Conducting fault boundaries are common features in reservoirs, but realistic modeling of flow through such systems is difficult because the flow is grossly distorted, particularly at the nodes of the permeability contrasts. Standard finite-difference simulators use an uneconomical number of gridblocks and still do not represent the correct physical features. Nevertheless, the realistic simulation of faulted systems is essential for practical waterflood planning and consideration of EOR schemes. This paper presents an extension of a curvilinear grid technique to model the complex crossflow processes that occur in heterogeneous systems where nodes and boundaries are well defined. To test our methods, we performed experiments in a model nodal system and obtained displacement and streamline profiles for unit and nonunit mobility ratios for a permeability contrast of 2.5 and viscosity ratio range of 0.3 to 3.0. Grids were constructed by the numerical solution of a system of generating equations and incorporated into existing simulators. We show that the number of gridblocks required to model the systems effectively may be substantially reduced. This work demonstrates that there is scope for modifying grid generation for current simulators and incorporates more of the physical reality of the displacement processes in heterogeneities with nodes, such as faulted systems.
All reservoirs are heterogeneous; i.e., the porosity, permeability, and saturation vary over the entire formation. The commonest forms of heterogeneity are permeability variations forming layers and lenses. These occur in a variety of combinations, with distortions giving rise to pinchouts and faulting and fractures creating nodes, i.e., points at which the permeability changes discontinuously in more than one coordinate direction. In this work we shall consider flow around such nodes.
Fluid flow in the region of nodal heterogeneities will not generally be aligned with the principal source/sink axis (crossflow). This will be especially prominent right at the node. The use of standard Cartesian grids for simulation will result in this crossflow being greatly underestimated because the predicted flow is preferentially oriented along grid lines. Such inaccuracies will be compounded by mobility-ratio effects.
To quantify these effects, two idealized systems have been studied in detail in this work. The models, shown in Fig. 1, are the lens and quadrant models.