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# 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.

## Applications of pressure transient 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
• Evaluate workover or stimulation treatments.

Descriptive reservoir tests are conducted to:

• Assess reservoir extent and geometry
• Determine hydraulic communication between wells
• Characterize reservoir heterogeneities
• Evaluate reservoir parameters.

## 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.[1]

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

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

where pD, 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. 1 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. 2) 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.

## Benefits of downhole shut-in

Fig. 3 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.

## 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. 4), a rigorous solution to deriving the dynamic reservoir parameters can be obtained for each layer.[2]

### Steps in a typical multilayer test

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

1. 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.
2. 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.
3. 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.
4. 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.

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. 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 kx, ky, and kz, 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. 5 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. 5a shows the response at the sink (packer) probe, and Fig. 5b 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 kh/μ was calculated as 1.0 md/cp, and the vertical mobility kv/μ was calculated as 0.3 md/cp. Fig. 6 shows the log-log plot of the buildup between times 3,800 and 4,700 seconds that occurred after the sample was taken.

## NODAL analysis

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 non-uniqueness 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:

....................(2)

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 non=geothermal fluid entries into the wellbore.

### Recommendations for temperature profiling

To obtain good-quality temperature profile data, the following procedures are recommended:

1. 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.
2. It may be possible to record a representative geothermal gradient if the well is shut in.
3. Record shut-in profiles if possible. Always compare shut-in profiles with the flowing profiles.
4. Repeat all runs.
5. In dual completions, run the temperature log in both tubing strings because the two logs are not identical.
6. Use short depth scales for presentation. They highlight temperature anomalies better than large depth scales.
7. 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.

## References

1. Joseph, 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
2. Kuchuk, F.J., Karakas, M., and Ayestaran, L. 1986. Well Testing and Analysis Techniques for Layered Rese