A mathematical model for numerical simulation of 2D water-oil phase reservoir concerning start-up pressure gradient is solved with full implicit finite difference scheme. A reduced-order model is established by projecting original model in low dimension space formed by basis functions, which is produced from collected snapshots; CVT-Lloyd algorithm is employed in cluster analysis to tackle with flaws from collecting snapshots of same time interval. Computational results show that reduced-order model established based on POD is able to approximate the original model effectively. With cluster analysis, data reduction is eliminated, which could create uniform snapshots in space resulting in enhanced accuracy of reduce-order model. On the other hand, extremely limited clustering groups may lead to loss of information and thus impairing accuracy of reduced-order model.

In a condensate gas reservoir welhest model of Xu & Lee, error function express of wellbore phase redistribution is adopted and a mathematical model of variable wellbore storage in triple porosity condensate gas reservoir is shown. With Laplace transformation and Stehfest inversion, effects of pressure parameters on pressure and differential of pressure are analyzed. Typical pressure curves are given.