Transient Flow Of Polymer Foam In Porous Media

Compared with the aqueous foam, the non-Newtonian property of the polymer foam liquid phase, which increases the viscosity of liquid film,decreases the discharge time of liquid film, lowers the gas diffusion velocity and enhances the foam stability, can improve the flooding efficiency. One dimension transient flow of the polymer foam in porous media is studied in this paper,whose results could provide a necessary theoretical support to polymer foam flooding after polymer flooding.The bubble population balance equation of the flow of the polymer foam in porous media is derived from the population balance principle. Based on the equations of the mass balance of polymer foam liquid phase,gas phase and the bubble population balance,the mathematical model of one dimension transient flow of the polymer foam in porous media is established;and the mathematical model of one dimension transient flow of the aqueous foam,which is as a special polymer foam, in porous media is given meantime.The numerical models of transient flow of the polymer foam and the aqueous foam in porous media is given by using the finite difference method.The numerical difference equations of the mass balance equations of the numerical models mentioned above are solved by using IMPES method and the difference equation of the bubble population balance equation of the numerical models mentioned above is solved by using TVD third-order method. The program of "Numerical calculation of one dimension transient flow of polymer foam in porous media" is programmmed by using the numerical calculation methods mentioned above.Through the experiments of the flow of HPAM foam and the aqueous foam in the artificial sandstone core and by using Levenberg-Marquardt algorithm,the correlation formulae of the generation coefficient and the coalescence coefficient,which change with the apparent viscosity of HPAM foam liquid phase and the sandstone core permeability, of one dimension transient flow of HPAM foam and the aqueous foam in the artificial sandstone core are established,and the mathematical model of one dimension transient flow of the polymer foam in porous media and the relavant numerical calculation method are verified.By using the program of "Numerical calculation of one dimension transient flow of the polymer foam in porous media", one dimension transient flow of HPAM foam in the artifical sandstone core is numerically calculated and analyzed. The profiles of the liquid phase saturation,the pressure drop and the number density of one dimension transient flow of HPAM foam in porous media with the dimensionless distance and the profiles of the pressure drop with dimensionless time are achieved.The relationship between the steady state pressure drop gradient and the liquid phase injection velocity,the gas injection velocity of one dimension transient flow of HPAM foam in the artifical sandstone core is numerically calculated.The results show that the steady state pressure drop gradient of one dimension transient flow of HPAM foam in the artifical sandstone core increases with the liquid injection velocity increasing,and the increasing velocity of the steady state pressure drop gradient gets higher with the liquid phase flow behavior index of HPAM foam lowering, which means the degree of the deviation from the Newton rheological characteristic get higher. The steady state pressure drop gradient of HPAM foam is about the same with the gas injection velocity increasing and increases with flow behavior index of liquid phase decreasing.The influences of the liquid phase flow behavior index of one dimension transient flow of HPAM foam in the artifical sandstone core on the liquid phase saturation,the pressure drop and the number density of HPAM foam are numerically calculated.The results show that the front flowing velocity of the liquid phase saturation increases and the liquid phase saturation inceases with the liquid phase flow behavior index decreasing;and the pressure drop increases with the liquid phase flow behavior index decreasing,the pressure drop of HPAM foam with non-Newton fluid liquid phase is bigger than that of the aqueous foam with Newton fluid liquid phase.The increase of the pressure drop of HPAM foam with the non-Newton fluid liquid phase with the dimensionless time increasing is faster than that of the aqueous foam with Newton fluid liquid phase and its steady pressure drop of HPAM foam is bigger than that of the aqueous foam. The front flowing velocity of the number density of HPAM foam increases and the number density of HPAM foam inclines to increase with the liquid phase flow behavior index decreasing. The number density of HPAM foam with non-Newton fluid liquid phase is bigger than that of the aqueous foam with Newton fluid liquid phase.The influences of the permeability of one dimension transient flow of HPAM foam in the artifical sandstone core on the liquid phase saturation,the pressure drop and the number density of HPAM foam are numerically calculated.The results show that the front flowing velocity of the liquid phase saturation increase and the liquid phase saturation of the upstream of the front is about the same with the permeability of the core decreasing.The pressure drops of the transient flow of HPAM foam in the artifical sandstone core are about the same under different permeabilities.The steady pressure drop inclines to increase with the permeability increasing. The number density of HPAM foam of the upstream of the front decreases with the permeability decreasing.Finally,the three basic injection modes in the artifical sandstone core after polymer flooding are numerically caculated and analyzed.The results show that,compared with the polymer flooding and the gas flooding,the polymer foam flooding could form a foam piston in the artifical sandstone core, which causes high pressure drop and improves the flooding efficiency.