Jeffrey Spath

Semi-analytical Solution for Multiple Layer Reservoir Problems with Multiple Vertical, Horizontal, Deviated and Fractured Wells

We present new semi-analytical solutions to the multiple layer reservoir problem, both in real-time and Laplace space. Assuming a vertically stacked system of layers, an analytic solution within each layer can be derived using a method of integral transforms. We fully account for crossflow between layers by coupling these analytic solutions together and solving Fredholm integral equations to obtain the flux field at the layer interfaces. The time evolution of these fluxes is governed by a Volterra integral equation. Also, the form of our equations allows us to stop a model execution and then restart from the exact terminated state.