Automated Type-Curve Matching in Well Test Analysis Using Laplace Space Determination of Parameter Gradients

This paper presents an investigation of automatic methods of type curve matching for the interpretation of drawdown tests in the presence of wellbore storage and skin. Gauss or Gauss-Marquardt nonlinear regression methods are used to estimate wellbore, reservoir and boundary parameters in single layered, unbounded reservoirs. The use of numerical Laplace Transform inversion techniques to obtain gradients of the solution with respect to the unknown reservoir parameters makes the problem particularly streamlined, and is a major improvement on existing techniques. In addition, constraining the reservoir parameters to positive values (where appropriate) is found to improve convergence of the nonlinear regression algorithms. Nonlinear regression algorithms require analytical expressions for the reservoir pressure drop and its derivatives with respect to the unknown reservoir parameters. These are frequently not available for existing type curves, which has prevented their automated fitting so far. This work was successful in calculating these functions by numerical inversion of the known analytical expressions in Laplace space, making the automated fitting procedure possible in a wide range of formerly inaccessible cases. Examples given demonstrate that the regression analysis in some cases can yield better results than the conventional graphical techniques.