In the analysis of gel placement to this point, only linear and purely radial flow geometries were considered. However, flow in reservoirs is often anisotropic—the effective permeability and/or the pressure gradient is greater in one horizontal direction than in another direction. Anisotropic flow can occur in both fractured and unfractured reservoirs.60 In the naturally fractured Spraberry field, Elkins and Skov61 reported that the effective reservoir permeability along the main fracture trend was 13 times greater than that at right angles to this trend. As expected,60 permeability anisotropy is significantly less in unfractured reservoirs. For example, Ramey62 reported only a 56% permeability anisotropy for a channel-sand reservoir (i.e., kx/ky=1.56).
In fractured reservoirs, gel placement can be treated effectively as a linear flow problem.16 However, unfractured anisotropic reservoirs can be viewed as flow geometries that are intermediate cases between linear and radial flow. In fact, a linear flow geometry can represent the extreme case of an anisotropic reservoir. Since the requirements for an effective gel placement are radically different for linear versus purely radial flow, questions arise about gel placement during anisotropic flow in unfractured reservoirs: How anisotropic must an unfractured reservoir be to allow gelant placement to approximate that for the linear flow case? Asked another way, how anisotropic must an unfractured reservoir be to achieve an acceptable gel placement during unrestricted gelant injection? These questions were addressed in Refs. 13 and 63 by developing two models of simple anisotropic flow systems and by performing sensitivity studies with these models. Both analytical and numerical methods were applied to solve the problem. We studied how the effectiveness of gel treatments is influenced by permeability variation, distance of gelant penetration, anisotropic pressure distributions, resistance factor, and residual resistance factor.
Our analyses showed that the range of permeability variations (permeability in the most-permeable direction divided by permeability in the least-permeable direction) must be greater than 1,000 (and usually greater than 10,000) before anisotropy can be exploited to achieve a satisfactory gel placement in unfractured wells. We doubt that any unfractured wells or reservoirs exist with this degree of anisotropy. In contrast, in wells and reservoirs where anisotropic flow is due to fractures, the linear flow geometry and the extreme permeability contrast between the fracture and the porous rock can aid gel placement substantially.63