Method of sequential changing of stationary states for one-dimensional filtration problem with limiting gradient of pressure

Taking into account nonlinear effects observed in experiments with low-permeability layers, at low pressure gradients (e.g., about $10^5$ Pa/m), refinement of Darcy law is proposed. On the basis of this model, by means of method of sequential change of stationary states and the problem of one-dimensional filtering is numerically solved. It is established that approximate solutions received by the method of sequential change of stationary states, for the description of distribution of pressure in layer and a well production, will be agreed with the numerical solution of the equation of a filtration in full statement. The analysis of influence of pressure gradient $q$ and limiting exponent defining the rate of yield of the nonlinear filtration law to the linear Darcy's law with increasing pressure gradient $\gamma$, on the features of hydrodynamic fields and well production is carried out.