  This article presents a priori error estimates of the miscible displacement
of one incompressible fluid by another through a porous medium characterized by
a coupled system of nonlinear elliptic and parabolic equations. The study
utilizes the $H(\rm{div})$ conforming virtual element method (VEM) for the
approximation of the velocity, while a non-conforming virtual element approach
is employed for the concentration. The pressure is discretised using the
standard piecewise discontinuous polynomial functions. These spatial
discretization techniques are combined with a backward Euler difference scheme
for time discretization. The article also includes numerical results that
validate the theoretical estimates presented.
