Pore Pressure Induced by Fluid Injection - Induced Seismicity Potential in Energy Technologies - page 203

Pore Pressure Induced by
Fluid Injection

The dependence of the induced pore pressure on the operation parameters (injection
rate, volume of fluid injected), on position and time, and on the hydraulic properties of the
reservoir is illustrated in this appendix by considering the simple example of fluid injection
in a disk-shaped reservoir. The analysis shows that different parameters control the pore
pressure at the beginning of the injection operation and once enough fluid has been injected
in the reservoir (see also Nicholson and Wesson, 1990).
The pore pressure induced by injection of fluid, Δρ, is to a good approximation governed
by the diffusion equation

c

2 Δρ = ∂Δρ/∂t + source

∇

where c denotes the hydraulic diffusivity equal to c = k/ μS. In the above, k is the intrinsic
permeability of the rock (generally expressed in Darcy), μ is the fluid viscosity, and S is the
storage coefficient, a function of the compressibility of both the fluid and the porous rock.
The diffusion equation imposes a certain structure on the link between the magnitude of
the induced pore pressure Δρ, the injected fluid volume V , and the rate of injection Q o .
As an example, we consider the injection of fluid at a constant volumetric rate Q o , at
the center of a disk-shaped reservoir of thickness H and radius R . It is assumed that the
reservoir is thin (i.e., H/R 1 ), and also that the pore pressure is uniform over the thickness

of the layer, which implies, depending on the manner the fluid is injected, that some time
has elapsed since the beginning of the operation.
At early time (to be defined more precisely later), the pore pressure perturbation in-
duced by injection of fluid has not reached the boundary of the reservoir. The induced pore
pressure field is then given by the source solution for an infinite domain, a solution of the
form (Wang, 2000)

≪

Δρ( r,t ) = ρ * F( r/ √ [ct]) (1)

where r is the radial distance from the injection well, t is time, and F is a known function.
The quantity where ρ * is a characteristic pressure (i.e., a yardstick for measuring the induced
pressure) given by

ρ * = μ Q o /kH