Performance of Wells in Solution-Gas-Drive Reservoirs

Abstract

Summary We examine buildup responses in solution-gas-drive reservoirs. The development presented here parallels the development for single-phase liquid flow. Analogs from pseudopressures and time transformations are presented and gas-drive solutions are correlated with appropriate liquid-flow solutions. The influence of the skin region is documented. The basis for the success of the producing GOR method to compute the saturation distribution at shut-in is presented. The consequences of using the Perrine-Martin analog to analyze buildup data are discussed. Introduction The objective of this paper is to discuss pressure-buildup responses for solution-gas-drive reservoirs. In a recent study, we show that it is possible to correlate solution-gas-drive solutions during the transient and boundary-dominated flow periods for production either at a constant surface oil rate or at a constant wellbore pressure with the van Everdingen-Hurst unit well solution (constant-rate production). With Ref. 1 as a basis, a theoretical framework for pressure-buildup analysis in solution-gas-drive systems is developed. The advantages of using time transformations such as pseudotime to analyze buildup data are also discussed. The influence of the skin factor on the buildup response is investigated, and Raghavan's suggestion that the producing GOR at shut-in can be used to compute a pseudopressure to analyze buildup data is extended to cases where s=0. Consideration of this aspect is an important contribution of this work. We also examine situations where the producing period is short and where both single-phase and two-phase regions exist at shut-in. This portion of our work should have applications to drillstem test analysis. Mathematical Model We consider flow to a well located at the center of a homogeneous cylindrical reservoir. The well can be produced either at a constant rate or at a constant pressure. The outer boundary of the reservoir is assumed to be closed or at a constant pressure equal to the initial reservoir pressure. The well penetrates the formation frilly. The skin region is modeled by considering an annular region that is concentric with the wellbore, with a permeability different from the formation permeability. Gravity and capillary pressure effects are considered to be negligible. Unless otherwise stated, the reservoir initially is assumed to be at the bubblepoint. The PVT properties for the fluids used in this work are shown in Figs. 1 and 2, and Fig. 3 presents the relative permeability data. The data sets shown in Figs. 1 through 3 are identical to the data sets considered in Refs. 1 and 6 and are used principally to preserve continuity. The conclusions presented here do not depend on the specific data used in the simulations. Table 1 lists other properties of the reservoir used in this study. Numerical Model A finite-difference model was used to obtain the results presented in this paper. This model simulates isothermal flow of oil and gas below the bubblepoint or the flow of oil above the bubblepoint. A detailed description of this model is given in Ref. 7 (also see Ref. 1). Steps taken to ensure the accuracy of our solutions included comparison with analytical solutions for single-phase flow, material-balance checks, and sensitivity checks (timesteps and mesh size) In addition, we duplicated the analytical expressions for saturation and pressure derived by Boe et al. for the infinite-acting flow period for both drawdown and buildup conditions and solutions for steady flow of gas and oil. Approximate analytical solutions also were derived in the course of this study for pressure distributions in a closed reservoir producing at a constant rate or at a constant pressure; these solutions served to verify the accuracy of our simulations. Theoretical Considerations In Ref. 1, we show that if we consider flow in a closed reservoir and define the reservoir integral (pseudopressure) by the relation (1) then it is possible to correlate solution-gas-drive responses with the liquid solution for both transient and boundary-dominated flow periods. Here, a(p, So) is given by (2) and r is the radius corresponding to the point at which pressure p(r)=p. For boundary-dominated flow, r∼0.54928re. Fig. 5 of Ref. 1 presents a correlation of r as a function of time. The dimensionless time scale to be used to correlate solutions with the single-phase liquid-flow solution is given by (3) Here, and ct represent the system mobility and system compressibility, respectively, corresponding to the average reservoir pressure, p (and also the average saturation, SO). Thus, T, and ct, are given by (4) (5) Eqs. 1 and 3 may be used for constant-rate or constant-pressure production. For computational purposes, the reservoir integral may be mapped as (6) The changes in the variables of integration are justified because a is a single-valued function of p(r) for all p(r) with r, less than r - F for a fixed time and also for all p(t') with 0 less than t' less than t for F fixed during the drawdown period for the initial conditions (uniform saturation distribution) assumed in this work. SPEFE P. 611^