AN APPROXIMATE SOLUTION OF LINEAR FLOW IN NATURALLY FRACTURED RESERVOIRS

Equations are presented for evaluation of linear flow in naturally fractured reservoirs represented by dual-porosity systems. The problem has not been treated previously in the petroleum engineering literature. This situation might happen, for example, in the case of drawdowns or buildups in dual-porosity systems which are hydraulically fractured or semi-infinite dual-porosity systems which are bounded by two parallel linear discontinuties. The equations apply only for oil systems. The extension to gas wells, however, is straightforward. The model assumes flow from the matrix into the fractures. There is no flow from a matrix block into another matrix block. It is shown that a conventional crossplot of log of delta p vs log of time should result in two parallel straight lines with a slope equal to 0.5 and a transition period which depends on the type of interporosity flow (pseudo steady-state, transient or gradient) and the shape of the matrix blocks. This plot allows determination of the storativity ratio, omega, fracture porosity and distance between natural fractures. A conventional crossplot of delta p vs square root of time on Cartesian coordinates should result in two distinct straight lines. The first straight line has a slope bigger than the second straight line. The ratio of these slopes squared gives the storativity ratio, omega. The analysis also permits calculation of the hydraulic fracture length.