Pressure transmission in a bounded randomly fractured reservoir of single-phase fluid

A double-porosity model for the pressure response of a naturally fractured reservoir of single-phase fluid is extended to allow for blocks that are of varying sizes. Previous studies with blocks of the same size have found that for a constant rate of withdrawal of fluid, plots of pressure change with the logarithm of time give parallel straight lines at early and late times. At intermediate times a third straight line has also been observed on such plots, with a slope of one half of the early and late time slopes. In this paper this phenomenon of semilog slope-halving is studied using analytical solutions in Laplace space, and conditions for observing it are derived.When the reservoir is finite with highly permeable fractures, slope-halving may be observed if the logarithm of the pressure change is plotted against the logarithm of time. This phenomenon of log-log slope-halving for finite reservoirs is also studied here.A simple formula that approximates the pressure response of a finite highly permeable naturally fractured reservoir when fluid is withdrawn at a constant rate, is derived. This solution is successfully fitted to data from three separate interference tests conducted at the Ngawha geothermal field in New Zealand.