Riemann Problem For A Hyperbolic System Of Conservation Laws Modeling Polymer Flooding

The hyperbolic system of conservation laws modeling polymer flooding can be used for the exploration of petroleum crude oil reserves in porous rock and to study how to improve the extraction rate of crude oil.In this thesis,we study a class of non-strictly hyperbolic system of conservation laws modeling polymer flooding.By the method of phase plane and characteristic analysis,we solve the Riemann problem for the system,and prove that the Riemann problem possesses a unique global entropy weak solution,and clarify the precise structure of Riemann solution.In the first chapter,we introduce the research status of the hyperbolic system of conservation laws modeling polymer flooding,and briefly summarize the main work of this thesis.In the second chapter,under the parabolic degeneration condition of the hyperbolic system of conservation laws modeling polymer flooding,the elementary waves and prop-erties of wave curves are analyzed at first.Secondly,the Lax geometric entropy condition of shock wave is given by using the viscosity vanishing method.Finally,the Riemann problem of the Buckley-Leverett equation is discussed with the convex hull.In the third chapter,we construct Riemann solutions for the hyperbolic system of conservation laws modeling polymer flooding.Firstly,with the classification of elemen-tary waves,we give the necessary and sufficient conditions for the combination of two elementary waves to construct a Riemann solution;Secondly,we introduce the curves?_R,?_Kand?_Kto divide the phase plane(s,c);Thirdly,according to the location feature of elementary waves,the phase plane is divided into two cases to construct global solution of the Riemann problem.Case 1,the wave velocity contour?_K~1of rarefaction wave,which starts from regional?and passes through the point(s~T,1),will intersect with the bound-ary c=0 in region?.Case 2,the rarefaction wave curve?_R~1starting from the region?and passing through the point(s~T,1)will intersect with boundary s=1 in the region?.For these two cases,according to the different positions of left states,the Riemann solutions are constructed by 10 subcases,respectively.In the fourth chapter,we present the conclusion and put forward the research prospect of the hyperbolic system of conservation laws modeling polymer flooding.