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ANALYSIS OF BOILING EXPERIMENTS USING INVERSE MODELING
S. Finsterle', C. Satik, and M. Guerrero2
'Earth Sciences Division
Lawrence Berkeley National Laboratory
University of California
Berkeley, CA 94720
2Stanford Geothermal Program
Stanford University
Stanford, CA 94305ABSTRACT
Numerical predictions of geothermal reservoir
behavior strongly depend on the assumed
steam-water relative permeabilities, which are
difficult and time-consuming to measure in
the laboratory. This paper describes the esti-
mation of the parameters of the relative per-
meability and capillary pressure functions by
automatically matching simulation results to
data from a transient boiling experiment
performed on a Berea sandstone. A sensitivity
analysis reveals the strong dependence of the
observed system behavior on effects such as
heat transfer from the heater to the core, as
well as heat losses through the insulation.
Parameters of three conceptual models were
estimated by inverse modeling. Each calibra-
tion yields consistent effective steam perme-
abilities, but the shape of the liquid relative
permeability remains ambiguous.
INTRODUCTION
The experimental determination of relative
permeability and capillary pressure functions
for nonisothermal, single-component, two-
phase flow problems as encountered in geo-
thermal reservoir engineering is very
challenging, mainly because of the need to
measure saturation, matric potentials, and flow
rates under high temperatures and pressures.
Moreover, the standard concept of characteris-
tic curves as saturation-dependent material
properties may be inappropriate in such
systems, because interfacial tension, wetting
characteristics, and pore-level condensation-
evaporation mechanisms are affected by
temperature changes. The need for steam-
water relative permeability and capillary
pressure functions in numerical simulations of
geothermal reservoirs prompted several inves-tigators to analyze enthalpy data from
production wells [e.g., Grant, 1977; Horne
and Ramey, 1978] or to conduct steam-injec-
tion and boiling experiments in the laboratory
[e.g., Ambusso et al., 1996; Satik, 1997]. In
this paper, we describe the estimation of the
parameters entering the relative permeability
and capillary pressure functions, by automati-
cally matching simulation results to data from
a transient boiling experiment performed on a
Berea sandstone. If we use inverse modeling
for parameter estimation, the functional form
of the characteristic curves is part of the
conceptual model, i.e., it cannot be directly
inferred from the data. However, by
subjecting competing conceptual models to
the estimation process, we can find the func-
tion that best matches the observed data. If the
match was achieved without overparameteriza-
tion, the most likely model is identified.
We first discuss the inverse modeling approach
implemented in ITOUGH2 [Finsterle,
1997a,b] and describe the boiling experiment.
Next, we analyze the temperature, saturation,
pressure, and heat flow data using inverse
modeling with ITOUGH2.
INVERSE MODELING
Inverse modeling is a technique to derive
model-related parameters from a variety of
observations made on a hydrogeologic system,
from small-scale laboratory experiments to
field tests to long-term geothermal reservoir
responses. In this section, we briefly summa-
rize the various steps involved in the iterative
procedure of automatic model calibration. A
detailed discussion of inverse modeling theory
can be found elsewhere (e.g., Carrera and
Neuman [1986]).1-
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Finsterle, S.; Guerrero, M. & Satik, C. Analysis of boiling experiment using inverse modeling, article, May 1, 1998; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc697625/m1/5/: accessed August 15, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.