An Experimental Investigation of Convergent Flow To Horizontal Wells

Abstract

Abstract If the problem of fluid flow in a reservoir toward a well cannot beapproximated as a two-dimensional one, the analytical treatment becomes verydifficult. This is especially true when horizontal wells are involved and theend-effect cannot be neglected. There are, in the literature, mathematical expressions to calculateproductivity of horizontal wells for various geometric configurations and manyof these include the effect of flow convergence. Some of them appear to besignificantly in error. The paper describes experiments with an electrolytic model. This approachuses the analogy between the flow of fluid particles, driven by fluidpotential, in a porous medium and movement of ions, driven by electricalpotential, in an electrolyte. A simple and low-cost experimental setup permitsthe testing of various theoretical equations and the results are presented. Introduction In many cases the flow of fluids in a homogeneous reservoir toward a well, vertical or horizontal, can be analyzed simply when the problem istwo-dimensional. In some situations this approach may be sufficient; but when, because of more complicated geometry, the effect of convergence toward the tipof a well (as, for example, in the case of a vertical well partiallypenetrating a liquid- bearing porous matrix layer) has to be taken intoaccount, the difficulties of establishing the flow pattern and, consequently, calculations of the well productivity, may be significant. A common simplification is the assumption of the uniform flux along theactive well length. But this approach, as pointed out by Muskat(l), does notgive the correct results, even for the relatively simple case of a partiallypenetrating vertical well and steady-state flow. The situation becomes more difficult for horizontal wells of finite lengthdraining bounded volumes. There is usually a problem of convergent flow towarda well in a plane perpendicular to the well's axis, but on top of this there isa three-dimensional convergence toward the tips of the well. Probably in somesituations when, for example, the well is very long and draining a thin layerand narrow pattern, this additional convergence can be neglected.