What does the diffusivity equation describe?

What does the diffusivity equation describe?

• A. The pressure profile in an infinite-acting, radial reservoir, with a slightly compressible and constant viscosity fluid.
• B. The diffusion of heat in rocks
• C. The flow of oil in a vertical well
• D. The change of formation porosity with time

Answer: (A)

The diffusivity equation describes how pressure diffuses through a porous medium, showing how the pressure field evolves in space and time. In reservoir engineering, this becomes a diffusion equation for pressure around a well in an infinite-acting radial reservoir when the fluid is slightly compressible and its viscosity is essentially constant. It comes from combining Darcy’s law with mass conservation, yielding a partial differential equation for pressure, often written in the form ∂p/∂t = (κ/(φ μ c_t)) ∇^2 p, where κ is permeability, φ is porosity, μ is viscosity, and c_t is total compressibility. This formulation captures how production or injection changes propagate as a pressure wave through the rock. The other topics—heat diffusion, vertical well flow, or porosity changing with time—involve different mechanisms or variables and are not described by this pressure diffusion equation.

The diffusivity equation describes how pressure diffuses through a porous medium, showing how the pressure field evolves in space and time. In reservoir engineering, this becomes a diffusion equation for pressure around a well in an infinite-acting radial reservoir when the fluid is slightly compressible and its viscosity is essentially constant. It comes from combining Darcy’s law with mass conservation, yielding a partial differential equation for pressure, often written in the form ∂p/∂t = (κ/(φ μ c_t)) ∇^2 p, where κ is permeability, φ is porosity, μ is viscosity, and c_t is total compressibility. This formulation captures how production or injection changes propagate as a pressure wave through the rock. The other topics—heat diffusion, vertical well flow, or porosity changing with time—involve different mechanisms or variables and are not described by this pressure diffusion equation.