Figure I Generalized map of the Wilbur Mining ... - University of Utah

Geothermal Resources Council, TRANSACTIONS, Vol. 3 Septetrher 1979
THE INFLUENCE OF STEAM-WATER RELATIVE PERMEABILITY CURVES ON
THE NUMERICAL MODELING RESULTS OF LIQUID DOMINATED GEOTHERMAL RESERVOIRS
ABSTRACT
Sensitivity analyses for modeling of a hypothetical
liquid dominated geothermal reservoir
indicate the strong dependence of the results on
the assumptions made about the steam-water
relative permeability curves. Of significant
importance are the critical saturation points for
the individual phases and the curvature of plots.
The effects are more evident on calculated
producing wellbore pressure and projected heat
recovery.
INTRODUCTION
The success of numerical modeling for hydrothermal
systems depends on the assumptions raade
about the rock and fluid property data. One piece
of information that strongly controls the results
of model studies for two phase flow in reservoirs
is the assumed values for relative permeabilities.
A review of literature shows that in previously
published model studies on geothermal
systems, the concept of relative permeability has
been treated lightly, perhaps because of lack of
information. Relative permeabilities used in the
past include systems similar to oil-water models
as used by Martin', or approximations by simple
models such as Corey's^ as used by Faust and
Mercer,^ Jonsson'' from his modeling work
indicated that relative permeability data had
little influence on pressure drop and saturation
d istr i but ion.
Recently, evidence of actual lab derived
relative permeability curves for steam-water
systems has appeared in the literature.^ * These
curves show that the end points, corresponding to
the critical water and critical steam saturation,
may be much different than the ones used in oilwater
or water-gas system.
In this study an effort was made'to look at
the sensitivity of numerical modeling results to
the assumed values of relative permeability data.
DESCRIPTION OF THE MODEL
The numerical model used in this study was a
modified version of a program originally developed
by Faust and Mercer. Relative permeability curves
H. Sun and I. Ershaghi
University of Southern California
697
were furnished to the program through the use of
an equation which allowed for selection of a
wide range of end points as well as curvatures.
The general form of the equation may be shown as
follows:
(S - S )
'I
w wc
b (1 S - S )
W SC
where S = water saturation, fraction
w
S = critical water saturation, fraction
WC
S = critical steam saturation, fraction
SC
a, b, n and n are constants.
The model was used for a one dimensional
reservoir initially containing hot water with
one producing well and no recharge. The heat
and mass recovery as a function of time were
computed using different sets of relative permeabilities.
Table I shows some of the specifications
used in the model.
Throughout the life of the system, flow
toward the wellbore occurs in three distinct
periods. The initial period of single phase
liquid flow, followed by a two phase liquid-vapor
flow and the eventual conversion to one phase
vapor flow. In assessing the importance of
accurate relative permeability data on modeling
. results, one must examine the outputs which can
be used for history matching purposes. The study
of saturation distribution and other profiles in
the reservoir as used by Jonsson may be somewhat
mi sleadi ng.
There are several ways to use numerical
modeling results for history matching purposes.
The results of this study are presented in terms
of heat recovery versus time and wellbore
producing pressure versus time.
The effect of assumed values for critical
saturation of water is shown in Fig. 1. During
the two phase flow, the Change of critical water
saturation from 0,3 to 0.5 could cause significant
differences in the performance projection for
1'
i!
I I
,1