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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
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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.SC (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 21C. 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

    dlh T\II rIP (flrh...,

    "l"IIt MTA AS nul*':

    !MIlt g;AVm , .... TG1 111. )lASS tLQI.'fI1![ ,lMII ~ U(J.~ I(U TlN!SI' CDr,.~!uII/~ &,O~I)/J

    ., III IlElll(AD ,

    .EtlM,FT O.O~ rtt!~.tl" 1I4.l'O llKr1AAltllt,' m,rT

    rIf[ t'N(UI 11$(' as fOlltN:

    , .. 1.0 rT " 1,.....&.1 n. till ~Tlt!lr[t ITIJ ..r.9." ' ,1M2 ' .reS& t.lZI, 0.50\51 11. UI1 7l ,r.>6! ,

    170.&. TU.59 315." 1!t.2t 0.711" O.01.'l:i 0.411} Mm "Q '.4In 71.1;00 .. ",." "'.n Pi,.' '1\1.2t 1,71" O.Cffi e .I~I' Mm IIM Mm 7um 0 lU.1O In,,. m.02 '''',11 1,71 t.oo:;, Mm c '.:;IoU , ... t. l tt2 n,Utt m.se "0.11 m,~ 127.:'0 1.7114 '.MS' 0.1122 Mm 11. 1.1..01 71,t!. '11," UI.:U 171.01 '1\1.10 "ml 0.0052 0.4171 MID ". 0.4211 It .4'02 mole 17MI m.SI ';!f.1O I.m. um 0.1210 I.me UI.II' . uu -7Ul?6 " lotO UP] m,Of m.le 0.1160 o.ma t,ms "m, ". Mnl 70.(m 11/,70 nUl 17".0 '..,.10 I,m, o.ooso 0,1~42 Mm IU~ 0.11:" u. nil 0 15]," '''.10 310,Of m.le t .lm f,O", I,me MUI 1t.1II! I,mo ",~I nl.n U1.:t 3:!M' ':>f.ZO '.7701 '.001' ' . I:!'"A Mm ,,~ 1.lm n.1041 ,

    Im .60 Ita." l8I.O'I ' 1'.10 G.7U3 o.om o.ms Mm ". Mm a ,6Sst E 110 .... ," ,11 JRI-5I' m.zo '.7641 uw 0.1211 Mm , ... 0,4241 61.ma ." UU.ZO ,.. .. ltU, 11'.:'0 O.I~ 12 1.0041 t.l2U 0.:;&01 '''' I.nu 61.?ln "-un,so 1'11." m,SI m,zo t.ml '.iI'I" I ,ml Mm "" o, lr. 61.]714 Ill .... tt l .t1 HM' ." . 0 ,7~1 O.H~ O,I)~' o.~ 11. 0.11"...8 IUS!S < .. mot , 10 lOl ,ll 18'.~ ,n.:o 0.1'171 . cm O. l lIt "nu "" Im U.5J1! 0 15]j.1t 20M2 HI,a. 12t," I,rnt '.OO~I a.1ll1 M~fJ IWI G.IW u.tm "" 1&]0,11 ~." lIl.1t m,:'O '.Xl' 1,0')11 '.ll1S ~ta I '.'" . m! 15.1192 170..00 201.S1 H..,e 12'9.20 1,1515 1.00ll . ~m Mm ,., I.lm Is.ml 17f1.30 10M3 lIS"1 m,to I,m! o.om "m! M'>!I IlAiI ',12110 "."~J 1116.60 210,21 la . ,. tlt.10 o.ml um o.tl ., o.sm ". 0,1:'85 U.~4R7 ~ ItU ,tO m.JI !1~," ,n,1O . 11SO '.e041 0,4405 Mm lUll ',4~A' 44 . I6~l 201/,tt m,,, m.3t m,2' 2,0300 '.om 0.1970 I,m! m! 0,7110 !o~ .m' lIlMO m .ll ... n m.:o 1 .1If~ I,C111 o,:SeJ< 1I.5:U1 ~!51 . ms 1~1 . m1 221 /.10 218./1 H9,]] '2Mt 1,'602 "om MO'I I M~ NISI 101110 102.111' '" 2301,1' 211022 l'1O,2f m.tt I.UOI Mm ..,152 ..,:;51 ml I.m~ 101.117] 2l11,~ 223," 111.21 r.t.lt I,ml um '.5210 Mm ..sf t.m. 11)0.]501 , 241J.7I 271.0. m." m,~ t.taU "O~ t.S:iO .. ",. ~Is! O. im ",2~:' ~ 2S~t," 22'. U 111.04 t2f.;t I .n&l t.Ol" Ml:'t .sm ~m ,./It, n.m' 2411 , )1 uo." JfJ ." "' .~ , .... t .ml e."" t.sm ~nT t.illl ".tlU mM' m.2t 19U2 m , tt I m o.ollfJ M~I t.ml "151 '.712' r.;em ltll,,. :.n.1O m.lI ':'9,:'0 I ,mo Mltl ' .S11O Mm IIm t,1241 'I.ml 2f~.2t m,,. ",",0 m,2t 1.1l1I Mill 0.:; ....... M'm '''' '.m3 'MOO! ,.., . " . It :no1.I' "'.~ '"14" 0.0111 Mm t.l~, l~oUI t.;'" '2.;!zt ' Oi .... m.12 lt~.'1 ..,. ~o l.om '.0192 . ml M I" I~III! ', I:OU ".uu 11:'4.'0 m,1t m ,Il ,,,'.10 2.1111 Mm "':'Cl t,:". I~M' I.m' ".ms ' 211,10 111.1

  • 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

    ~ .,.

    ~ --~

  • 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'

    ~

    '" .. "'-~ ~