A Least Squares Approach to Estimating the Average Reservoir Pressure

Least squares method (LSM) is an accurate and rapid method for solving some analytical and numerical problems. This method can be used to estimate the average reservoir pressure in well test analysis. In fact, it may be employed to estimate parameters such as permeability (k) and pore volume (Vp). Regarding this point, buildup, drawdown, late transient test data, modified Muskat method, interference test, and other methods are equivalent to a separable least squares problem. The main advantage of LSM in the well testing problems is that the results would be confident and no trial and error is required. Furthermore, the given method requires a short time. The fast rate of convergence and high accuracy of the LSM are demonstrated through two examples. The current study concerns a modified Muskat method. The results of LSM combined with the modified Muskat method are compared with the other iterative and qualitative methods. The preliminary numerical results with both simulated and field data suggest that the method be capable of producing smooth interpretable estimates of reservoir parameters from data.