Numerical modeling of temperature and species distributions in hydrocarbon reservoirs

Abstract

[1] We examine bulk fluid motion and diffusion of multicomponent hydrocarbon species in porous media in the context of nonequilibrium thermodynamics, with particular focus on the phenomenology induced by horizontal thermal gradients at the upper and lower horizontal boundaries. The problem is formulated with respect to the barycentric (mass-averaged) frame of reference. Thermally induced convection, with fully time-dependent temperature distributions, can lead to nearly constant hydrocarbon composition, with minor unmixing due to thermal gradients near the horizontal boundaries. Alternately, the composition can be vertically segregated due to gravitational effects. Independent and essentially steady solutions have been found to depend on how the compositions are initialized in space and may have implications for reservoir history. We also examine injection (to represent filling) and extraction (to represent leakage) of hydrocarbons at independent points and find a large distortion of the gas-oil contact for low permeability.

Modeling of multicomponent diffusions and natural convection in unfractured and fractured media by discontinuous Galerkin and mixed methods

“…Note that the coefficients (B K ) E,E ′ , (B K ) E,E ′ , and K,E depend on the geometrical shape of the elements and the local mobility coefficient. By imposing the flux continuity across the cell interfaces, (q K,E = q K ′ ,E ; E = K ∩ K ′ ), one can eliminate the flux unknowns q K,E from Equation 11. As a result, the following linear system with primary unknowns, ie, the cell average pressures in P and the edge average pressures in T P , becomes…”

“…Let K be a grid block that contains a 1D fracture element I. By applying the mixed hybrid finite element formulation to Darcy's law over K, the flux q K,E across the edge E of K can be expressed as a function of the cell pressure average p K and the edge pressure averages (pressure traces)tp K,E , as shown in Equation 11. The same approach can be applied to discretized Darcy's law in the fracture element I.…”

“…These include (i) natural convection, (ii) different diffusion mechanisms, and (iii) reservoir filling and leakage. 11 Natural convection is mainly affected by horizontal temperature gradient. Diffusions are from temperature, pressure, and composition gradients.…”

“…() There are 3 distinct processes that affect species distribution in hydrocarbon reservoirs. These include (i) natural convection, (ii) different diffusion mechanisms, and (iii) reservoir filling and leakage . Natural convection is mainly affected by horizontal temperature gradient.…”