Fluid mechanics simulations modelled in terms of the Navier–Stokes partial differential equations require equations of states for mathematical completeness. In general, equations of states for ideal fluids include the incompressibility assumption for liquids where the density is constant, the polytropic assumption where the pressure depends on a known power of the density, and the ideal gas assumption for gases. The ideal gas equation is frequently combined with the assumptions of a specific heat and thermal conductivity that are independent of the pressure and only depend on the temperature. Real gases on the other hand, exhibit non-ideal behaviour with complex algebraic mathematical models for microfluidic flows where different physics of flow phenomena are present. In order to address current equations of states limitations, microfluidic behaviour in this study is modelled with a new mathematical non-linear model that incorporates a coupled pressure-density-viscosity equation of state. A numerical method is then developed for solving a nonlinear Reynolds integral equation that incorporates real gas effects, and is used to perform a mathematical analysis in order to determine real gas accuracy effects. Results from this study demonstrate that ideal gas assumptions can have a detrimental effect on accuracies for microfluidic simulations.