Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method
Tao Liu, Zijian Ding, Jiayuan Yu, Wenwen Zhang
Abstract
This paper studies a parameter estimation problem for the non-linear diffusion equation within multiphase porous media flow, which has important applications in the field of oil reservoir simulation. First, the given problem is transformed into an optimization problem by using optimal control framework and the constraints such as well logs, which can restrain noise and improve the quality of inversion, are introduced. Then we propose the widely convergent homotopy method, which makes natural use of constraints and incorporates Tikhonov regularization. The effectiveness of the proposed approach is demonstrated on illustrative examples.
Topics & Concepts
Tikhonov regularizationRegularization (linguistics)Homotopy analysis methodHomotopyMathematical optimizationInverse problemApplied mathematicsNonlinear systemComputer scienceMathematicsMathematical analysisArtificial intelligencePhysicsQuantum mechanicsPure mathematicsReservoir Engineering and Simulation MethodsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems