Geomechanical Reservoir Models

Geomechanical models simulate changes in rock properties with time and pressure. In performance-based reservoir analysis, a geomechanical model may be coupled with the fluid flow model (analytical or numerical). Geomechanical models are useful for (and may be necessary additions to) analyses of overpressured reservoirs. The primary properties of interest are porosity, formation compressibility (pore compressibility), and permeability.

Pressure Dependent Permeability: Modified Pseudo-Pressure & Pseudo-Time

In the standard pressure transient equations, permeability is usually considered to be constant. There are several situations where this may not be a valid assumption:

• Compaction in overpressured reservoirs
• Very low permeability reservoirs in general
• Unconsolidated and/or fractured formations

One way to account for a variable permeability over time is to modify the definition of pseudo-pressure and pseudo-time.

The Pseudo-Steady State (PSS) equation for gas is follows:

where

The modified PSS equation, which incorporates a variable permeability with pressure, is as follows:

where

Alternatively, the modified equation may be written in two parts as follows:

1. Depletion Part:

(1)

2. Inflow Part:

(2)

The equation, 1. Depletion Part, is a material-balance equation, and thus, has no dependence on the mobility terms k and m. The mobility terms only enter into the inflow, 2nd part of the PSS equation. When the PSS equation is coupled, however, the k/m term must be included in pseudo-time.