Scaled Fluid-Flow Models with Geometry Differing from that of Prototype

Experiments on oil displacement from homogeneous porous media have shown that the component porous media have shown that the component oil flow across the layer is often negligibly small compared with that parallel to it. This result is applied in the inspectional analysis of the equations governing the macroscopic displacement processes. It is shown that in rectangular homogeneous models the dimensionless groups l/h and a can usually be neglected. This finding has been proved experimentally in rectangular models of various dimensions, two extremes of which are described in this paper. The work has been extended to curved models. An additional requirement is that the angles of dip must be small. Comparative experiments have been carried out in three-dimensional models of various geometrical configurations. The results of both studies indicate a greater flexibility in the use of models than has previously been assumed. Introduction The production behavior of petroleum reservoirs can to a large extent be investigated with the help of scaled models, although the great number of parameters to be scaled in such processes precludes parameters to be scaled in such processes precludes complete simulation. However, not all parameters have an equally important influence on the process; and it is therefore necessary to select the most important ones and investigate which parameters can possibly be neglected. To date, oil reservoirs have almost always been represented by models of similar geometry. In other words, the characteristic length, width and height are scaled down by the same factor. For many reservoirs, however, the length-height ratio is extremely large, and laboratory models become inconveniently long or very thin. In such cases it would be desirable to make the model too thick relatively. It will be demonstrated that this is in a number of cases a justifiable solution. DERIVATION OF THE SIMILARITY GROUPS IN SCALING RECTANGULAR MODELS For the purpose of this paper, it is sufficient to derive the similarity groups for the displacement of oil by water in a homogeneous, isotropic, porous medium where the reservoir pressure is roughly maintained; thus an incompressible flow can be simulated. For more complex cases the scaling rules can be derived in a way similar to that given here. The following equations apply to the simultaneous flow of two incompressible fluids such as oil and water in a two-dimensional porous medium (see Fig. 1). We distinguish here two regions in which either water or oil flows, the regions being separated by a transition zone. (1) ox u = (2) oy u = (3) wx u = (4) wy u = JPT P. 220