Page 275 - Geothermal Energy Systems Exploration, Development, and Utilization

5.3 Reservoir Characterization 251
• Heterogeneity: Deep geothermal reservoirs are extremely heterogeneous.
Fractures determine the flow, transport, and geomechanical properties to a large
extent (Section 5.3.1).
• Nonlinearity: Owing to the large imposed changes of the thermodynamical state
variables (e.g., pressure, temperature, stress), fluid and rock properties behave
nonlinearly (Section 5.3.2).
• Uncertainty: Data on material properties rely on a few measurements; therefore,
the information about geothermal reservoirs is to a large degree uncertain
(Section 5.3.4).

5.3.1
Reservoir Properties

5.3.1.1 Reservoir Permeability
Reservoir permeability is one of the most important hydraulic parameters governing
advective transport processes. At the same time, it is most difficult to determine as
pumping tests give information only about the near field area. In most sedimentary
rocks the porosity is interconnected, which makes the rock permeable for flow.
A rough estimate of reservoir permeability can be calculated by the steady-state
method directly using Darcy’s Law and thus assuming laminar flow conditions
l
Q µ
k =− l (5.10)
A∇p
with the flow rate, dynamic viscosity, cross-section of the flow path, and pressure
gradient, respectively (see list of symbols for parameter definitions and units).

5.3.1.2 Poroperm Relationships
The suitability of existing empirical relationships in order to correlate porosity and
permeability changes such as the well-known Kozeny–Carman equation (Kozeny,
1927; Carman, 1937) is a matter of question for fractured rocks. During geothermal
power production using a borehole doublet consisting of a production and injection
well, the reservoir conditions will change. Besides, a temperature decrease at the
injection well results in a thermoelastic response, and the pore pressure will also
vary. This leads to a poroelastic response of the reservoir rocks depending on
effective stress (difference between confining stress and pore pressure), resulting
in a change in permeability and porosity. Various previous studies continued to
investigate the effective pressure dependency of these rock properties. (Carroll and
Katsube, 1983) developed a theory of hydrostatic poroelasticity in terms of porosity
and bulk volume. By means of this theory changes in effective pressure can be
related to changes in porosity (Zimmerman, 1991) (Figure 5.3)

s
l
n =− (1 − n)β p − β s (σ − p ) (5.11)
p
where the parameters are bulk compressibility and compressibility of the solid.
The permeability can always be expressed as a function of confining and pore
pressure (Al-Wardy and Zimmerman, 2003). If the permeability follows the effective