Open AccessMETHOD OF SEQUENTIAL CHANGINGOF STATIONARY STATES FOR ONE-DIMENSIONAL FILTRATION PROBLEM WITH LIMITING GRADIENT OF PRESSURE
Author(s) -
О. В. Белова,
В. Ш. Шагапов
Publication year - 2014
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2014-20-7-75-84
Subject(s) - pressure gradient , limiting , exponent , nonlinear system , darcy's law , mathematics , yield (engineering) , distribution (mathematics) , mathematical analysis , mechanics , porous medium , thermodynamics , physics , porosity , geology , geotechnical engineering , engineering , mechanical engineering , linguistics , philosophy , quantum mechanics
Taking into account nonlinear eects observed in experiments with low-per- meability layers, at low pressure gradients (e.g., about 105 Pa/m), renement 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 lter- ing 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 ltration in full statement. The analysis of inuence of pressure gradient q and limiting exponent dening the rate of yield of the nonlinear ltration law to the linear Darcy’s law with increasing pressure gradient γ, on the features of hydrodynamic elds and well production is carried out.