On the estimation of fluid pressure in porous media based on noisy boundary observations

A filtration problem (Friedman, A., 1982), (Elliott, C. M. and Friedman, A., 1985) is one of typical nonlinear problems in the fluid mechanics and the filtration problem often appears in the fluid flow in the porous media. The characteristics of the filtration problem considered in this paper is that time evolution of the system state at the boundary is governed by the stochastic partial differential equation and the boundary condition contains the partial differential inequality. This paper is concerned with the pressure estimation of the fluid in the porous media. First, the mathematical model of the system dynamics is given. And the existence of the unique solution of the system equation is proved. Secondly, with the help of the nonlinear filtering theory, the estimator dynamics of the fluid pressure in the porous media is derived under the noisy boundary observation and some approximation techniques for the nonlinear estimator dynamics are proposed. Finally, the efficiency of the approximations are shown by the simulation experiments.