(179d) Van Der Waals Phenomenological Transport Equation of State for Dense Viscosities of the Ultra-Deep Petroleum Reservoirs in the Gulf of Mexico

Even though there is no universal agreement on whether transport properties resulted from the concept of the attractive and repulsive forces, nonetheless, on the microscopic scale both density and viscosity reflect the effects of molecular motion and interaction. As the measurements of both density and dynamic viscosity are based on thermodynamic state variables of temperature and pressure, density and viscosity are functions of the thermodynamic state of the fluid and as such, both properties can be treated by the VDW 1873 theory of cubic equations of state and the law of corresponding states. Consequently, on the basis of the phenomenological similarity between the Van der Waals PVT graph and the morphological profile of transport properties TηP or TλP graph (η denotes dynamic viscosity and λ denotes thermal conductivity), a non-statistical mechanics approach is applied to construct a mathematical expression of the Van der Waals (VDW) type for transport equation of state. Thus, analogy between the spinodal shape of the PVT and TηP graphs in which the positions of pressure and temperature are interchanged and the dynamic viscosity (η) or (thermal conductivity, λ) takes the position of molar volume in the Van der Waals theory of cubic equations of state has been accorded the name, Van der Waals theory of Transport Equation of State or simply Van der Waals Transport Equation of State.

The reformulated VDW 1873 equation typified by the Lawal-Lake-Silberberg (LLS) generic cubic equation of state is applied as a framework for the construction of transport equation of state for fluids and mixtures. In contrast to the 1986 formalism by the author, the improved LLS transport equation incorporate dilute-gas and dense-gas temperature functions and critical viscosity is used as a correlating parameter. The analysis of results shows that the LLS transport equation of state predicts accurate transport property of gases, dense-gas, liquid states and supercritical fluids over the entire PVT states and it is internally consistent at the gas-liquid phase transition critical point without recourse to the judicious choice of density correlations or to any of the thermodynamic properties as correlating parameters.