Deconvolution of well-test data as a nonlinear total least-squares problem

We present a new time-domain method for the deconvolution of well test data which is characterized by three novel features: (1) Instead of the rate-normalized pressure derivative itself, we estimate its logarithm, which makes explicit sign constraints necessary; (2) the formulation accounts for errors in both rate and pressure data, and thus amounts to a Total Least Squares (TLS) problem; and (3) regularization is based on a measure of the overall curvature of its graph. The resulting separable nonlinear TLS problem is solved using the Variable Projection algorithm. A comprehensive error analysis is given. The paper also includes tests with a simulated example and an application to a large field example.