We consider the numerical solution of coupled fluid flow and heat or mass transport in porous media. The aim of this work is to provide some new mathematical development and algorithm to reduce the CPU costs of the solution of these strongly non-linear coupled equations widely used in geosciences and environmental sciences, without lost of accuracy. Usually, the flow equation is solved first. We show that, by solving the transport equation first, the CPU time can be significantly reduced. This new algorithm is not dependent on the numerical scheme and is quite easy to implement in a numerical code. The accuracy of this new way of coupling flow and transport equations is evaluated with 2D and 3D numerical tests.