Analytic Methods And Application On Nonlinear Porous Flow Groups

Abstract:In the article, with stable successive displacement thinking, a series methods were suggested to solved the nonliear porous flow groups basing on the three parameters of nonlinear mathematical model putting forward by Huang Yanzhang. For example of calculation, the vertical wells, the nonlinear production decline laws and nonlinear factors were compared and analyzed; for example of calculation, the nonlinear porous bottomhole pressure variation on vertically fractured wells were analyzed and the effects of nonlinear parameters on bottomhole pressure changes were compared under the constant production.For stress sensitive formations, two approximation methods were proposed by inducing additional start-up pressure gradient with establishing similar stratigraphic concepts and additional skin factor. Additional skin factor method discussed with additional start-up pressure gradient method bottomhole pressure and production decline laws.The production decline laws were discussed with additional skin factor method and additional start-up pressure gradient method under constant bottomhole pressure.Nonlinear partial differential equations coupled the stress sensitivity, basing on homotopy transformation principle were scheduled to discuss the bottomhole pressure and fixed yield in both cases. We analyzed the characteristics of pressure distribution, and discussed the impact of the factors of production decline laws and bottomhole pressure drop of the law, and verified the correctness of the method by nonlinear degradation method. Furthermore, the additional skin factor and additional start-up pressure gradient method results were compared.A new method based on the principle of homotopy transformation was proposed for solving partial differential equations coupled nonlinear stress sensitivity.The characteristics of pressure distribution were analyzed, and the impacting factors on production decline laws and bottomhole pressure drop of the law were discussed. We verified the correctness of this method by nonlinear degradation method, and the additional skin factor method with additional start-up pressure gradient method results were compared.This article established a production decline model for segmented-fractured horizontal well with finite conductivity, and their effects on production were discussed about nonlinear and stress sensitivity. The horizontal wellbore pressure drop and Reynolds number variation law as well as its effect on production were analyzed. The laws of crack were discussed about pressure drop and propagation, as well as production changing in early single linear flow, early double linear flow and later quasi steady state flow phase; and the resean for nonlinear’s less affection to production of staged-fractured horizontal wells were analyzed.Based on the point source function theory, the nonlinear density function and its linearation method were proposed. In the article, we demonstrated that analytical methods about nonlinear porous flow meets the Newman conditions and proposed a standardization quasi time, discussed the impact of vertical permeability on production decline laws.We analyzed production decline law of vertical well in nonlinear bounded closed formation, and compared our results with the literature, and draw a conclusions that there is a limit supply radius in nonliear porous. With the Laplace transform and numerical inversion method, contour integration was used to solve the nonlinear reservoir bottomhole pressure drop laws, considering the effect of wellbore storage and skin factor, and the nonlinear well test chart were given.