MATHEMATICAL MODEL OF NONLINEAR FLOW LAW IN LOW PERMEABILITY POROUS MEDIA AND ITS APPLICATION

Abstract

Two thousand and four hundred millions tons of proved and undeveloped low permeability reserves are a great potentiality for Chinese petroleum industry to develop.A problem on nonlinear flow in low permeability porous media is a basic one in exploiting low permeability oil and gas fields.It is also one of up to date research fields of modern mechanics of fluids in porous media.It is the first time that a mathematical model expressed in a continuous function for the nonlinear flow was established based on experiments.It lays a foundation of studying the nonlinear flow from qualitative analysis to quantitative one.Nonlinear mathematical models for steady and unsteady flow are given according to the model.Formulas of pressure distributions are presented.A formula of pressure disturbance radius of the unsteady flow is derived by means of average conservation of mass.An example is discussed on the authority of experiments.Pressure distributions and a movement law of the radius for the nonlinear flow,and their comparisons with those for the linear flow are obtained.It is shown that there is much difference between results based on nonlinear flow law and linear flow law.Thus,it is necessary that influence of nonlinear flow on development indexes of the fields be taken into account.