FIGURE 1: Proposed time-dependent relative permeability correlation (the arrow in the curve points to the direct of more released gas).
A fully coupled reservoir-geomechanics model is developed to simulate the enhanced production phenomena both in heavy-oil reservoirs (i.e., Northwestern Canada) and conventional oil reservoirs (i.e., North Sea). The model is implemented numerically by fully coupling an extended geomechanics model to a two-phase reservoir flow model. A sand erosion model is postulated fter the onset of sand production, which is determined based on the degree of plastic deformation inside the reservoir formation calculated by the coupled reservoir-geomechanics model. Both the enhanced oil production and the ranges of the enhanced or sanding zone are calculated, and the effect of solids production on oil recovery and enhancement are analyzed. Our studies indicate that the enhanced oil production can be the result of the combined effect of higher fluid velocity due to the movement of the sand particles according to a modified Darcy's flow and an effective permeability increase due to sand erosion. Another benefit from this process is that such an improvement in mobility may reduce the near well pressure gradient so that the sanding potential is reduced given a flow rate, and it permits a less sand-prone environment which is favorable for further sand control. In addition, two-phase flow can affect pressure gradient and formation residual cohesion due to capillary pressure change, which is also critical for sand control. Such an analogy can also be used for a completion strategy by allowing a certain amount of sand produced before a sand control strategy is implemented in a high flow-rate reservoir, when the optimum production is desirable, and when the reservoir productivity does not vitally rely on sand production. This article demonstrates the feasibility of such a model to simulate both sanding and enhanced oil production. Our initial attempt was to simulate the field performance in Northwestern Canada. As we were unable to match the field data using those input data for the onset of the stable sand production, we suggest that either new data is obtained for massive sand production (skeleton collapse), or such an erosion model should be used in the stable sanding period only, before the onset of massive sand production. Introduction Sand production is a phenomenon that occurs during aggressive production induced by the combined effect of viscous fluid flow and the in situ stress concentration near a wellbore and perforation tips in poorly cemented formations. Such solids production may compromise oil production, increase completion costs, and reduce the life cycle of equipment downhole and on the surface. Sand production has been a major concern to production engineers for decades, either in poorly consolidated reservoirs or from those offshore formations which are weakly cemented. These sanding effects often are associated with high fluid viscosities and production rates, and are becoming more critical these days as operators are following more aggressive production schedules. Sand production can, however, have benefits. It has been proven an effective way to increase well productivity both in heavy oil and light il reservoirs(1, 7).
A fully coupled reservoir-geomechanics model is developed to simulate the enhanced production phenomena both in heavy-oil reservoirs (i.e. Northwestern Canada) and conventional oil reservoirs (i.e. North Sea). The model is implemented numerically by fully coupling an extended geomechanics model to a two-phase reservoir flow model. A sand erosion model is postulated after the onset of sand production, which is determined based on the degree of plastic deformation inside the reservoir formation calculated by the coupled reservoir-geomechanics model. Both the enhanced production and the ranges of the enhanced or sanding zone are calculated, the effect of solid production on oil recovery and enhancement are analyzed. Our studies indicate that the enhanced oil production can be contributed by a combined effect of higher fluid velocity due to the movement of the sand particles according to the modified Darcy's flow and an effective well radius increase or negative skin development due to sand erosion. Despite of such an improvement on mobility may reduce the near well pressure gradient so that the sanding potential is weakened, it permits an easier path for oil to flow into the well due to an enhanced permeability. Two-phase flow can affect pressure gradient and formation residual cohesion due to capillary pressure buildup. Indirectly, production enhancement strategy can be controlled by the water saturation distribution and development, as the success and economic value of a field operation can depend on whether sand production can be induced or not. Such an analogy can also be used for a completion strategy by allowing a certain amount of sand production before sand control strategy implemented in high flow-rate reservoir, when the optimum production is desirable and when the reservoir productivity does not vitally rely on sand production.2
Three methods (Gauss-Legendre method, Stehfest method and Laplace transform method) are used to evaluate a solution of a coupled heat-fluid linear diffusion equation. Comparing with the results by Jaeger, the accuracy and efficiency of the Stehfest and Gauss-Legendre methods and the limitations of the truncated solutions obtained by Laplace transformation are discussed. It is concluded that the Stehfest method gives accurate results and is numerically more efficient than the other two methods, particularly for the solutions in early time. Two transformations with u = -In(x) and u = arctan(xn/2), where u is the original integral variable, are considered in the Gauss-Legendre method.
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