Excerpt from On the Simulation of Heterogeneous Petroleum Reservoirs This problem has been analyzed with greater generality The theoretical solution of this problem for general angles and boundary conditions is complicated by the fact that the elliptic equation has a singularity at the node (the velocity is (usually) either zero or infinity). Nevertheless an approximate deflection law can be obtained by introducing an averaging length scale on the scale of the ignored physical phenomena, e.g. Capillarity. The resulting equations will be discussed on another occasion In the next section we describe a simple algorithm that will give an approximate method for deflection, evolution, and lateral bifurca tion of a front as it passes a layer. We make two simplifying assumptions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.