Analytical Solutions for Pressure Buildup and Falloff Analysis of Water Injection Tests of Partially Penetrating Wells: Nonunit Mobility Ratios (1984)

Analytical Solutions for Pressure Buildup and Falloff Analysis of Water Injection Tests of Partially Penetrating Wells: Nonunit Mobility Ratios R.K.M. Thambynayagam R.K.M. Thambynayagam Search for other works by this author on: This Site Google Scholar Paper presented at the European Petroleum Conference, London, United Kingdom, October 1984. Paper Number: SPE-12965-MS https://doi.org/10.2118/12965-MS Published: October 22 1984 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Thambynayagam, R.K.M. "Analytical Solutions for Pressure Buildup and Falloff Analysis of Water Injection Tests of Partially Penetrating Wells: Nonunit Mobility Ratios." Paper presented at the European Petroleum Conference, London, United Kingdom, October 1984. doi: https://doi.org/10.2118/12965-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 Europec featured at EAGE Conference and Exhibition Search Advanced Search Thambynayagam, R.K.M., British Petroleum Plc Plc SPE MemberAbstractApproximate analytic solutions are presented for pressure build-up and fall-off analysis of water pressure build-up and fall-off analysis of water injection tests of partially penetrating wells. The three basic cases of interests, infinite, bounded and constant pressure outer boundary reservoirs are considered. The validity of the analytic solutions are demonstrated by comparison with the results of a conventional black oil finite difference program. The method allows reservoir characteristics to be determined from short-tern water injection tests.IntroductionInjection-well test analysis corresponds very closely to that of production well testing provided the mobility ratio between the injected and in situ fluids is near unity. When the injected and in situ fluids have widely differing properties the unit mobility ratio assumption is not satisfied and the analogy between injection well testing and production well testing is not straight forward. Morse and Ott, Mathews and Russell and Earlougher present good discussions on injection well testing, particularly for fall-off testing. Until recently, systems with non-unit mobility ratio have received relatively little attention.When a fluid that is different to the in situ reservoir fluid is used to displace the reservoir fluid it creates a saturation discontinuity between the region where the injected fluid predominates and the region where the original reservoir fluid predominates. Consequently, the problem is of very complex predominates. Consequently, the problem is of very complex nature. In the past the problem has been studies by several researchers. Verigin and Ramey used Boltzmann's transformation to solve problems associated with such a moving boundary. A semi-analytic solution for the pressure transients during injection tests of geothermal reservoirs has been presented by Tsang and Tsang. Benson and Bodvarson studied water injection tests of a geothertnal reservoir using a numerical simulator, from which they derived expressions to allow calculation of the transmissibility and skin factor. These two methods account for the property variations between the injected and in situ water zones and is thus applicable to non-unit mobility ratio tests. The form of the results are, however, complicated and the general applicability of these methods to water injection tests of oil reservoirs are not immediately apparent. Recently Woodward and Thambynayagam have presented analytical solutions for the pressure presented analytical solutions for the pressure buildup and fall-off analysis associated with a water injection test of an undersaturated oil reservoir. The solution is applicable to the case in which a water bank surrounds the well at the commencement of injection and is extended to include non-isothermal effects.All the methods mentioned above assume that the well is perforated over the entire thickness of the formation. Wells, of which the fluid entry section is less than the formation they penetrate, are called partially penetrating wells. Unlike the flow from a partially penetrating wells. Unlike the flow from a fully penetrating well where the flow is radial, the flow from a partially penetrating well is three dimensional. The effects of partially penetrating wells on systems with unit mobility ratio have been studied by numerous authors. Hantush derived an expression for the pressure distribution in an infinite reservoir. Seth extended Hantush's work to a bounded reservoir. Kazemi and Seth have presented a good discussion on the effects of anisotrophy and stratification on pressure transient analysis of wells with restricted flow entry. Recently Onyekonwu and Horne have developed analytical methods using Laplace transform techniques with numerical inversion procedures to study reservoirs with spherical procedures to study reservoirs with spherical discontinuities.Non-unit mobility injection well tests of partially penetrating wells has received relatively partially penetrating wells has received relatively little attention in the past. The purpose of this work is to extend the analysis of Woodward and Thambynayagam to accommodate partially penetrating wells. The basic cases of interest, infinite, bounded and constant pressure outer boundary reservoirs are considered.THEORYThe physical model considered in this analysis consists of a well located in an anisotropic medium of uniform thickness. The formation and fluid properties are independent of pressure, the fluids of properties are independent of pressure, the fluids of small compressibility and gravity effects negligible.p. 83 Keywords: upstream oil & gas, equation, analytic solution, water injection test, pressure buildup, woodward, wellbore, reservoir, expression, spe 12965 Subjects: Formation Evaluation & Management, Drillstem/well testing This content is only available via PDF. 1984. Society of Petroleum Engineers You can access this article if you purchase or spend a download.