Analytical Models Clause Samples

Analytical Models. Dinske [4] gives the analytical solution of the diffusion equation in spherical geometry for a time-dependent source function representing a pressure source that is linearly increasing with time: (6) The pore pressure perturbation p(r, t) as function of radial distance from the centre of the sphere (where the injection pressure source is located) and time is calculated using the following parameters:  Source terms q0 = 4πDa0p0 and qt = 4πDa0pt with - p0 being the initial injection source pressure (Pa) - pt being the injection source pressure gradient (Pa/s) In consideration of switching off the injection source after a shut-in time t0, Dinske extended equation (6) to simulate the post shut-in period via the summation of two injection sources, leading to the following formula: (7) ▇▇▇▇▇▇▇▇ [5] gives an exact analytical solution for spherical pore pressure spreading from a point source of constant flux fluid mass injection: (8) Here q is the mass flux rate (kg/s), ρ0 is the fluid density (kg/m3), λ and λu are the drained and undrained Lamé parameters, α is the Biot coefficient (dimensionless), μ is the shear modulus (Pa) and k is the permeability (m2). The variable ξ is: (9) In the computations that follow we compare the solutions of numerical and analytical models for identical injection and reservoir characteristics in order to verify the developed.