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