Summary
Several pressure buildup tests are analyzed with a view to evaluate the potential of the ideas given in the literature. A broad range of tests is examined to demonstrate the characteristics of responses in wells producing below the dew point. Methods to obtain quantitative information that is consistent for different tests are outlined. The specific contributions of this article are as follows. First, in this article we examine field data, second, we look at multiple rates, third, we examine unfractured and fractured wells, fourth, we look at wells that have been produced for a short time and those produced for a long time, fifth, we consider both depletion-type and cycling scenarios, and, sixth we tie pressure data to relative permeability and PVT data. Many of these issues are addressed for the first time.
Introduction
Because of the extraordinary success of the diffusivity equation in enabling us to analyze pressure measurements and the conveniences derived there from, the analysis of pressure responses subject to the influences of multiphase flow is, at best, provided as only a perfunctory treatment in the literature. Single-phase flow is the paradigm in this area of reservoir engineering. The reluctance in shifting from this paradigm may be partially attributed to the perception that relative-permeability measurements are not reliable enough for us to analyze the rapid changes in pressure that occur over a very short period of time. The other principal reason is that a simple method needs to be devised to relate the relative permeability to pressure, although studies have suggested procedures to address this issue.1,2
In this article we provide information for those interested in using multiphase-flow concepts for analyzing pressure-buildup tests in wells producing gas-condensate reservoirs. This class of tests was chosen for a number of reasons besides the fact that the gas-condensate system provides an opportunity to combine both single-phase and two-phase flow concepts.
Since we consider multiphase flow under multiple-rate conditions, there are very few theoretical ideas to guide us. The simulations of Jones et al.2,3 provide us with a starting point. These works merely examine a single buildup following a single drawdown with the well flowing at a constant rate or a constant pressure. Since no theoretical evaluations of multirate tests are available, we have conducted a number of simulations using a compositional model to ensure that the explanations we provide are plausible. We do not concentrate on the synthetic situations, however, because the same information may be conveyed by the field-case illustrations. In the following, we examine five tests to demonstrate important features of buildup responses in gas-condensate reservoirs. Four of these tests are in "depletion" systems and the fifth one discusses buildup tests in a pressure-maintenance project.
Background
The depletion tests we consider presume that the results of a constant-composition-expansion (CCE) test on a representative sample are available. An equation of state, tuned to this sample, provides information on molar density and viscosity. In addition, we assume that appropriate relative-permeability measurements are available. Using this information, we proceed to analyze buildup tests using the concepts suggested by Jones, Vo, and Raghavan.3 The buildup tests for the pressure-maintenance system are evaluated using the single-phase analog because information on the in-situ composition (pressure-maintenance project) is unavailable to us. These tests are analyzed by the composite-reservoir formulation.4Figs. 1 and 2 present the pertinent CCE and relative-permeability information used in this work. We consider a wide range of mixtures with the maximum liquid dropout in the range of 0.07 to 0.35. Mixtures 1, 2, and 3 are for depletion experiments, and mix 4 applies to the test for the well in the pressure-maintenance project. Justification for the use of relative-permeability curves is based on the fact that these curves are also used in matching performance and making production forecasts. As expected, the relative permeability to oil is negligibly small until the liquid saturation becomes quite large. Table 1 presents properties that are needed to analyze the buildup tests. Our primary focus in all of the following is to obtain a consistent interpretation of multiple buildup tests after the wellbore pressure has fallen below the dew-point pressure.
Theoretical Considerations
We use single-phase and two-phase analogs to analyze pressure measurements. Our focus will be the interpretation of buildup measurements. The single-phase analog given by $$m(p)={\int {p {wf, s}}^{p {ws}}}\,{\rho {g}\over \mu {{\rm g}}}\,{\rm d}p,\eqno ({\rm 1})$$ is essentially identical to the analog commonly used for dry-gas systems. Here, ? is the molar density, ? is the viscosity, pwf, s is the pressure at the time of shut-in, pws is the shut-in pressure, and the subscript g refers to the gas phase. This analog takes advantage of the unique character of the condensate system, namely that, under normal circumstances, the condensate is immobile over substantial portions of the reservoir. Thus, if the variation in the relative permeability for the gas phase is negligibly small over the region where liquid is immobile, then this analog should be useful whenever this region of the reservoir begins to influence the well response. (In all of the following, we assume that water is immobile.)
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