Perforation Inflow Test Analysis (PITA)

Well testing has served the industry faithfully for decades as the primary and most reliable means of:

• Quantifying deliverability
• Characterizing the reservoir
• Evaluating the condition of the well

However, for the last few years, oil and gas producers have been searching for alternatives that would yield the desired information in less time, in a more environmentally friendly manner, and at a cheaper cost than conventional well tests.

The trend has inevitably been towards tests of shorter duration. Although it is accepted that results from short tests may not be as reliable as those from conventional well tests, it is reasonable to accept that the results are valuable in assisting with decisions about field development, when an increased margin of error can be tolerated. Offshore, in addition to the potentially exorbitant cost of testing (several millions of dollars), the drive towards "green" (shorter) tests is fuelled by environmental considerations such as flaring of hydrocarbons. In North America, the marginal economics of low deliverability wells requires the use of "cheap" tests. Either way, there is an increasing trend towards green tests to replace conventional well tests.

One such green test consists of simply allowing the well to flow into the closed wellbore after perforating (closed chamber test). The buildup pressure data is collected for a period of hours or days, depending on the reservoir's flow potential. These tests have been variously called: Slug test, Surge Test, Perforation Inflow Diagnostic (PID), or Closed Chamber Test.

Theory
Following a critical review of the literature, and in collaboration with Dr. Mehran Pooladi-Darvish of the University of Calgary, we have developed a complete and systematic analysis that yields an estimate of initial reservoir pressure, permeability and skin. We have called this procedure "Perforation Inflow Test Analysis" (PITA). Two publications containing full technical details have been submitted for presentation at the CIPC in Calgary (June 2005) and at the SPE ATCE, in Dallas (October, 2005).

Starting with the fundamental equations in Laplace space, we derived early-time and late-time solutions of the transient pressure behaviour. Early-time data is used to estimate skin, and late-time data is used to estimate initial pressure and permeability. In gas wells, the pressure data is usually measured at the wellhead and converted to bottomhole.

This conversion is primarily due to hydrostatic head because the influx rate into the wellbore diminishes rapidly (and friction is negligible). The influx flow rate is not measured but can be estimated using closed chamber calculations, provided the assumption of single-phase flow can be justified. Figure 1 shows the typical profiles of measured pressure and calculated gas influx rate for a "perforation test" of a gas well. As shown here, the influx rate declines rapidly.

Flow Regimes
It is obvious that the data for PITA is significantly influenced by wellbore storage. It is also evident that the data is directly influenced by the flow capacity (k * h) and skin. The critical part of any analysis is distinguishing between the data that is dominated by wellbore storage (afterflow), and the data that is dominated by the reservoir response (reservoir flow).

Just as in traditional well testing, the best way to differentiate between these flow regimes is to plot the derivative. However, the derivative for PITA is different from the traditional derivative of well testing. The PITA derivative, also known as the "impulse 2 derivative," is defined as t dp/dt, the product of the square of time and the well known primary pressure derivative (PPD). A typical derivative is shown in Figure 2. It illustrates that the early-time data (wellbore storage) has a slope of 2 (well test derivative has a slope of 1), and the late-time data (reservoir flow) has a slope of 0 (flat line- same as well test derivative). Once the derivative has been plotted, it is easy to recognize if reservoir flow exists. If it does, reservoir pressure and permeability can be determined. At least some of the late-time data should fall on the flat part of the derivative, as shown in Figure 2, in order to get a reliable analysis. If this data exists, then skin can be calculated from the early-time data. If there is no reservoir flow, then an unique interpretation is not possible.

Analysis

In traditional well test interpretation, we start analyzing the data from early-time to late-time. In PITA, we start with late-time data to obtain reservoir pressure and permeability. We then analyze the early-time data (where the derivative slope is 2) to obtain skin. Even though a complete analysis can be obtained from the derivative plot alone, it is useful to generate the inverse pseudo-time plot to confirm the analysis.

The fundamental equations were derived in terms of liquid flow (pressure and time). However they are easily converted to gas flow by replacing pressure with pseudo-pressure and time with pseudo-time.

A summary of the procedure for analyzing a Perforation Inflow Test for a gas well is presented below:

1. Convert measured wellhead pressure to sandface pressure (in some tests, the sandface pressure is measured directly).
2. Convert sandface pressure to pseudo-pressure.
3. Convert time to pseudo-time
4. Calculate impulse derivative and plot versus pseudo-time on log-log scales (Figure 2).
5. Determine start of late-time reservoir dominated flow (Figure 2).
6. Analyze late-time data by plotting Y vs 1/t on reverse a Cartesian coordinates (Figure 3). A straight line through the valid late-time data gives permeability and reservoir pressure from:
7. Analyze the early-time data by plotting pseudo-pressure vs. pseudo-time on a Cartesian coordinates (Figure 4). If permeability has first been determined from step 6, skin can be obtained from the slope of a straight line, anchored on pseudo-pressure, the minimum wellbore pressure (cushion pressure), and passing through the valid early-time data (corresponding to derivative slope = 2)
   

The analysis procedure is well grounded in theory. We now have a much better sense of the interpretation and the validity of these short tests because of our clear understanding of the flow regimes. In practice, we know that the longer we flow, the better the results. Therefore, it is important to validate the PITA results by comparing them with those from other tests (e.g. permeability obtained from longer flow/buildup or reservoir pressure obtained from static gradient). Because of well cleanup and other such considerations, the value of permeability and skin can be different between various tests. Until we have enough experience to determine to what extent PITA can be relied on, IHS recommends comparing results as often as possible, and we encourage analysts to publish their results.

Conclusions

1. We have developed a systematic and comprehensive analysis of data obtained from Perforation Inflow Tests.
2. We have developed clear diagnostics to identify when the analysis is applicable and when the results are reliable.
3. When the influx is very small, is it because of low permeability or is it formation damage? If sufficient data is available, it is possible to determine the difference between low permeability or damage. If the data quality is poor, or the test duration is inadequate, one must rely on "gut feeling" or experience, or consider more elaborate testing procedures, such as downhole shut-in.
4. Validate PITA by comparing results to those obtained from other tests.

Martin Santo, Senior Technical Advisor, IHS Energy
Posted September 24, 2015

This article was published by S&P Global Commodity Insights and not by S&P Global Ratings, which is a separately managed division of S&P Global.