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Calibri 83ffff̙̙3f3fff3f3f33333f33333.'TU Delft Repositoryg T(uuidrepository linktitleauthorcontributorpublication yearabstract
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departmentresearch group programmeprojectcoordinates)uuid:37fb1813-9567-4f92-a643-028c5049da27Dhttp://resolver.tudelft.nl/uuid:37fb1813-9567-4f92-a643-028c5049da27OA semi-analytical model for productivity testing of complex well configurationsLFokker, P.A.; Brouwer, G.K.; Verga, F.; Ferrero, D.; TNO Bouw en Ondergrond This paper presents a semi-analytical method for the modeling of productivity testing of vertical, horizontal or multilateral wells. The method, which is applicable to both oil and gas reservoirs, automatically accounts for well interference. The use of analytical expressions ensures proper handling of transient short time behavior and semi-steady-state longtime behavior, both close to the well and further into the reservoir. Calculation times are still very limited, in the order of a few minutes down to a few seconds when there are vertical wells only. This makes the tool suitable for well testing evaluation. The approach is based on an earlier derived productivity prediction tool, in which the steady-state equations were solved. It has now been extended to solve the time-dependent diffusion equation and it is thus more rigorous than the extension to time-dependent behavior using solutions to the Laplace equation and moving pressure boundaries, which was presented recently. In our current method, the equations have first been transformed using the Laplace transformation. The expressions for the producing wells are combined with auxiliary sources outside the reservoir. The core of the semi-analytic method involves an adjustment of the positions and strengths of these sources in order to approximate the boundary conditions at the reservoir boundaries. The solution that is obtained is transformed back into the time domain using a Stehfest algorithm. The new approach has been validated with numerical tools, including both reservoir simulators and well-test interpretation software. Validations were performed with artificial cases using both single-well and multiple-well production tests. The results of these tests were excellent.Energy Efficiency; Geosciences; Energy / Geological Survey Netherlands; Equations of state; Laplace transforms; Petroleum reservoirs; Productivity; Tools; Well testing; Analytical expressions; Interpretation software; Laplace transformations; Semi-analytical methods; Steady-state equations; Time dependent behavior; Time-dependent diffusion; Well-testing evaluation; Software testingenconference paper9European Association of Geoscientists and Engineers, EAGESponsors: Shell)uuid:86764b57-cf60-4625-a4c4-96288b221bddDhttp://resolver.tudelft.nl/uuid:86764b57-cf60-4625-a4c4-96288b221bddBA semi-analytical model for productivity testing of multiple wellsoFokker, P.A.; Brouwer, G.K.; Verga, F.; Ferrera, D.; Nederlands Instituut voor Toegepaste Geowetenschappen TNO This paper presents a new, semi-analytical method for calculation of the productivity of vertical, horizontal or multilateral wells draining either gas or oil reservoirs. Well interference effects and the presence of natural or induced fractures are accounted for. The method is based on an earlier derived productivity prediction tool in which now moving pressure boundaries have been implemented to account for time dependence. The semisteady-state pressure equations are solved using combinations of exact solutions around the well in an infinite reservoir and additional solutions to the Laplace equation are introduced to approximate the boundary conditions. The pressures and rates for all the flowing wells are solved in a single step for each required value of the time. Both numerical and analytical approaches have been used to validate the new method. The validity of the moving-boundary approach for the transient well behaviour has been checked against analytical results, whereas a numerical method has been empl<oyed to analyse the multi-well response in homogeneous, isotropic reservoirs. Finally, the new method has been applied to real production test data. Both single-well and multi-well production tests performed in different types of reservoirs have been analysed with satisfactory results.Mathematical models; Natural gas; Petroleum reservoirs; Productivity; Isotropic reservoirs; Moving-boundary approach; Multi-well production tests; Pressure equations; Well testing
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