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Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume VI – Emerging and Peripheral Technologies

H.R. Warner Jr., Editor

Chapter 9 – Geothermal Engineering

By J.L. Renner, SPE, G.M. Shook, SPE, Idaho Natl. Engineering and Environmental Laboratory, S. Garg, SPE, Science Applications Intl. Corp., J.T. Finger, SPE, Sandia Natl. Laboratories, P.W. Kasameyer, Lawrence Livermore Natl. Laboratory, K.K. Bloomfield, SPE, Idaho Natl. Engineering and Environmental Laboratory, P.N. Hirtz, Thermochem Inc., and G.L. Mines, Idaho Natl. Engineering and Environmental Laboratory

Pgs. 399-451

ISBN 978-1-55563-122-2
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Introduction

The word "geothermal" comes from the combination of the Greek words gê, meaning Earth, and thérm, meaning heat. Quite literally, geothermal energy is the heat of the Earth. Geothermal resources are concentrations of the Earth ’

s heat, or geothermal energy, that can be extracted and used economically now or in the reasonable future.

Spatial variations of the thermal energy within the deep crust and mantle of the Earth give rise to concentrations of thermal energy near the surface of the Earth which can be used as an energy resource. Heat is transferred from the deeper portions of the Earth by conduction through rocks, by movement of hot magma toward the surface, and by deep circulation of water. Most high-temperature geothermal resources are associated with concentrations of heat caused by the movement of magma (melted rock) to near-surface positions where the heat is stored. Because rocks have relatively small thermal conductivity, very large intrusions of magma may take millions of years to cool.[1]

Exploration for geothermal resources most commonly uses geologic mapping, geochemical analysis of water from hot springs, and geophysical techniques commonly used by the mining industry. With advances in seismic techniques, reflection seismic surveys are increasingly being used. Geothermal drilling relies on technology used in the oil/gas industry modified for high temperature applications and larger well diameters. Well testing and reservoir engineering rely on techniques developed in the oil/gas industry for highly fractured reservoirs because the high flow rates needed for economic production usually require fractures.

Occurrence of Geothermal Energy


Temperature increases with depth within the Earth at an average of about 25°C/km. So if the average surface temperature is 20°C, the temperature at 3 km is only 95°C. Although direct use applications of geothermal energy can use temperatures as low as about 35°C, the minimum temperature suitable for electrical generation is about 135°C. Geothermal resources occur in areas of higher than average subsurface temperatures.

Heat Flow and Temperature

The heat of the Earth is derived from two components: heat generated by the formation of the Earth and heat generated by subsequent radioactive decay of elements in the upper parts of the Earth. Birch et al.[2] found that heat flux can be expressed as q = q * + DA, where q* is the component of heat flow that originates from the lower crust or mantle, and DA is the heat generated by radioactive decay in the shallow crust. DA is the product of depth (D) and the energy generated per unit volume per second (A). Because A varies with depth, calculation of heat flow and, consequently, temperature with depth is complex. For most general heat flow studies in conductive areas, the change in heat flow with depth can be ignored.

Temperature at depth (T) is given by T = Tsurface+ DΓ, where Γ (temperature gradient) is related to heat flow and K (rock conductivity) by q = –KΓ. Diment et al.[1] provide a generalized review of temperatures and heat flow with particular emphasis on heat content in the U.S.

In older areas of continents, such as much of North America east of the Rocky Mountains, heat flow is generally 0 to 60 mWm–2. This heat flow coupled with the thermal conductivity of rock in the upper 4 km of the crust yields subsurface temperatures of 90 to 110°C at 4 km. It is apparent that depths on the order of 5 to 7 km are needed to attain the temperature (~ 135°C) required for electrical generation from geothermal energy in stable continental areas of moderate to low heat flow. Hence, exploration for geothermal energy focuses on areas where higher than normal heat flow is expected.

Tectonic Controls

The unifying geologic concept of plate tectonics provides a generalized view of geologic processes that move concentrations of heat from deep within the Earth to drillable depths and areas where geothermal development is likely to be successful. The heat can be related to movement of magma within the crust or deep circulation of water in active zones of faulting. Fig. 9.1 shows the major geothermal provinces in the world.

The brittle and moving plates of the lithosphere (crust and upper mantle) are driven by convection of plastic rocks below. Convection causes the crustal plates to break and move away from zones of upwelling hot material. Magma moving upward into a zone of separation brings with it substantial amounts of thermal energy, but most spreading zones are within ocean basins and unsuitable for geothermal development. The ocean spreading centers give rise to the midoceanic ridges.

Rifting of the Earth ’ s crust can also occur in continental blocks. Two of the better-known examples of such rifting are the East African rift and the Rio Grande rift in New Mexico. These rift zones contain young volcanism and host several geothermal systems, including Olkaria in Kenya and the Valles Caldera in New Mexico.

Where continental and oceanic plates converge, the oceanic plate (because it is usually more dense) is thrust or subducted under the continental plate. The subduction causes melting near the leading edge of the subducted plate and, as a result, lines of volcanoes form parallel to the plate boundary and above the subducting plate. Many of the world’ s most important geothermal regions are associated with these features: Indonesia, Japan, Mexico, New Zealand, the Philippines, and the fields in Central and South America.

Translational plate boundaries, locations where plates slide parallel to one another, may develop extensional troughs, known as pull-apart basins such as the Salton Trough of Southern California. [3] Volcanism associated with the Salton Trough generated the heat in the Salton Sea, Cerro Prieto, and Imperial Valley geothermal fields. Tensional features further north on the San Andreas and related faults may be the source of the volcanism thought to be the heat source for The Geyser’

s geothermal field about 90 miles north of San Francisco.

A third source of elevated heat flow and volcanism are "hot spots" (volcanic centers thought to overlie rising plumes of hot mantle material). Hot spots most commonly occur in the interior of plates but can occur on ocean ridges as well. Several important geothermal systems are associated with recent volcanism caused by hotspots: Yellowstone, U.S., the geothermal fields in Iceland, and those of the Azores.

Geothermal resources also have been developed in areas of anomalously high temperatures with no readily apparent active volcanism, such as the Basin and Range physiographic province in the western United States. Although the tectonic framework of the Basin and Range is not fully understood, the elevated heat flow of the region is likely caused by a thinner than average continental crust undergoing tensional spreading. The elevated heat flow and deep circulation along recently active faults have generated many geothermal sites exploited in Nevada. These geothermal fields are not associated with recent volcanic activity, and while there is no evidence of midlevel crustal magmatic activity, it cannot be ruled out.

Several geothermal fields are, however, associated with recent volcanism along the margins of the Basin and Range. The Coso and Mammoth Lakes fields in California and the Cove Fort and Roosevelt Hot Springs fields in Utah are examples.

Types of Geothermal Systems


Exploitable geothermal resources are hydrothermal systems containing water in pores and fractures with sufficient permeability to produce fluids in adequate volume. Most hydrothermal resources contain liquid water, but higher temperatures or lower pressures can create conditions where steam and water, or steam alone, are the continuous phases. [4][5] Examples of steam-alone fields are among the oldest developed geothermal fields—Larderello in Italy and The Geysers in Northern California. These types of geothermal fields are termed "vapor-dominated" because the initial pressure follows a vapor-static gradient, as opposed to hydrostatic gradients in liquid-dominated fields.

Other geothermal systems that have been investigated for energy production are (1) geopressured-geothermal systems that contain water with somewhat elevated temperatures (above normal gradient) and with pressures well above hydrostatic for their depth, (2) magmatic systems, with temperature from 600 to 1,400°C, and (3) hot dry rock (HDR) geothermal systems, with temperatures from 200 to 350°C. HDR systems are characterized, as are subsurface zones, with low natural permeability and little water. Currently, only hydrothermal systems shallower than about 3 km and containing sufficient water and high natural permeability are exploited.

A more recent addition is "enhanced geothermal systems" (EGS), which fall between HDR and hydrothermal systems. These may lack enough fluid or have low permeability for commercial use, and ongoing research focuses on injecting fluids and enhancing permeability for improved efficiency. Currently, only hydrothermal systems less than 3 km deep with sufficient water and high natural permeability are actively utilized for energy production. Another option is utilizing the heat from beneath the Earth's surface with low hydraulic conductivity, occasionally termed deep heat mining (DHM). Given that the continental crust is primarily composed of granite or gneiss, HDR systems specifically target granitic heat reservoirs. HDR systems typically aim for temperatures above 200 °C, requiring the drilling of wellbores reaching depths of 6 to 10 km in the continental crust, which maintains an average geothermal gradient[6].

Geothermal Energy Potential


Estimates of potential for geothermal power generation and thermal energy used for direct applications are available for most areas. The most recent review of worldwide electrical generation reports 12,810 MWe (megawatts electric) of generating capacity is online in 23 countries (Table 9.1). Since that report, additional 4,013 kWe capacity has been added in Indonesia, the most additional capacity of all countries. [7] The expected capacity in 2005 is 19,757 MWe. Geothermal resources also provide energy for agricultural uses, heating, industrial uses, and bathing. Fifty-five countries have a total of 16,209 MWt (megawatts thermal) of direct-use capacity. [8] The total energy used is estimated to be 45,000 TW-hrs/yr (terawatt-hours per year).


Gawell et al. [9] estimate that identified geothermal resources using today's technology have the potential for between 35,000 and 73,000 MW of electrical generation capacity. The Gawell study relied on expert opinions and generally focused on identified resources. Stefansson[10] prepared an estimate of identified and unidentified worldwide potential based on the active volcanoes of the world. He estimates a resource of about 11,200 ± 1,300 TW-hrs/yr using conventional technology and 22,400 using conventional and binary technology (Table 9.2). Stefansson[11] points out that his estimate is in general agreement with that of Gawell et al.,[9] although individual regions may not be in agreement.


The U.S. Geological Survey has prepared several assessments of the geothermal resources of the United States. [12][13][14] Muffler[13] estimated that the identified hydrothermal resource, that part of the identified accessible base that could be extracted and used at some reasonable future time, is 23,000 MWe for 30 years. That is, this resource would operate power plants with an aggregate capacity of 23,000 MWe for 30 years. The U.S. undiscovered resource (inferred from knowledge of Earth science) is estimated to be 95,000 to 150,000 MWe for 30 years.

Muffler[13] also provides an explanation of the terminology used to define the various categories of resources. Resource base is all of the thermal energy contained in the Earth. Accessible resource base is that part shallow enough to be reached by production drilling. Resources are those portions of the accessible base that can be used at some reasonable future time. Reserves are that portion of the resource that has been identified and can be used under current economic conditions. Resources are also divided into categories of "identified" and "undiscovered," based on knowledge of the certainty of their existence.

Geothermal Exploration


Geothermal resource exploration, development, and production draw on the techniques of both the mining and oil/gas industries. The geologic setting of geothermal resources is similar to deposits of metal ores, and geothermal systems are thought to be the modern equivalent of metal ore-forming systems. Hence, exploration draws most heavily on the techniques of the mining industry. Development of the resource and its production as hot fluid uses the techniques of the oil/gas industry with modifications because of the high temperatures and the much higher flow rates needed for economic production.

Exploration begins with selection of an appropriate area based on general knowledge of areas with above average heat flow. The best guides for more detailed investigation are the presence of thermal springs (the equivalent of oil seeps). However, to develop undiscovered resources, geologists must rely on other techniques. Because the target is a region of above average temperature, heat flow studies can indicate elevated subsurface temperatures. Among other methods being used and investigated for regional exploration are remote sensing of elevation changes, age of faulting, and geochemical techniques.

Hydrothermal systems suitable for geothermal development must have adequate temperature and sufficient flow for economic production. Geochemical techniques can be used to determine subsurface temperatures when hot springs are present, and shallow temperature-gradient holes can be used to project subsurface temperatures below the level of drilling. Geophysical tools are also used to determine the approximate size of the reservoir. Because high flow rates are needed for geothermal production, most geothermal production comes from highly fractured reservoirs. Geophysical methods that can determine fracture intensity are of great importance to the explorationist.

Geochemical Studies

The interpretation of the chemistry of hot springs and fumaroles is an important tool used in geothermal exploration. The solubility of minerals strongly depends on temperature, and the kinetic rate of rock-water reactions is relatively slow. Thus, water equilibrated with rocks in a geothermal system can retain their dissolved mineral content as they move to the surface, and the composition of hot springs can be used to determine the temperature of equilibration. The geochemistry of thermal springs is the most widely used geothermal exploration tool for estimating subsurface temperatures prior to drilling wells.

The most widely used geothermometer is based on the solubility of silica. Because more than one form of silica, with different solubilities, can be present in the subsurface, caution must be used in applying the thermometer. The two most common forms of silica in geothermal systems yield the following composition-temperature relationships over the temperature range of 0 to 250°C.

RTENOTITLE....................(9.1)

and

RTENOTITLE....................(9.2)

where SiO2 is the concentration of silica in mg SiO2 per kg water. [15]

The second most widely used geothermometer, Na-K-Ca, was developed by Fournier and Truesdell, [16] and a magnesium correction was added by Fournier and Potter. [17]

RTENOTITLE....................(9.3)

The concentration units are moles/kg, β = 1/3 for water equilibrated above 100°C, and β = 4/3 for water equilibrated below 100°C.

Because of the importance of geothermometers for exploration and for interpreting chemical changes in geothermal reservoirs during production, a rich literature on the geochemistry of geothermal systems is available. Four publications[18][19][20][21] provide a particularly useful understanding of the chemistry of geothermal systems, how to sample thermal springs, and the application of geochemistry to understanding geothermal systems.

Geophysical Techniques

Geophysical Methods in Geothermal Exploration and Field Operations

Geophysical methods can help locate permeable structures with high-temperature water or steam and estimate the amount of heat that can be withdrawn from the ground in a given time period. Once a field is developed, geophysical measurements can be used to help site additional production and injection wells, to understand the details of the permeability structure, and to provide constraints on reservoir models used in the management of the geothermal field. The primary exploration targets are colocated heat, fluid, and permeability. Wright et al.[22] provide a useful review of geophysical techniques for geothermal exploration.

Geophysical interpretation in geothermal fields is complicated by two factors. First there are a great variety of rock types in which different geothermal systems might be found (e.g., young sediments in the Salton Trough, California; the Franciscan mélange at The Geysers, California, or a mixture of rocks such as tuffs, flows, mudslides, and intrusive rocks at Pacific rim, volcanic-hosted fields). Second, the geologic structures at geothermal systems are often quite complex, and structure may not determine the location or economic viability of the geothermal field. Consequently, the exploration strategy for geothermal energy differs from that for petroleum fields and is more similar to mineral exploration.

Temperature at depth can be sensed directly in boreholes or estimated by extrapolation of heat-flow measurements in both shallow and deep holes. Heat-flow measurements combine observed temperature gradients and thermal conductivity measurements to determine the vertical heat transport in areas where conduction is the primary mechanism of heat transport. If the temperature gradient changes dramatically with depth, these measurements indicate areas where heat transfer is dominated by advection. Heat-flow measurements provide evidence both of regions where geothermal systems are more likely[23][24][25][26][27] and of the extent of localized convecting systems. [28] Because the fluid flow patterns can be complex, the deeper zones of hot fluids are often not directly beneath the shallow high heat-flow anomalies.

Subsurface temperatures can also be inferred from physical properties of rock masses. Laboratory measurements[29][30][31][32] of the density, seismic, electrical and mechanical properties of rocks as a function of temperature, pressure, porosity, matrix material, alteration, and saturation provide the information needed to plan and interpret a geophysical campaign.

Locating zones of sufficient permeability for economic production is difficult. Electrical self-potential (SP) provides the only direct signal from subsurface fluid flow; all other methods require the inference of permeability from causes (i.e., zones of extension, intersecting faults, state of stress, or seismicity) or secondary effects (i.e., temperature distribution or zones of mineral alteration). Surface geophysical methods have provided important information for siting early wells at many geothermal fields. For example, the gravity anomalies caused by dense, thermally-altered sediments in the Imperial Valley, California, guided much early drilling. However, surface and borehole geophysics is much more important later in the development of a field, when wells must be sited to provide adequate production or injection capability, or to provide constraints to tune reservoir models.

Examples of Specific Methods as Applied to Geothermal Both natural and induced seismicity reflect physical processes occurring within or beneath the geothermal system. The significance of these events, or of their absence, depends on the specific setting of the geothermal system being examined. It has been argued that for fluids to keep moving from hot regions toward cooler regions, microseismicity must occur to keep fractures open. Consequently, passive seismic techniques for the detection of microseismicity have long been used to explore for geothermal fields. [33] However, several fields, such as Dixie Valley, Nevada and Olkaria, Kenya have little or no detectable seismicity, and for others, such as The Geysers, California, we do not know whether there was seismicity before production began. On the other hand, seismicity can provide information about the tectonic setting in which the geothermal system occurs. For example, in the Salton Trough, the natural seismicity outlines the plate boundaries, whose oblique motion provides the extension required for the shallow injection of magma and the resulting fluid circulation. Historical and paleoseismic information may also provide valuable information about the setting of a geothermal system. For example, Caskey et al.[34] have found that the Dixie Valley field sits in a seismic gap indicated by both 20th-century events and Holocene fault ruptures. Finally, if seismicity only occurs at shallow depths, then the brittleductile transition may shallow because of locally high heat flow.

Microearthquakes can also be useful to constrain the processes occurring during operations in a field. For example, Beall et al.[35] and Smith et al.[36] showed that much of the seismicity at The Geysers can be used to map the descending plume of injected fluid, and microearthquakes detected from a deep borehole seismic systems have been used to map artificial fractures (e.g., Fehler et al.[37] at Fenton Hill, New Mexico, or Weidler et al.[38] at Soultz, France).

Passive seismic observations are also used to generate velocity images of the crust. By simultaneously solving for the earthquake locations, time, and the velocity and attenuation structures, three-dimensional (3D) images of geothermal fields can be developed. [39][40][41][42][43] Inferences about steam saturation and porosity can be drawn by comparisons of the P- and S-wave images[44] or by comparing the velocity and attenuation images. [45][46] Inferences about fracture orientation can be inferred if shear-wave velocity depends on polarization. [47] These surveys can be repeated to look at the effects of production and injection. [48]

Exploration seismology has historically not been successful in delineating economic geothermal fields, probably because of the complex structures in which they occur and the somewhat tenuous relationship between the structure and the producing fields. Recent work[49] has focused on using the large number of first arrival times to develop a two-dimensional (2D) or potentially a 3D velocity model that can be used for migration to image steeply dipping structures. The velocity image provides valuable information about the structure as well as improving the imaging of discrete reflectors.

Many electrical methods have been applied to geothermal exploration and characterization. Passive electrical SP anomalies have been interpreted to indicate zones of strong upward flow of hot water. [50][51][52][53][54] DC and induction methods with a broad variety of geometries, frequencies, penetration depths and resolutions have identified high-conductivity anomalies that are nterpreted to be warm or heavily altered areas, or to indicate structures that might control fluid movement. [55][56][57] Repeated electrical methods have also been used to identify zones where cool recharge is entering a geothermal system.

Potential field methods, including gravity and magnetics, are used in traditional ways to delineate faults, basin geometries and other structures, and to identify intrusions or buried eruption deposits that might provide heat or influence flow paths as demonstrated by Soengkono. [58] The interpretation of these data depends strongly on the nature of the particular system being studied. For example, in the sedimentary section in the Salton Trough, California, the known resource areas are all marked by gravity highs caused by alteration of the sediments by high temperature circulating fluids. [59][60] However, in most fields, an area of relatively high gravity would typically not be related to the geothermal system.

Although they are not traditionally thought of as geophysical techniques, geodesy and deformation measurements can provide valuable information about the processes occurring within a geothermal system. [61][62]

Other than temperature-depth logging and spinner surveys to identify inflow areas, borehole logging has not been extensively used in geothermal areas. Several factors contribute to this. The high temperatures can be a problem for traditional logging tools. The tool designs and standard interpretation principles are optimized for relatively flat sedimentary sections, a situation which is unusual in geothermal environments. Finally, geothermal wells often have severe lost circulation zones that require casing to be set rapidly to save the hole. This can preclude openhole logging. High-temperature logging tools can alleviate some of these problems. [63][64][65]

Two scientific projects have provided public access to logging data sets from drillholes in geothermal systems. The Salton Sea Scientific Drilling project[66] collected a large suite of traditional well logs, [67] repeated temperature logs, [68] borehole gravity, [69] and vertical seismic profile (VSP) measurements. [70] At Dixie Valley, extensive borehole televiewer studies and mini-hydraulic fracture tests to determine effective stress have led to an understanding of which fractures are open and why. [71][72] If interpreted as measurements of specific formation properties rather than as a means to correlate between wells, additional borehole geophysical measurements could provide valuable information in operating geothermal fields.

Integrated geophysical methods can provide valuable information about a geothermal system both during exploration and exploitation. The specific methods that are valuable, and the way disparate data sets might be combined, strongly depend on the nature of the system being examined and the questions being asked. The value of geophysical measurements is enhanced if they are interpreted in terms of a conceptual or numerical model that is also constrained by other information, whether it be geological and geochemical exploration data or knowledge gained during the operation of a field. This integration is potentially most effective during exploitation when the reservoir models calculate the geophysical effects as well as the pressure drawdowns and fluid flows. [73][74][75][76] A similar approach to exploration might prove to be very valuable.

Geothermal Drilling

Background

Compared to the oil/gas industry, geothermal drilling activity is minuscule. Worldwide installed geothermal generating capacity is approximately 8,000 MW (Table 9.1), [77] and for typical production from a geothermal well of 6 to 10 MWe, along with injection wells equal to one-third the number of producers, this represents a total of only 1,000 to 1,600 active wells. This number is somewhat misleading because many more wells have been drilled than are currently active. There are exploratory wells that were needed to identify and evaluate the geothermal reservoirs, many former production or injection wells have been plugged and abandoned, and much workover drilling for active power plants is required by the corrosive and solids-laden brines in many geothermal reservoirs. In spite of all this, the market is still so small that few drilling contractors or service companies can be sustained solely by their geothermal drilling business.

Nature of Geothermal Formations

Typical rock types in geothermal reservoirs include granite, granodiorite, quartzite, greywacke, basalt, and volcanic tuff. Compared to the sedimentary formations of most oil/gas reservoirs, geothermal formations are, by definition, hot (production intervals from 160°C to above 300°C) and are often hard (240 + MPa compressive strength), abrasive (quartz content above 50%), highly fractured (fracture apertures of centimeters), and underpressured. They often contain corrosive fluids, and some formation fluids have very high solids content[ total dissolved solids (TDS) in some Imperial Valley brines is above 250,000 ppm] . These conditions mean that drilling is usually difficult—rate of penetration and bit life are typically low; [78] corrosion is often a problem; [79] lost circulation is frequent and severe; and most of these problems are compounded by high temperature.

Lost circulation and reservoir damage deserve special mention. Lost circulation is often massive; complete loss of returns at pumping rates of hundreds of barrels per hour is common. Geothermal wells have been abandoned because of the inability to drill through a loss zone, [80] and many more have needed an unplanned string of casing to seal off a problem interval. Lost circulation treatment is complicated by the requirement that the treatment not damage the producing formation, and this distinction is often difficult. Geothermal wells have been drilled into "live" production zones; that is, the hole is producing steam or hot brine during drilling. This is conventional practice in The Geysers, where the production zone is air-drilled and the produced fluid is dry steam; this is often described as "drilling a controlled blowout." Drilling with brine inflow is much riskier, so an alternative is to allow moderate losses and to lose drilling mud into the producing fractures, with a later backflow from the production interval to clean up the formation. Productivity of most production wells up to 340 mm casing is up to 0.6 million kg/hr, so the formation has very little skin damage initially. If wells are to be drilled after brine production has begun (often a clean-out workover), this requires mufflers, rotating heads, mud coolers, and high-temperature wellhead/blowout preventer (BOP) equipment. It also means making connections in a hot hole and sometimes running liners in a live well. Although some of these operations are similar in principle to underbalanced drilling (UBD), the temperature and flow rates mean that the problems are much different from oil/gas UBD and must be well understood to avoid damage or injury from loss of well control.

Lost circulation material (LCM) is sometimes effective[81] but often fails because losses are through fractures with apertures of several centimeters so that the LCM particles are not large enough to bridge the loss zone. If zones with fractures must be sealed, cement is usually the treatment of choice but is hard to place accurately. It is much more important to repair loss zones where casing will later be set than in production intervals. Cotton-seed hulls are used to provide temporary LCM in Imperial Valley production zones because they eventually disintegrate and produce little residue in the wellbore flowback for cleanup. Cement plugs are not used because extensive lost circulation in the reservoir indicates good fractures, which are productive. Time and materials for lost circulation treatment can represent 15% of well cost, and the underpressured formation aggravates differential sticking, so these can be major impacts on drilling cost.

Depth and temperature of geothermal resources vary considerably. Several power plants, (e.g., Steamboat Hills, Nevada and Mammoth Lakes, California) operate on lower-temperature fluid (below 200°C) produced from depths of approximately 330 m, but wells in The Geysers produce dry steam (above 240°C) and are typically 2,500 to 3,000 m deep. In the most extreme cases, an exploratory well with a bottomhole temperature of 500°C at approximately 3,350 m has been completed in Japan, [82] and experimental holes into molten rock (above 980°C) have been drilled in both Hawaii and Iceland.

Slimhole Drilling

Typical geothermal exploration comprises drilling a large-diameter, production-size well and, if it shows the presence of fluid and high temperature, producing steam or brine from it while measuring the fluid temperature, and, ideally, downhole pressure. These flow tests, which usually last for days to weeks, directly evaluate the energy or enthalpy output of the well and indicate whether the reservoir pressure is drawndown significantly over the course of the test.

This method has major disadvantages: it is expensive (U.S. $1 to 3 million per well) and there is significant environmental impact from roads, large drill sites, and fluid-handling requirements. In addition, if the operator hopes to turn an exploration well into a production well, it may be located at the fringe of the resource where it is not convenient for eventual construction of a power plant. If data from a smaller hole is adequate to evaluate the reservoir, then slimhole exploration is typically much less expensive.

Drilling slimholes is cheaper than production-size wells because the rigs, casing and cementing, crews, locations, and drilling fluid requirements are all smaller; because site preparation and road construction in remote areas is significantly reduced; and because it is not necessary to repair lost-circulation zones before drilling ahead. [83] Core rigs, most often used by the minerals industry to explore for ore bodies, use diamond bits which cut a thin-kerf hole 51 to 150 mm in diameter with corresponding core diameters of 25 to 100 mm. Cores are wireline-retrieved, so the drill string is not tripped except to change bits. Weight on bit or rate of penetration is usually controlled by a hydraulic feed cylinder. Because the cuttings produced by the diamond bits are very fine and make up a smaller fraction of the hole volume than in rotaryrig coring, minerals-type core drilling can continue without drilling fluid returns, in contrast to conventional rotary rigs producing cuttings large enough to stick the drillstring, if they are not circulated out of the hole.

There are tradeoffs between rotary and core drilling, but small hole sizes have generally favored core rigs. These rigs may not be cost-effective in oil/gas exploration because, in many sedimentary formations, rotary drilling has much faster penetration and can therefore drill those intervals more cheaply. However, the advantage of being able to drill through lost circulation zones in geothermal formations can offset faster penetration.

After drilling an exploratory geothermal slimhole, it is essential to evaluate the reservoir ’

s potential for commercially viable production. The two most important reservoir qualities are its temperature and its resistance to fluid flow. Because permeability is a local measurement and most geothermal production is through fractures, flow resistance is quantified as permeability integrated over some wellbore length. This is called transmissivity and has units of m3. Well testing is discussed in Section 9.8 of this chapter.

Reservoir temperature can usually be determined easily, either through logs after drilling and completion, or even from logs or maximum-reading thermometers during drilling (most geothermal drilling permits require periodic downhole temperature measurements as a criterion for casing programs.) Because of the low circulation rates used for slimhole core drilling (typically 0.75–1.25 L/s), the formation temperature recovers from the cooling effect of the drilling fluids much more quickly than in conventional rotary drilling.

Direct cost comparison of slimhole and rotary drilling in the same reservoir is provided by two wells drilled in Oregon in the 1990s. The rotary hole, "slim" by oilfield standards, was drilled approximately 3 km away from and before the slimhole. The slimhole was rotary drilled for approximately 950 m and then core-drilled to total depth (TD). Costs for the wells are summarized in Table 9.3.


Several points are evident in the following comparison:
  • Even though charges by the drilling contractor were considerably greater for the slimhole than for the rotary hole, lower ancillary costs for the slimhole made the total project much cheaper. Rate of penetration for core drilling is typically less than that for rotary rigs, so part of the greater rig cost was caused by the longer time required for the slimhole, and the remainder is because of the rig day-rates.
  • The drilling-fluids expense was slightly greater for the slimhole, but it was inflated by the complete loss of circulation in the lower part of the hole.
  • Even though more than half the total footage was rotary drilled, the smaller bits used in the rotary section and the less expensive core bits in the cored section greatly reduced the cost of bits and tools. There were no stabilizers or drill collars in the cored section.
  • Smaller sizes of the rig, pad, and sump reduced rig mobilization and site construction costs.
  • A mud-logging service company and contract drilling supervision were only used for the rotary section of the hole.
  • Smaller casing sizes, with correspondingly smaller cement volumes, were less expensive for the slimhole.


Geothermal Drilling Technology

The drilling conditions described above have led to the following practices, which are reasonably uniform, in the geothermal drilling industry.

Bits Because of the hard, fractured formations, roller-cone bits with tungsten-carbide inserts are almost universally used for geothermal drilling. The abrasive rocks mean that bit life is usually low (50 to 100 m), but many bits are also pulled because of bearing failures caused by rough drilling and high temperature. Polycrystalline diamond compact (PDC) bits have the dual advantages of more efficient rock cutting and no moving parts, but experience with PDC bits in geothermal drilling is both scant and unfavorable. Much research and development in hard-rock PDC bits is under way, [84][85] so it is possible that these bits will come into wider use in geothermal drilling.

Tubulars Because of the low-value fluid (steam or hot water), geothermal wells must produce large fluid volumes and so tend to be larger diameter than oil/gas wells; typical geothermal production intervals are 219 to 340 mm in diameter. Unlike oil/gas wells, geothermal production is from the open hole or through a slotted liner, not through tubing. This means that both drillpipe and casing are usually larger than for oil/gas wells at the same depth.

Drillpipe suffers both erosion and corrosion. Both of these problems are aggravated by high temperature. Erosion is common when air drilling, which is often done to avoid damaging the production interval with mud invasion, but properly hard-banding the tool joints will mitigate erosion. Most drilling contractors and operators establish an inspection schedule, based on experience in the geothermal field being drilled, to track drillpipe condition. Casing problems, other than cementing (discussed later), usually deal with corrosion and scaling. Brine quality varies greatly, ranging from near-potable in moderate-temperature systems to highly corrosive with high dissolved solids in some high-temperature systems.

Many techniques—cement-lined casing, exotic alloys, and corrosion-resistant cement—have been applied to the casing corrosion problem, which is especially severe in the Imperial Valley. Shallow and hot, CO2-bearing zones there drive an external corrosion rate approaching 3 mm of carbon steel per year, necessitating plugging after 10 to 12 years even after well life was extended by cementing in smaller production strings. Most production wells in the Imperial Valley have been completed or retrofitted with titanium casing, which has proved to be cost effective in spite of its very high capital investment.

Many high-temperature drilling problems with downhole tools and drilling fluids could be avoided or mitigated by using insulated drill pipe (IDP), which delivers cooler fluid to the bottom of the hole. [86] IDP has been demonstrated in the laboratory and in limited field experience, and is commercially available but has not seen significant use by industry.

Drilling Fluids Most geothermal drilling fluids are a fairly simple water/bentonite mixture with possible polymer additives. [87] Large hole volumes and frequent lost circulation mean that expensive muds have a significant impact on drilling cost. Drilling records from a number of geothermal wells in several reservoirs showed the following typical property ranges.

Density 1.03 to 1.15 g/cm3
Funnel viscosity 35 to 55 sec
pH 9.5 to 11.5
Plastic viscosity 0.01 to 0.02 Pa-s
Yield point 35 to 125 kPa

Well Control Because formations are usually underpressured (pore pressure less than fluid pressure in a full wellbore), influx into the wellbore is rare. There are two primary causes for loss of control: an unexpectedly hot formation is encountered at a shallow depth where the annulus pressure is insufficient to keep the drilling fluid or the formation fluid from flashing to steam; or lost circulation causes the fluid level and, thus, the pressure in the wellbore to suddenly fall far enough for the same thing to happen. If complete control is not lost, simply pumping cold water into the wellbore can usually kill the well.

Directional Drilling Neither positive displacement motors nor steering and measurement-while-drilling (MWD) tools operate reliably at high temperature, so most corrections are done at depths where the formation is cooler than 175°C. Kickoffs in higher temperature formations can be done with whipstocks, if they can be oriented with high-temperature survey instruments. High-temperature turbines have been demonstrated and service companies offer "high-temperature" positive displacement motors (PDM), but neither is extensively used in geothermal drilling. If moderate fluid loss occurs while drilling with mud motors, the addition of fresh mud sometimes makes it possible to continue drilling for the life of the bit in a hot hole. Motors are usually burned up on trips back in the hole. High-temperature electronics for steering tools can also be a problem, but technologies exist for operating unshielded electronic components above 260°C.

Cementing The principal differences between cementing geothermal and oilfield casing are the requirements on the cement itself because of high temperature, and the requirement that geothermal casings are cemented completely to surface to withstand thermal cycling. [88] The major modification in composition of geothermal cement is the addition to standard Class G cement of retardants and approximately 40% silica flour. A fairly typical bill of materials for primary cement of 406 mm casing at approximately 460 m in a geothermal production well is the following: 82 m3 Class G cement mixed 1:1 with perlite and 40% silica flour, 4% bentonite, and 1% CaCl2. The perlite is usually omitted and the Class G cement mixed with 40% silica flour, if there is no loss zone that makes the lighter slurry desirable. Foam cement has also been successful in cementing casing in areas of lost circulation, while latex is extensively used in some areas to offer more corrosion protection in high-CO2 areas.

Geothermal Well Completions

Thermal cycling in geothermal production and injection wells requires a complete cement sheath around the casing, and high production flow rates (often > 100,000 kg/hr) mean that casing is usually larger in diameter than for many oil/gas wells. Other factors that influence completion design include brine chemistry; how the well is produced—pumped or self-energized; possible two-phase flow in the wellbore; multibranch completions; presence of lost-circulation zones that would prevent lifting the cement column back to surface; and whether the production interval is stable enough to be openhole or must be completed with a slotted liner.

Brine chemistry can cause two major problems: corrosion and scaling. Corrosion can be so severe that titanium casing is economic, even at a cost approaching $1,000/ft, while scaling, either inside the casing or in the production interval, can lead to frequent workovers. Scale is sometimes removed with jets on coiled tubing, but scaling in the wellbore often seals the formation and must be drilled out with an underreamer.

The requirement for a cement sheath to surface means that lost circulation zones must usually be plugged before cementing. Other methods—stage cementing, nitrogen foam cement, top jobs with a tremie line (small diameter line inserted from the surface into the annulus between casing and wellbore), and perforate and squeeze—have been used, sometimes successfully, but the cement job is much simpler and less expensive if conventional cementing practices will suffice. It is also critical that no water be trapped between the cement and the casing, especially in intervals where one casing is inside another, because the water can become hot enough to flash to steam as the well goes on production and heats up. If the collapse rating of the inner casing is lower that the saturation pressure of the water, the casing will buckle (if the trapped-water location has formation outside it, the fracture gradient is usually low enough to allow the pressure to bleed off into a fracture.)

Case Histories of Two Geothermal Wells

To give more intuition for actual geothermal drilling, case histories for two wells are summarized in Tables 9.4 through 9.7. Because certain data related to specific wells are proprietary, the wells are identified only as "steam well" and "brine well." Both wells were drilled in the mid-1990s, so an inflation factor should b applied to the costs, and both wells were drilled in geothermal fields where there was extensive previous experience. In both tables, ROP means rate of penetration.

Steam Well This well was designed to be a two-leg well with casing to approximately 1,500 m and two openhole branches to approximately 3,000 m, but the first leg encountered no steam entries. It was plugged back and two additional branches were drilled (i.e., three holes were drilled from approximately 1,350 to approximately 3,000 m). Although drilling three legs is not required for all wells in this reservoir, it is not uncommon, and drilling records from this well can be extrapolated back to one- or two-branch wells. The hole was drilled with mud to the 1,500 m casing point; then, all branches were air-drilled.

Total time over the hole was approximately 90 days, and total well cost was approximately U.S. $3 million. There was no significant lost circulation in the mud-drilled part of the hole. Other events included milling two windows in the 298 mm casing and four twist-offs—three of them in the air-drilled intervals. Although more footage was drilled than planned, this was considered a relatively trouble-free well.

Brine Well This is a self-energized geothermal production well drilled in sedimentary formations. The well is cased to approximately 640 m and has an openhole production interval from there down to approximately 1,500 m. The corrosive nature of the brine requires titanium casing, but standard practice is to avoid drilling inside this very expensive tubular. Procedure is to drill 375-mm hole to TD and flow the test well through 406-mm casing, then run and cement the 340-mm production string inside the 406-mm casing.

Total time over the hole was approximately 50 days (but approximately 10 days went to flow testing the well and cementing the titanium casing), and total well cost was approximately 3.7 million dollars, with approximately 1.4 million dollars of this total for the titanium production string. There were four significant events of lost circulation (total mud lost > 7,000 bbl), all of which were controlled with LCM. Problems in stage-cementing the 406-mm casing led to a major fishing job. There were no fishing jobs during drilling. This was also considered a relatively trouble-free well.

Additional References

Both the Society of Petroleum Engineers (www.spe.org) and the Geothermal Resources Council (www.geothermal.org) provide searchable databases of publications that include detailed descriptions of geothermal drilling technology. The U.S. Bureau of Land Management provides a summary document describing regulatory requirements for exploration, drilling, production, and abandonment on federal geothermal leases. [89] The Standards Association of New Zealand has printed a 93-page manual that combines regulatory requirements with suggestions on operational practices for drilling, maintenance, repair, and abandonment. [90]

Reservoir Engineering


Geothermal reservoir engineering, having its roots in petroleum reservoir engineering, has historically relied on conventional petroleum methods with slight modifications to account for inherent differences in conditions. It was not until the late 1960s and early 1970s that engineers recognized they must include a rigorous energy balance to account for interphase mass and energy exchange[91][92] and other heat transfer mechanisms that arise from vaporization of fluid during extraction operations. There are a variety of phenomena that make geothermal reservoir engineering unique compared to conventional reservoir engineering, including:

  • The reservoir fluid has no inherent value in and of itself. The fluid (either liquid or vapor) can be viewed as a working fluid whose sole value is the energy (heat) it contains.
  • Geothermal reservoirs in the native state are rarely static and are usually neither isothermal nor of uniform fluid composition. Large spatial variations in pH occur. Highly-corrosive reservoir fluids are not uncommon and lead to additional expense of drilling, completions, and production.
  • Geothermal reservoirs are rarely completely closed. More often, a zone of recharge and multiple zones of discharge (including springs and fumaroles) are associated with the resource.
  • Phase behavior is deceptively complex. In its simplest form, the reservoir fluid is a single component that may partition into up to three phases: liquid, vapor, and adsorbed phases. Usually, there are additional components such as noncondensible gases (CO2, H2S, etc.) and salts.
  • Geothermal reservoirs are typically found in highly fractured igneous or metamorphic rocks; very few are found in sedimentary rocks worldwide. While rock matrix properties would make the resource commercially unattractive as a petroleum reservoir (e.g., permeability can range as low as a 10–20 m2, porosity is in the 0.02 to 0.10 range), the relatively large dimensions (thickness may range to thousands of meters) ensure a substantial resource (heat) is in place.


While there are important distinctions between classical petroleum engineering and geothermal reservoir engineering, much of the latter can be considered an extension of the former. In this section, we emphasize these extensions of conventional engineering.

Reservoir Characterization

Well Testing Geothermal well testing is similar in many respects to transient pressure testing of oil/gas wells, with some significant differences. Many geothermal wells induce boiling in the near-well reservoir, giving rise to temperature transients as well as pressure transients. Substantial phase change may also take place in the well, further complicating analysis. Pressure tools must be kept in a high-temperature environment for long periods of time, and production intervals are frequently very small portions of overall well depth. Production intervals, which are usually associated with fracture zones, may be at substantially different thermodynamic conditions. Finally, pressure and temperature changes induce fluid property changes that require correction. Nevertheless, the principles of geothermal well testing are the same as petroleum well testing. And with the caveats already noted, standard interpretation methods can be used.

Because the primary objective in geothermal well testing is to determine the ultimate productivity of a well prior to completion, injectivity testing is perhaps the most useful kind of well test. In contrast with a production test, cold water injection does not induce flashing (phase change) near the wellbore. Injection testing in an all-liquid reservoir can therefore be interpreted conventionally to yield formation transmissivity and well skin factor. For a well with a single feed zone, an injection test will yield unambiguous values for formation properties. Most wells have multiple feed points, however, and it is necessary to relate the outflows (or inflows) from the well to the difference between the pressure gradient in the well and that in the reservoir. A fluid entry that accepts fluid during injection may nevertheless prove to be unproductive in a production test. [93]

Because of changes in temperature (and therefore fluid density and viscosity) with time, it is imperative to obtain downhole measurements of pressure and temperature. As an example, replacement of a 2,500-m fluid column at 150°C with cold fluid at 20°C results in a pressure increase of ~

20 bar at the base of the column. Pressure, temperature, spinner (PTS) logs are frequently run to obtain estimates of feed-zone locations and pressure and temperature profiles. However, convective effects in a geothermal wellbore often totally dominate the measured pressure and temperature profiles. Interpretation of such data is treated by White, [94] Stefansson and Steingrimsson, [95] and Grant. [96][97] The heat and mass transport mechanisms involved in the intersecting wellbore and reservoir system are reviewed here to illustrate the difficulties inherent in characterizing reservoir permeability structure and fluid state from downhole measurements.

Three possible types of temperature profiles that may be observed during cold water injection into a geothermal well are shown in Fig. 9.2. The well in this example has two permeable horizons whose limits are marked by crosses on the depth (vertical) axis. Profile 1 is the simplest. Water enters at the wellhead (z = 0). The measured temperature increases slowly to depth z2, and then it increases rapidly. The rapid increase below z2 indicates that the depth z2 is the major zone of fluid loss and that little or no cold water penetrates below z2.


A break in gradient at depth z1, followed by a sharp increase in gradient at z2, is shown in Profile 2. This indicates some fluid loss at depth z1 and loss of all or nearly all of the balance of the injected fluid by depth z2. Except in permeable zones, the fluid gains heat by conduction from the surrounding formation. If W is the mass flow rate down the well, Tw(z) is the fluid temperature, and Tr(z) is the formation temperature, then the conductive heating (caused by the temperature difference TrTw) of the descending water is given by

RTENOTITLE....................(9.4)

where
Cpw = specific heat of the fluid (J/kgK),
d = wellbore diameter (m),
and
U = overall heat transfer coefficient (W/m2K).

The temperature gradient dTw/dz is inversely proportional to the flow rate W. Therefore, an increase in temperature gradient (see Profile 2, Fig. 9.2) implies a decrease in W and, hence, water loss from the well at the depth of gradient change. In many cases, flow rates are so large that dTw/dz is small or, within measurement error, zero. Essentially no change in Twbetween wellhead and datum z2 is indicated in Profile 1 (an "isothermal" profile).

A jump in temperature at z1 is shown in Profile 3. This indicates fluid influx at this depth. Hot fluid enters the well at z1, mixes with the cold water from the wellhead, and the entire flow is injected at z2. Given the enthalpy/temperature of the inflow at z1, the amount of the inflow can be calculated by a heat balance. If H(T +

) is the enthalpy in the well above z1, H(T) is the enthalpy below z1 and H1 is the inflow enthalpy, then the inflow W1 is given by

RTENOTITLE....................(9.5)

Alternatively, the inflow at z1 can be directly measured by a spinner or other downhole flowmeter, and the inflow enthalpy can then be estimated from Eq. 9.5.

To quantitatively compare the fluid gain or loss at the two depths (z1 and z2), it is essential to compare the pressure profile in the well with that in the reservoir. Two possible pressure profiles are shown in Fig. 9.3. A much larger difference between wellbore and formation pressure at z2 than at z1 in Profile 1 need not imply less permeability at z2 than at z1. Pressure Profile 2 corresponding to temperature Profile 3 in Fig. 9.2 indicates that fluid enters the well at z1 and is injected into the formation at z2.


A typical temperature profile in a discharging geothermal well with several liquid feed zones is shown in Fig. 9.4. The feed zones are indicated by discontinuous changes in temperature gradient; the isothermal intervals between the feed zones denote impermeable zones. In this figure, the middle feed zone is a zone of cooler fluid, giving the temperature reversal. The ascending water boils at some depth (flash depth) in the wellbore; above this depth, the temperature profile follows the saturation curve for water. If the inflows from the various feed zones are known (say from a spinner survey), then Eq. 9.5 may be used to compute the feed-zone temperatures. Location of feed zones in a well with in-situ boiling (i.e., two-phase feed zones) is somewhat involved. The interpretation of PTS surveys in wells with two-phase feeds is discussed by Kaspereit[98] and by Spielman. [99]

The behavior of the well as it warms up after cold-water injection (or production with insitu boiling and the consequent drop in formation temperature around the wellbore) provides additional information regarding permeable zones. Permeability is often indicated by a marked feature, in successive surveys, such as a persistent cold zone, rapid warming, and interzonal flow. The permeable zone, which has accepted water during injection, may appear as a persistent cold feature as the well heats up (similar to the middle feed zone in Fig. 9.4). If the injected cold water does not move to other parts of the reservoir, it will take longer to heat this portion of the well than the impermeable sections of the well that have not accepted fluid. Alternatively, the permeable zones may permit rapid circulation of the injected water away from the well, and there appears a marked peak in the heating surveys. Finally, the disturbed pressures may initiate flow between two permeable zones of the well. Such a transient flow during warm-up is manifested by an isothermal temperature profile and implies permeable zones at both the end points of the isothermal interval.

Because of boiling, convection, and interzonal flow in the wellbore, it is necessary to carefully interpret downhole temperature data to deduce the reservoir temperature distribution. Great care must be exercised to identify those measurements affected by convection/interzonal flow and by boiling in the wellbore; such data often mask the true formation temperatures and should be discarded. Stable temperatures measured at feed depths usually provide the most reliable measures of reservoir temperatures. Liquid feed-zone temperatures are best determined from temperature surveys recorded in discharging wells. Additionally, in impermeable sections of the borehole, it is often possible to extrapolate the measured temperatures to estimate the formation temperatures. [96]

The pressure profile in a geothermal well can be measured directly by a downhole gauge. It is also possible to compute the downhole pressure from the water level data and the temperature gradient survey. Basically, this involves numerically integrating the differential equation,

RTENOTITLE....................(9.6)

together with the boundary condition p = poat z = zo(e.g., wellhead pressure). Here, zodenotes the water level in the well (measured downwards from the wellhead), ρ (p,T) denotes the fluid density, and g is the acceleration because of gravity. Given T(z) and p(z), density ρ (p,T) can be obtained from the thermodynamic equation-of-state data for liquid water. This procedure for calculating downhole pressures from water level data works only in single-phase (all liquid) wells. The presence of boiling conditions anywhere in the wellbore (below the water level, zo) invalidates the use of this method. Experience has shown that the downhole pressures computed from water level and temperature data are often more accurate than those recorded by downhole pressure gauges.

Regardless of how the downhole pressures are obtained, the pressure profiles can provide information regarding formation permeability by showing a "pivot" as the well warms. The mechanism is illustrated in Fig. 9.5. The well in Fig. 9.5 has a single entry at z1. Profile 1 is during cold-water injection. As the well heats up, two physical mechanisms affect the downhole pressures: the transient decay of the pressure buildup caused by injection and the change in gradient caused by the warming of the water column in the well. For injection into a homogeneous single-phase reservoir, the time required for the pressure transient to decay is proportional to the injection time; in practice, the pressure decay is usually complete before much warming of the water column has occurred. This produces pressure Profile 2, with the coldwater pressure gradient but where the pressure at z1 has reached equilibrium with reservoir pressure. As the well contacts the reservoir only at its permeable point, only here does it equilibrate with the reservoir pressure. The pressures measured at other depths in the well merely reflect the weight of the fluid column present in the well. As the well warms up, the water column lightens to produce Profiles 3 and 4. The successive profiles pivot about the reservoir pressure at depth z1.

The pressure pivot works best for wells in reservoirs with good permeability, where the pressure transients are small. If substantial transient effects are present, the pivot is displaced above the feed zone. As a check on the pivot, it should be defined by the intersection of more than two pressure surveys and preferably with as wide a range of temperatures as possible. Large temperature differences mean more contrast in pressure gradient. If the well has two significant permeable zones, the pressure pivot appears between them at a point weighted by the productivity ratio of the two zones. In this case, the pressure at the pivot lies between the reservoir pressures at the two zones and probably corresponds roughly to the reservoir pressure at the depth of the pivot. Having identified the well ’ s permeable depths, measured pressures at these different depths in the various wells can be used to construct a reservoir pressure profile. [96][97]

In practice, the application of the techniques discussed here to actual field data sometimes proves to be difficult. Temperature and pressure profiles in wells of poor permeability often fail to provide any definite indications of feed zones. Geothermal wells are frequently drilled with foam or air to avoid damaging the formation; in these cases fluid gain zones often go unnoticed. Because of the economic desirability of putting a geothermal well on production quickly, long-term temperature recovery is in many cases not recorded; this makes the determination of stable reservoir temperatures very difficult. Because of variations in hole diameter and condition (slotted and blank intervals) and changes in fluid state downhole, spinner data (in the absence of simultaneous pressure and temperature surveys) may yield ambiguous interpretations. In spite of these limitations, the interpretation methods discussed herein have been used in numerous cases to successfully locate a well’ s permeable horizons. [96][97][99]

Pressure Transient Data Pressure transient tests are conducted to diagnose a well’ s condition and to estimate formation properties. The test data may be analyzed to yield quantitative information regarding (1) formation permeability, storativity, and porosity, (2) the presence of barriers and leaky boundaries, (3) the condition of the well (i.e., damaged or stimulated), (4) the presence of major fractures close to the well, and (5) the mean formation pressure. After well completion, testing is performed by producing one or more wells at controlled rates and monitoring downhole pressure changes within the producing well itself or nearby observation wells (interference tests). A comprehensive review of techniques for analyzing pressure transient data may be found in monographs by Matthews and Russell, [100] Earlougher, [101] and Streltsova. [102] Also, see the Reservoir Engineering and Petrophysics volume of this Handbook. Much of the existing literature[101] deals with isothermal single-phase (water/oil/gas) and isothermal two-phase (oil with gas in solution, free gas) systems. Geothermal reservoirs commonly involve nonisothermal, two-phase flow during well testing. In addition, geothermal wells, unlike most oil/gas wells, do not usually penetrate a formation with uniform properties. In this section, these and other problems that are specific to geothermal well testing are briefly discussed.

Partial Penetration The line source solution forms the basis of most of the existing techniques for pressure transient analysis. It is assumed that the production (or injection) well fully penetrates an aquifer of uniform and homogeneous permeability. In a geothermal reservoir, the bulk of formation permeability is associated with thin stratigraphic units and/or a fracture network. The well is open to the reservoir only at the depths where it intersects the permeable zones, and for the balance of its depth, the well penetrates impermeable rock. A geothermal well is comparable to an oil/groundwater well that only partially penetrates the permeable formation. The mathematical theory for a partially penetrating well has been developed by Nisle[103] and Brons and Marting. [104] Partial penetration is detectable from the shape of the buildup (or drawdown) curve. A Horner plot of the buildup data shows the existence of two straight lines. The penetration ratio is given by the ratio of the slope of the late part to that of the early part of the buildup curve. In at least some geothermal wells, the permeable interval(s) constitutes such a small fraction of the "total formation thickness" that it is not meaningful to define a penetration ratio. For small flow/shut-in times, the well in these cases exhibits a pressure response resembling that of an spherically symmetric source/sink and not a line source/sink. The mathematical theory for a geothermal well undergoing spherical flow is presented by Tang. [105] For the spherical flow period, a plot of pressure drop or pressure buildup vs. tp–0.5 orΔt–0.5 (tp= total production time, Δt = shut-in time) yields a straight line; the slope of the straight line can be used to compute the formation permeability. One important consequence of partial penetration in geothermal systems is that the transmissivity value determined from interference tests frequently exceeds that of single-well tests.

Drawdown/Buildup Analysis for Two-Phase Wells A geothermal system may be two-phase before production begins or may evolve into a two-phase system as a result of fluid production. Theoretical analysis of pressure drawdown and pressure buildup data from single wells in such systems has been published by Grant, [106] Garg, [107] Garg and Pritchett, [108] Moench and Atkinson, [109] and Sorey et al.[110] For a constant rate of mass production, W, a Horner plot of pressure buildup vs. log[ (t + Δt)/Δt]

gives a straight line at late times. (For drawdown tests, well pressure vs. logarithm of production time, t, yields a straight line.) Here, t denotes the production time, and Δt is the shut-in time. The slope m of the straight line is related to the "kinematic mobility,"

RTENOTITLE....................(9.7)

where

RTENOTITLE....................(9.8)

In Eqs. 9.7 and 9.8, k is the absolute formation permeability, Htis the formation thickness, krℓ (krg)is the liquid (gas) phase relative permeability, and υ(υg) is the liquid (gas) phase kinematic viscosity.

Given the specific flowing enthalpy Hf, it also is possible to estimate the separate liquid and vapor phase mobilities.

RTENOTITLE....................(9.9)

and

RTENOTITLE....................(9.10)

where H(Hg) denotes the specific liquid (gas) phase enthalpy. The flowing enthalpy, Hf, is given by

RTENOTITLE....................(9.11)

where mg is the vapor mass fraction of the fluid flow. Substituting from Eq. 9.11 into Eq. 9.9 and Eq. 9.10, it follows that

RTENOTITLE....................(9.12)

To evaluate krg and krℓ separately, an additional relation is required between krg and krℓ.

The previously described analysis procedure for drawdown/buildup data is only approximate. Because of the nonlinear nature of two-phase flow, buildup and drawdown tests yield different values for kinematic mobility k/νt; this introduces an element of uncertainty in the determination of k/νt.

A second complicating factor arises in the calculation of well skin factor, S. Grant and Sorey[111] showed that the compressibility of two-phase mixtures of steam and water in porous rock can be written as

RTENOTITLE....................(9.13)

where Cpr and Cpw are the specific heat capacities of rock and water respectively; ρr, ρw, and ρv are the densities of rock, water, and steam, respectively; Lv is the enthalpy change because of boiling; Psat and Tsat are the saturation pressure and temperature; and Φ is the porosity. This expression does not include the compressibility of each phase; it merely accounts for the volumetric change because of phase change. For typical geothermal problems, however, this compressibility is 102 larger than steam compressibility and 104 larger than liquid. Grant and Sorey[111] also show that the compressibility can be approximated by

RTENOTITLE....................(9.14)

where compressibility, ct, is in bar–1; bulk volumetric heat capacity ρCp is in kJ/m3-°C; and pressure, P, is in bars.

An additional complication frequently arises in practice. If the pressure gauge is not located adjacent to the major entry for a well, then the pressure data must be corrected for the pressure difference between the gauge location and the feed point. If the well contains two-phase fluid, it will generally be necessary to correct the measured pressures by different amounts for different drawdown/buildup times. In Fig. 9.6, taken from Riney and Garg, [93] a semilog plot is presented of the pressure buildup for Well B-20 at a depth of 1,372 m, where most of the downhole pressure recordings were made. The primary production zone for this well is located at a depth of 1,220 m. Several pressure gradient surveys made during the buildup period show that the well is two-phase. Riney and Garg[93] used these pressure gradient surveys to estimate the buildup pressures at the feed-point depth of 1,220 m; the replotted Horner plot is given in Fig. 9.7. A comparison of Fig. 9.6 and 9.7 shows that the slope of straight line in Fig. 9.7 is approximately one-half of that in Fig. 9.6.

Decline Curve Analysis A method that has enjoyed extensive use in geothermal engineering for production forecasting is decline curve analysis. Two types of decline curve analysis are used: empirical rate-time analysis using the Arps method[112] and Fetkovich-type curves. [113] Their application and limitations of use are discussed below.

Empirical decline curves consist of plotting rate as a function of time in either Cartesian, semilog, or log-log coordinates. The usual goal is to establish a linear trend between rate and time and use that relationship to forecast future production schedules, abandonment rates, production cumulatives, etc. It requires a continuous history of static reservoir pressure and/or flow rates at constant flowing wellhead pressure. These data are often not available for a variety of reasons, but can be estimated from production data. First, the well mass flow rate, W, must be normalized against a standard flowing wellhead pressure, Pstd. [114]

RTENOTITLE....................(9.15)

where W is the measured flow rate, p is the estimated (or measured) static wellhead pressure, and Pwf is the measured well flowing pressure. This relationship was developed for steam wells; for liquid-dominated wells, the appropriate equation is

RTENOTITLE....................(9.16)

Having normalized the rate against a reference pressure, decline analysis can then be used. It is important to note the dangers in extrapolating rates too far into the future, given that a phase change, for example, may lead to orders of magnitude change in density, kinematic viscosity, compressibility, etc. The normalized rate can then be analyzed with either Arps-type decline curves or Fetkovich-type curves.

Decline-curve analysis is based on the empirical rate decline equations originally given by Arps. [112] The general rate-time equation can be written as

RTENOTITLE....................(9.17)

Di is decline rate, b is the Arps exponent (0 ≤ b ≤ 1), and t is time. Depending on the value of b, the following forms of rate decline can be identified.

RTENOTITLE....................(9.18)

RTENOTITLE....................(9.19)

RTENOTITLE....................(9.20)

These decline equations can be used to estimate abandonment flow rates or time.

Fetkovich-type curves[113] can also be used to estimate decline rates and reservoir properties. These type curves were originally developed to provide a theoretical basis for decline curve analysis and are used to estimate the decline parameters Di and b. The type curves also provide estimates of permeability-thickness product and wellbore skin properties. The Fetkovich decline equations can be used with the relevant changes in units (e.g., from volumetric flow rate to mass flow rates).

RTENOTITLE....................(9.21)

and

RTENOTITLE....................(9.22)

For vapor-dominated reservoirs, one can also use a pseudo-pressure approach (e.g., Faulder[115]). The application of Fetkovich-type curves for geothermal well analysis is similar to that of oil/ gas wells, with a few caveats. Most importantly, if reservoir conditions are two-phase, or if boiling is induced in the vicinity of the wellbore, the effective compressibility follows from Grant and Sorey. [111] If conditions change (e.g., if boiling is induced, or if the reservoir becomes superheated), the compressibility is discontinuous, changing by more than two orders of magnitude. Also, if phase conditions change, the well decline rate will also be incorrect. It is thus dangerous to predict geothermal well behavior too far into the future if such phase change possibilities exist.

With the above caveats, one applies the Fetkovich-type curves in the following fashion:

  • Normalize the well flow rates against a standard flowing well pressure using the backflow equations (Eqs. 9.15 or 9.16) as appropriate. The flow rates may have to be renormalized occasionally, if for example, substantial disruption of production occurs and transient conditions again prevail.
  • Plot the normalized rate vs. time on log-log tracing paper of the same size as the type curve to be used.
  • Shift the tracing paper, keeping the axes aligned, to obtain agreement between the real data and the type curve. A match point can be selected from the overlay, and reservoir properties (kh, re, and S) can be determined from the match point.
  • From the pseudo-steady-state portion of the production, the decline parameter, b, can be determined. Note that an attempt to estimate b from the transient data may either give a nonunique[113] or nonphysical value[116] for b.


Tracer Testing

Tracers are used in geothermal reservoir engineering to determine the connectivity between injection and production wells. Reinjection of spent geothermal fluid is nearly universal—to address environmental concerns as well as to provide reservoir pressure maintenance and improve energy extraction efficiency. Because injected fluids are much cooler than in-situ fluids, knowledge of injectate flow paths helps mitigate premature thermal breakthrough. As in other applications of tracer testing, the goal of the tracer test is to estimate sweep efficiency of a given injection pattern. [117] Because geothermal systems tend to be open, tracer tests can also be used to estimate the extent of recharge/discharge or total pore volume. [118][119] Currently, however, the primary use of geothermal tracers is to estimate the degree of connectivity between injectors and producers. That information is subsequently used to develop an injection program that either minimizes or postpones injection returns in production wells while providing pressure maintenance.

Geothermal Tracers Because geothermal reservoirs are not usually developed on regular well spacing, well pairs may exhibit weak connectivity, and tracer tests must be conducted over long times, using large volumes of tracer to overcome thermal decay and dilution effects. For these and other reasons, extensive work has been invested in evaluating so-called "natural tracers." These can be thought of as compounds that are present in geothermal fluids naturally and whose concentrations may change during production and injection and may therefore be used to trace injectate. Examples of natural tracers include chloride, [120] ammonia, [121] and various stable isotopes of water. [122][123][124]

Artificial tracers have also been used extensively to determine flow paths in geothermal reservoirs. Tritium was the first artificial tracer used to trace geothermal injectate. [125] Since the early 1990s, various new compounds have been evaluated for use in geothermal reservoirs. Liquid-phase tracers have evolved from carboxylic and benzene sulfonic acids[126] to polyaromatic sulfonates, [127] which are stable thermally at temperatures greater than 300°C and have detection limits in the range of 102 parts per trillion (ppt). Vapor-phase tracers have evolved from chlorofluorocarbons used in the early 1990s to hydrofluorocarbons in the late 1990s. [128] To date, criteria for selection of tracers focus on thermal stability, low background concentrations, low detectability, and being environmentally benign. More recently, issues such as sorptivity and volatility have been recognized as equally relevant characteristics that influence analysis. [129]

Tracer tests have been conducted for over 25 years in geothermal fields, including early work in New Zealand, [130] The Geysers in Northern California, [125] Lardarello in Italy, [131] and various Japanese fields. [132] In the last decade, more than 50 tracer tests have been conducted worldwide in geothermal fields.

Interpretation Methods Early workers in the field recognized that tracer tests could be used quantitatively to evaluate volumetric sweep efficiency of an injection program. Lovekin and Horne[133] applied optimization methods to maximize the residence time of injectate. This involved minimizing a tracer breakthrough function.

RTENOTITLE....................(9.23)

where the cij are referred to as the arc cost function for the travel arc between a given injection and production well pair (e.g., a streamline), and qri is the injection rate for injector i. The cost function is related to operational and geologic information for the field, including tracer first arrival and peak arrival times, horizontal distances and elevation differences between wells, injection and production rates, etc. The method was applied to optimizing production operations at the Wairakei Field in New Zealand. [133]

In 1991, Macario extended the previous work to use a natural tracer, chloride, to optimize reinjection in the Philippine field, Palinpinon. Shortly after commissioning the power plant in 1983, an increasing trend of chloride in the production wells was observed. This was interpreted as evidence of rapid return of reinjected fluids to the production sector of the field. [134] Because the chloride trend is associated with all injectate (i.e., not a specific injector), Macario[135] developed a linear combination method that expresses the chloride concentration as a linear combination of the injection wells active during the time interval considered. Produced chloride for a given well, Clp, is expressed as a linear function of the chloride injection rates.

RTENOTITLE....................(9.24)

The coefficients ai are coefficients of correlation between a given producer and injector. A large coefficient implies strong production contribution from a given injector. These coefficients can subsequently be used in the arc cost function. These methods appear to work well if there is operational flexibility to use the appropriate wells and work equally well for either natural or artificial tracers.

Noting that fluctuations in injection rates manifest themselves as changes in produced chloride concentrations over and above the underlying trend in time, Sullera and Horne[120] applied wavelet analysis to two geothermal fields: Palinpinon in the Phillipines and Dixie Valley in Nevada. The chloride production data and injection rates are decomposed into progressively lower-frequency detail, and multiple regression techniques are applied to identify the degree of connectivity between individual injectors and producers. Care must be taken to avoid decomposing the signal too far; however, Sullera and Horne[120] show the method yields large, positive correlation coefficients for well pairs identified by tracer tests to have strong connectivity, and low positive, or negative coefficients for well pairs with known poor connectivity. The authors also showed that the data set being transformed must have sufficient temporal "texture" for wavelet analysis to be useful.

Some additional quantitative analysis has been done using synthetic tracer tests. One reservoir management concern is to identify the velocity of thermal fronts in the reservoir. The velocity of a temperature front, vT, is related to the fluid velocity, vw, in a fixed manner. [136]

RTENOTITLE....................(9.25)

By transforming tracer production data at each production well, Shook[117] showed that thermal velocities can be predicted from tracer tests. These studies were restricted to heterogeneous, nonfractured media and single-phase conditions, where thermal conduction is largely a secondorder effect. Efforts to extend the method to fractured media have met with limited success, in particular because of fracture geometry. Likewise, quantitative analysis of tracers in two-phase or superheated steam reservoirs is difficult. Because the tracer is transported by either of the phases at various times (e.g., vaporizing here and condensing there), mean residence times are more difficult to interpret. Under certain conditions, a boiling interface may develop between the fluid originally in place and the cooler injectate. [137] The velocity of this boiling front has been studied analytically, [138][139] and can be predicted for simple geometries and homogeneous reservoir conditions. In cases where buoyancy is important, however, the vaporized tracer may not trace injectate flow paths, making the interpretation still more difficult. Predicting thermal velocities in fractured media remains an active research topic in geothermal tracing.

Analysis of tracer tests conducted in geothermal fields ranges from purely qualitative to quantitative, volumetric analysis of pore volume. Matsunaga et al.[140] show an analysis of seven tracer tests conducted at the Hijiori, Japan, engineered geothermal system. By comparing mean residence times[141] for consecutive tracer tests, they showed that the flow system was evolving during the injection of cool (25 to 50°C) liquid into initially hot ( ~

150°C) dry rock. They concluded in part that anhydrite scaling was plugging some of the fractures, thereby modifying the flow field. They also noted a rapid decline in produced temperature during the injection tests, but did not correlate the thermal velocities with tracer velocities. The Hijiori geothermal reservoir is among the most instrumented and studied engineered geothermal systems in the world. A variety of tracer tests have been conducted and reported on over a number of years. [140][142][143]

Other than the analyses for the Hijiori field tracer tests, a majority of tracer test interpretations remains qualitative. Fig. 9.8 is an example of analysis of several tracer tests conducted at Dixie Valley, Nevada. The geothermal field has been a test facility for testing naphthalene sulfonates for a number of years, and seven such tests have been conducted since 1997. [127] The relative size of the arrows is indicative of the relative contribution of an injector on a set of producers. Estimates of reservoir pore volume have also been calculated on the basis of tracer dilution. [144] However, the interpretation in the figure (i.e., relative contribution of injectors to production areas) remains the most-used information from these tracer tests.


An example of tracer test interpretation in vapor-dominated reservoirs is given in Fig. 9.9. This figure summarizes the interpretation of a tracer test conducted in The Geysers geothermal field in Northern California. In this test, two hydrofluorocarbons, R23 and R134a, and tritiated water were injected into a zone containing moderately (~ 15°C) superheated steam. Fig. 9.9 shows the cumulative mass fraction of R134a and tritium recovered from wells surrounding the injector. Tritiated water is a nearly ideal geothermal tracer because its properties are nearly identical with those of water and, therefore, tracks the injectate very well. Adams et al.[128] suggest that the similarity in recovery between the tritium and R134a suggests both compounds remained with the injectate, indicating R134a is a useful tracer for areas with low or moderate superheat. Another tracer test conducted in a highly superheated zone at The Geysers showed substantial separation between tritiated water and the chlorofluorocarbon R13. [128] The authors concluded that a large degree of superheat exaggerates the effect of volatility, and caution should be exercised in using tracers whose volatility greatly exceeds that of water when superheated conditions prevail.


While some tracer tests have been modeled, [145] this is one aspect of tracer test analysis that has tended to lag behind oilfield practices. Recent advances have been made in improving the phase behavior routines for vapor-liquid partitioning tracers, [119][146] and use of modeling tracer tests is expected to increase.

Numerical Simulation

Simulation of geothermal processes involves solution of highly nonlinear, coupled equations describing mass and energy transport in complex, heterogeneous media. The first models of geothermal simulation appeared in the 1970s. [147][148][149] However, it was not until the 1980 Code Comparison Study[150] that numerical models for reservoir management were generally accepted. In that code comparison study, a suite of six geothermal problems were made available to geothermal code developers, and results of the problem set were published. The results showed that numerical models were capable of solving these complex equations. Since that time, numerical models have been developed for more than 100 geothermal fields. O ’ Sullivan et al.[151] present an excellent overview of geothermal reservoir simulation.

Coupled mass and energy (heat) transport in heterogeneous media is a complex problem. The primary component of geothermal reservoirs is water, which can exist in a vapor, liquid, or adsorbed state. [152] Phase behavior is further complicated by vapor pressure lowering[153] and by the presence of noncondensible gases (e.g., CO2) and salts. Phase changes (condensation and vaporization) occur in native state heat pipes[4][154] and also because of injection/production operations. Minerals may also precipitate or dissolve in response to phase change, affecting permeability and porosity in near-well regions.

The basic equations that are solved in geothermal simulation are the same as in thermal petroleum (or hydrology) simulation: conservation of mass for each component and conservation of overall energy. These can be found in standard references[155] and are not repeated here. The significant differences are discussed next.

Conceptual Models and the Native State

Geothermal reservoirs frequently exhibit conditions not encountered in petroleum reservoirs. Convection cells arising from local differences in heat flux are encountered in the native (i.e., pre-exploited) state, and both energy and mass are in a state of dynamic equilibrium. In addition to the more conventional issues of reservoir structure, fault locations, permeability structure, etc., there exist other concerns that impact initializing a geothermal simulation model. Reservoir boundaries are typically not sealed, and conceptual reservoir models must capture heat flux from a localized or variable heat source from below, heat loss to caprock or atmosphere (e.g., via fumaroles, steaming ground, etc.), and fluid recharge and discharge locations and magnitude. Large chemical changes occur spatially, in part, because of Rayleigh condensation patterns[156] and fluid recharge.

Effect of Fractures Reservoirs are nearly universally fractured, requiring accurate treatment of flow through primary flowpaths, storage in bulk porosity, and mass and energy transfer between the two. While many petroleum reservoirs are also fractured, a "representative" pressure diffusivity κ = k/Φ μc for geothermal reservoirs is 1 to 2 orders of magnitude lower than for petroleum reservoirs, because, in large part, of lower matrix permeability and larger effective compressibility. This invariably implies that either a Multiple Interacting Continua (MINC) or MINC-like[157][158] method or other variation of dual-porosity model[159] be used to simulate pressure and temperature transients. Some studies have included explicit representation of dominant fractures[160][161]; however, most hydrothermal reservoir models employ some type of continuum model.

Simulation Process As already noted, a typical geothermal reservoir is in dynamic equilibrium with its surroundings, with boundaries at least partially open and large heat flux both into and out of the reservoir. For these reasons, a reservoir simulation study usually commences with a native state model, in which the initial (dynamic) state is simulated over geologic time. At steady state, temperature distributions, locations, and strength of observed discharge (e.g., hot springs), and chemistry are compared against simulated results, and the reservoir structure is adjusted accordingly. Input parameters that may be changed during this stage include the permeability structure and location and strength and chemical makeup of inflow (both heat and mass). After obtaining a good match between simulated and observed initial conditions, what production history exists is then history matched. Data used in this effort include production rates, enthalpy, and geochemistry of the produced fluids, either by an individual well or a combination of wells. Relatively recent history match exercises have included tracer test results[162] and geophysical measurements[163][164][165][166] to assist in the model-calibration exercise.

Recent Advances Since the mid-1990s, several new capabilities have been developed to facilitate geothermal reservoir simulation. In particular, inverse modeling and uncertainty analysis[167] are used to replace the tedious and often subjective, manual history-match exercises with automated methods. More recent work has focused on extending those concepts by adding geophysical measurements to the model calibration work, and several research groups are working towards using this combined suite of tools to estimate reservoir parameters and reduce the associated uncertainty.

Geothermal reservoir fluids are geochemically complex, typically not neutral pH, and exhibit a large degree of rock-fluid interaction. Until recently, geothermal simulators treated the fluids as pure water. That has changed within the last decade, with equations of state available to treat mixtures of water, CO2, and dissolved solids. [168][169][170] More sophisticated multicomponent chemical models have been developed for geothermal application but are largely restricted to phase behavior routines that neglect flow. [171][172][173] More recent attempts have been made to develop fully coupled transport and chemical interaction models. [174][175] While not fully developed as yet, these models have been used to evaluate minerals extraction from geothermal brines. [176]

While not normally considered for hydrothermal reservoir simulation, coupled thermal, hydrologic, and mechanical (T-H-M) models are being developed for studying enhanced geothermal systems (EGS) reservoirs. [177] Other groups are extending the thermodynamic limits of fluid properties to super-critical conditions to study deep-seated geothermal zones. [178][179][180]

Field Operations

Stimulating Production

Higher-temperature wells are normally self-energized and produce without stimulation. Initial production of a well is usually allowed to discharge to a surge pit to allow for cleanup of the wellbore of debris from drilling operations. If a well is self-energized, it is also important to know whether the produced fluid remains single phase in the wellbore. Friction losses are much greater for two-phase flow, so increasing the casing diameter at the point where the fluid flashes to vapor will increase production. A well that does not discharge spontaneously will require stimulation. There are several methods of stimulation used.

Swabbing This technique involves lowering a swab down the well, below the water or mud line. A one-way valve in the swab permits the fluid to pass by the swab as it is lowered into the well. Raising the swab lifts the water column out of the well to reduce the hydrostatic pressure on the producing formation so the well begins to discharge fluids spontaneously. This method may take several trips in and out of the well to initiate flashing and induce flow.

Coil Tubing and Liquid Nitrogen The removal of fluid from the top of the column can be achieved by running tubing into the well below the fluid level and injecting liquid nitrogen to lighten the column and induce boiling in the well. This method is the most common method of bringing a well back online after well remediation or surface facility shutdowns.

Compressed Air Compressed air can be deployed instead of nitrogen and is preferred over swabbing, mainly for safety and well control reasons. Standard air compressors are used in conjunction with drill pipe. The annulus is pressurized with air and the column of liquid is reverse-circulated through the drill pipe.

Foaming Agents Foaming agents help reduce the weight of the water column by emulsifying air or nitrogen in the liquid, thus keeping the gas entrained in the liquid and providing greater lift.

Decompression This method has been used to stimulate water wells for agricultural purposes and is sometimes effective in starting a geothermal well. This method consists of pressurizing the wellbore with compressed air and quickly depressurizing the well to atmospheric pressure to induce boiling.

Pumped Wells If the well does not produce spontaneously and does not respond to stimulation or if the power production facility is designed to only handle geothermal liquids and not two-phase or vapor flows, it will be necessary to install a pump. Conventional technology for many years was a line-shaft pump with the motor at the surface and the impeller set some distance below the drawdown water level in the well. This arrangement requires a straight, vertical wellbore down to the pump depth. There also may be restrictions on pump depth because line-shaft pumps have limits on how far torque can be effectively transmitted down the wellbore. Recently, high-temperature-capable submersible pumps have been developed that give good service up to about 200°C. The pump must be located at a depth sufficient to avoid cavitations at all flow rates expected.

Curtailments Curtailments are planned or unplanned circumstances that require wells to either be shut-in completely or throttled. Examples of curtailments include intentionally throttling production back during off-peak power needs (load following), unexpected tripping of generation equipment, or other surface problems that may require forced outages. Some wells may load up with liquid and stop flowing if any flow constraint is imposed. These wells might then require stimulation to restart production. In cases where short down-time is expected, or to prevent the well from cooling, a plant bypass system might be installed at the surface to keep the well flowing. The bypass system can be a turbine bypass that passes the steam through a condenser (and the condensate back into the resource) or route steam to an atmospheric muffler system. When venting steam to atmosphere is a safety or environmental concern, a condensing system is generally used.

Injection Injection initially started as a disposal method but has more recently been recognized as an essential and important part of reservoir management. Sustainable geothermal energy use depends on reinjection of produced fluid to enhance energy production and maintain reservoir pressure. A simple volumetric calculation shows that over 90% of the energy resides in the rock matrix; hence, failure to inject multiple pore volumes results in poor energy recovery efficiency. When the usable energy is extracted from the fluid, the spent fluids must be disposed, reused in a direct use application, or injected back into the resource. Despite efforts to maximize the fraction of fluids reinjected, it is common for losses to approach 50%, mainly through evaporative cooling tower loss. Frequently, makeup water is used to augment injection. Failure to reinject can lead to severe reductions in production rates from falling reservoir pressure, [181] interaction between cool groundwater and the geothermal resource, [182] ground subsidence, [183] or rapid dryout of the resource. [184]

Measurements in Geothermal Production Applications


Measurements of mass flow and the constituents of the mass produced are integral in the productionof geothermal fluids. From regulatory and royalty payment issues to monitoring the condition of the resource and abatement of corrosive constituents in the geothermal fluid, physical and chemical measurements are a necessity for geothermal production and utilization.

Mass Flow

Single-Phase Flow Depending on the phase being produced, the operator has a choice of many instruments for measuring flow. Conventional methods are typically used to measure flow for single-phase systems. The choice of flow element and meter initially depends on the mass and/or volumetric flow rate, turn-down ratio (range of flow to be measured), the pressure, temperature, and extent of flow surging. Fluid chemistry is also a factor that can affect reliability because geothermal fluids may be very corrosive and can deposit scale or contain solids that plug the instrument and produce inaccurate measurements. [185] Differential producer-type flowmeters, such as orifice, venturi, V-cone, annubar and pitot tubes, are often used for steam, water and gas-flow rate measurement. Vortex and ultrasonic flowmeters are also sometimes used.

Because of the harsh conditions of geothermal production, conventional flowmeters may not maintain their calibration or even survive long in geothermal service. Because a large number of wells, consisting of many single- and two-phase flow streams, may produce to a power plant, a sufficient number of flowmeters is seldom installed to provide a complete mass balance on the system. In fact, many geothermal fields are produced without continuous flow-rate monitoring of the wells or total fluid through the power plant. Therefore, flow measurement is often necessary using portable, point-by-point, nondisruptive techniques.

One technique for single-phase vapor or brine flow measurement is a pitot tube traverse using an S-type pitot tube. The measurement principle is similar to that of an annubar, but the pitot tube can be easily inserted and removed through a small valve on the pipeline. This allows measurement of flow in any straight section of pipe that has an access port at least 1 in. [ 2.54 cm] in diameter. The pitot tube can traverse across the pipeline diameter to obtain high-resolution velocity profiles and accurate bulk flow rate measurements. These flow measurements are made in single-phase pipelines where conventional flowmeters either do not exist or require external calibration.

This pitot tube is referred to an S-type because of the shape of the tip. The velocity pressure tube bends into the flowstream and the static pressure tube bends downstream. This configuration results in a compact tip assembly less than 1 in.[ 2.54 cm] in diameter and has the added benefit of amplifying the differential pressure reading by up to 2 times that of a standard pitot tube or annubar. A thermocouple sheath usually extends slightly beyond the pressure-sensing tubes to protect the tubes from impact against the pipe wall and to allow for concurrent temperature measurement to temperature-compensate the change in density of the fluid.

The differential pressure is typically measured by a transducer with an accuracy of about+ /–0.2% of full scale. Temperature is also measured so that saturation temperature and/or superheat values can be determined at each traverse point for the final volumetric and mass flow calculation. One of the most important features of a properly designed pitot tube system is the back-purge capability. The pressure sensing lines must be flushed with pressurized nitrogen or air at regular intervals during the measurement process to ensure that no condensate or brine accumulates in the lines. The presence of liquid in pressure sensing lines is the most common cause for error in standard differential-pressure flowmeters.

Another technique for nondisruptive, portable flow measurement is tracer flow testing (TFT). This method was originally developed for two-phase flow[186] but has the same applications for single-phase flow as the pitot tube. The basic principle behind the TFT method is to inject a conservative liquid or vapor tracer at a known rate upstream of a sample point. At the sample point, mass of tracer can be measured in the sample and calculations of flow rate can be determined. This method can be used to accurately calibrate stationary flowmeters.

Two-Phase Flow Two-phase fluid-flow measurement by conventional mechanical devices is a more difficult problem. [187] The most conventional method is to install production separators at the wellhead and measure the separated liquid and vapor produced by the techniques already described. Because of the high capital cost of wellhead separation systems, fluid gathering systems are usually installed, and vapor and fluid are separated at a more centralized facility.

In two-phase geothermal fields, monitoring the enthalpy of produced fluids is important in understanding the reservoir performance. Decreasing enthalpy can indicate breakthrough of injection water or invasion of cooler groundwater, while increasing enthalpy can indicate reservoir boiling and the formation of a steam cap. Enthalpy is essential for the interpretation of geochemical data because it determines the steam fraction at sampling conditions and allows the correction of chemical concentrations back to reservoir conditions. Enthalpy and mass flow rate govern the amount of steam available from each well and ultimately the energy output of the power plant.

Mass flow rate of steam and water phases and total enthalpy of the flow can be measured directly for individual geothermal wells that produce to dedicated separators. However, because of the high capital cost of production separators, most geothermal fluid gathering systems are designed with satellite separation stations in which several wells produce to a single separator. In many cases, all of the two-phase fluids produced from a field are combined by the gathering system and separated in a large vessel at the power plant. Without dedicated production separators for each well, the steam and water mass flow rates and total enthalpy of individual wells cannot be measured during production.

An atmospheric separator, James tube and weir box can provide reasonably accurate enthalpy and mass-flow rate values. [188] However, as this method requires diversion of flow from the power plant, with subsequent revenue losses, it is most frequently used during development production tests. In some fields, atmospheric venting of steam may not be allowed because of environmental regulations for hydrogen sulfide emissions and brine carryover.

The injection of chemical tracers into two-phase flow (i.e., TFT) allows the determination of steam and water mass flow rates directly from tracer concentrations and tracer injection rates, without disrupting the normal production conditions of the well. There are currently no other online two-phase flowmetering systems available for geothermal applications, but testing of a vortex shedding flowmeter (VFM) with a dielectric steam quality sensor (DSQS) was performed at the Okuaizu field, Japan in October 1998. [189] The VFM/DSQS system was calibrated against the TFT method, and two of the three tests agreed within 10%. The DSQS is sensitive to liquid and vapor phase electrical conductivity, so large corrections are required for dissolved salts in brine and noncondensable gases (NCG) in steam. It was also concluded that the sensors would be adversely affected by scale deposition if used in continuous operation.

The tracer flow test technique requires precisely metered rates of liquid- and vapor-phase tracers injected into the two-phase flow stream. Samples of each phase are collected with sampling separators at a location downstream of the injection point to ensure complete mixing of the tracers in their respective phases. The water and steam samples are analyzed for tracer content, and the mass flow rate of each phase is calculated based on these measured concentrations and the injection rate of each tracer.

The mass rate of liquid (WL) and steam (WV) is given by

RTENOTITLE....................(9.26)

where

WL,V = mass rate of fluid (liquid or steam),
WT = tracer injection mass rate,
and
CT = tracer concentration by weight.
The mass rates calculated for each phase are valid for the temperature and pressure at the sample collection point. The total fluid enthalpy can then be calculated from a heat and mass balance equation using the known enthalpies of pure liquid and steam at the sample collection pressure/temperature. Enthalpy corrections can be made for high-salinity brine and high-NCG steam, if necessary. [186]

The TFT liquid tracer can be measured directly on site and even online to obtain real-time liquid mass flow rate data using a dedicated portable analyzer. [190] Data resolution is greatly improved over the discrete grab-sampling technique, especially under surging flow conditions. The gas tracer, usually sulfur hexafluoride (SF6), can also be sampled on site using portable instrumentation so that single-phase steam and two-phase flow-rate results are immediately available. Automated online systems can be used for continuous metering of multiple single and two-phase flow streams.

Examples of data from online brine flow measurements are shown in Figs. 9.10 and 9.11, as measured by a portable field analyzer for the liquid tracer. Note that the first well (Fig. 9.10) was producing at a stable rate, while the second well was surging significantly (Fig. 9.11). Well behavior and detailed flow resolution can be obtained by continuous real-time monitoring.

During flow testing, the continuous total mass flow rate can also be monitored using a two-phase orifice meter. In this case, TFT is used at regular intervals to determine the total discharge enthalpy, which is needed for the two-phase orifice calculation, and to calibrate the orifice meter. This technique is used at some power production facilities for continuous monitoring of wells in production to the power plants, with intermittent measurements by TFT. An example of the correlation between the two-phase orifice meter and TFT measurement for total flow is shown in Fig. 9.12 for the production wells at the Coso, California power plant. Although two-phase orifice metering is accurate to only about +

/– 20%, it provides useful real-time trending data for total flow rate.


Flow Measurement Errors in Well Testing

The errors typically associated with the TFT measurement process are summarized in Table 9.8. For comparison, an error analysis performed for a standard James-tube well test in the Philippines is given in Table 9.9, with calculations for two types of weirs used in brine flow measurement. The James-tube technique was a common well test method before the development of TFT. Drawbacks to the James-tube technique are the requirement that the well must be discharged to atmosphere and limited accuracy, especially at higher enthalpies.

Fluid Compositions

Sampling of two-phase geothermal fluid requires special techniques involving inertial separation of phases. [191] Geothermal steam frequently contains small amounts of entrained liquid water, noncondensable gases such as CO2, and other constituents such as silica. [192] Some impurities, such as NaCl, may be present as dissolved species in the liquid or as solid particulate. [193] These other constituents affect power generation efficiency and corrosion, [194] but extensive discussion of their measurement is beyond the scope of this section. Relevant terminology is summarized briefly next.

  • Steam purity is the proportion of pure water (both liquid and vapor) in a fluid mixture. Typically, only steam impurity is discussed in quantitative terms and is expressed in units of concentration by mass in the mixture.
  • Total dissolved solids is the concentration by mass of nonvolatile, dissolved impurities in the steam. These typically include silica, salts, and iron. Semivolatile constituents such as boric acid are not usually considered as part of the TDS.
  • Noncondensable gases (NCG) are the other constituents that have a pronounced affect on geothermal operations. NCG is typically defined as a mass fraction, or weight percent. Principal


NCG constituents include CO2, H2S, NH4, CH4, and H2. The amount of NCG produced with geothermal fluids must be known to correctly size NCG removal systems.

Geothermal Energy Conversion Systems for the Production of Electrical Power


The type of energy conversion system used to produce electrical power from a geothermal resource depends on the type and quality (temperature) of the resource. Vapor-dominated resources use conversion systems where the produced steam is expanded directly through a turbine. Liquid-dominated resources use either flash-steam or binary systems, with the binary conversion system predominately used with the lower temperature resources.

Direct Steam Systems/Vapor-Dominated Resources

When the geothermal resource produces a saturated or superheated vapor, the steam is collected from the production wells and sent to a conventional steam turbine (see Fig. 9.13). Before the steam enters the turbine, appropriate measures are taken to remove any solid debris from the steam flow, as well as corrosive substances contained in the process stream (typically removed with water washing). If the steam at the wellhead is saturated, steps are taken to remove any liquid that is present or forms prior to the steam entering the turbine. Normally, a condensing turbine is used; however, in some instances, a backpressure turbine is used that exhausts steam directly to the ambient. [195] The steam discharges to a condenser where it is condensed at a subatmospheric pressure (typically a few inches of Hg). The condenser shown in Fig. 9.13 is a barometric condenser. In a barometric condenser, the cooling water is sprayed directly into the steam, with the cooling water and condensate being pumped to a cooling tower where the condensing heat load is rejected to the ambient. Some plants use surface condensers where the latent heat from the condensing steam is transferred to cooling water being circulated through the condenser tubes. With a surface condenser, the cooling water and condensate are typically pumped to the cooling tower in separate streams. The steam condensate provides a makeup water source for the evaporative heat rejection system. Any excess condensate, together with the tower blowdown, is injected back into the reservoir.

Hydrothermal resources typically contain varying amounts of dissolved minerals and gases that impact both the design and operation of the energy conversion systems. In power cycles where steam is extracted from the geothermal resource and expanded in a condensing turbine, the cycle design must account for the removal of the noncondensable gases extracted from the resource with the steam. If not removed, these gases accumulate in the condenser, raising the turbine exhaust pressure and decreasing power output. When hydrogen sulfide is present in the process steam, it also accumulates in the condenser, though a portion partitions or dissolves in the condensate or cooling water. When the hydrogen sulfide levels are sufficiently high so that some abatement process of the condensate or cooling water is required, surface condensers are typically used to minimize the quantity of water that has to be treated. In addition, the noncondensable gas stream containing hydrogen sulfide must also be treated prior to being released to the atmosphere.

Flash Steam Systems/Liquid-Dominated Resources

With few exceptions, the fluid in hydrothermal resources is predominantly liquid. Frequently, the reservoir pressure is insufficient to overcome the hydrostatic head in the wellbore and bring the fluid to the surface as a liquid, at flow rates sufficient for commercial production. Depending on the power cycle used, it may be necessary to use downhole pumps to provide the necessary flow. In instances when the reservoir temperature is sufficiently high, the fluid is allowed to flash in the wellbore. This reduces the hydrostatic head in the wellbore and allows more production flow. When flashing occurs in the well, a two-phase fluid is produced from the well. The conversion systems used with this flow condition are typically flash-steam power cycles. In a single-flash cycle, a separator is used to separate the fluid phases, with the steam phase being sent to a turbine. Typically, in this cycle, the fluid pressure immediately upstream of the separator is reduced, which results in additional flashing of the liquid phase and produces additional steam flow. This single-flash steam power cycle is depicted in Fig. 9.14. Once the steam leaves the separator, the cycle is very similar to that for a vapor-dominated resource (Fig. 9.13). The saturated liquid brine leaving the separator is reinjected along with cooling tower blowdown and excess condensate.

The dual-flash steam power cycle adds a second low-pressure flash to the single-flash cycle. In the dual-flash cycle, the liquid leaving the first (high pressure) separator passes through a throttling device that lowers fluid pressure, producing steam as the saturated liquid flashes. The steam from this second flash is sent either to a second turbine or, if a single turbine is used, to the turbine at an intermediate stage. The steam exhausting the turbine(s) is condensed with a heat-rejection system similar to that of the steam plant used with a vapor-dominated resource. In the dual-flash cycle, the optimum pressure of the first separator is higher than the optimum flash/separator pressure in a single-flash cycle. Unless the resource temperature is high, the optimum first-stage pressure can be found using an initial approximation that this separator temperature is at the mid-point of the temperature where flashing starts to occur (liquid reservoir temperature) and 100°C. The second, or low pressure, flash is typically just above atmospheric pressure. As the resource temperature increases, the optimum pressures for the two flash stages increase.

As with the direct steam systems (vapor-dominated resource), flash plants must have provisions to remove noncondensable gases from the heat-rejection system, to remove liquid from the saturated steam before it enters the turbine and, if levels are sufficiently high, remove hydrogen sulfide from the noncondensable gas and condensate streams. In addition, mineral precipitation is generally associated with the flashing processes. This requires the use of chemical treatment in the wellbore, separators, and injection system to prevent the deposition of solids on piping, casing, and plant-component surfaces. The potential for mineral precipitation increases as the fluid is flashed because the dissolved minerals concentrate in the unflashed, liquid phase.

Binary Systems/Liquid-Dominated Resources

A binary conversion system refers to a power cycle where the geothermal fluid provides the source of energy to a closed-loop Rankine cycle that uses a secondary working fluid. In this closed loop, the working fluid is vaporized at pressure using the energy in the geothermal fluid, expanded through a turbine, condensed, and pumped back to the heat exchangers, thus completing the closed loop. This type of conversion system is used commercially with liquid-dominated resources where the fluid temperatures are below ~

200°C. Typically, this conversion system requires the use of pumped production wells to provide necessary well flow and to keep the fluid in a liquid phase to prevent minerals from scaling of heat exchanger surfaces. The system is depicted schematically in Fig. 9.15 with an evaporative heat-rejection system.


In some areas where geothermal resources are found, there is little water available for evaporative heat-rejection systems. In these cases, the cooling tower and condenser, shown in Fig. 9.15, are replaced with air-cooled condensers. A commercial plant that uses this sensible heat-rejection system is shown in Fig. 9.16. Typically, all of the geothermal fluid that passes through the binary plant heat exchangers is injected back into the reservoir. This is environmentally desirable, as it effectively eliminates all emissions to the ambient and, more importantly, provides a recharge to the reservoir to maintain its productivity. The working fluids used in these plants are volatile and typically are in a gas phase at room temperature and atmospheric pressure. They liquefy at moderate pressures, and the entire working-fluid system is generally operated at above atmospheric pressure to prevent the leakage of air into the closed loop. Existing plants use isobutane, pentane, or isopentane working fluids.

The performance of the binary system depends on a number of factors, including the resource conditions and the selection of the working fluid. These plants are usually used with lower temperature resources because, relative to the flash-steam power cycles, the binary cycle can produce more power from a given quantity of geothermal fluid. Cycles can be designed to maximize the conversion of the geothermal energy to power. [196][197] In simple cycles, the working fluid is boiled at a single pressure. One method of improving performance is to boil at multiple pressures (the working-fluid flow stream is split into high- and low-pressure stream paths). Another proposed technique is the heating and vaporization of the working fluid above the fluid ’

s critical pressure. [197] Both of these design strategies attempt to match the working fluid heat addition process to the sensible cooling of the geothermal fluid (as depicted on a plot of temperature vs. total heat transferred). While the supercritical cycle has a higher associated component and pumping costs because of the higher operating pressures, these cycles have fewer components and are less complex than the multiple boiling cycles. They also are more efficient in converting the geothermal energy into electrical power. [198]

Conversion efficiency is maximized by minimizing the temperature differences during the heat-addition and heat-rejection processes. [199] The conversion systems that more efficiently convert the geothermal energy to electrical power also tend to be more equipment intensive, especially with regard to heat-transfer areas. If there is a significant cost associated with the production of the geothermal fluid (resource exploration, drilling, surface piping, etc.), these costs will offset the additional energy-conversion-system cost and the more efficient plants will produce power at lower cost.

Studies have shown that power cycles using working fluids of mixed hydrocarbons have superior performance (in terms of power produced from a unit quantity of geothermal fluid) to those having single-component working fluids. [197] Mixtures have an advantage because their isobaric phase changes (boiling and condensation) are nonisothermal. This allows the vaporization of the mixture to more closely match the sensible cooling of the geothermal fluid. Perhaps more importantly (in terms of reducing cycle irreversibility), this characteristic allows the desuperheating and condensing of the working fluid to more closely approach the sensible heating profile of the cooling fluid (water or air).

A binary cycle is being commercially developed that uses an ammonia-water mixture as the working fluid instead of a hydrocarbon. In this cycle, a great amount of recuperative preheating of the working fluid is accomplished with the superheat in the turbine exhaust. Though the cycle has a more complex heat-exchanger train than indicated by the flow schematic in Fig. 9.16, it is more efficient in converting the geothermal energy into electrical power. The systems using this cycle are called Kalina Cycle® systems. [200]

Binary Systems/Liquid-Dominated Resources
Fig. 9.17—Geothermal combined-cycle plant adapted from ORMAT[201].
Certain geothermal power plants utilize a combined cycle approach, which integrates a traditional Rankine cycle to harness electricity from what would otherwise be considered waste heat in a binary cycle (IEA-ETSAP, 2010) (Figure 7). This dual-cycle setup is designed to achieve relatively high electrical efficiency[202][203]. The size of these combined-cycle plants typically ranges from a few megawatts (MW) to 10 megawatts of electricity generation (MWe) [204][205]

Hybrid geothermal power plants follow similar principles to standalone geothermal plants but incorporate an additional heat source into the process, such as heat from a concentrating solar power (CSP) plant. This extra heat is introduced to the geothermal brine, elevating its temperature and enhancing power output.

An example of such a hybrid system is the Stillwater project in the United States, managed by ENEL Global Renewable Energies, which combines CSP and solar photovoltaics with a binary system[206]. ENEL is also exploring two other hybrid systems: one in Italy incorporating biomass to raise brine temperature, akin to CSP systems[207]; and another in Cove Fort, Utah, merging hydropower with geothermal to generate electricity from re-injection water flow, offering improved re-injection control and reduced maintenance costs[208].

Nomenclature


ai = correlation coefficients between a given wells’

produced chloride and theith injection wells ’ injected chloride concentration

ao = initial chloride concentration for a given production well
A = the energy generated from radioactive decay, per unit volume per second
b = Arps exponent (0 ≤ b ≤ 1)
cij = arc cost function for the travel arc between a given injection and production well pair (e.g., along a streamline)
cr = rock compressibility
cw = liquid compressibility
Clp = produced chloride for a given well
Cpr, Cpw = specific heat capacities of rock and water, respectively
ct = total compressibility, including effects of phase change
CT = tracer concentration by weight
d = wellbore diameter
D = depth
Di = decline rate
g = acceleration because of gravity
Ht = formation thickness
Hf = flowing enthalpy
H(Hg) = liquid (vapor) phase enthalpy, respectively
i = injector
k = absolute formation permeability
krℓ (krg) = liquid- (gas-) phase relative permeability
K = rock conductivity
Lv = enthalpy change because of boiling
m = slope of pressure buildup or drawdown test
mg = vapor mass fraction
P = estimated (or measured) static wellhead pressure
po = reference pressure at a datum z = zo
Psat = saturation pressure
Pstd = standard flowing wellhead pressure to normalize flow rates for decline curve analysis
Pwf = measured well flowing pressure
PI = initial formation pressure
q* = the component of heat flux that originates from the lower crust or mantle
q = total heat flux
qDd = dimensionless flow rate W/WI
qi = chloride injection rate in well i
qri = re-injection rate at well i
QL,V = mass rate of fluid (liquid or steam)
QT = tracer injection mass rate
re = effective radius
rw = wellbore radius
S = well skin factor
Sw = liquid saturation
t = production time
tDd = dimensionless time used in decline curve analysis
tp = total production time
T = temperature at depth
Tr(z) = formation temperature
Tsat = saturation temperature
Tw(z) = fluid temperature
U = overall heat transfer coefficient
vT = velocity of temperature front
vw = fluid velocity
W = mass flow rate
WI = initial mass flow rate
z = vertical distance
zo = water level in the well (measured downwards from the wellhead)
z1, z2 = depths to permeable horizons, see discussion of wellbore temperature gradients and Figs. 9.2 and 9.3
zo = water level in the well (measured downwards from the wellhead)
β = mixing rule parameter for geothermometers
Δt = shut-in time (buildup test)
κ = pressure diffusivity
Γ = temperature gradient
μ = dynamic viscosity
ρ (p,T) = fluid density
ρr, ρw, ρv = densities of rock, water, and steam, respectively
υ(υg) = liquid- (gas-) phase kinematic viscosity
υt = kinematic viscosity
Φ = porosity

Acknowledgments


Prepared for the U.S. Dept. of Energy, Assistant Secretary for Energy Efficiency and Renewable Energy, under DOE Idaho Operations Office Contract DE-AC07-99ID13727.

Copyright Notice


The submitted manuscript has been authored by a contractor of the U.S. Government under DOE Contract DE-AC07-99ID13727. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes.

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SI Metric Conversion Factors


bbl × 1.589 873 E – 01 = m3
ft × 3.048* E – 01 = m
°F (°F–32)/1.8 = °C
in. × 2.54* E+

00

= cm


*

Conversion factor is exact.