In-Place Determination of Reservoir Relative Permeability Using Well Test Analysis

Abstract

In-Place Determination of Reservoir Relative Permeability Using Well Test Analysis A-J.A. Al-Khalifah; A-J.A. Al-Khalifah Stanford U. Search for other works by this author on: This Site Google Scholar R.N. Horne; R.N. Horne Stanford U. Search for other works by this author on: This Site Google Scholar K. Aziz K. Aziz Stanford U. Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 1987. Paper Number: SPE-16774-MS https://doi.org/10.2118/16774-MS Published: September 27 1987 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Al-Khalifah, A-J.A., Horne, R.N., and K. Aziz. "In-Place Determination of Reservoir Relative Permeability Using Well Test Analysis." Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, September 1987. doi: https://doi.org/10.2118/16774-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Annual Technical Conference and Exhibition Search Advanced Search SPE MembersAbstractThis paper describes a new method to estimate two- and three-phase relative permeabilities in-situ, using pressure transient analysis. The technique requires a short drawdown test, consisting of a number of steps of increasing flow rate. The resulting relative permeabilities reflect the properties of the whole drainage area, rather than those of a small laboratory core. The proposed technique is a major improvement over current historical performance methods. These existing methods need data over long periods, yet only cover a range of saturation up to present conditions - all future projections require extrapolation. By contrast, the new method estimates relative permeabilities at sandface saturations, which cover a range of future reservoir conditions. The well test can be repeated at a later stage of depletion to forecast still further into the future.The proposed technique applies the solutions of multiphase diffusivity equation in terms of the pseudopressure function, m(p). These solutions have already been reported for constant rate tests in solution gas-drive reservoirs. This paper extends the pseudopressure solutions to three-phase systems. Two- and three-phase solutions are then superposed to obtain mutiple-rate solutions, the basis for two- and three-phase relative permeability equations. A saturation equation developed originally by Boe et al. for solution gas-drive reservoirs, is also extended here to three-phase reservoirs. These pressure-saturation equations can be used to estimate sandface saturations during the test.Using a commercial black-oil simulator, example well tests were simulated over a 40% range in gas saturation. Both two- and three-phase results show close agreement with input relative permeability curves. In cases where relative permeability is not homogeneous within the drainage area, the resulting estimates of relative permeability curves were very representative of in-situ heterogeneities.The proposed technique offers a means to estimate two- and three-phase relative permeabilities at in-situ reservoir conditions, accounting for heterogeneities, wettability and fluid composition. It also seems to be the most appropriate way to obtain estimates for subsequent reservoir engineering analysis.IntroductionMultiphase flow may be described by a modified single phase flow equation. During multiphase flow, there are more than one phase flowing simultaneously. Therefore, the flowing conductivity of the formation to each of the phases is different and less than that during single phase flow. While the latter is represented by the absolute permeability, k, the former is specific for each phase and is called effective phase permeability, kl. Phase l effective permeability, kl, is normalized to a specific base permeability, such as absolute permeability, k, to define the relative permeability of phase 1, krl. Relative permeability is a function of several rock and fluid properties, besides its phase saturation. Therefore, the single phase flow equation is modified using both phase relative permeability and saturation terms. While relative permeability goes into the transmissibility term, the saturation is also inserted into the storage term. Using this modification, multiphase equations are written as: for oil:(1)for gas:(2)for water:(3)Extensive work has been done on the theory, instrumentation and procedure of several laboratory methods to measure two-phase relative permeability curves. Steady state and unsteady state methods are the two conventional choices in the laboratory. In the steady state method, the two phases flow simultaneously till the same stable rates are measured at both ends of the core. In the unsteady state method, the core is saturated with one phase and then the other phase is made to flow through the core at one end and produced at the other end. Several versions of these methods are currently in use.Three-phase relative permeabilities are not easily obtained in the laboratory. Experimental procedure is more tedious and less advanced compared to that of two-phase flow. Results of the few experiments done are controversial. An alternate approach to estimate three-phase relative permeabilities is to use probability models. These models combine the two sets of two-phase relative permeabilities to obtain three-phase relative permeabilities.P. 339^ Keywords: saturation, permeability curve, spe 16774, drillstem/well testing, penneability, flow in porous media, heterogeneity, fluid dynamics, oil saturation, relative penneability Subjects: Reservoir Fluid Dynamics, Formation Evaluation & Management, Flow in porous media, Pressure transient analysis, Drillstem/well testing This content is only available via PDF. 1987. Society of Petroleum Engineers You can access this article if you purchase or spend a download.