Gas flow in a reservoir under transient conditions can be approximated using which two equations?

Gas flow in a reservoir under transient conditions can be approximated using which two equations?

• A. Bernoulli's equation and the mass balance
• B. Navier-Stokes equations and Fick's law
• C. Darcy's law and the continuity equation
• D. Energy balance and mass balance

Answer: (C)

Modeling transient gas flow through reservoir rock hinges on conservation of mass in a porous medium and a constitutive relation that links flow to pressure gradients. Darcy's law provides the relationship between the fluid flux and the pressure gradient, scaled by the rock’s permeability and the gas viscosity. The continuity equation enforces that mass is conserved as gas density and flow change with time and space, which is essential for compressible gas where pressure variations cause density changes and storage effects in the pore space. Put together, these two form the standard framework that describes how pressure evolves during transient flow in a reservoir. Other options don’t fit as well because they describe different situations: Bernoulli’s equation applies to inviscid, along-flow energy conservation and isn’t appropriate for flow through a porous medium; the full Navier–Stokes equations model viscous flow in open domains and are more detailed than needed for reservoir-scale porous media; Fick’s law governs molecular diffusion of species rather than bulk flow through a porous rock; an energy balance focuses on heat transfer, which is not the primary driver of transient gas movement in this context.

Modeling transient gas flow through reservoir rock hinges on conservation of mass in a porous medium and a constitutive relation that links flow to pressure gradients. Darcy's law provides the relationship between the fluid flux and the pressure gradient, scaled by the rock’s permeability and the gas viscosity. The continuity equation enforces that mass is conserved as gas density and flow change with time and space, which is essential for compressible gas where pressure variations cause density changes and storage effects in the pore space. Put together, these two form the standard framework that describes how pressure evolves during transient flow in a reservoir.

Other options don’t fit as well because they describe different situations: Bernoulli’s equation applies to inviscid, along-flow energy conservation and isn’t appropriate for flow through a porous medium; the full Navier–Stokes equations model viscous flow in open domains and are more detailed than needed for reservoir-scale porous media; Fick’s law governs molecular diffusion of species rather than bulk flow through a porous rock; an energy balance focuses on heat transfer, which is not the primary driver of transient gas movement in this context.