Well Test Analysis of Naturally Fractured Vuggy Reservoirs with an Analytical Triple Porosity – Double Permeability Model and a Global Optimization Method

Abstract

The aim of this work is to study the automatic characterization of Naturally Fractured Vuggy Reservoirs via well test analysis, using a triple porosity-dual permeability model. The inter-porosity flow parameters, the storativity ratios, as well as the permeability ratio, the wellbore storage effect, the skin and the total permeability will be identified as parameters of the model. In this work, we will perform the well test interpretation in Laplace space, using numerical algorithms to transfer the discrete real data given in fully dimensional time to Laplace space. The well test interpretation problem in Laplace space has been posed as a nonlinear least squares optimization problem with box constraints and a linear inequality constraint, which is usually solved using local Newton type methods with a trust region. However, local methods as the one used in our work called TRON or the well-known Levenberg-Marquardt method, are often not able to find an optimal solution with a good fit of the data. Also well test analysis with the triple porosity-double permeability model, like most inverse problems, can yield multiple solutions with good match to the data. To deal with these specific characteristics, we will use a global optimization algorithm called the Tunneling Method (TM). In the design of the algorithm, we take into account issues of the problem like the fact that the parameter estimation has to be done with high precision, the presence of noise in the measurements and the need to solve the problem computationally fast. We demonstrate that the use of the TM in this study, showed to be an efficient and robust alternative to solve the well test characterization, as several optimal solutions, with very good match to the data were obtained.