Constant-Pressure Production in Solution-Gas-Drive Reservoirs: Transient Flow

Abstract

Summary This paper presents procedures to obtain reservoir parameters from constant-pressure drawdown data in solution-gas-drive reservoirs. A novel procedure to determine the mechanical skin factor is introduced. Examples, including a field case, illustrate the use of this procedure. An estimate of the drainage area can be obtained with the derivative of rate data. A theoretical basis for analyzing data by the pressure-squared, p2, approach is presented; this procedure permits the approximate determination of sandface effective permeabilities in the transient flow period. For damaged wells, it is possible to obtain rough estimates of the size of the skin zone and the ratio of reservoir/skin-zone permeability when early transient data are available. The expression of the appropriate dimensionless rate in terms of physical properties for solution-gas-drive systems is presented. Finally, this paper presents a procedure to obtain an estimate of the change in sandface saturation during the transient flow period. Introduction The purpose of this work is to introduce procedures to obtain reservoir parameters from constant-pressure drawdown data in solution-gas-drive systems. Theoretical results in Refs. 1 and 2 are used as a basis for the procedures to determine effective permeabilities to flowing phases and the skin factor and its related parameters. In multiphase flow, it is generally not possible to correlate well responses with the liquid flow solutions in terms of conventional parameters. Specifically, for constant-pressure production during the transient flow period, one cannot use a plot of the inverse of rate vs. the logarithm of time in the standard manner to compute formation flow capacity and mechanical skin factor. The only procedure currently available to estimate skin factor values from constant-pressure production-drawdown data in solution-gas-drive reservoirs is the use of type-curve matching with single-phase flow equations in the interpretation procedure. Refs. 1 and 2 show that it is possible to correlate solution-gas-drive solutions during transient and boundary-dominated flow periods for production at either a constant surface oil rate or at a constant wellbore pressure with the van Everdingen-Hurst unit well solution (constant-rate production). With this result as a basis, practical methods are proposed to compute mechanical skin factor, approximate estimates of sandface effective phase permeabilities for the infinite-acting period, and drainage area. This paper is divided into four parts. In Part 1, theoretical results given in Ref. 2 are summarized to establish a background for the timings presented. Part 2 is devoted to obtaining the mechanical skin factor, s, and drainage area, A. In Part 3 a theoretical justification for the p2 approach to analyze rate data is provided. Part 4 presents a procedure to obtain approximate estimates of effective sandface permeability. It is also shown that rough estimates of the ratio of reservoir/skin-zone permeabilities and the size of the skin region can be obtained for damaged wells when early transient data are available. The expression of the appropriate dimensionless rate in terms of physical properties for solution-gas-drive reservoirs is presented. The numerical results presented were obtained with a finite-difference black-oil model that simulates the isothermal flow of oil and gas. A detailed description of this model, including steps taken to ensure the accuracy of the solutions, is given in Ref. 1 (see also Ref. 2). Mathematical Model How to a fully penetrating well located at the center of a homogeneous cylindrical reservoir is considered. The well is produced at a constant-pressure mode with a closed outer boundary. The skin region is modeled by considering an annular region that is concentric with the wellbore, with a permeability different from the reservoir permeability. Gravity, capillary pressure, and non-Darcy flow effects are considered negligible. The PVT properties for the fluids and the relative permeability data used in this work are identical to the two data sets considered in Refs. 1, 2, and 5 and are used principally to preserve continuity. Fig. 1 presents the relative permeability data for the two data sets. The results presented here do not depend on the specific data used in the simulations. Table 1 presents details on the range of variables examined in this study.