Title
A semianalytic model for the productivity testing of multiple wells
Author
Fokker, P.A.
Verga, F.
TNO Bouw en Ondergrond
Publication year
2008
Abstract
We present a semianalytic method for modeling the productivity testing of vertical, horizontal, slanted, or multilateral wells. The method is applicable to both oil and gas reservoirs and automatically accounts for well interference. The use of analytic expressions ensures that short-time transient behavior and long-time semisteady-state behavior are handled appropriately, whether close to the well or further into the reservoir. Calculation times are still very limited - on the order of a few minutes to a few seconds when all wells are vertical. This makes the tool suitable for evaluating well testing and determining well productivity. We based the approach 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. 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 crux of the semianalytic 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 obtained is transformed back into the time domain by use of a Stehfest algorithm. The new approach has been validated with numeric tools, including both reservoir simulators and well-test interpretation software. Validations were performed with artificial cases and with field production data, using both single-well and multiple-well production tests. The results of these tests were excellent. Copyright © 2008 Society of Petroleum Engineers.
Subject
Geological Survey Netherlands
Geosciences
Energy / Geological Survey Netherlands
Boundary conditions
Differential equations
Equations of state
Horizontal wells
Oil wells
Petroleum reservoir engineering
Productivity
Interpretation software
Oil and gas reservoirs
Reservoir simulators
Well interference
boundary condition
hydrocarbon reservoir
Oil production
Reservoir characterization
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TNO identifier
280042
ISSN
1094-6470
Source
SPE Reservoir Evaluation and Engineering, 11 (3), 466-477
Document type
article