As we have already seen, in the pressure range of , the group can be considered to be approximately constant. With this simplification, we can remove the group from the spatial derivative on the left-hand side of Equation 5.37 to obtain:
This is the diffusivity equation for real gases in terms pressure, p. While this may at first glance appear to be linearized, it is not. Both the gas compressibility term, , and the gas viscosity term, , are pressure dependent. When using the pressure formulation, we typically evaluate these terms at either the initial pressure condition, , or the average condition, . (Note: other more rigorous methods are available for the evaluation of the product; however, they are beyond the scope of this course.)