Improvement of Levenberg-Marquardt algorithm during history fitting for reservoir simulation

In order to estimate reservoir parameters more effectively by history fitting, DE (Differential Evolution) was proposed to estimate the optimum damping factor so that the standard Levenberg-Marquardt algorithm was improved, and the improved algorithm was validated by analysis of examples. The standard LM algorithm uses trial-and-error method to estimate the damping factor and is less reliable for large scale inverse problems. DE can solve this problem and eliminate the use of line search for an appropriate step length. The improved Levenberg-Marquardt algorithm was applied to match the histories of two synthetic reservoir models with different scales, and compared with other algorithms. The results show that: DE speeds up the convergence rate of the LM algorithm and reduces the residual errors, making the algorithm suitable for not only small and medium scale inverse problems, but also large scale inverse problems; if the iteration termination criteria of LM algorithm is preset, the improved algorithm will save the number of iterations and reduce the total time greatly needed for the LM algorithm, leading to higher efficiency of history matching.