We analyze the effect of numerical integration in finite element procedures applied to a nonlinear parabolic system describing compressible miscible displacement in a porous medium. We shall consider the use of the numerical quadrature scheme to approximate the pressure and velocity by a mixed method using a Raviart-Thomas space of index k and the concentration by a standard finite element method. We also give some sufficient conditions on the quadrature scheme, and obtain a bound of the form

mixed methods, Raviart-Thomas space, quadrature scheme, molecular dispersion.