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WELL TESTING INTERPRETATION
AND
NUMERICAL SIMULATION STUDY ON WELL KJ-20. KRAFLA
Soeroso * UNU Geothermal Training Programme
National Energy Authority
GrensBsvegur 9, 108 Reykjavik
ICELAND
* Permanent address:
PERTAMINA
Geothermal Division
Head Office, p,a. Box 12, Jakarta
INDONESIA
ABSTRACT
The reservoir engineering techniques dealing with interpretation
of well tests and simulation studies are presented for well
KJ-20 at the Krafla Geothermal Field , Iceland .
These teats are both fall-off and injection tests made at the
completion of the well, and build-up test after prolonged
production for more than a year . The interpretation methods used
consist of MDH, Horner and type curve matching. The results
indicate a transmissivity in the range 1.35 x 10- 8 m3 /P •• B to
1.89 X 10-8 m3 /P •. s.
A conceptual model was made of the drainage volume for well
KJ-20, Krafla. This model was then transformed for a solution
with a numerical simulator to simulate and predict the future
behaviour for the production from the well.
The numerical simulator, SHAFT 79 developed at the Lawrence
Berkeley Laboratory at the University of California was applied
for the prediction of the future reservoir behaviour in the
vicinity of well KJ-20, Krafla. The simulations were processed
on the VAX 11-750, VAX/VMS 4.2 computer, installed at the
National Bnergy Authority in Reykjavik, Iceland. Two cases
were considered in this study, one with the drainage volume
for well KJ-20 closed on all sides and the other with the
northern boundary for the drainage area open. In the closed
boundary case the depletion time for well KJ-20 is about 8
years which in that case is also the depletion time for the
drainage volume of the well. For the open boundary case the
depletion time for well KJ-20 is increased to about 13 years.
In that case the drainage volume has not been depleted.
TABLE OF CONTENTS
ABSTRACT . . . . . . . . . . . . . . . . . .
1. INTRODUCTION
1.1. Scope of work
1.2. Problem Statement
2. WELL TESTING THEORY
2.1. Basic Solution
2.2. Wellbore Storage and Skin
3. APPLICATION TO WELL KJ - 20 KRAFLA
3.1. Fall-off and Injection Tests
3.2. Build-up Test
3.3. Analysis and Result of Well Tests
4. SIMULATION ON WELL KJ - 20 KRAFLA
4.1. Conceptual Model ..
4.2. Numerical Simulation
4.3. Result of Simulation
4.4. Discussion
4.5. Conclusion
ACKNOWLEDGEMENT
2
6
6
6
8
8
10
13
13
16
20
22
22
23
25
26
27
28
REFERENCES . . . . . . . . . . . . . . . . . . • . . .. 29
LIST OF TABLES:
Table 1 Pressure build-up data for well KJ-20, Krafla.
Table 2 Wellbore simulation results for well KJ-20, Krafla.
LIST OF FIGURES:
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Fall-off and injection test in well KJ-20, Krafla.
Semilog plot of fall-off test in well KJ-20, Krafla.
Type curve matching with fall-off test in well
KJ-20, Krafla.
Semilog plot of injection test in well KJ-ZO,
Krafla.
Type curve match in, with injection test in well
KJ-20, Krafla.
Pressure 10, before well KJ-ZO, Krafla was shut-
in.
Temperature log before well KJ-20, Krafia was
shut-in.
Static temperature 10' in well KJ-20, Krafla.
Horner plot for well KJ-20, Krafla.
Type curve matching with build-up test in well
KJ-20, Krafla.
Loa log plot of fall-off and injection testa in
well KJ-20, Krafla.
Map showing the location of well KJ-20, Krafla.
Model used for simulation.
The South - North section of the simulation model.
A. Closed boundary ; B. Open boundary toward North.
Pressure behaviour for the closed boundary case.
Temperature behaviour for the closed boundary case.
Vapour saturation behaviour for the closed boundary
case.
Enthalpy behaviour for the closed boundary case.
Pressure behaviour for the open boundary case.
Temperature behaviour for the open boundary
case.
Figure 21 Vapour saturation behaviour for the open boundary
case.
Figure 22 Bnthalpy behaviour for the open boundary case.
NOMENCLATURE:
A = area, ma
c = compressibility, Pa- 1
C = wellbore storage coefficient, m3 /Pa
• = acceleration of gravity, m/sec 2
h = thickness (reservoir), metre
k = permeability, ma
m = slope of semilog line, Pa/cycle
P = pressure, Pa
P = changes of pressure, Pa
q = flow rate, m3 /sec
r = radial distance, metre
t = time, second
t = changes of time,second
V = volume, m'
Greek symbols
~ = porosity, fraction
~ = dynamic viscosity, Pa.s
r = density, kg/m)
Subscripts:
a = apparent
A = area
D = dimensionless
f = flowing
i = initial
s = sf =
t = " =
shut-in
sandface
total
wellbore
6
1. INTRODUCTION
1.1. Scope of work
This report is the final part of the author's work during the
six months trainina in reservoir engineering at the United
Nations University (UNU) geothermal trainin~ programme at the
National Energy Authority (NEA) in Reykjavik, Iceland.
The training programme as a whole included introductory
lectures in various disciplines of geothermal technology such
as; geology, geophysics, geochemistry, production and utiliz
ation, and reservoir engineering, for approximately six
weeks. The next six weeks were spent on specialized lectures
in borehole geophysics and reservoir engineering.
Before commencing the specialized training in reservoir
engineering, two weeks of field excursion and seminars were
undertaken which included visits to both low and high temperature
geothermal fields with various types of utilization of geothermal
energy. The author also obtained a brief training in the use
of the IBM Personal Computer installed in the UNU.
1.2. Problem Statement
There are various types of tests which have been applied in
geothermal wells to enhance the understanding of the reservoir
behaviour. The first tests performed after well KJ-20 had reached
total depth were fall-off and injection tests, both of these
tests measured water level in the wellbore. The tests are
conducted to obtain data that can be analyzed to get an estimate
for the transmissivity and storativity in the reservoir
formation.
The other test called pressure build- up test reflects the
condition of a well. The results obtained from this test give
an idea of the average reservoir properties, i.e quantitative
value for the transmissivity in the drainage volume of the well,
7
and mean reservoir pressure. The analysis of the test can also
indicate whether the well is damaaed or stimulated, and gives
quantitative information concerning the shape of the reservoir
either homogeneous or heterogeneous.
In order to make a prediction of the future possibilities of
the reservoir behaviour in the neighborhood of well KJ- 20, in
the Krafla Geothermal Field, a simple conceptual model was made.
The conceptual model was made on the basis of geology and data
from the tests. This model was then transformed to enable a
solution with a numerical simulator.
8
2. WELL TESTING THEORY
2.1. Basic Solution
The basic equation for transient flow in porous medium is the
diffusivity equation. The diffusivity equation is a combination
of the law for conservation of mass, an equation of state and
Darcy's law. The diffusivity equation in radial coordinates
can be written:
5r' 5r k
li 5t
(2.1)
Matthews and Russel present a derivation of the diffusivity
equation and point out that it assumes horizontal flow,
negligible gravity effect, a homogeneous and isotropic porous
medium and a single fluid of small and constant compressibility.
The parameters ~,~, Ct and k are assumed independen t of
pressure.
In dimensionless form, pressure drop can be written:
P. (t.,r.) = 2 x k h (~ - P (t,r))
q ~
(2.2)
In transient flow, PD is always a function of dimensionless time,
which is when based on wellbore radius:
tu = k t ( 2 • 3 )
or when based on drainage area
tu" = k t = ( 2 • 4 )
~ Il Ct A
Dimensionless pressure also varies with location in the
r eservoir, as indicated in equation (2.2) by dimensionless radial
distance from the operating well. The radial dimensionless
distant is defined as:
(2.5)
rw
9
Substitution of these variables into the radial diffusivity
equation ~ive6:
§..a~J) + L ~D (2.6)
The dimensionless diffusivity equation can t hen be solved for
the appropriate initial and boundary condition (Earlougher 1977,
S.P. Kjaran 1982, Sigurdsson. 0, lectures),
During the initial transient flow period, it has been found
that the well can for most practical purposes be approximated
by a line source. This assumes that in comparison to the
apparently infinite reservoir, the wellbore radius is negligible
and the wellbore itself can be treated as line source. For
the infinite acting reservoir the boundary and initial condition
are give n as:
lim
r. o = 1
for all
for all
tD » 0
The solution to the radial diffusivity equation with these
boundary and initial conditions is the exponential integral
solution to the flow equation (also called the line source
or Theis solution). The exponential integral solution is:
PD (tD ,rD) ::; - i El (=--.!:.D2) ( 2 • 7 )
4 t.
or
PD (tD, rD ) ::; i [ In L.t"_) + 0.80907 1 ( 2 • 8 )
10
The difference between equation 2.7 and equation 2.8 is only
about two percent, when tD/rD 3 ~ 5.
At the operating well (in a single well system) rD = 1, Ba
tD/rD Z = tD and equation 2.8 becomes:
P. (t.) - 9 = ! [In t. + 0.80907 1 ( 2 • 9 )
Substitution f o r the dimensionles8 parameters into equation 2.9.
(Pi - P (t,r)) = g u [ In k t ) + 0.80907 + 2 91
4 ~ k h Ii!i Ct rw a
(2.10)
or
Pw' = Pi ± 0.183 ll.....I.t [log t + log k + 0.3514 + 0.868691
k h IiJJlCt rw:i
where: + for injection
for production
2.2. Wellbore S tor age a nd Skin
We llbore Stora,e:
(2.11)
Wellbore storage also called after flow, after production,
after injection, and wellbore loading or unloading, has long
been recognized as effecting short time transient pressure
behaviour (Earlougher,1977). This effect exists in the well
when the well is opened for production, the fluid flow from
the well is larger than the c orresponding flow from the
reservoir into the well.
Similarly when the well is shut - in, fluid still continues to
pass through the sandface into the hole. Wellbore storage is
characterized by a wellbore constant, defined as:
c = t:.v
t:.P
11
(2.12)
For the wellbore with chan.ing liquid level, the wellbore
constant is: C = Y. __ (2.13)
r /I where: V. is the wellbore volume per unit length.
The diaensionles8 wellbore storage coefficient, C. is defined
as:
c. = c (2.14)
2 " " et h r.a
The sand face flow rate at the foraation can be calculated
from the following equation:
q., = q + C dP. (2.15)
dt
and
q., = q [ 1 - C. ~ P. (t •• C ••••• )] (2.16)
dt.
In logarithaic term:
10" llo' = - 10/1 C. - log A P. + loaA t.
q
or
laiC At. = loa: A PI! + 1011 C. + 10/1 (9..,) (2.17)
q
At the beginning of a well test the sandface flow is
approximately zero , 80 the wellbore storage constant can be
found from a straight line with slope in the early time data
on a log log plot of preSBure change, A P versus elapsed time,
~t . The wellbore storage coefficient, can then be calcUlated
fro.:
C = q L>t L>p
12
(2.18)
The diffusivity equation including wellhore storage in the well
was solved by Everdingen and Hurst (1949) for the infinite
reservoir case . In that case the inner boundary condition for
equation 2.6 are changed to:
lim (2.19)
r. o
Skin Effect.
The skin characterizes the condition of the well, in terms of
damaged or stimulated. These conditions can be described with
additional pressure drop in the reservoir near the well .
According to van Everdingen (1953) the additional pressure drop
close to the well is defined:
p = 069 11 S (2.20)
2 " k h
From the skin factor an apparent wellbore radius can also be
determined as:
rv. = rwe- I (2.21)
A positive skin factor therefore indicates that the well is
damaged or has solid deposition near the well face . A negative
value for the skin factor, on the other hand indicates that
permeability is higher near the well commonly due to sections of
oversized hole, removal of debris from permeable zones or
intersection of fractures .
13
3. APPLICATION TO WELL KJ-20 KRAFLA
3.1. Fall-off and Injection Tests
Well KJ-20 was drilled during June - August 1982 with directional
drilling (N 12.6 E) and cut fracture at 1270 meter depth.
A 13 3/8 " casing were set to 212.5 meter depth, 9 5/9 " casing
to 650 meter depth and completed with 7 " blind and slotted liner
from 596.20 meter (liner hanger) to 1762.7 meter. The total depth
of well KJ-20 was 1823 meter. This well was finished with a
completion test. The test were both fall-off test and injection
test.
Well completion procedure: Before starting the completion test,
pressure gauge was lowered into the well to certain depth with
water still pumped into the well at a rate of 25.76 l/s. The
first fall-off test started on the 20tb of August 1982 at 17:08
with initial pressure 15.24 bar at 200 meters depth and finished
after approximately 8 hours (484 minutes). Then followed by an
injection test which started on August 21, 1982 at 01:26 with
an injection rate of 30.86 lis. This test was carried out for
approximately 7 hours (431 minutes). A second fall-off test was
performed after the injection was stopped which lasted for about
93 minutes. These tests are illustrated 8S shown in Figure 1.
The aim of completion test: The aim of the completion test (fall
off and injection) is to reveal the condition or characteristics
of the well. These conditions or characteristics of the well
can be shown from calculation result i.e transmissivity,
formation storativity, wellbore storage and skin factor. The
result can indicate whether the well has a good or poor potential
and also if the well is damaged or stimulated.
Analysis: The completion test of well KJ-20 Krafla was analyzed
using Miler, Dykes and Hutchinson (MDH) method. This method
involves graphing the pressure during the test versus logarithm
of the time. For comparision type curve match were also used
for this test.
14
Fall-off test:
MDH method: Changes of pressure or declining pressure after
pumping was stopped are plotted versus logarithm of time as shown
in Figure 2. A straight line can be fitted to the data which
gives a slope m equal to 2.5 bar/cycle. From equation 2.11 the
transmissivity of well KJ-ZO can be calculated as follows:
equation 2.11:
P •• = PI -0.1832 ~ [log t + log ( ____ ~k~ __ ) + 0.3514 +
0.8686 sj
with the slope
k h
m = 0 . 1832 ~
k h
The injection rate prior to the fall - off test was 25.76 lIs
or 0.0257 m'/s.
The transmissivity : k h = 0.1832 -lL
~ m
k h = 0.1832 x 0.02576
~ 2.5 x 10-
1.89 X 10- 8 m3 /Pa.s
Type curve match: The changes of pressure (delta P) versus
changes of time (delta t) are plotted on log la, paper
(Figure 3). From type curve match for infinite acting reservoir
with skin and wellbore storage the following match points
were obtained:
CD = 1 E+05 p = 6.0 bar t = 47.5 minutes
s = - 5 t» = 4.0 X 10&
15
Then from equation 2.2 we have:
P. = 2 x k h P
q "
" 2 • P
transmissivity: k h = 0.02576 x 3
~ 2 x 6.0 X 10,
And from equation 2.3:
storativity: ~ Ct h = k h (-!'-' t.
M.P
= 2.05 x 10- 8 m3 /Pa.8
M.P
'" Ct h = 2.05 x 10-' x 47.5 x 60 = 1.12 x 10' m/Pa
0.012 x 4.0 x 10'
Injection test:
MDH method: The MDH plot is shown in Figure 4, and the straight
line gives a slope m = 3.6 bar/cycle. Followina the same
procedure as for the fall - off test :
m = 0.1832 ~
k h
and the injection rate during the test was 30.86 lis or
0.03086 m'/s.
16
Then the transmissivity is: k h
~
= 0.1832 -!L
m
k h = 0.1832 x 0.03086 = 1.57 x 10-' m'/Pa.s
3.6 x 10'
Type curve match: The changes of pressure (delta P) versus
the changes of time (delta t) during the injection test are
plotted on log log paper as shown in Figure 5. From type curve
match for infinite acting reservoir with skin and well bore
storage one obtains:
CD = 1E+05
s = - 5
P = 6.6 bar
PD = 3
t = 47 minutes
tD = 4.0 X 10&
with the same procedure as for the fall - off test using equation
2.2 and equation 2.3 one obtains:
transmissivity: k h
~
= LX> _) P M.P
k h
~
= 0.03086 x 3 = 2.23 X 10- 8 m3 /Pa.s
2 x x 6.6 X 105
and
storativity: ~ Ct h = k h (_t_)
t>
~ Ct h = 2.23 X 10- 8 x 47 x 60
4.0 x 10-
3.2. Build-up Test
M.P
= 1.3 x 10- 9 m/Pa
The production from well KJ-20, Krafla was initiated on
October 5, 1982 and continued for more than a year. A break
in electrical power generation from the Krafla Geothermal
Power Plant was planned beainnina from May to early September
17
1984 (Sigurdsson et al.,1985). Therefore well KJ-20 was shut
in on June 6,1984 and pressure build-up monitored.
Procedure: Before closing the well for build-up test, pressure
and temperature logs were made to determine the setting depth
for the pressure iauge to ensure the setting depth to be below
water level and the main feed point, see Figure 6 and Figure
7. This was done on June 1, 1984 and the well was shut in for
about one hour during each log and then put in production
again until June 6, 1982.
The aim of the teat: The aim of the build-up test was as for
the completion test to reveal the condition or characteristics
of the well after it had been producing for more than a year
and also to compare the results, with parameters determined
from the completion test. In this case Horner plot and type
curve matching method were used for determine reservoir para
meters.
Data: The pressure build-up data is tabulated in Table 1.
Because of lack of flowing pressure at the feed zone at the time
of shut-in, a wellbore simulator (Ambastha wellbore simulation
program) was used to simulate the flowing condition of the well
before shut-in with total flow rate as 10.6 k~/s and discharge
fluid enthalpy as 1929 kJ/kg at 11.7 bar well head pressure.
The wellbore simulation results are shown in table 2.
For well KJ-20 the discharge enthalpy exceeds the enthalpy of
water at the maximum reservoir temperature of 302.S·C (see Fi~ure
8) i.e: hw = 1382 kJ/kg. It is therefore assumed that two
phase fluid mixture enters the well and for evaluating the
reservoir parameters the mixture density is used.
Horner plot:
When the well was shut-in, the response of the bottom-hole
shut-in pressure can be expressed by using the prinsiple of
superposition in time. For a well producing at rate q until time
t, and at zero rate thereafter. The effect of this on pressure
18
build-up can be looked on as if an imaginary well located at
the same point started injecting with the same rate as the prior
production rate. Earlougher 1977 described that the pressure
at any time after shut-in as:
Pw. - PI = 2 m { PD (t t t.) )
From equation 2.9:
P. (t.) - s = t [ In t. + 0 . 80907 1
Assuming that the logarithmic approximation to the dimensionless
pressure solution applies, and the equation for the shut-in
pressure can be written as:
or
Where
Pw. - PI = m { log (t + t) - log
Pw f - PI = m [ log t + t]
t
m = - 0.1832 ~
k h
t 1
The static presBure during the build-up is plotted versus the
sum of production time and shut-
as shown in Figure 9. From
pressure can be found by
to log (t + t)/ t equal one .
logarithm of the time ratio (the
in time divided by shut-in time)
this graph the average reservoir
extrapolating the straight line
For well KJ-20 this pressure is
bar/cycle.
98 bar, for the slope m = 11.7
It is assumed that the fluid flow in the well is isoenthalpic
(the enthalpy of the fluid entering the well is equal to the
flowing enthal py
the steam tables)
at the surface). For that case one obtains (from
kJ/ki; r· = at 99 bara:
54.79 kg/m'; r· =
H. = 2726.5 kJ/kg;
690.15 kg/m'.
The mixture density is given by Grant et al.,1982
H. = 1403.2
19
_1_ = -lL + 1 - x
r, r· r· And
x = H.t --=--1!w H. - H.
Where: x = steam fraction; Ht = total discharge enthalpy, kJ/kg;
H. = steam enthalpy, kJ/kgj Hw = water enthalpy, kJjkg,
For our case
x = 1929 - 1403.2 = 0.3973
2726.5 - 1403.2
_1_ = 0.3973 + ( 1 - 0.3973)
r, 54.79 690.15
r, = 123.08 kg/m'
Flow rate before the well was shut-in was 10.6 kg/s which
corresponds to (10.6)/(123.08) = 0.086 mats, and with the
slope m = 11.7 bar/cycle.
k h = 0.1832 ~ = 0.1832 x 0.086
ID 11.7 x 10'
k h = 1.35 X 10- 8 m3 /P •. 8
~
Type curve match:
From the type curve match shown in Figure 10, for infinite
reservoir with skin and wellbore storage the following is
obtained at the match point:
CD = lE+05
s = -5
to = 2.0 x 10 1
PD = 3.8
t = 3.0 X 10 2 hra
p = 64 bars
Based on equations 2.2 and 2.3 and following the same procedure
as for the completion test one obtains:
20
Transmissivity: k h :::: ~ (~D) :::: 0.1832 x 3.8
Storativity
2 " p 2 x 64 x 10 5
k h :::: 0.832 x 10- 8 m'/P •• B
~
~ c. h = ~ ( t) rw :::: 0.1095 m
jJ rw"' tD
~ et h :::: 0.832 x 10- ' x 3.0 x lOa X 3600
0.012 X 2.0 X 10'
o Ct h:::: 3.744 X 10-- m/P.
3 . 3. Analysis and Result of Well Tests
The completion test both the injection and fall-off test indicate
that well KJ-ZO, Krafla is connected to a high conductivity
fracture.
This indication can be observed in the early time data on the
10' log plot of delta P versus delta t (10, la, strai,ht line
of half slope), see Figure 11.
The injection test in Figure 11 shows oscilation at a certain
point, which in this case may be caused of reservoir behaviour
(ioe temperature effect). Homogeneous behaviour can also been
seen in the log log shape durin, the completion test, which
corresponds to an in f inite acting behavior.
From the completion test it is very difficult to determine or
to predict the nature of the outer boundary from the late
time data, because of the short duration of the test.
The magnitute of transmissivity from the fall-off test is
2.36 x 10- 1 m3/Pa.s and f r om the injection test 1.57 x 10- 1
21
m'/P •. s usina MDH method and the ma.nitute of transmissivity
from the pressure build up test is 1.35 x 10- 8 m3/Pa.S using
Horner plot which is not very different from the former two.
The formation storativity of the pressure build-up test is
approximately ten times .rester than from the completion
t e st, which in this case indicates the presence of more
compressible two phase fluid in the reservoir at the time of
the build-up test.
22
4. SIMULATION ON WELL KJ-20 KRAFLA
4.1. Conceptual Model
In order to simulate the reservoir behaviour in the vicinity
of well KJ-20 Krafla a simple conceptual model was made. The
model is based on geological, production output and reservoir
parameters from the Krafla area (Sudurhlidar). An aerial overview
of the Krafla Geothermal field and the l ocation of well KJ-20
can be seen in Figure 12. Based on the conceptual model and the
output potential of well KJ-20 and its surrounding wells, the
simplified three dimensonal reservoir model, and the South -
North section used in the simulation were made as shown in Figure
13 and 14 respectively. Different boundary conditions were used
in order to give some ideas about the possible reservoir
behaviour that may occur in the future. Two cases were selected
as follow:
Closed boundary:,
To simulate the reservoir behaviour in the vicinity of well
KJ - 20, Krafla, a drainage area of fixed shape was selected. The
shape of the drainage area was selected in accordance with
the ratio of the today output potential for the neiahbourina
production wells at the Sudurhlidar Field. These neighbourina
wells confine the boundaries of the drainage area to the East,
South and West. To the North an existing East-West fracture marks
the northern boundaries for the drainage area. This model has
an area of 0.124 km2• The drainage volume is made up of 200 meter
thick caprock, and a 2000 meter thick reservoir rock. For this
case all the boundaries were taken as closed boundaries.
The reservoir domain is divided into four layers each 500 meter
thick. Circular elements with 50 meter radius are imbedded in
the cent er layers of the reservoir domain. Furthermore the lower
circular element encloses another circular element with 10 meter
radius and the sink is emplaced in it. The model for the
simulation study in this case consists therefore of three
materials for the three domains including atmosphere. They are
23
divided into 9 elements varying in size from 1.0 x 10' ma to
1.0 x 10 20 m3 with 13 interface connections between them.
The initial conditions for this case are described in section
4.2.
Open boundary:
This model is the same as for the closed boundary case, but the
north boundary is now open and connects to a fracture which
is further open to a large reservoir element to the north. This
model therefore, consists of 4 materials for the various
reservoir domains. They are divided into 16 elements varying
in size and volume from 1 x 10' .' to 1 x 1030 mS with 32
interface connections between elements. The initial temperature
and pressure conditions of the large reservoir element used
in this study were put as 320 ' e and 114 bar. respectively.
4.2 . Numerical Siaulation
To run the simulation some assumptions were made as:
1. All of the material for the various reservoir domains is
assumed to have the same value for rock density and porosity.
2. The caprock thickness is assumed 200 m and reservoir thickness
is assumed 2000 m divided into 4 layers with the same
thickness (500 m).
3. Relative permeability in fractured media were assumed to
be linear functions of vapour saturation.
4 . No recharge is from the basement to the system.
5. Constant conditions are kept at the surface.
24
Data for the nu.erical ai.ulation.
1. Total production of well KJ - 20 is 10.6 kg/s, based on
measurement of the well output before shut-in with well
head pressure 11.7 bar gauge and total discharge fluid
entha1py 1929 kJ/kg.
2. The values used for rock density and porosity are 2650 ka/m3
and 5% (Bodvarsson et al., 1982) and are assumed the same
for all of the zones.
3. The initial conditions for pressure and temperature were taken
from average pressure and temperature profiles in the Krafla
field (Sudurhlidar). The values used correspond to the depth
to the center of each layer and it assumed that initially
there is no boiling in the reservoir. Then the initial
pressure and temperature conditions for the sink at 1350 meter
depth are 114 bar and 320 · C (Bodvarsson et al., 1982).
4. Permeability was taken from the result of the injection test
analysis (Bodvarsson et al., 1982),i.e: 2.0 x 10-15 ma,
and it assumed that horizontal and vertical permeability
are the same. This value is only valid for the reservoir
domains. For the caprock permeability was estimated 2.0 x
10- 18 ma, this value was used for both horizontal and
vertical directions.
Permeability of the fracture was guessed as 2.0 x 10-14 ma
in the horizontal direction and 1.0 x 10- 14 ma in the
vertical direction. The guessed values for the fracture
permeability were su.gested by Omar Sigurds8on.
5. The values of irreducible liquid saturation, irreducible
vapour saturation and perfectly mobile vapour saturation were
taken from Bodvarsson et al., 1982 i.e: 35% , 5% and 65%
respectively.
25
6. Thermal conductivity of caprock is 1.5 J/m,s, ' C and 1.7
J/m.8 ,' C for fracture and reservoir rocks (Bodvarsson et
al.,1982).
7. Heat capacity of all materials for the various reservoir
domains were taken as: 1000 J/kg · C (BodvarsBon et al., 1982).
In these simulation studies, the computer program SHAFT 79
from the Lawrence Berkeley Laboratory, University of
California (K. Pruess and R:C Schoeder, 1980) was used to
simulate the reservoir behaviour of the drainage volume
for well KJ-20 , Krafla i.e: pressure, temperature, vapour
saturation and discharge enthalpy. The simulation processing
was done on the VAX 11-750, VAX/VMS 4.2 computer, installed
at the National Energy Authority in Reykjavik, Iceland.
4.3. Result of Simulation
The chan.es in some of the reservoir parameters during the
simulation studies of well KJ-20 Krafla for both the closed
boundary and the open boundary cases are summarized in Figure
15 to Figure 22.
Closed Boundary
Pressure and temperature in the outer elements seem to decrease
slowly and vapour saturation inc reases gradually with time
but in the sink element pressure and temperature quickly drop
within the first few months of production and continue to
decrease drastically with time. From the initiation of production
in the s ink element, vapour saturation falls rapidly and
fluctuates up to a period of 1 year. This is due to encroachment
of fluids from outer element into sink element at the initiation
of production.
Vapour saturation and enthalpy behaviour in the sink element
remains constant from the fourth year until the eighth year.
This is because boiling is depressed in the sink element due
26
to increasing flow of cooler fluid from the layer above, and
decreasing of lateral fluid flow from the surrounding,
The vapour saturation for both outer element and sink element
representing well KJ-20 Krafla reaches a maximum value (100%)
in 8.3 years, see Figure 17. At that time the pressure in the
sink element has dropped to 3.62 bar as shown in Figure 15,
and well KJ-20 is depleted.
Open Boundary
The simulation results for the open boundary case are
characterized by slowly decreasing pressure and temperature
in the outer element which continuous until the end of simul
ation. Maximum pressure drop in the outer element from the
beginning to the end of simulation is 28 bar and maximum
temperature drop is 21·C. In the sink element both pressure
and temperature rapidly drop from the beginning to the end of
simulation.
From Fi~ure 21 vapour saturation in the outer element reaches
a maximum value of 80.17% but vapour saturation in the sink
element reaches a maximum value of 100% in 13 years. When the
vapour saturation in the sink element has reached 100% the
pressure quickly drops as well KJ-20 is depleted, as shown in
Fi.ure 19.
4.4. Discussion
In the simple mode l used in this simulation studies, the sink
element was embedded within a larger circular element, which
in the open boundary case had a small common interface with the
fracture, Actually from drilling reports for well KJ -20, Krafla,
the well intersects fracture at 1270 m depth. If the sink element
would have been placed interface with the fracture or in the
fracture itself the result would most likely indicate a longer
depletion time for well KJ-20 than the present study gives.
27
From the initiation of production in the sink element for both
the closed and the open boundar y case the pressure and
temperature drop rapidly. This is because the model used in the
simulation study is very coarse, especially for the open boundary
case where the large reservoir to the north is simulated by one
element. These pressure and temperature behavior would be
smoother if the large reservoir element in the north would be
divided into layers like for the main drainaie volume.
4.5. Conclusion
The results of the simulation study indicate that well KJ-20
in the Krafla Geothermal Field has a depletion time of 8
years for the closed boundary case and 13 years for the open
boundary case under the condition of no recharge from the
basement to the production element, 5% porosity (BodvarsBon
et al., 1982), and a 500 meter thick production zone.
The simulation study gives also information or ideas about the
reponses for well KJ-20 in the Krafla Geothermal Field
(Sudurhlidar) that may occur in the future.
28
ACKNOWLEDGEMENT
I would like to convey my deep gratitude to Mr. Omar Sigurdsson
for his diligent supervision and guidance in the specialized
training, the National Energy Authority of Iceland for releasing
the data from the Krafla Geothermal Field (well KJ-20), Mr. Jen
Steinar GuOmundsson the Director of United Nations University
Geothermal Trainina Programme for his excellent organization
of the 1986 training session.
Special thanks are due to the PERTAMINA management for granting
me si x months leave of absence to pursue this valuable trainin,.
29
REFERENCBS
1. Abaneth Wale (1985): Reservoir Engineering Study of The Krafla
- Hv i tholar Geothermal Area, Iceland., Report 1985.
2. Asgrimur Gudmundsson, Benedikt Steingrimsson, Gudjon
Gudmundsson, Gudmundur O. FreidleifssoD, Hilmar Sigvaldsson,
Omar Siaurdsson, Steinar P. Gudlauasson and Valgardur Stefansson
(1983) : Krafla Well KJ-20 Report; val 1 - 4, in Iceland.,
Desember 1982 - February 1983.
3.Charles B. Haukwa (1985): Analysis of Well Test Data in The
Olkaria West Geothermal Field Kenya" Report 1985.
4. Gudmundur S. Bodvarsson and Sally M. BensoD, Omar Sigurdsson
and Vol~ardur Stefansson, Einar T. E1i8880n (1984): The Krafla
Geothermal Field, Iceland val 1 - 4., Water Resources Research.,
Novenber 1984.
5. H. J. Ramey. Jr: Reservoir Engineering Assessment of
Geothermal System, Department of Petroleum Engineering Stanford
University.,1981.
6. Jaime Ortiz - Ramizes (1983); Two Phase Flow in Geothermal
Wells: Development and Uses of a Computer Code., June 1983.
7. Kjaran S.P and Elliason J. (1983): Geothermal Reservoir
Engineering Lecture notes UNU, Iceland.
8. K. Pruess and R.C Schroeder (1980): SHAFT 79 User's Manual,
Lawrence Berkely Laboratory University of California Berkely,
California 94720., March 1980.
9. Malcom A. Grant, Tony Donaldson, Paul F. Bixley (1982):
Geothermal Reservoir Eniineering.,1982.
10 . Omar Sigurdsson, Benedikt S. SteingrimsBon and SteffansBon
(1985): Pressure Build Up Monitoring of The Krafla Geothermal
30
Field, Iceland, Tenth Workshop on Geothermal Reservoir
Engineering Standford University, January 22 - 24., 1985.
11. Pratomo Harry (1979): Build Up Test Analysis of Niawha and
Kamojang Wells, report., November 1979.
12. R.A. Dawe and D.e. Wilson (1985): Development in Petroleum
Engineering - 1., 1985.
13. Robert C. Harlouger. Jr (1977): Advances in Well Test
Analysis. J t977.
14. Sulaiman Syafei (1982): Kawah Kamojang Reservoir Simulation,
report., November 1982.
31
Table 1: Pressure build up data for well KJ - 20
Date Time Pressure Depth Temperature Flowrate bar m ·c lIs
840606 111 2 ----- ------ 268.70 13.80
840606 1230 43.50 1300.00 268.70 0.00
840606 1655 56.54 1300.00 268.70 0.00
840607 1850 66.50 1300.00 268.70 0.00
840608 1120 69.44 1300.00 268.70 0.00
840613 1105 76.43 1300.00 294.40 0.00
840621 0132 79.84 1300.00 294.90 0.00
840715 1123 84.54 1300.00 299.90 0.00
840809 1734 86.83 1300.00 299.90 0.00
32
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33 20'~ ____________________________________________________________ -.
Well J(J-20
15
10
c '"
5
,.
0+----.----,----,-----,----,----r----,----,----.----,~
TiMe (Minute)
Figure 1 Fall - off and injection test in well KJ - 20, Krafla.
34
dt iminutes)
Figure 2 Semi log plot of fall-off test in well KJ-20, Rrafls .
. ',---,-------,--- ,--------,
.. '\-- ------1I----- --j--- -t;;-;:-;--c-;-;-;;;-;= It., . • •.• • 11' " . 1 • • I.'
' '', •. n .' .1. I.'" .•.•••. e. · ,.... . .. • ? . r. :!;:: .
' . 01 . I. "' •• f • • • •
• , ••• U '~I . • "f, " ., I ,
1." • , ..... " ,
"'i--r--==:=+=====ll V V- _\.~
7~------_7.------_7 .. ,------_7.,------~.
Figure 3
lit (minute.s )
Type curve matching with fall-off test in well KJ-20, Rrafls .
Figure 4
35
At (m inu tes)
Semilog plot of injection teat in well KJ - 20, Krafla.
, ... r-------r-------.------,----~
··I~t=~-:::;:;;;;=-~~ ",I •••.• • 't" •• h • I.' I." . . " .,., •• , . ...... .
=:~-;: v.· ··~· \'!'~P .. t ;':;; ':';~:: • • • o. ~ '.n. ,.-. ,' '', ..
'" ··U'~I . • •• • ' I .,' , ,.' . \' -.. , ..
.. f------+------+-- ---l-----
,." L,---------'.c. --------'.,.-- - -----,L,..-'-------.J, ..
Figure 5
Cl! (minutes)
Type curve matching with injection test in well KJ-20, Krafla.
'" ~ ..!I " S d
,~
od ~
'" " 0
36
o ~--~-------------------------------------
- 200
- 400
-600
-800
- 1000
- 1200
-1400
- 1600
- 1800
-2000 +-------.-------r------.-------,-------r------~ 20 30
Figure 6
40 50 Pressure in bars
60 70 80
Pressure log before well KJ-20, Krafla was shut - in.
~ ~ ~ ~
~ e ~
.~
.Q ~
"-~
Q
37
0,---------------------------________________ ___
-200
-400
- 600
- 800
-1000
- 1200
- 1400
- 1600
- 1800 + ________ .-______ -r ________ r-______ ,, ___ '_~ ___ JI -2000
240 250
Figure 7
260 270 280 290 Temperature in celcius
Temperature log before well KJ-20,' Krafla was shut - in.
38
0,--------------------------------------------------,
-200
-400
- 600
" - 800 ... oS ~
S d - 1000 .~
.d .. Cl.
-1200 ~ Q
-1400
-1600
- 1600
-2000 +-------,-------,--------.-------r-------r------~ 200 220 240 260 260 300 320
Temperature in celcius
Figure 8 Static temperature log in well KJ - 20, Krafla.
39
Figure 9: Horner plot for well KJ-20, Krafla .
.. i------+------j------t.;;;-;-;:;-;w;;:;:-:-c:;-i " . 1 ••• •• • '0'1'01 • • • . • ,,,, ..•••• " ,.rI . . ..... . e. " .· .. . . _ • ........... I~. I . ....... 10' · • , . I''' ' •. , •. .•
• • Lb. ' -l.11, • , .. " .. , . .. ,,' • 11-' " ' ,
.. I---~I-----II-----II-------I
.. '-----!r------,~--____;s__--~ -;: .. ' 00'
Figure 10
lit [hours)
Type curve matching with build-up test in well KJ-20, Krafla.
40
",,"clioft 1nl
,,' L------+-------r----:-:-:~-_t_;:~_:::;_--___j I hn.tt I •• r
/' '.
Figure 11
... ...
• .' At !miMeS)
Log log plot of fall-off and injection tests in well KJ-20, Kraf l a.
HOLUR SEM SOFNUOU GASI
SUMARIO 1984
N
Cl) ;
~, .
41
-'
+
, $KYRINGAR
/"":) Sprengl9'gur
-;'--MiSgel'lQi
_- GossPN'l9"
i ........ j , \ ,~
, iut mQbltfg Ira Iokum $100;1$10 jO klllskeib, ('0 12.000 g'ol
r" I } Holur. sem sofnuC,u gosi 1984 'J
:I~
MYND6
Figure 12: An aerial overview of the Krafla field and the location of well KJ - 20.
42
~===~,-,.. fracture
impermeable
boundar y
~1odel used f o r simu l a 1:.)on .
43
close boundary
reservoir
sink element
A
~ open boundary
t"""'" ' -""""'''';
Figure 14
.,"'" -,--~ , , " , , ".:: - - - --
reservoir : ~ r eservoir I I/,
u, ~ " ' " B sink element fl"~C~'
The South - North section of the simulation model. A. Closed boundary i B. Open boundary toward North.
44
120
80
~ ~
'" .0
9 60 v a ~ ~ v ~
'"
r\ .~
.~ IS-.:.
"'" ~ .~
f'\
\ ~ I'
"
100
40
'\ 20
o o 1 2 3 4 5 6 7 8 9 10
Year o Outer Element + Sink Element
Figure 15 Pressure behaviour for the closed boundary case.
350
325
'\
300 00 ~ ,~
~ ~
~ 0
,8 ~
275 ~ ~ ." ~ ~ ~
'" S ~ 250 ...
225
200 o J
Figure 16
--~,
2 3
45
\ ~~
4
"
5 Year
~ ['I;, \
6 7 8
o Outer Element + Sink Element
\
--.j 9 10
Temperature behaviour for the closed boundary case,
100
90
80
70
:B 60
~ .~
~ 50 0
:;l ~ ~ 0 40 ~
~ f/)
30 ~ ~
20
/
j 10
o o
Figure 17
46
/ d'
/ /'
.I' ~
; H-t- J
if I!
/ r! VI [l
1 2 3 4 5 6 7 8 9 Year
o Outer Element + Sink Element
Vapour saturati on behaviour for the c l osed boundary c ase .
10
47
3000
2750
2500
~
'" ~ "'- 2250 i;! ~
r ~ .~
>-
'" 2000 ~
" :!3 c '"
1750
/ ~
I \ /
1500
1250 o 1 2 3 4 5 6 7 8 9 10
Year o Sink Element
Figure 1 8 Entha l py behaviour for the closed boundary case.
48
120
~ ""
80
~ ~ ~ .0
100 t ~ fl-
T
~ .,.
~ --~
<I .~
60 ~ ~ ~ ~ ~ ~ ~
'" 40
~
~ ~
'" f\ , 20
o o 3 6 9 12 15
Year <> Outer Element + Sink Element
Figure 19 Pressure behaviour for the open boundary case.
49
320
It '" "'-
~ 300 ~
260 m ;; .~
" ~ ~ " C
.~
~ 260
~~ "..
~ ;; .. " ~ ~
"" E ~ 240
'""'
1\ 220
,. 200
o 3 6 9 12 15 Year
o Outer Element + Sink Element
Figure 20 Temperature behaviour for the open boundary cas e .
100
60
!J d 60 ~ ~ ... ~
'" .9 d 0
:;:l ~ 40 ...
A :l ~ Ul
20
o o
Figure 21
50
lA / J
I
3 6 9 12 15 Year
<> Outer Elemen t + Sin k Element
Vapour saturation behav iour for the open boundary case.
51
3000
~
2600
~...I-¥I' /
..vi'
~
'" .. "'-~ ~
<I 2200 .~
,.., ... -• :S I1 d
'"
1800 I
1400 o 3 6 9 12 15
Year + Sink Element
Fi ture 22 Enthalpy behaviour for the open boundary case.
top related