THERMO-HYDRO-MECHANICAL MODELING OF WORKING FLUID INJECTION AND THERMAL ENERGY EXTRACTION IN EGS FRACTURES AND ROCK MATRIX Page: 4 of 11
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mechanics) are tightly coupled, the solution
can become inaccurate and require very
small time steps (Valocchi et al., 1981). For
most potential EGS reservoirs, fluid flow,
heat transport, and rock deformation will be
strongly nonlinearly coupled. The changes
in flow and energy transport properties due
to fracturing and/or dissolution add further
complexity and nonlinearity to the problem.
For such situations, the global implicit
approach (GIA) solves all solution variables
simultaneously during each time step by
seeking the solution of a large system of
nonlinear equations via some form of
Newton's method and is a more robust
solution than the other two approaches
(Chacon and Lapenta, 2006; Hammond et
al., 2002; Molins et al., 2004).
One potential limitation of the GIA
approach is the need to compute, store and
invert the Jacobian matrix. This could
become problematic for large systems that
would be expected for reservoir-scale
geothermal problems. As the number of
solution variables grows, the matrix holding
the Jacobian entries also grows. The
increased size of the Jacobian matrix results
in greater memory usage and more CPU
time to solve the resulting system of linear
equations within the Newton iterations. For
highly nonlinear processes involving strong
fluid-reservoir interactions and significant
changes of flow and transport properties due
to fracturing, the true Jacobian is often
difficult to describe in analytical formulas.
For reasons such as these, during the past
three decades, despite its numerical merits
of greater robustness and the ability to take
larger time steps, the fully-coupled GIA
method was considered to be too CPU-time
and memory-intensive (Yeh and Tripathi,
1989) or to be computationally inefficient
(Steefel and MacQuarrie, 1996). It has been
used primarily only as a research tool for
small one- or two-dimensional problems
with a few thousands of unknowns. Since
the first attempts of implementing the GIA
approach in the early 1980s (Valocchi et al.,
1981; Miller and Benson, 1983), only a
handful of examples based on this approach
have been reported in the literature,
compared with numerous examples of
applications based on an operator splitting
approach (Xu et al., 2006; Yeh et al., 2004;
Rutqvist et al., 2004).
Reliable reservoir performance predictions
of enhanced geothermal reservoir systems
will require accurate and robust modeling
for the coupled thermal-hydrological-
mechanical processes. As stated above,
these types of problems are solved using
operator-splitting methods, usually by
coupling a subsurface flow and heat
transport simulator with a solid mechanics
simulator via input files. An alternative is to
solve the system of nonlinear partial
differential equations that govern the system
simultaneously using a fully coupled
solution procedure for fluid flow, heat
transport, and solid mechanics using a GIA
approach. This procedure solves for all
solution variables (fluid pressure,
temperature/enthalpy and rock displacement
fields) simultaneously, which leads to one
large nonlinear algebraic system that is
solved using a strongly convergent nonlinear
solver. Developments over the past 10 years
in the area of physics-based conditioning,
strongly convergent nonlinear solvers (such
as Jacobian Free Newton methods) and
efficient linear solvers (such as GMRES),
make this approach competitive.
In this paper, we describe the application of
a globally implicit geothermal reservoir
simulator, as applied to EGS reservoir
simulations, using the INL code Fracturing
And Liquid CONvection, FALCON
(Podgorney et al., 2011).
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Podgorney, Robert; Lu, Chuan & Huang, Hai. THERMO-HYDRO-MECHANICAL MODELING OF WORKING FLUID INJECTION AND THERMAL ENERGY EXTRACTION IN EGS FRACTURES AND ROCK MATRIX, article, January 1, 2012; Idaho Falls, Idaho. (digital.library.unt.edu/ark:/67531/metadc835377/m1/4/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.