PEH:Reservoir Pressure and Temperature

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 7 – Reservoir Pressure and Temperature

David Harrison, Schlumberger, and Yves Chauvel, Gamma Experts

Pgs. 683-717

ISBN 978-1-55563-120-8
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The practice of using bottomhole pressure measurements to improve oil and gas production and solve problems of reservoir engineering began around 1930. Initially, pressures were calculated using fluid levels; a later method was to inject gas into the tubing until the pressure became constant. The earliest bottomhole pressure measurements were made with one-time-reading pressure bombs and maximum-indicating or maximum-recording pressure gauges that lacked the accuracy, reliability, or durability of present-day technology.

The varied uses of bottomhole pressure and temperature measurements have increased in scope during the past two decades as instrumentation technologies have produced more reliable and accurate tools. These advances have made more applications possible, including use in multilayer reservoirs, horizontal wells, interference testing, and drawdown test interpretation.

This chapter is focused mainly on the types of measurements made and the tools available. Some information is included on interpretation techniques to connect the data acquisition with its use in characterizing a reservoir and its contents. Detailed explanations of these interpretation techniques can be found in other chapters in this Handbook.

Reservoir Pressure

The measurement commonly referred to as "bottomhole pressure" is a measurement of the fluid pressure in a porous reservoir. The reservoir pore-fluid pressure is a fraction of the overburden pressure that is supported by the fluid system. The other portion is supported by the rock and generates the in-situ rock stress. The overburden pressure is created by the weight of the rocks composing the lithostatic column at the point of observation. Hence, the difference between the overburden pressure and the vertical rock stress can approximate the pore pressure.

At original, or virgin, conditions, the vertical pressure profile reflects the distribution of fluids in the reservoir and may also indicate compartmentalization resulting from fluid flow barriers. Within any reservoir compartment, the pressure gradient reflects the density of the continuous fluid phase in the reservoir, hence the position of fluid contacts. Fig. 7.1 illustrates a typical pressure profile showing gas-, oil-, and water-bearing intervals of a reservoir at initial conditions.

Fig. 7.1 – Pressure gradients in a well drilled in a virgin reservoir.

In a developed reservoir, differential depletion of lithostatic layers with various permeabilities and the movement of fluid contacts can change the pressure profile. Monitoring the static pressures vs. time in developed reservoirs is a crucial tool for reservoir management.

Pressure Distribution in the Reservoir During Fluid Flow

The Fluid Flow chapter in this volume of the Handbook explains the factors that govern the flow of fluids through porous media for steady-state, pseudosteady-state, and transient flow conditions.

Steady-State Flow. Steady-state flow is characterized by simultaneous constant pressure and flow rate. From the equation for steady-state radial flow,^[1]

....................(7.1)

the pressure profile away from a producing well can be calculated. A typical result is shown in Fig. 7.2.

Fig. 7.2 – Pressure profile away from the wellbore.

Pseudosteady-State Flow. Pseudosteady-state flow behavior is observed when a well reaches stabilized production from a limited drainage volume. For constant-rate production under pseudosteady-state conditions, the difference between the flowing wellbore pressure and the average reservoir pressure in the drainage volume is constant, and the pressure drawdown is a linear function of time. The late-time buildup pressure will level off to the average reservoir pressure if the buildup duration is sufficiently long. Pressure depletion occurs with continued pseudosteady-state production.

Transient Flow. Transient flow is most often modeled with the radial diffusivity equation, which allows modeling pressure vs. time and pressure vs. distance from an observation point (typically, a well).

At a sufficiently large time, the pressure disturbance anywhere in the reservoir is proportional to the logarithm of the inverse square of the radius away from the origin of the disturbance. Thus, the magnitude of the disturbance is maximum near its origin (the wellbore) and rapidly terminates away from the wellbore. Because the pressure wave is affected by the reservoir fluid transmissibility, kh/μ, higher transmissibility results in smaller pressure differentials and vice versa. This effect explains why high-resolution pressure gauges are necessary to measure meaningful pressure differentials in reservoirs with high transmissibility. The radius of influence of a pressure disturbance is proportional to the square root of time. This is why the well testing time necessary to observe distant boundaries becomes prohibitively expensive, particularly in low-productivity reservoirs.

The variations of pressure as a function of time, which can be formulated by solving the radial diffusivity equation for specific cases, have given rise to well-testing applications.

Reservoir Temperature

Reservoir temperature is governed primarily by the reservoir’s proximity to the earth’s mantle, and by the relative heat exchange capacities and thermal conductivities of the formations forming the lithostatic sequence that includes the reservoir.

The geothermal gradient resulting from the heat-exchange process varies from basin to basin, but within a specific area the variations are small. In most hydrocarbon-producing areas, the gradient is usually in the range of 0.6 to 1.6°F per 100 ft of depth increase (Fig. 7.3). Areas where the earth’s crust is thinner than average, such as volcanic and geothermal areas, have much higher gradients. In thin-crust areas the gradient change averages 4°F per 100 ft of depth increase. Local temperature gradients at depth have been reported as high as 10°F per 100 ft approaching singularities (e.g., major faults, areas of tectonic movement) in the earth’s crust in geothermal areas.

Fig. 7.3 – Definition of an average geothermal gradient.

To determine a precise geothermal gradient, the selected well must be shut in, without disturbance, for a period of time sufficient to let conduction effects equilibrate the temperatures. The temperature survey should be conducted from surface to bottom on the first descent into the well and at a slow speed (ideally, no more than 30 ft/min to accommodate the thermal inertia of the sensor). This procedure is necessary because the passage of the thermometer alters the static gradient. Even if a precise gradient is not required, following the procedure is still recommended for running temperature surveys in wells (shut-in, injecting, or flowing). Anomalies present during the first descent—whether observed or not—may disappear on subsequent surveys after disruption of the initial thermal equilibrium.

The virgin reservoir temperature may be determined when drilling initial exploration and appraisal wells by using the maximum temperatures recorded on successive logging runs or wireline sampling operations. The technique^[1] calls for plotting T_bh vs. (t_k + Δt_c)/Δt_c on a linear scale.

These data are interpreted in Horner analysis fashion by drawing a straight line through the data points and extrapolating to the reservoir temperature at (t_k + Δt_c)/Δt_c = 1, which corresponds to infinite shut-in time. Even though this approach is not mathematically rigorous, it provides reliable estimates of the static temperature when short circulation times are assumed. This technique is especially applicable to regions with high geothermal gradients, where the temperatures recorded at the time of logging runs can be significantly lower than the static temperature.

Metrology of Bottomhole Pressure and Temperature Gauges

Metrology is the science and process of ensuring that a measurement meets specified degrees of accuracy and precision. Bottomhole pressure-gauge and temperature-gauge performance depends on the static and dynamic metrological parameters described here. The pressure measurement equipment consists of the pressure transducer, associated electronics, and telemetry. Each component uniquely influences the measurement quality.

Static Metrological Parameters

The main static metrological parameters affecting gauge performance are accuracy, resolution, stability, and sensitivity.

Accuracy. Accuracy is the maximum pressure error exhibited by the pressure transducer under the following applied conditions: fitting error, pressure hysteresis, and repeatability. The fitting error, also called the mean quadratic deviation (MQD), is a measure of the quality of the mathematical fit of the sensor response at a constant temperature. Pressure hysteresis is the maximum discrepancy of the transducer signal output between increasing and decreasing pressure excursions. Repeatability is defined as the discrepancy between two consecutive measurements of a given pressure at the same temperature.

Resolution. Resolution is the minimum pressure change detected by the sensor. When referring to the resolution of a bottomhole pressure gauge, it is important to account for the associated electronics, because the gauge is always used in series with the electronics. Thus, the resolution of the measurement is the lower of the resolution of the gauge and its electronics. Another important consideration is that the resolution must be evaluated with respect to a specific sampling rate, because an increase of the sampling rate worsens the resolution. The electronic noise of strain-gauge transducers is often the major factor affecting resolution. Mechanically induced noise may further limit gauge resolution because some gauges behave like microphones or accelerometers. This effect may be significant during tests when there is fluid or tool movement downhole.

Stability. A pressure sensor is stable if it can retain its performance characteristics for a relatively long time period. Stability is quantified by the sensor mean drift (psi/D) at a given pressure and temperature. Three levels of stability can be defined: short-term stability for the first day of a test, medium-term stability for the following 6 days, and long-term stability for a minimum of one month.

Sensitivity. Sensitivity is the ratio of the transducer output variation induced by a change in pressure to that change in pressure. The ratio represents the slope of the line produced by a plot of the transducer output vs. pressure input. The plotted sensitivity should be, but is not always, linear with respect to pressure.

Dynamic Metrological Parameters

Four aspects are used to evaluate the dynamic metrology of pressure gauges.

Transient Response During Temperature Variaton. The sensor response is monitored under dynamic temperature conditions while holding the applied pressure constant. The transient response characterizes the time required to get a reliable pressure measurement for a given temperature variation. Peak error and stabilization time are calculated.

Transient Response During Pressure Variation. The sensor response is recorded before and after a pressure variation at a constant temperature. Peak error and stabilization time are calculated.

Dynamic Response During Pressure and Temperature Shock. The sensor response is recorded before and after a temperature shock.

Dynamic Temperature Correction on the Pressure Measurement. The most advanced quartz-gauge transducers are based on a single-crystal sensor design. The crystal is activated on two distinct resonating modes, which are sensitive to both pressure and temperature but with different sensitivities. An advantage of this design is that the measured temperature is the temperature of the crystal. "Dynamic temperature correction" is used to adjust the pressure measurement of single-crystal sensors in real time for any remnant temperature effect. The nonuniform temperature of the crystal, especially while undergoing strong pressure or temperature variations or both, may induce such effects.

Calibration and Standard Evaluation Tests for Pressure Gauges

Calibration is essential for obtaining good temperature and pressure data. To ensure that a pressure gauge gives a pressure as close as possible to the real pressure over its entire operating range, it must be calibrated. Calibration involves establishing transfer functions to convert raw output from the pressure and temperature data channels into scaled pressure and temperature readings. These transfer functions are 2D (in pressure and temperature) polynomial models—the degree of which is a function of the accuracy required for the measurement.

The calibration process consists of applying known pressures and temperatures to the desired operational ranges. The raw pressure and temperature output signals are received and entered into a polynomial optimization routine. Input pressures are applied with a dead-weight tester, and input temperatures are generated by an oil bath. The following steps are required for a complete master calibration.

Choosing the Pressure-Temperature Calibration Points

Clearly, more calibration points yield a more accurate calibration; however, the inertia in temperature equilibration is a limiting factor. The best practice is to never use fewer than 100 pressure-temperature calibration points and distribute the points in a scheduled time routine, such as shown in Fig. 7.4.

Fig. 7.4 – Scheduled time routine for a pressure gauge calibration test.

Deriving the Pressure Calibration Function

The pressure calibration function is a polynomial of order N in pressures and order M in temperatures:

....................(7.2)

in which the A_ij calibration coefficients are determined by a linear regression providing a least-squares minimization; S_p and S_t are the pressure and temperature outputs, respectively; and S_po and S_to are the corresponding offsets. Usually the number of A_ij coefficients can be limited to approximately 15. During this step, the peak error and MQD are determined.

Temperature Calibration Function

It is often useful, though not always necessary, to calibrate the transducer to output a scaled temperature measurement. The temperature calibration function is a polynomial of order N in temperatures and order M in pressures:

....................(7.3)

in which the A_ij′ calibration coefficients are determined by a linear regression providing a least-squares minimization; S_p, S_t, S_po, and S_to are as described previously.

Determining Nonlinearity in Pressures and Temperatures

Several other tests supplement the master calibration.

Pressure Thermal Sensitivity. The pressure thermal sensitivity represents the error (psi) that results if the temperature measurement is in error 1°C.

Maximum Hysteresis During the Calibration Cycle. This test is determined from calibration data.

Calibration Check. A calibration check verifies the consistency of the sensor readings when the applied pressures and temperatures are different from those used during the calibration cycle. The calibration check is performed in the laboratory at the time the sensor is evaluated and is essentially a rerun of a master calibration.

Other Procedures and Tests. Standard procedures are typically used in evaluating pressure transducers to compare different technologies and certify the calibration parameters. The most commonly used standard procedures are as follows:

Complete master calibration.
Calibration check.
Stability tests: middle term and long term.
Repeatability test.
Resolution test.
Noise or short-term stability test.
Dynamic tests: temperature shock, temperature transient, temperature response time, and pressure shock.

Metrology of Temperature Gauges

When the temperature is used to correct pressure gauge readings, it must come from the pressure-sensing element, not from the wellbore fluid. On the other hand, bottomhole-fluid temperature measurements are performed with sensors that are in immediate contact with the wellbore fluid and have a minimum thermal inertia (1 or 2 seconds) to follow the variations of the fluid temperature as closely as possible. For this reason, temperature measurements available from pressure-gauge technology are rarely valid for traditional wellbore temperature profiling, which uses the wellbore fluid temperature as a diagnostic tool to detect anomalies in the expected flow patterns in and around the wellbore.

Typical wellbore-fluid temperature measurements have a resolution in the range of 0.05°F and accuracy in the range of 1°F. Accuracy in thermometry is not always a prerequisite because temperature measurements are often normalized between themselves—e.g., from pass to pass or from flowing run to shut-in run in production-logging applications. Accuracy is necessary, however, to compare absolute bottomhole temperatures to draw geothermal maps; to design temperature-sensitive operations, such as stimulation or drilling operations using temperature-sensitive chemicals; or to operate close to the limitations of equipment, such as in geothermal or other high-temperature oil and gas fields.

Resolution is of brmount importance for applications such as the diagnosis of flowing wells or when the measured temperature is the temperature of a pressure-sensing element—the reading of which is affected by minute changes in sensor temperature. High-resolution wellbore-fluid thermometry is also used in extremely slanted and horizontal wells, in which true vertical depth (TVD) variations, and therefore geothermal temperature variations, are small.

Pressure Transducer Technology

All pressure transducers operate on the principle of converting a pressure change into a mechanical displacement, or deformation. Deformation of the sensing element is then converted into an electrical signal that is processed by the measuring system. Types of pressure transducers available in the field, either individually or in combination, are mechanical, capacitance, strain gauge, and quartz gauge.

Mechanical Pressure Transducers

The first pressure transducers had mechanical-force-summing elements that converted energy into mechanical displacement, or deformation, and then coupled the generated force to a recording device. In the Amerada gauge, a popular mechanical pressure transducer, the pressure-sensing element is a helical Bourdon tube. The tube is of sufficient length to rotate a clock-driven stylus a full circumference inside the cylindrical chart holder. The chart, usually made of coated metal, is recovered at the end of the test, unfolded until flat, and read on a high-precision optical machine. The transducer also incorporates a vapor-type recording thermometer to make temperature corrections on the pressure measurements.

Mechanical transducers have largely been abandoned because of their obsolete metrological characteristics and lack of surface readout (SRO). They are still used occasionally for basic applications at the lower end of the economic spectrum, for some very high-temperature applications, or as backup for an electronic pressure gauge.

Capacitance Pressure Transducers

Capacitance transducers have a variable-gap capacitor in which the sensing element is formed by two metallic or quartz plates. As the external pressure increases, the deflection of the sensing plate creates a change in the capacitance that can be mathematically related to the applied pressure. Capacitance transducers have the advantages of good frequency response, low hysteresis, good linearity, and excellent stability and repeatability. The disadvantages are high sensitivity to temperature, acceleration, orientation, and mechanical noise.

Fused quartz has excellent elastic behavior (low hysteresis) and is chemically inert. These properties make it an almost ideal material for manufacturing small capacitor modules with a high temperature rating.

Strain Pressure Transducers

Many types of strain-gauge transducers are in use. Strain gauges have become very popular because of their ruggedness, low cost, and good dynamic behavior. Their metrological characteristics have greatly improved in recent years; gauges with an accuracy of a few psi and resolution as low as 0.05 psi are available. The primary limitation of strain gauges is their tendency to drift, although that aspect of the measurement has improved.

A strain gauge has a strain-sensitive resistor directly attached to a measuring sensor; when the sensor is subjected to pressure, it deforms. The resulting displacement changes the resistor length, hence its resistance. The applied pressure is calculated from a calibrated relationship to the change in resistance at a given temperature.

Bonded Wire Transducers. In this design, introduced by the Paine Corporation in the 1970s, two sets of wire, called the "active" windings, are wrapped around a cylindrically shaped tube-sensing member. As pressure increases, the tube bore is stretched, causing a change in the wire resistance. Another two sets of wire—the reference, or "passive," windings—are wrapped on the upper part of the tube, which is not exposed to pressure. These four sets of wire form a Wheatstone bridge that allows the electrical output to be reduced to a pressure reading.

Thin-Film Transducers. The thin-film sensor consists of a resistor pattern that is vaporized or sputter-deposited onto the force-summing element (the measuring diaphragm). In some transducers the resistors are not directly mounted on the diaphragm but are on a beam linked to the diaphragm by a push rod.

Sapphire Transducer. In the Schlumberger improvement of the diaphragm-type thin-film transducer, the sensing resistors are mounted on a miniature substrate of industrial sapphire. The Sapphire* pressure-gauge system is vacuum-filled and the resistor pattern forms a Wheatstone bridge. This system benefits from the elastic performance of the sapphire and its stable deformation properties. The result is a sensor with good repeatability, good stability, low hysteresis, and low drift. A high-gauge factor improves the resolution over traditional designs. The main disadvantages are low output level and high cost.

Quartz Pressure Transducers

Quartz-crystal pressure transducers vibrate at their resonating frequency when excited by a suitable external energy source. The resonating frequency is affected by both the pressure and temperature to which the crystal is exposed. Because of the excellent gauge factor yielded by this physical process, quartz-crystal pressure transducers have exceptional accuracy, resolution, and long-term stability. The disadvantages are high cost and high sensitivity to temperature, although the most recent designs are much less temperature-sensitive.

Hewlett-Packard Design. The Hewlett-Packard (HP) design has been in use since the early 1970s. It features a two-crystal arrangement of a measure and a reference crystal. The measure crystal is exposed to both pressure and temperature. The reference crystal is exposed only to temperature and is used to compensate for temperature effects on the measure crystal. Both crystals are factory-matched so that their frequency characteristics in temperature are approximately the same. The measure crystal senses the pressure directly rather than through a mechanical linkage or other force-summing device. This has the effect of optimizing the metrology of the measurement.

The output from the crystal pair and associated electronics is calibrated to yield the measured pressure by means of a 2D cubic polynomial including 16 coefficients. The values of these coefficients are determined at least annually during the gauge master calibration.

Quartzdyne Design. The Quartzdyne design features three resonating crystals: the measure crystal, which is exposed to both pressure and temperature, and the temperature and reference crystals, which are exposed only to temperature. The measure crystal is a thick-walled, hollow quartz cylinder closed at both ends. The resonating element is a disk placed in the center, which divides the cylinder into halves. Separate conductive plates are located on the front and back of the resonator disk. Fluid pressure on the exterior walls hydrostatically compresses the quartz cylinder, producing internal compressive stresses in the resonator. The oscillating frequency of the resonator changes in response to these internal stresses.

The reference crystal oscillates at a fixed high frequency, which is subtracted from both the measure crystal and temperature crystal resonating frequencies. The temperature compensation is performed based on these low-frequency signals. The calibration procedure involves a fourth-order polynomial.

Because of its small size, the Quartzdyne design provides good thermal performance and low cost, although somewhat at the expense of accuracy.

Schlumberger Design. In the Schlumberger CQG* Crystal Quartz Gauge design, the transducer features a single quartz crystal structure in which a resonator is coupled with a dual-mode oscillator. The resonant frequency of the first mode is highly sensitive to pressure, and that of the second mode is more sensitive to temperature. The sensor consists of a cylindrical quartz body fitted with two end caps. The end caps maintain a vacuum inside the sensor. The resonator is a plate etched out of the quartz cylinder that features shaped surfaces acting as vibrating lenses. The resonating frequency of the plate varies with changes in pressure and temperature.

From a static point of view, the main advantage of this design is that pressure and temperature are measured at the same location, which minimizes time and space delays for thermal corrections. From a dynamic point of view, this design leads to very small peak transient errors in the thermal response that can be further minimized by using real-time dynamic compensation. The calibration involves a fourth-order polynomial.

The main disadvantages of the CQG design are fragility and high cost.

Paroscientific Design. The Paroscientific design uses a quartz crystal operating in flexure mode to measure force. To derive a pressure output, a force-summing device such as a Bourdon tube or bellows must be used. Thus, the transducer senses pressure through the force-summing device and is not in direct contact with the wellbore fluid. This design tends to improve temperature characteristics but dampens the response and downgrades the measurement metrology. A temperature sensor comprising a quartz torsional tuning fork provides temperature compensation.

Quartztronics Design. The Quartztronics design is a modified HP design, with a specially cut resonator and a noncylindrical cell geometry. The result is a smaller, lower cost pressure transducer with a higher pressure range.

The transducer features a temperature-sensing crystal and a reference crystal, both located close to the measure crystal. This configuration provides improved pressure- and temperature-transient responses in comparison with the HP design. The two crystals are thermally matched to the measure sensor and within a pressure-proof package bonded to one of the end caps of the measure sensor.
*

Mark of Schlumberger

Temperature Sensors

Mechanical Transducers

The first bottomhole thermometers were mechanical. They were identical to bottomhole mechanical pressure gauges, except that a thermometer sensor was substituted for the pressure sensor. This type of thermometer has been mostly replaced by sensors and recording elements that are easier to use and have higher precision and accuracy.

Thermistors

Thermistors are temperature-sensitive resistive elements made of semiconductor material with a negative coefficient of resistance. The physical effect governing a thermistor’s change of resistance is the increased number of conducting electrons for a corresponding increase in temperature. Thermistors can be built up to 100 times more sensitive to temperature change, for the same resistivity change, than resistance temperature detectors (RTDs), which are described next. The main drawback of thermistors is their operating temperature limitation of approximately 300°F.

Resistance Temperature Detectors

RTDs rely on the increase in resistance of metals in response to increasing temperature. The resistor consists of a coil of fine metal wire or a film of pure metal deposited on a nonconductive surface. Different metals with different resistances are used, but platinum has become the most popular because of its excellent accuracy, large linear range of operation, and wide temperature range (higher than 1000°F is possible). The RTD is usually encased in a probe that is directly exposed to the well fluids. The RTD is commonly the active leg of a Wheatstone bridge.

Optical Fiber Measurement of Pressure and Temperature

Several systems are being developed to provide pressure and temperature measurements distributed over the length of an optical fiber that is permanently deployed in the completion. An advantage of fiber optic technology is that the sensors have no electronic components at depth, so they tend to be more reliable. Furthermore, optical sensors are immune to shock, not prone to electromagnetic interference, and operable at high temperatures.

Fiber optic technology is based on exposing the fiber to periodic ultraviolet (UV) light patterns that induce a "grating" on it. Pressure and temperature variations change the reflection wavelength of the gratings and can be decoded with respect to the fixed, incipient operating wavelength. The system is self-referencing.

Every point distributed along the length of the fiber has the potential to generate a different temperature measurement. The advantages are measurement of a permanent temperature gradient over the length of the fiber and the ability to select specific measurement points. Single-point and distributed temperature sensors have been reported to operate successfully in steamflood wells up to 575°F. In one reported case, temperature measurements taken along a horizontal wellbore at different times showed steamchests, water breakthrough, crossflow, and flow behind pipe.

Pressure is measured by sensors located at discrete, fixed points along the fiber. At the sensors, the fiber is cut, and its ends are placed face-to-face in a proximal arrangement. The face-to-face spacing is measured by successive reflections of the light wave. Changes in the value of the spacing reflect the environmental pressure around the fiber at that point. The self-referencing technique uses the distributed temperature measurement for suitable corrections.

Acquiring Bottomhole Pressure and Temperature Data

The acquisition of bottomhole pressure and temperature data can be planned and executed in a cost-effective manner with a minimum disruption to normal operating routines. In many cases, early on-site interpretation is useful in guiding decisions about continuing the acquisition program. Several questions should be answered at the design stage.

What are the objectives of measurement: static pressure, reservoir dynamics, fluid characterization, vertical pressure and temperature profile, well flow characterization, or other?
Is the environment openhole or cased hole? An exploration or development well?
Is there a need for real-time SRO measurements or can the data be recorded downhole and reviewed later?
What metrology is needed for the measurements (e.g., maximum temperature and pressure, measurement resolution and accuracy)? ^[2]
How will the gauges be conveyed to the bottomhole measuring points?
Is there a need to perform continuous or repeated measurements over months or years?
What economics apply, and do they imply a possible tradeoff with the quality or quantity of the measurements?

This section addresses these issues within the categories of SRO vs. downhole recording (DHR), surface vs. downhole shut-in, mode of conveyance, drillstem tests (DSTs), openhole wireline formation testing, production logging, measurement while perforating, and permanent installations in "smart" completions.

Surface Readout vs. Downhole Recording

Measurements can be transmitted to the surface, usually via an electric cable, or recorded in downhole memory powered by batteries.

SRO has the obvious advantage of providing data in real time. Real-time readouts are especially beneficial for transient measurements that require time for the pressure to stabilize and radial flow to develop. Because stabilization times depend on reservoir and fluid properties and because the determination of these parameters is often the purpose of pressure measurements in well tests, predicting the duration of stabilization periods is often difficult. SRO is preferred in these cases.

Some applications, usually those in the lower economic tier, can be conducted without the need for SRO. The benefits include lower operating costs and a fixed operations schedule. The drawback is the difficulty of guaranteeing the quality of the acquired data, including the potential for significant operating losses if the bottomhole recording equipment malfunctions. For these reasons, DHR should be chosen only when the measurement target does not necessarily depend on stabilization times or when stabilization times are already known (e.g., to measure the average reservoir pressure in a reservoir of known mobility).

Many industry tools provide both SRO and DHR. The measuring section of these tools is common to both options. In the SRO option, the sensor electronics are coupled to a telemetry system for uphole transmission, and the cable supplies downhole power. In the DHR option, downhole batteries supply power, and the data are stored in memory boards for future readout or downloading to suitable computer systems.

Surface Shut-In vs. Downhole Shut-In

The practice of downhole shut-in during a buildup test as opposed to surface shut-in is discussed in "Pressure Transient Testing." The advantages of downhole shut-in include control of the wellbore volume (afterflow), reduction of the duration of buildup tests, and choice on the recording mode (SRO or DHR).

Downhole shut-in can be performed during conventional DSTs or during tests performed on production wells. In a DST, the downhole shut-in valve is usually the main test valve. Shut-in is performed at the end of a flow period by actuating the test valve. Traditionally buildup pressures are recorded in DHR mode. Another procedure is to use the DST valve as the main shut-in valve while the DataLatch* electrical wireline downhole recorder/transmitter is used to observe pressures in real time during the buildup. DataLatch technology is described in "Drillstem Testing."

In producing wells, downhole shut-in is performed by setting a valve assembly in the tubing before performing the test. The tubing must have been previously equipped with locator nipples so that the valve can be anchored at the appropriate depth. The valve is run on either a slickline carrying a DHR pressure gauge or an electric line equipped with an SRO recording gauge. The shut-in valve is actuated by a sequence of pulls and releases on the slickline or cable. Commonly operated shut-in valves can perform in the range of up to 12 open-close cycles, after which the valve assembly is released from the setting nipples by an appropriate pull on the line. Other versions of shut-in valves can be operated by a clock, small explosive squib, or battery.

Bottomhole Conveyance of Gauges

Pressure and temperature gauges can be conveyed to the downhole environment by a number of methods, possibly in tandem with other measurements. Several possibilities are discussed here.

Drillstem Test String. Refer to the DST subsection 7.10.4.

Electric Line. Electric line operations provide surface readout and can be conducted any time during the life of the well. In openhole, wireline pressure testing offers a unique opportunity to efficiently collect distributed pressure data on the entire stratigraphic sequence penetrated by the well. In cased holes, pressure and temperature measurements are taken repeatedly along with other production logging measurements to monitor well performance and diagnose flow and completion problems. In addition, pressure buildups and other transient tests are frequently conducted in producing wells, using production logging tools or with "hanging" gauges, to check for variations in the productivity index and for skin development and to monitor multilayer producing systems. In the exploration environment, however, electric lines are not typically used because of the risks associated with having cable in the well while flowing. These risks include difficulty closing safety valves or subsea trees with cable in the borehole and sticking of the cable because of sanding from unconsolidated formations or hydrate formation in subsea wells. The DataLatch electrical wireline downhole recorder/transmitter, introduced in the late 1980s, has largely mitigated this risk. The DataLatch system is briefly described in "Drillstem Testing."

Slickline Slickline pressure and temperature surveys are performed with hanging gauges in situations that do not require SRO. Slickline operations are more cost-effective than electric line operations; however, the data quality usually does not match that of SRO data. Depth control is one of the critical factors affecting data accuracy. On the other hand, surface pressure control is easier in slickline operations because of their smaller diameter, typically in the range of 0.1 in. in diameter. A promising development is the "slick conductor line," a thin, hollow-core, 100% steel cable laid around an electric conductor to provide limited SRO capabilities.

Coiled Tubing. A popular alternative to drillpipe, coiled tubing is used to convey downhole gauges and other equipment in deviated holes when gravity is insufficient to pull the tools to the bottom of the well. Insufficient gravity occurs where well deviation exceeds values in the range of 60 to 70°, depending on tool weight and length, friction coefficients, pipe roughness, and the presence and type of completion components. In horizontal wells, the coiled tubing may not reach the toe of the completion because of a helical lockup of the coil inside the completion. Coiled tubing may be equipped with an internal electric cable running the length of the coil to support SRO operations.

Tractors. Tractors are an emerging technology that complements the use of coiled tubing in difficult, deviated completions. Tractors are self-powered and operated by electric line. They can negotiate bends, crawl up or down, and overcome the limitations of coiled tubing in long horizontal wells. Their main limitation is the large amount of cable power required for operation.

Wireless Transmission. Wireless transmission is a technique that has been in use since the late 1980s. It attempts to provide the advantages of SRO without using an electric line. The downhole tool, a sub that is part of a DST string, features a pressure gauge, battery pack, telemetry, recorder board, and antenna. The antenna sends the signals collected from the pressure recorder at a frequency suitable for transmission through the formation strata. At the surface, the signals are picked up by an array of suitably deployed stake antennae. This technique is limited to land operations and depths of approximately 8,000 ft.

Drillstem Testing

A DST string is a complex array of downhole hardware used for the temporary completion of a well. DSTs provide a safe and efficient method to control flow while gathering essential reservoir data in the exploration, appraisal, and development phases of a reservoir or to perform preconditioning or treatment services before permanent well completion. Fig. 7.5 shows a typical DST string with its essential components. In exploration well testing in particular, the DST string usually includes tubing-conveyed perforating (TCP) guns, which are shot underbalanced (i.e., wellbore pressure is less than reservoir pressure) at the initial well completion.

Fig. 7.5 – Pressure-controlled DST string.

DST strings include gauge carriers, which are collars that normally contain up to four pressure gauges bundled together, affording redundancy in long tests in which one or more gauges are likely to fail. These gauges perform only DHR measurements.

Most modern DST strings are fullbore strings, which means they have a flush opening running completely through the string of tools. The opening enables running pressure gauges and other slim tools (typically 1 ¹¹/₁₆ in.) in SRO mode.

The DataLatch system is a DST string component that combines the advantages of DHR (typically during flow periods) with the advantages of SRO (typically during shut-in periods). Pressure data are recorded in the tool’s memory boards. In suitable conditions, a LINC* Latched Inductive Coupling tool is run with an electric cable and latched into the DataLatch mandrel. This combination is used to read out the memories, reprogram the gauge acquisition schedule if necessary, and monitor the test in real time. The DataLatch system is unique for bottomhole pressure measurement applications. It allows simultaneous and continuous acquisition of three different measurements during the course of a DST test: rathole or reservoir pressure, cushion or tubing pressure, and annulus pressure.

Openhole Wireline Pressure Testing

Wireline pressure testing is conducted using tools lowered on an electric cable or coiled tubing in deviated wells. The tools consist of function-specific modules selected for a specific operation. Fig. 7.6 shows the modular arrangement of a modern wireline pressure tester.^[3] In a complete configuration, the tools may include a single-probe module for basic pressure testing and sampling, a dual-probe module for permeability applications, a flow-control module for flexible schedule testing, a fluid analyzer module for optical fluid properties monitoring in real time, multisample module for representative fluid sampling at reservoir pressure-volume-temperature (PVT) conditions, sample modules for large-volume fluid sampling, a pumpout module that can recirculate mud filtrate and other unrepresentative fluids out of the tool flow system before representative sampling, and a dual-packer module for very large area sampling, interference testing, and DST emulation.

Fig. 7.6 – Wireline tool components.

Wireline pressure testing encompasses several applications described in "Specific Applications and Interpretations." The applications include measuring static reservoir pressure, collecting representative fluid samples, determining anisotropic permeability, identifying reservoir permeability barriers, determining reservoir fluid gradients and densities, and determining rock stress components.

As in conventional well testing, a wireline sampling operation must be carefully designed beforehand to achieve the desired objectives. Key parameters that require special attention include the test type, fit of the probe type to the reservoir’s mechanical and hydraulic deliverability characteristics, volumes to be withdrawn, type of pressure gauges for the expected reservoir permeability, test sequence, number of pressure points to be taken, and interpretation objectives. The actual downhole tool configuration and the test sequence directly reflect the design study that precedes the operation.

Production Logging

The uses, benefits, and interpretation techniques of production logging are discussed in another chapter in this section of the Handbook.

Measurements While Perforating

Pressure and temperature measurements may be performed concurrently with shaped-charge perforating. This technique, called measurement while perforating (MWP),^[4] includes the following applications:

Before perforating, MWP verifies the completion fluid density, directly measures the wellbore pressure, and adjusts the perforating underbalance.
During perforating, MWP positively detects the detonation of the perforating gun.
After perforating, MWP observes the pressure responses and interprets them as a transient test, and it monitors the fluids produced by the perforation.

The MWP system is especially adapted to low-flow-rate or short-duration tests such as IMPULSE* measurement while perforating tests, closed-chamber tests, and slug tests. Flow tests can also be analyzed.

MWP must be performed in SRO mode; otherwise, the technique offers no benefit. An SRO tool such as the DataLatch recorder/transmitter or an electric line tool must be used. The production well environment is preferred for MWP, with the perforating guns conveyed on an electric line with the MWP sub above the guns. A typical MWP sub for pressure and temperature measurements incorporates a gamma ray detector and casing collar locator for depth control and suitable shock absorbers to mechanically decouple the guns from the measurement system. An optional bottom electric adapter can fire the guns electrically, which is often the procedure in non-TCP applications.

Because MWP also measures the wellbore fluid temperature, it is used for the same applications as production logging.

Permanent Pressure Measurement Installations

Permanent monitoring systems are placed downhole with the completion string near the depth of the reservoir to be monitored. They are connected to the surface by a cable that runs the full length of the completion string and exits the wellbore through suitable connectors crossing any subsurface safety systems and the wellhead. Advanced telemetry allows querying these sensors at any time throughout the life of the reservoir. Most systems in operation today record bottomhole pressure and temperature.

Permanent systems^[5] are engineered specifically for monitoring applications and have a life expectancy of several years. The digital electronics within the gauges are designed for extended exposure to high temperature without required maintenance. The metrology characteristics emphasize long-term stability rather than fast dynamic response. Quartz crystals as well as sapphire-based sensors can be used.

The cables for permanent installations are designed to withstand pressure, temperature, and exposure to highly corrosive fluids. They must also be mechanically rugged to prevent damage during installation. Usually single conductor cables are used.

The connections are similarly designed for durability. They include bottomhole connectors (power and pressure) to the permanent gauge mandrel and uphole connectors that cross through the wellhead. The complexity of the surface installation varies, depending on whether the wellhead is located at the surface—as on a land well or wellhead exposed above the sea on a platform—or subsea. For subsea wells, the acquisition system is typically through existing data-gathering systems through umbilicals. On platforms, several permanent gauges may be connected to an autonomous surface unit that records the measurements and communicates with shore facilities through standard or advanced (satellite) transmission links.

Fig. 7.7 shows a continuous data stream from an 80-day recording in which the pressure measurement was used to optimize production. The surface production rate was repeatedly adjusted to yield an acceptable bottomhole flowing pressure.

Fig. 7.7 – Readout of a recording over an 80-day period from a permanent gauge.

Wellhead Environments

Although the focus of this chapter is bottomhole measurements, it is worthwhile to mention a few interesting points about the environments of surface and subsea measurements.

Surface Acquisition of Downhole Data

Current specifications of surface acquisition systems, sensors, umbilicals, and piping commonly used in the industry are 0 psi and –40°F for the lower range of pressures and temperatures, respectively. The temperature specification in particular presents no obstacle to testing operations in extremely cold areas, such as the Arctic and similar cold-weather territories.

Subsea Acquisition of Pressure and Temperature

Pressure and temperature measurements are sometimes required at the subsea tree level. The measurements are mainly used to monitor the operating conditions of the landing string near the ocean floor. Applications include ensuring that the maximum temperature rating of the elastomers in the blowout preventer (BOP) is not exceeded, and providing data to help prevent hydrate formation during deep-sea cleanup and well testing operations.

Specific Applications and Interpretation

Bottomhole pressure data are vital for understanding reservoir performance and predicting future behavior. Applications include volumetric calculations (e.g., reserves), reservoir dynamic properties (e.g., permeability), drainage volumes (e.g., compartmentalization and flow barriers), fluid properties (e.g., density, phase behavior), well tubular and artificial lift design (e.g., size selection and lifting systems), evaluation of reservoir energy and fluid contacts with time, and input to numerical reservoir simulation models.

Depth Datum of Pressure

Static pressures should be corrected to a fixed depth datum to eliminate the influence of the fluid pressure gradient for building isobaric maps, using bottomhole pressure to calculate inflow performance relationship (IPR) diagrams for multilayer pressure data sets, or interpreting vertical permeability barriers from a pressure differential between two reservoir layers.

Pressures are adjusted to a fixed datum by calculating the hydrostatic potential (also called the datum-corrected pressure) as follows:

....................(7.4)

The potentials (adjusted pressures) reflect the dynamics of fluid movement in the reservoir better than the raw pressure data can. Reservoir layers with different potentials flow into one another if put in communication (e.g., if they are completed in the same wellbore). Isobaric maps built on datum-depth-corrected pressures reveal flow within a specific reservoir layer if this layer shows different potentials in different regions of the reservoir. In addition, vertical permeability barriers are qualified in terms of potential differences between the two adjacent reservoir units separated by the barrier.

D₀, the datum depth, can be arbitrary and has no influence on the interpretation of the hydrostatic potential, assuming a constant reservoir fluid density across the different wells or layers. Typically, a datum at the midpoint of the hydrocarbon column is selected to study pressure trends across the reservoir and phase behavior effects. A datum within a well may prove more useful for analyzing potential differences between multiple reservoir layers crossed by the well.

Static Pressure

Static pressure measurements always result from some form of transient test, in which a large or small amount of fluid is withdrawn from the well before the pressures are allowed to stabilize. Static pressures are acquired during wireline testing at the rate of approximately one measurement every few minutes because only very small amounts of fluid samples are withdrawn. Conversely, static pressures take much longer to stabilize in conventional well testing because the much larger fluid samples withdrawn create much greater pressure disturbances.

Static Pressure From Buildup Tests. The static pressure of a reservoir is one of the interpretation outputs of pressure transient tests. Many short-duration buildup tests (including wireline pressure "pretests") are designed solely for measuring the static reservoir pressure. The interpretation of buildup tests to determine the static reservoir pressure is discussed in another chapter in this section of the Handbook.

Average Reservoir Pressure. The average reservoir pressure can be determined arithmetically by averaging the datum-corrected pressures of a given layer in all wells, with each pressure weighted by the net thickness of the reservoir at the well. A better average pressure is determined by recording the pressures, either actual or weighted, on a map of the area and drawing isobars from which the average pressure weighted for an area is determined by planimetery (or gridding) of the isobars.

Static Pressure Determined From the Productivity Index. The productivity index (PI) of a producing layer, J, is defined as the ratio of the downhole production rate of the layer to the pressure drawdown under which the layer produces:

....................(7.5)

On a plot of bottomhole flowing pressure vs. downhole flow rate, the PI is represented by the inverse of the slope of the IPR line describing the pressure-rate characteristics of the producing layer (Fig. 7.8).

Fig. 7.8 – PI of a reservoir with a single producing layer.

The static reservoir pressure and PI of a reservoir with a single producing layer can be determined with production logging measurements without the need to shut in the well. The well must be flowed at several different flow rates (typically three or four) and allowed to stabilize between successive rate changes. Bottomhole pressure and flow-rate measurements are performed for each value of the surface flow rate. The IPR is drawn through the data points on a pressure vs. rate plot, and extrapolation of the IPR line to a zero-flow condition gives the static pressure.

In most gas wells and in oil wells drawn below the bubblepoint pressure, the IPR may not be linear. Although the same procedure can be used, the IPR shape should fit the curved nature of the data (e.g., a quadratic fit if turbulence is the cause of the nonlinearity of the IPR). Once properly fitted, the y-axis intercept (zero flow) of the modeled IPR gives the static pressure, and the x-axis intercept (atmospheric pressure) gives the absolute open flow (AOF) potential. The AOF potential of a gas well is generally a better indicator of its performance than its PI because PI is not constant and the IPR is represented by a curved line. The AOF of a gas well is determined by plotting the gas potential, m(p), as a function of the flow rate of each flow period of an isochronal test. In some cases of low reservoir pressure, Δp² can be used instead of m(p). More information on determining gas flow potential and reserves is in another chapter in this Handbook.

The same procedure applies to multilayer completions—plotting bottomhole pressure vs. rate for each layer of the system. To interpret the pressure data of combrble layers, however, the pressures must be corrected to a common arbitrary datum depth to readily differentiate whether the layers belong to the same hydraulic system. The results of the procedure, called selective inflow performance (SIP), include the static pressure and the PI per layer. The SIP procedure has become very popular for commingled producing systems, especially in gas wells because of the shorter stabilization times involved. SIP overcomes a fundamental limitation of commingled producing systems where the layer static pressures are not available by direct measurement, not even by shutting in the well, unless all the reservoir layers are in a strict hydraulic equilibrium.

Fig. 7.9 shows this technique applied to a multilayer reservoir comprising four layers: A, B, C, and D. The "Total" curve represents the global performance of the whole system, intersecting the pressure axis at a value that represents the wellbore pressure when shutting in the well. Obviously, this shut-in pressure differs from the pressure of each of the individual wells because the whole system is not at hydraulic equilibrium. Crossflows develop when shutting in this well, and high-pressure Layers A and B flow into depleted Layers C and D.

Fig. 7.9 – SIP analysis of a four-layer commingled reservoir with crossflow.

Pressure-Depth Plots

Vertically distributed wellbore and formation pressures, such as those measured by a wireline pressure tester, can be used to build mud and reservoir pressure profiles. If the measured interval is sufficiently thick, accurate pressure gradients may be established. As already mentioned, the gradients can in turn be used to spot permeability barriers and reservoir fluid contacts and to determine the reservoir fluid density.

Thick beds have a greater pressure change from top to bottom than thin beds. Therefore, the resolution of the pressure gauge becomes increasingly important the thinner the beds are. Another important factor is the number of pressure measurements taken within the bed of interest. Fig. 7.10 shows that increasing the number of pressure points greatly reduces the statistical error in determining the true gradient.

Fig. 7.10 – Gradient accuracty vs. bed thickness.

In some plots, the recorded pressures may not fall on a linear gradient. One example of this condition is when pressure points are not taken in a uniform depth-increasing or depth-decreasing sequence. This situation favors dispersion of the pressure measurements because of gauge hysteresis and lack of temperature stabilization. A procedure to help determine the reservoir fluid density consists of comparing the fluid density with the mud density over a set of tests taken with a wireline tester. As shown in Fig. 7.11, if the fluid pressures vary by Δp_fl and the mud pressures vary by Δp_m over the depth interval ΔD and a vertical well is assumed, then the following can be written:

....................(7.6)

....................(7.7)

then by elimination:

....................(7.8)

Because mud pressures are consistent over greater depth intervals, ρ_m is usually known. Eq. 7.8 then can be used to improve the reservoir fluid density determination.

Fig. 7.11 – Plot of reservoir (formation) pressure vs. mud (hydrostatic) pressure.

Virgin Reservoirs. In virgin reservoirs, the static reservoir pressures are unaffected by fluid withdrawal and the observed gradients therefore reflect the density of the original fluids. The "breaks," where the slope changes in the gradient, reflect the original fluid contacts as illustrated in Fig. 7.12.

Fig. 7.12 – Fluid types and contacts in a virgin reservoir.

Permeability barriers can also be identified as illustrated in Fig. 7.13. The barrier is indicated in Fig. 7.13a by the hydrostatic potential difference between the layers above and below the detected permeability barrier of approximately 20 psi. The line with a gradient of 0.497 psi/ft represents the mud pressure, which was measured in the same trip in the well while acquiring the formation pressure. In Fig. 7.13b, the reservoir fluid gradients differ across the permeability barrier. Nevertheless, a potential difference of approximately 140 psi across the barrier is interpreted as indicating a no-flow barrier. Zero permeability is implied. Otherwise, the pressure would have equilibrated on both sides of the barrier over geologic time.

Fig. 7.13 – Detecting permeability barriers.

Sometimes the gradients must be extrapolated to confirm fluid contacts. The gas/water contacts in Fig. 7.14 cannot be identified by the pressure profile of Well 1 or Well 2. By extrapolating the water gradient of Well 1 and the gas gradients of Well 2, however, it is possible to determine the position of the gas/water contacts in three zones. This extrapolation shows that pressure readings taken near the wellbore in this case reflect pressures that exist deep within the formation. From the gradient interpretation, the fluid in the upper formation is water, and there are two gas/water contacts in the lower formation.

Fig. 7.14 – Extrapolation of pressure gradients to fluid contact levels.

It is important to note when extrapolating gradients from reservoir pressures in low-permeability reservoirs that the pressures may be affected by supercharging. Supercharging is caused by the nonzero, small value of the mudcake permeability. This permeability allows a finite continuous flow of filtrate across the mudcake. In a low-permeability formation, the resistance to fluid flow created by the mudcake can be on the same order of magnitude as the resistance of the formation to accepting fluid. A standard wireline pressure measurement is therefore insufficient to measure the pressure of the virgin formation because a residual finite pressure difference remains between the formation at the mudcake interface and the virgin formation some distance away. Supercharged points plot to the right of a normal fluid gradient line.

Developed Reservoirs. Differential depletion is most likely to occur in developed reservoirs, destroying the original gradients. In addition, differential depletion generates vertical flow in the reservoir. Vertical flow may also result from partial completion effects that superimpose the corresponding pressure gradients on the fluid density gradients. A typical pressure-depth profile in a well drilled in a field under production is in Fig. 7.15. The well was completed in an interval in Zone 1. The pressure profile taken some time after initial completion clearly shows that the pressure in Zone 1 has been drawn down by fluid withdrawal. The pressure in Zones 2, 3, 4, and 5, which were not perforated, has also been affected by vertical flow through the reservoir. The measured gradients reflect the pressure drop created by vertical flow. The sharp pressure drop across Zone 2 reflects the very low permeability of this zone.

Fig. 7.15 – Pressure profile of a well in a developed field.

In spite of the blurring of fluid gradients in developed reservoirs, vertically distributed reservoir pressures are still useful for correlating formations hydraulically from well to well. The initial correlation made on the basis of openhole logs (left side) in Fig. 7.16 had to be modified because of the reservoir pressure data. Although time equivalent and present in both Wells 1 and 2, Zones A and B show different pressure regimes in the two wells and are not in hydraulic communication (right side).

Fig. 7.16 – Hydraulic correlation between two wells.

Pressure Probes in Duplex or Triplex

Taking pressure points with a multiple-probe wireline tester eliminates the uncertainty of the depth measurement for the set of points taken at a tool station. Modern wireline testers include a multiple-probe system that can measure pressure at a sink, or flowing, probe, at the same depth at a "horizontal probe" opposite the sink probe, and at a "vertical probe" at some vertical distance on a generatrix (i.e., parallel to the tool axis) with the sink probe. Both data density and data consistency increase greatly when this probe arrangement is used.

Effect of Capillary Pressure

Several studies have shown that a wireline formation tester actually measures the pressure of the continuous phase in the invaded region around a wellbore; typically this is the drilling fluid filtrate. The measured tester pressure is thus different from the reservoir pressure by the amount of capillary pressure. The capillary pressure affects the saturation of the wetting phase in the reservoir. The combined effects of rock wettability and capillary pressure can be reflected as changes in the pressure gradient, fluid contact level, or both on pressure-depth profiles, especially those recorded with oil-base mud in the borehole.^[6]^[7]

The principles, measurement techniques, and applications of capillary pressure measurements are discussed in another chapter in this Handbook. Refer to that chapter for information on the variation of water saturation with height, entry or threshold pressure, free-water level (FWL), and oil/water contact (OWC).

The first and most conspicuous effect of capillary pressure on wireline tester pressure gradient profiles is the creation of a break in the gradient at the FWL that may not coincide with the OWC interpreted from other measurements such as resistivity logs. The depth difference increases as the displacement pressure (a function of pore-throat diameter) increases. Fine-grained reservoirs with small pore throats are most likely to exhibit potentially large depth differences between the OWC and FWL.

The second, potentially more deleterious effect of capillary pressure on wireline tester pressure gradient profiles is that the measured pressure may differ from the true formation pressure. The difference results in an unrecognized shift of the gradient to the right or left of the true reservoir fluid gradient. The effect of the gradient shift, which is equal to the amount of capillary pressure, is to displace the observed break in the gradient. Interpreting this break as the FWL yields an erroneous depth, located either above or below the true FWL, depending on the conditions described next.

Fig. 7.17 presents pressure-depth plots and capillary pressure profiles in a water-wet reservoir drilled with water-base mud and oil-base mud. Fig. 7.17c shows the capillary pressure profile expected in a water-wet oil-bearing section of the reservoir. The capillary pressure is greater in the virgin zone because oil is the nonwetting fluid. The wireline tester measures a filtrate pressure in the invaded zone that is lower because of the absence of capillary pressure. The result is a gradient shift to lower pressure values and the FWL is interpreted above its true location. There is no shift in the water-bearing section of the reservoir because the capillary pressure is zero in both the virgin zone and invaded zone.

Fig. 7.17 – Pressure-depth plots and capillary pressure profiles – water-wet reservoirs.

When oil-base mud is used in a water-wet reservoir, the effect of the capillary pressure causes the measured pressures to differ from the true formation pressures only in the water-bearing section of the reservoir (Fig. 7.17b). Fig. 7.17d shows the capillary profile in the water-bearing section of the reservoir for this case.

Similar data and effects for water- and oil-base muds used in oil-wet reservoirs are shown in Fig. 7.18.

Fig. 7.19 – Pressure-depth plots and capillary pressure profiles – oil-wet reservoirs.

One possible method to correct for wettability and capillary pressure effects on wireline formation tester pressures is the Leverett J-function^[8]:

....................(7.9)

Laboratory measurements of p_c, k, and ϕ are used to develop a relationship for a reservoir. The amount of capillary pressure determined by the J-function is added to the measured pressure:

....................(7.10)

where p_c(S_xo) is the capillary pressure in the filtrate-invaded zone, for which the water saturation is traditionally called S_xo.

Alternatively, if a nuclear magnetic resonance log (NMR) is available, the in-situ capillary pressure correction can be performed directly. NMR logs have the capability to model the pore-size distribution. The method also makes use of laboratory experiments on cores to calibrate the correction.^[9]^[10]

Pressure Transient Testing

The interpreted pressure transient test is a primary source of dynamic reservoir data. Tests on oil and gas wells are performed at various stages of drilling, completion, and production. The test objectives at any stage range from simple measurement of reservoir pressure to complex characterization of reservoir features. Most pressure transient tests can be classified as either single-well productivity tests or descriptive reservoir tests.

Productivity tests are conducted to determine well deliverability, characterize formation damage and other sources of skin effect, identify produced fluids and determine their respective volume ratios, measure reservoir pressure and temperature, obtain representative fluid samples suitable for PVT analysis, evaluate completion efficiency, and evaluate workover or stimulation treatments.

Descriptive reservoir tests are conducted to assess reservoir extent and geometry, determine hydraulic communication between wells, characterize reservoir heterogeneities, and evaluate reservoir parameters.

Detailed information on the use and interpretation of transient pressure data is presented in another chapter in this Handbook. Some special analytical techniques follow.

Pressure Flow Convolution and Deconvolution

The pressure-flow convolution involves simultaneous bottomhole flow rate and pressure measurements to correct for the variations of bottomhole pressure caused by flow rate fluctuations during drawdown tests.^[11]

The bottomhole pressure and flow rate are mathematically convolved (coupled) as follows:

....................(7.11)

where p_D, the pressure function equivalent to a constant flow rate situation, is obtained by mathematical deconvolution of the pressure from the flow-rate fluctuations. When software deconvolution operators are used, trial and error is required to convolve a flow-rate schedule with a pressure function that approximates the true constant rate-equivalent pressure function, thus reproducing the measured pressures. The process can be made to converge rather rapidly for a pressure measurement of a given resolution, as long as the results allow for an acceptable margin of error.

Fig. 7.19 shows an example in which the transient consists of a step-rate change from a high value with a downhole spinner flowmeter rotation rate of approximately 17 revolutions per second (rps) to a lower value with a flowmeter response of approximately 7 rps. Clearly, the pressure and flow-rate data mirror each other, which is precisely the effect of the convolution. A constant flow-rate function was sought to interpret this test. The technique used here makes use of semilog analysis, in which rate-normalized pressures are plotted vs. the "sandface convolution time" (a time function akin to a generalized superposition function). The result (Fig. 7.20) is a straight line on the semilog plot, which in turn can be interpreted to yield the test objectives of the permeability and skin effect.

Fig. 7.19 – Pressure and spinner data in a step-rate change test.
Fig. 7.20 – Interpretation of test data in Fig. 7.19.

Benefits of Downhole Shut-In

Fig. 7.21 shows superimposed log-log plots for two buildup tests run on the same well. The surface shut-in test barely reaches radial flow after 200 hours. However, a large fraction of the wellbore volume is eliminated in the downhole shut-in test, and consequently radial flow is detected almost as early as the first minute after shut-in, and confirmed after 1 hour. This test, which lasts 100 hours, could well have been aborted after a maximum of 5 hours without any loss of information.

Fig. 7.21 – Compared pressures of a surface shut-in and downhole shut-in test.

Multilayer Tests

To interpret tests when several layers are producing in a commingled environment, a generalization of the pressure-flow convolution is used. Conventional well tests performed on commingled multilayer reservoir systems normally do not yield interpretable data. The different dynamic reservoir parameters (i.e., kh, skin effect, static pressure, boundary condition, heterogeneity) of each layer induce off-phase flow rate events in the layer that do not superimpose themselves to yield a predictable sandface pressure response. By using simultaneous bottomhole pressure and flow rate measurements and designing the drawdown test as a succession of step-rate tests (Fig. 7.22), a rigorous solution to deriving the dynamic reservoir parameters can be obtained for each layer.^[12]^[13]

Fig. 7.22 – Typical design for a three-layer multirate test (PL = production logging).

The following steps describe a typical design for a three-layer multirate test:

The well is shut in, and the pressure and flow sensors (typically conveyed by a production logging tool) are positioned above the top of the uppermost layer. The well is opened to the smallest choke opening, and the ensuing transients of rate and pressure are recorded until stabilization occurs. Finally, a continuous flow profile is recorded across the set of producing layers.
The pressure and flow sensors are repositioned above the top of the middle layer. The well is opened to the intermediate choke opening, and the ensuing transients of rate and pressure are recorded until stabilization occurs. A second continuous flow profile is recorded across the set of producing layers.
The pressure and flow sensors are repositioned above the top of the lowermost layer. The well is opened to the largest choke opening, and the ensuing transients of rate and pressure are recorded until stabilization occurs. A third continuous flow profile is recorded across the set of producing layers.
In a last, optional step, the pressure and flow sensors are repositioned above the top of the uppermost layer and the well is shut in again. The observed transients of rate and pressure are recorded as in a traditional buildup test.

The interpretation of this data set (which includes SIP data) makes extensive use of the pressure-flow convolution to extract the individual layer parameters. After the results are obtained, it is advised to verify their quality by forward-simulating the commingled pressure and flow response of the layered system and by matching the simulated responses to the measured data. A single-well numerical simulator is used with the layered system described by the interpreted values of permeability and skin effect for each layer. The surface flow rate schedule is input, and the simulator predicts the commingled pressure response of the system as well as the individual layer flow history for the entire test, which must match the measured downhole pressure and flow rate records.

Wireline Pressure Transient Tests

Some interpretation techniques are unique to wireline testers because of the specific hardware used to perform the tests. Wireline testers investigate a smaller region around the wellbore because of the smaller volumes flowed. Wireline pressure testing offers unique advantages over drillstem testing, however, because of the variety of options available in the downhole hardware configuration, multiprobe arrangements, and packer devices. Stewart and Wittmann first described some salient techniques specific to wireline pressure testing in 1979.^[14]

In wireline pressure testing, the static pressure is measured by shutting in the sampling system after retrieving a small sample, typically 5 to 20 cm³. The subsequent buildup duration is short, and the stabilized static pressure is typically obtained within a few seconds to a maximum of approximately 30 minutes.

In low-permeability situations, the buildup may take much longer. Continued testing with the tool hanging stationary at the same depth, firmly seated against the formation, may be impractical. In addition, pressure measurements may be affected by the supercharging phenomenon as described previously, resulting in understated pressures.

Packer Probe Tests: Small-Scale Drillstem Testing. A packer probe fitted into the string of a modern wireline tester increases the area of the formation open to the flow during formation sampling, typically by a factor of up to several thousand. This increase multiplies flow rates by the same factor, which in turn greatly increases the depth of investigation. In some cases, a packer probe test has a depth of investigation similar to that of a small-scale DST.

Packer and Multiple-Probe Tests for Vertical Interference Testing. A packer probe can be used in tandem with a vertical probe to test for vertical permeability.^[15] The vertical probe is located on a generatrix (parallel to the tool axis) with the sink (packer) probe of the downhole tool. The distance of the vertical probe from the sink probe is adjustable. Whereas the pressure response at the sink probe depends on the local values of the permeability tensor, called k_x, k_y, and k_z, which are the permeabilities along arbitrary axes x, y, and z, respectively, the pressure response at the vertical probe (which is considered an observation probe) is a function of both the horizontal permeability at the vertical probe and the vertical permeability being measured. Thus, both pressure responses must be modeled simultaneously by a numerical parameter estimator.

Fig. 7.23 depicts the results of a tandem test. The dots are pressure measurements and the dashed curves are the pressures reconstructed from probe responses calculated from the interpretation results. Fig. 7.23a shows the response at the sink (packer) probe, and Fig. 7.23b shows the response at the vertical probe, which was set approximately 1 hour after the packer was set. The test sequence included a number of open-close cycles generated at the sink probe by the use of a flow-control module. A sample was also taken between times 2,800 and 3,800 seconds. The vertical probe response clearly shows the delayed interference response that occurred after that probe was set. From this data set, the horizontal mobility k_h/μ was calculated as 1.0 md/cp, and the vertical mobility k_v/μ was calculated as 0.3 md/cp. Fig. 7.24 shows the log-log plot of the buildup between times 3,800 and 4,700 seconds that occurred after the sample was taken.

Fig. 7.23 – Sink probe (a) and vertical probe (b) pressure responses during a vertical interference test conducted with wireline tester.
Fig. 7.24 – Log-log plot of post-sampling buildup from the vertical interference test of Fig. 7.23.

NODAL Analysis

The techniques and uses of NODAL* production system analysis are explained in another chapter in this Handbook. The objective of NODAL analysis is to predict well-producibility characteristics, also referred to as vertical lift properties (VLP), for various tubular and pressure configurations. If the pressure data are limited to sandface and wellhead measurements, the normal procedure is to generate several sets of VLP characteristics and select the one that best represents the measured pressure data. There may not be a unique solution. Recording a continuous profile of pressure vs. depth can alleviate nonuniqueness because the profile constitutes a precise measurement of the multiphase pressure losses that take place in a well. Using a continuous profile for input leads to better optimization of production rates with NODAL analysis.

NODAL analysis, aided by distributed pressure measurements, is the best way to design gas-lift systems. Gas-lift valve placement involves matching the pressure drop in the valves with the amount of pressure available in the well above the valve opening pressure. The pressure drop in the tubing, in turn, depends on the location and flow capacity of the valves.

Using Pressure To Characterize Reservoir Fluids

Pressure and temperature provide important information about the phase behavior and calibration of the equation-of-state for a fluid and average fluid density in flowing wells.

The average fluid density can be calculated by differentiating the pressure measurement vs. depth. In the absence of fluid friction on pipes, the acceleration and kinetic terms can be written as follows:

....................(7.12)

In a well flowing above the bubblepoint, the bubblepoint pressure can be inferred from a plot of the fluid density in the tubing. At the depth where the pressure reaches bubblepoint pressure, gas starts evolving from solution, and the density of the fluid shows a break to lower values. Density can be measured by differential pressure measurements.

Similarly, the pressure gradient in wet gas wells shows a break when the dewpoint is reached and condensate forms.

Temperature Profiles in Production and Injection Wells

All the mass-transfer processes taking place in and around a wellbore produce changes in the wellbore temperature. Measuring the wellbore temperature is a good diagnostic tool for applications such as identifying fluid entries into and exits from the wellbore, monitoring exothermic reactions such as cement hydration, determining the effects of temperature change on compression or decompression (Joule-Thompson effects), detecting the movement of fluids behind the casing, and identifying nongeothermal fluid entries into the wellbore. Another chapter in this section of the Handbook explains the use and interpretation of these data.

Recommendations for Temperature Profiling. To obtain good-quality temperature profile data, the following procedures are recommended.

Record a complete profile from surface to total depth (bottom of the well) on the first descent into the well. If the well is shut in, the thermal equilibrium becomes disrupted after the first passage of the temperature sensor, and unrecorded temperature anomalies may be lost forever. If the well is flowing, the first descent is a unique opportunity to diagnose leaks, spurious flow, or loss of completion integrity.
It may be possible to record a representative geothermal gradient if the well is shut in.
Record shut-in profiles if possible. Always compare shut-in profiles with the flowing profiles.
Repeat all runs.
In dual completions, run the temperature log in both tubing strings because the two logs are not identical.
Use short depth scales for presentation. They highlight temperature anomalies better than large depth scales.
Always interpret temperature logs together with flowmeter data.

Detecting Cement Tops. Cement hydration is an exothermic reaction that generates sufficient heat for determining the presence of cement behind a casing string by a temperature survey up to several days after cementing. The character of the anomaly above the cement top may be a large, sharp increase, in some cases up to 50°F, or a very slight increase in gradient.

The principal influence on the survey is the time elapsed between placing the cement and running the survey. Other influential conditions include cement texture, chemical composition, rate of hydration, mass of cement in place, and the thermal conductivity of the adjacent formation. The maximum temperature usually occurs 4 to 9 hours after cementing, but reliable data can be determined in most areas after 48 hours. The rate of hydration affects temperature change more than the total amount of heat liberated. Although hydration continues indefinitely, the rate decreases rapidly from the peak. A washed-out section of hole may be responsible for a large, sharp increase in temperature that falsely indicates a cement top. A small temperature change or slight change in gradient could be caused by a small annular area or dilution of the cement with drilling mud. These factors, which influence the size of the temperature anomaly at the top of the cement in a well, vary widely in their effect. Even for an unfavorable combination of factors, however, sufficient heat is typically generated to determine the cement top.

Vertical Extent of Fracturing and Detecting Lost Circulation. The temperature of fluids and solids injected during a frac job is low relative to that of the formation which causes anomalies in the geothermal profile. This effect also applies to lost circulation zones that receive excessive amounts of drilling mud. Diagnosis of these anomalies with temperature surveys can supply quantitative data on the fracture size and amount of mud lost.

Nomenclature

A_ij	=	pressure calibration coefficient of orders i and j, dimensionless
A_ij′	=	temperature calibration coefficient of order i and j, dimensionless
B	=	formation volume factor, RB/STB
C	=	wellbore storage coefficient, bbl/psi
D	=	depth along the wellbore, ft
D₀	=	depth along wellbore of the reference datum, ft
g	=	acceleration of earth’s gravity, ft/sec²
h	=	reservoir thickness, ft
J	=	productivity index, B/D/psi
J(S_w)	=	Leverett J-function, dimensionless
k	=	reservoir permeability, md
k_h	=	reservoir horizontal permeability, md
k_x	=	permeability along arbitrary axis x, md
k_y	=	permeability along arbitrary axis y, md
k_z	=	permeability along arbitrary axis z, md
m(p)	=	real gas pseudopressure, psi²/cp
p	=	pressure, psi
p_c	=	pressure calibration function, dimensionless
p_c(S_xo)	=	capillary pressure in filtrate invaded zone, psi
p_D	=	observed pressure response at the wellbore, dimensionless
p_D′	=	derivative of the sought constant rate pressure response, dimensionless
p_fl	=	fluid pressure, psi
p_i	=	original reservoir pressure, psi
p_m	=	mud pressure, psi
p_o	=	oil-phase pressure, psi
p_r	=	reservoir pressure, psi
p_w	=	water-phase pressure, psi
p_wf	=	bottomhole flowing pressure, psi
q	=	flow rate, STB/D
q_D(τ)	=	variable sandface flow rate, dimensionless
Q	=	downhole flow rate, B/D
r	=	distance from wellbore axis, ft
r_e	=	external boundary radius of the well, ft
r_w	=	wellbore radius, ft
s	=	skin effect, dimensionless
s_d	=	skin effect due to damage, dimensionless
S_p	=	pressure output of a pressure gauge, psi
S_po	=	pressure output offset of a pressure gauge, psi
S_t	=	temperature output of a pressure gauge, °F
S_to	=	temperature output offset of a pressure gauge, °F
S_w	=	water saturation, fraction
t_D	=	dimensionless time
t_k	=	circulation time, hr
T_bh	=	observed temperature in a well, °F
T_c	=	temperature calibration function, dimensionless
δ	=	deviation of the well, assumed constant between D and D₀, deg
ΔD	=	vertical depth differential, ft
Δp	=	pressure change, psi
Δp_fl	=	fluid pressure differential, psi
Δp_m	=	mud pressure differential, psi
Δt_c	=	time after circulation, hr
μ	=	fluid viscosity, cp
ρ	=	reservoir fluid density, g/cm³
ρ_fl	=	reservoir fluid density, g/cm³
ρ_m	=	mud density, g/cm³
σ	=	surface tension, psi.ft
τ	=	integration variable, dimensionless
ϕ	=	reservoir porosity, fraction
ϕ	=	hydrostatic potential, psi

References

↑ ^1.0 ^1.1 Dowdle, W.L. and Cobb, W.M. 1975. Static Formation Temperature From Well Logs - An Empirical Method. J Pet Technol 27 (11): 1326-1330. SPE-5036-PA. http://dx.doi.org/10.2118/5036-PA.
↑ Veneruso, A.F., Ehlig-Economides, C., and Petitjean, L. 1991. Pressure Gauge Specification Considerations in Practical Well Testing. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 6-9 October 1991. SPE-22752-MS. http://dx.doi.org/10.2118/22752-MS.
↑ Colley, N. et al. 1992. The MDT Tool: A Wireline Testing Breakthrough. Schlumberger Oilfield Review (April): 58.
↑ Davies, J., van Dillewijn, J., Herve, X. et al. 1997. Spinners Run While Perforating. Presented at the Offshore Europe, Aberdeen, United Kingdom, 9-12 September 1997. SPE-38549-MS. http://dx.doi.org/10.2118/38549-MS.
↑ Eck, J. et al. 1999. Downhole Monitoring: The Story So Far. Schlumberger Oilfield Review (Winter): 20.
↑ Elshahawi, H., Fathy, K., and Hiekal, S. 1999. Capillary Pressure and Rock Wettability Effects on Wireline Formation Tester Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6 October 1999. SPE-56712-MS. http://dx.doi.org/10.2118/56712-MS.
↑ Elshahawi, H., Samir, M., and Fathy, K. 2000. Correcting for Wettability and Capillary Pressure Effects on Formation Tester Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October 2000. SPE-63075-MS. http://dx.doi.org/10.2118/63075-MS.
↑ Leverett, M.C. 1941. Capillary Behavior in Porous Solids. Trans. of AIME 142 (1): 152-169. http://dx.doi.org/10.2118/941152-G.
↑ Lowden, B. 2000. Some Simple Methods for Refining Permeability Estimates From NMR and Generating Capillary Pressure Curves. DiaLog, The On-Line Newsletter of the London Petrophysical Society 8 (1). http://www.lps.org.uk/site_pages/dialog.htm#top.
↑ Marschall, D. et al. 1995. Method for Correlating NMR Relaxometry and Mercury Injection Data. Trans., Intl. Symposium of the SCA, San Francisco, 12–15 September.
↑ oseph, J., Ehlig-Economides, C.A., and Kuchuk, F. 1988. The Role of Downhole Flow and Pressure Measurements in Reservoir Testing. Presented at the European Petroleum Conference, London, United Kingdom, 16-19 October 1988. SPE-18379-MS. http://dx.doi.org/10.2118/18379-MS.
↑ Kuchuk, F.J., Karakas, M., and Ayestaran, L. 1986. Well Testing and Analysis Techniques for Layered Reservoirs. SPE Form Eval 1 (4): 342–354. SPE-13081-PA. http://dx.doi.org/10.2118/13081-PA.
↑ Ayestaran, L. et al. 1987. Layered Reservoir Testing. Schlumberger Technical Review 35 (4): 4.
↑ Stewart, G. and Wittmann, M. 1979. Interpretation of the Pressure Response of the Repeat Formation Tester. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23–26 September. SPE-8362-MS. http://dx.doi.org/10.2118/8362-MS.
↑ Head, E.L. and Bettis, F.E. 1993. Reservoir Anisotropy Determination With Multiple Probe Pressures. J Pet Technol 45 (12): 1177-1184. SPE-26048-PA. http://dx.doi.org/10.2118/26048-PA.fckLR

SI Metric Conversion Factors

bbl	×	1.589 873	E − 01	=	m³
cp	×	1.0*	E − 03	=	Pa•s
ft	×	3.048*	E − 01	=	m
°F		(°F − 32)/1.8		=	°C
in.³	×	1.638 706	E + 01	=	cm³
psi	×	6.894 757	E + 00	=	kPa
psi²	×	4.753 8	E + 01	=	kPa²

*

Conversion factor is exact.

[r1-1] 1.0 ^1.1 Dowdle, W.L. and Cobb, W.M. 1975. Static Formation Temperature From Well Logs - An Empirical Method. J Pet Technol 27 (11): 1326-1330. SPE-5036-PA. http://dx.doi.org/10.2118/5036-PA.

[r2-2] Veneruso, A.F., Ehlig-Economides, C., and Petitjean, L. 1991. Pressure Gauge Specification Considerations in Practical Well Testing. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 6-9 October 1991. SPE-22752-MS. http://dx.doi.org/10.2118/22752-MS.

[r3-3] Colley, N. et al. 1992. The MDT Tool: A Wireline Testing Breakthrough. Schlumberger Oilfield Review (April): 58.

[r4-4] Davies, J., van Dillewijn, J., Herve, X. et al. 1997. Spinners Run While Perforating. Presented at the Offshore Europe, Aberdeen, United Kingdom, 9-12 September 1997. SPE-38549-MS. http://dx.doi.org/10.2118/38549-MS.

[r5-5] Eck, J. et al. 1999. Downhole Monitoring: The Story So Far. Schlumberger Oilfield Review (Winter): 20.

[r6-6] Elshahawi, H., Fathy, K., and Hiekal, S. 1999. Capillary Pressure and Rock Wettability Effects on Wireline Formation Tester Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 3-6 October 1999. SPE-56712-MS. http://dx.doi.org/10.2118/56712-MS.

[r7-7] Elshahawi, H., Samir, M., and Fathy, K. 2000. Correcting for Wettability and Capillary Pressure Effects on Formation Tester Measurements. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October 2000. SPE-63075-MS. http://dx.doi.org/10.2118/63075-MS.

[r8-8] Leverett, M.C. 1941. Capillary Behavior in Porous Solids. Trans. of AIME 142 (1): 152-169. http://dx.doi.org/10.2118/941152-G.

[r9-9] Lowden, B. 2000. Some Simple Methods for Refining Permeability Estimates From NMR and Generating Capillary Pressure Curves. DiaLog, The On-Line Newsletter of the London Petrophysical Society 8 (1). http://www.lps.org.uk/site_pages/dialog.htm#top.

[r10-10] Marschall, D. et al. 1995. Method for Correlating NMR Relaxometry and Mercury Injection Data. Trans., Intl. Symposium of the SCA, San Francisco, 12–15 September.

[r11-11] seph, J., Ehlig-Economides, C.A., and Kuchuk, F. 1988. The Role of Downhole Flow and Pressure Measurements in Reservoir Testing. Presented at the European Petroleum Conference, London, United Kingdom, 16-19 October 1988. SPE-18379-MS. http://dx.doi.org/10.2118/18379-MS.

[r12-12] Kuchuk, F.J., Karakas, M., and Ayestaran, L. 1986. Well Testing and Analysis Techniques for Layered Reservoirs. SPE Form Eval 1 (4): 342–354. SPE-13081-PA. http://dx.doi.org/10.2118/13081-PA.

[r13-13] Ayestaran, L. et al. 1987. Layered Reservoir Testing. Schlumberger Technical Review 35 (4): 4.

[r14-14] Stewart, G. and Wittmann, M. 1979. Interpretation of the Pressure Response of the Repeat Formation Tester. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 23–26 September. SPE-8362-MS. http://dx.doi.org/10.2118/8362-MS.

[r15-15] Head, E.L. and Bettis, F.E. 1993. Reservoir Anisotropy Determination With Multiple Probe Pressures. J Pet Technol 45 (12): 1177-1184. SPE-26048-PA. http://dx.doi.org/10.2118/26048-PA.fckLR

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