Analytical solutions for one-dimensional two-phase multicomponent flows in porous media describe processes of enhanced oil recovery, environmental flows of waste disposal, and contaminant propagation in subterranean reservoirs and water management in aquifers. We derive the exact solution for 3x3 hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. Using the potential function as an independent variable instead of time allows splitting the initial system to 2x2 system for concentrations and one scalar hyperbolic equation for phase saturation, which allows for full integration of non-self-similar problem with wave interactions.

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Exact Solution for Non-Self-Similar Wave-Interaction Problem during Two-Phase Four-Component Flow in Porous Media

Analytical models of gasflooding are important for enhanced-oilrecovery (EOR) screening, for interpretation of laboratory data, and for streamline modeling. Introduction of two Lagrangian coordinates linked with one of the components and with the overall two-phase flux results in splitting the compositional model into an auxiliary system and an independent scalar equation. The number of equations in the auxiliary system is less by one if compared with the compositional model, making analytical modeling possible for more practical cases. The auxiliary system contains only thermodynamic functions and is independent of transport properties. Therefore, phase transitions and minimum miscibility pressure for gas injection are also independent of transport properties. The new splitting method is applicable for both self-similar solutions of continuous gas injection and nonself-similar solvent-slug problems. Analytical solution for four-component oil displacement by a nitrogen-based solvent was obtained using the splitting technique. The compositional two-phase model contains an elliptic region if and only if an elliptic region is also present in the auxiliary system. Calculations for several four-component mixtures exhibit existence of an elliptic region in compositional modeling.

A New Splitting Scheme and Existence of Elliptic Region for Gasflood Modeling

Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, Australian School of Petroleum, 2016.

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Analytical modelling of two-phase multi-component flow in porous media with dissipative and non-equilibrium effects

For two-phase compositional flow with mass transfer in porous media, it is shown that the existing steady-state solutions are unstable for gas-liquid systems, which are characterized by a high relative phase mobility. Instead of them the process model allows stable “semi-stationary” solutions which correspond to a limit model when the liquid-gas mobility ratio tends to zero. In a semi-stationary model the pressure and phase concentration fields are quasi-stationary, while the liquid saturation, in conditions of a continuous condensation/evaporation, is strongly non-stationary and has no a stationary limit in time. Within the framework of the semi-stationary model we have obtained a full splitting between hydrodynamics and thermodynamics, thanks to the fact that N-2 equations describing the phase concentration transport allow an explicit first integration along streamlines. This enables to transform them into differential equations of thermodynamic type (out of space and time) with differentiating over pressure. Being added to the usual equilibrium and EOS equations, such a system constitutes a new closed thermodynamic model which depends on the pressure only. This model describes the thermodynamic behaviour in an open system which corresponds to gas-liquid flow along each streamline. The remaining two flow equations determine the pressure and the saturation fields, with coefficients dependent on thermodynamics. To determine them it is sufficient to calculate the thermodynamic system one time, in contrast to the full compositional model where the thermodynamics is calculated at each space and time point. The obtained hydrodynamic model allows obtaining the analytical solutions along streamlines, by using the singular perturbation method with respect to the relative phase mobility parameter. The irregular character of the asymptotic expansions is determined by the fact that the formal limit solution corresponds to an immobile liquid, which means a full pore plugging by liquid and breaking of gas movement. The full analytical solutions to the non self-similar multicomponent flow problems towards a well were constructed with using the matching asymptotic expansion method. This result was used to propose a new method of gas-condensate well representation in reservoir simulations. The comparison of the solutions obtained for the split thermodynamic and hydrodynamic models with numerical ECLIPSE-based full-compositional simulations has shown a very good agreement. The suggested method was used to develop a new kind of the streamline compositional simulator. We illustrate some examples of its functioning. The research was financed by the Schlumberger Abingdon Technology Center.

Splitting the Thermodynamlics and Hydrodynamics in Compositional Gas-Liquid Flow through Porous Reservoirs

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Splitting the Thermodynamlics and Hydrodynamics in Compositional Gas-Liquid Flow through Porous Reservoirs