Geothermal reservoir characterization

Characterizing geothermal reservoirs draws on techniques common to petroleum reservoirs. Key differences create special challenges to gaining a good understanding of geothermal reservoirs. This article covers appropriate approaches and caveats for well testing, drawdown/buildup analyses and decline curve analysis for characterizing geothermal reservoirs.

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, 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.

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, Stefansson and Steingrimsson, and Grant. 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.

• 

  Fig. 1—Schematic of a typical temperature profile in a geothermal well under cold water injection at successive times 1, 2, and 3. Changes in temperature gradient indicate permeable zones.

Three possible types of temperature profiles that may be observed during cold water injection into a geothermal well are shown in Fig. 1. 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, T_w(z) is the fluid temperature, and T_r(z) is the formation temperature, then the conductive heating (caused by the temperature difference T_r –T_w) of the descending water is given by

....................(1)

where

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

The temperature gradient dT_w/dz is inversely proportional to the flow rate W. Therefore, an increase in temperature gradient (see Profile 2, Fig. 1) 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 dT_w/dz is small or, within measurement error, zero. Essentially no change in T_wbetween 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 ....................(2)

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. 2.

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. 2. 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. 1 indicates that fluid enters the well at z₁ and is injected into the formation at z₂.

• 

  Fig. 2—Schematic of a typical pressure profile in a geothermal well during an injection test.

A typical temperature profile in a discharging geothermal well with several liquid feed zones is shown in Fig. 3. 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. 2 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 and by Spielman.

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. 3). 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.

• 

  Fig. 3—A typical temperature profile in a discharging geothermal well with liquid feed zones. Cooler water is inflowing into the middle feed zone, which results in a temperature reversal.

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.

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,

....................(3)

together with the boundary condition p = p_oat z = z_o(e.g., wellhead pressure). Here, z_odenotes 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, z_o) 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. 4. The well in Fig. 4 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.

• 

  Fig. 4—Schematic of a wellbore pressure profile after cold water injection. As the well heats up the hydrostatic pressure in the well falls (density is reduced). The wellbore pressure pivots about the reservoir pressure at the depth of a single feed zone. In the case of multiple feed locations, the pivot point is a weighted average. The differences in pressure gradient are exaggerated in the figure.

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.

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.

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:

• Formation permeability, storativity, and porosity
• The presence of barriers and leaky boundaries
• The condition of the well (i.e., damaged or stimulated)
• The presence of major fractures close to the well
• 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, Earlougher, and Streltsova..

Much of the existing literature 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 page, 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 and Brons and Marting. 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. For the spherical flow period, a plot of pressure drop or pressure buildup vs. t_p^–0.5 orΔt^–0.5 (t_p= 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, Garg, Garg and Pritchett, Moench and Atkinson, and Sorey et al. 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," ....................(4)

where

....................(5)

In Eqs. 4 and 5, k is the absolute formation permeability, H_tis the formation thickness, k_rℓ (k_rg)is the liquid (gas) phase relative permeability, and υ_ℓ(υ_g) is the liquid (gas) phase kinematic viscosity.

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

....................(6)

and

....................(7)

where H_ℓ(H_g) denotes the specific liquid (gas) phase enthalpy. The flowing enthalpy, H_f, is given by

....................(8)

where m_g 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

....................(9)

To evaluate k_rg and k_rℓ separately, an additional relation is required between k_rg and k_rℓ.

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/ν_t; this introduces an element of uncertainty in the determination of k/ν_t.

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

....................(10)

where C_pr and C_pw are the specific heat capacities of rock and water respectively; ρ_r, ρ_w, and ρ_v are the densities of rock, water, and steam, respectively; L_v is the enthalpy change because of boiling; P_sat and T_sat 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 also show that the compressibility can be approximated by

....................(11)

where compressibility, c_t, is in bar_–1; bulk volumetric heat capacity ρC_p 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. 5, taken from Riney and Garg, 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 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. 6. A comparison of Fig. 5 and 6 shows that the slope of straight line in Fig. 6 is approximately one-half of that in Fig. 5.

• 

  Fig. 5—Pressure buildup for Well B-20 following flow test 4. A pressure gauge is set at 1373 m below ground surface (bgs); primary fluid entries are at 1220 m bgs. Time-varying two-phase conditions in the wellbore require corrections to the measured pressure that also vary in time. A corrected pressure buildup for this test is given in Fig. 6. The figure is modified from Riney and Garg by permission of the American Geophysical Union (after Riney and Garg).

• 

  Fig. 6—Corrected pressure buildup for Well B-20 following flow test 4. Effects of transient boiling in the wellbore are corrected for in the plotted pressure at 1372 m. Note the Horner plot slope is half that of Fig. 9.6. Individual data points (e.g., S3, S4, etc.) are pressure measurements at different times. An H₂O-CO₂ EOS was used for pressure-depth corrections required. The figure is modified from Riney and Garg by permission of the American Geophysical Union (after Riney and Garg).

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
• Fetkovich-type curves

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, P_std.

....................(12)

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

....................(13)

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. The general rate-time equation can be written as

....................(14)

D_i 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.

....................(15)

....................(16)

....................(17)

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

Fetkovich-type curves 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 D_i 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).

....................(18)

and

....................(19)

For vapor-dominated reservoirs, one can also use a pseudo-pressure approach (e.g., Faulder). 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. 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. 12 or 13) 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, r_e, 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 or nonphysical value for b.

Nomenclature

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
Hℓ(Hg)	=	liquid (vapor) phase enthalpy, respectively
i	=	injector
k	=	absolute formation permeability
krℓ (krg)	=	liquid- (gas-) phase relative permeability
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
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
W	=	mass flow rate
WI	=	initial mass flow rate
z	=	vertical distance
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
υℓ(υg)	=	liquid- (gas-) phase kinematic viscosity
υt	=	kinematic viscosity
Φ	=	porosity

Noteworthy papers in OnePetro

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External links

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See also

Geothermal reservoir engineering

Modeling geothermal reservoirs

Tracer testing in geothermal reservoirs

PEH:Geothermal_Engineering