This paper considers the design of an algorithm for analyzing multirate horizontal well pressure transient data using nonlinear regression techniques. Measured data is modeled using the analytical solution for a uniform-flux horizontal well in a rectangular parallelepiped reservoir. Parameter optimization is achieved using the public-domain Levenberg-Marquardt algorithm, LMDER, from Argonne national Laboratory.
We focus on efficient methods for calculation of analytical partial derivatives of the model pressure response which are required by the optimization routine. Complete expressions for all required partial derivatives are provided in Appendices, along with details on a method of evaluating these derivatives which requires minimal computational effort. We demonstrate the utility of the method by analyzing field buildup pressure data.