Tímarit Verkfræðingafélags Íslands - 01.08.1981, Blaðsíða 16

Capacitive perturbations in
well interference testing*
by Gunnar Böðvarsson,
School og Oceanography and Department of Mathematics,
Oregon State University, Corvallis, Oregon, 97331, U.S.A.
Gunnar BöOvarsson lauk f.h. prófi í
vélaverkfrœði frá TH í Munchen 1936,
verkfrœðiprófi í stœrðfræði, kraftfrœði
og skipavélfrœði frá TH í Berlín 1943.
PhD-próf frá California Inst. of
Technology t Bandaríkjunum 1957.
Verkfrœðingur hjá vélsmiðjunni Atlas
AS í Khöfn 1943-45, hjá Rafmagnseftir-
liti ríkisins í Rvík 1945-47. Yfirverk-
frœðingur við Jarðboranir ríkisins og
jarðhitadeild Raforkumálaskrifstofunn-
ar 1947-61. Fór á vegum Sþ, til Santa
Lucia í Vestur-lndíum 1951, Mexíkó
1954, Costa Rica 1963, fjölmargar
ferðir til El Salvador, Guatemala og
Nicaragua 1965-76, Chile 1972, íslands
1972 og Kína 1981 til að athuga mögu-
leika á vinnslu jarðvarma. Námsdvöl
við Cal. Inst. og Technology 1955-57.
Meðstofnandi ráðgefandi verkfrœði-
fyrirtœkisins Vermis sf. og starfaði við
það 1962-64. Prófessor I stœrðfræði og
jarðeðlisfrœði við Oregon State Univer-
sity í Bandaríkjunum frá 1964.
(conductance) A and an equivalent
capacitance C. That is to say, that given
the ambient time-varying pressure field
to be measured p(t) and the pressometer
reading pm(t), the mass flow into the
meter system satisfies the following
equations
INTRODUCTION
Conventional well interference testing
is applied to obtain observational data
on reservoir parameters such as fluid
conductivity, fluid diffusivity, and struc-
tural inhomogeneities or boundaries.
Test results are usually interpreted on
the basis of forward type curve-
matching methods (Ramey, 1970).
Field procedures are generally based
on the use of standard size wells for
both injection and response monitoring.
The pressure sensors are placed into the
wells that serve as observational ports.
Obviously, the monitoring wells con-
stitute capacitive inhomogeneities that
can perturb the reservoir flow field and
thereby distort the pressure readings. In
particular, the capacitance of wellbores
with two-phase fluids, gas caps or even
a free fluid surface is relatively large and
the perturbation can then be substan-
tial. Quite erroneous test results may be
obtained in such situations. Moreover,
analog perturbations can result from
the prensence of inactive high-capacitance
wells and other reservoir „soft spots” in
the neighborhood of the test wells. For
example, geothermal systems that ap-
pear liquid-dominated may actually in-
clude local spots with two-phase pore
fluids that have a higher compressibili-
ty than the pure liquid. In particular,
such soft spots are likely to develop in
regions with temperatures close to boil-
ing and/or high gas content liquids.
As a matter of course, the capacitive
effects are weli known and are in the
petroleum industry usually referred to
as wellbore storage effects. A con-
siderable literature exists, mainly
relating to such effects in single-well
pressure-buildup or drawdown testing
(see, for example, Ramey, 1970;
* Paper given at the Fifth Workshop on Geother-
mal Reservoir Engineering at Stanford University,
California, U.S.A., December 1979.
Earlougher and Ramey, 1973; Raghav-
an, 1976; Chen and Brigham, 1978;
Miller, 1979). For further references, we
refer to the monograph by Earlougher
(1977). A number of aspects relating
specifically to interference testing have
been discussed by Prats and Scott
(1975), Jargon (1976) and Sandal et. al.
(1979).
In passing, it is of interest to remark
that sensor capacitance is a matter of
extremely general relevance. For exam-
ple, capacitive effects interfere with the
measurement of time-varying temp-
eratures. Just as we refer to temperature
gauges as thermometers, we will here
apply the term pressometers for the
pressure monitoring devices. In in-
terference testing, the pressometer con-
sists of the entire monitoring well setup.
The purpose of the present short note
is to discuss the capacitive effects from a
rather general point of view and, in par-
ticular, to derive some basic expressions
to enable us to correct for pressometer
and soft spot capacitance. The ap-
proach will be based on the assumption
of a forward type interpretational pro-
cedure. In other words, the develop-
ment is based on definite field models
that lead to a well-posed problem set-
ting. By varying the model parameters,
the solutions yield the type-curves that
are used to interpret field data. Data in-
terpretation on the basis of so-called in-
verse procedures is usually not feasible
and would lead to a practically impossi-
ble problem setting.
Notation and basic equations are as
given in the paper by Bodvarsson
(1978).
In the case of slowly varying fields,
well pressometers can quite often be
lumped into an equivalent admittance
q = A(p-pJ, q = pCDpm (1)
where D = d/dt and p is the density of
the fluid. Let tQ = pC/A be the
pressometer relaxation or response time
and the above equations can then be
combined into one equation.
Pm + toDPm = P <2>
including only the parameter tQ. It is
convenient to introduce the correction
pressure p, that has to be added to pm to
obtain the ambient field p such that
P = (Pm + P i)* We have then the
relation
AN ULTRASIMPLE MODEL
60 — TÍMARIT VFÍ 1981