DECLINE CUMULATIVE PRODUCTION ANALYSIS (DCPA) – ALGORITHM, FOR GEOTHERMAL FIEL

GEOTHERMAL FIELD

Listiana Satiawati1*)_{, Djoko Sulistyanto}2)_{, Kris Pudyastuti}3)

1* 2 3)_{Program Studi Teknik Perminyakan Fakultas Kebumian dan Energi Universitas}

Trisakti, Jakarta 11440

*)_{e-mail: listianasatiawati@yahoo.com}

Abstract

Forecasting of geothermal production decline is one of the main tasks in reservoir engineering, in order to manage the reservoir and maintain the sustainability of the resource utilization. Studies on the analysis of production decline in geothermal fields have been widely implemented, one of which is the DCPA conducted by H.A. Davila J. (Davila,2017), and applied in Kamojang geothermal field - West Java Indonesia. DCPA 'Davila' in Kamojang (steam dominated) geothermal field, appears to be more accurate than previous studies. This study is to support the DCPA by creating a computer program (algorithm and numeric calculation written in Fortran90/95 programming languages (Imam,2009) (Tanja,2005)), thus it can expected to speed up the data matching process or the analysis process.

Keywords: Steady state, Decline cumulative production analysis, Steam dominated, Liquid dominated, Geothermal field, Algorithm, Fortran

Introduction

In order to improve the economicsof a field (hydrocarbons or geothermal), it is necessary to implement the reservoir management; part ofthat is an optimum reinjection design. The beginningof an optimum reinjection design is a declinecumulativeproductionanalysis (DCPA) .The applicationof DCPA can be used to predict a cumulativeproductiondecline in a well.

Departed from DCPA’sDavilawhoreportedthattherewas a good match between DCPA and production rate measurements at the KMJ-11 well. The well is completed in the waterdominatedreservoir and mostlyproduce 100% steam (S. Sudarman, et.al., 1995). Thisstudyaimed at making the DCPA algorithmusingprograminglanguage. It is expectedthatthisstudywill be continued at a later stageofmaking DCPA software.

Fig. 1 shows the flow rate forecastingwith the DCPA’sDavilamethod (red line) plotveryclosewith the production rate data (red cycle), the stochastic and exponentialarerepresented by green and brownlinerespectivelydiverging from the data KMJ-11.

DeclineCumulativeProductionAnalysis (DCPA)

Analysis to predict the declineofproduction by using Decline Cumulative Production Analysis (DCPA) method has beendone by several researcher ; oneofthem is Davila (2017).

Figure 1: Production rate forecast KMJ 11(Davila,2017).

Mathematical Model

A formula to forecast the geothermal production has been developed base on the linear relationship of decline cumulative production versus cumulative production and decline cumulative production versus production time charts (Afken,2005) (Boas,2006) (Kreyszig,2011). The analysis is taken under steady state condition (Davila,2017).

Derivation of cumulative production (Q) is,

(1)

q is the production rate.

The decline cumulative production (QD) is,

(2)

The linear relationship of QDand Q is,

(3)

so (4)

The linear relationship of QDand t (time) is,

(5)

so (6)

(8)

(9)

Eq. (9) is the production rate-time equation,

where (10)

is initial rate,

and (11)

is time decline exponent. The flow rate is

(12)

and the natural logarithm is,

(13)

is the slope in flow rate versus time.

The algorithms, sequences or steps to calculate qi, , and q and to plot production rate versus time as follow,

read q and t data

calculate Q, ln(Q),

q/Q, ln(q/Q) and ln(t)

write ln(Q), ln(q/Q)

and ln(t) data

finish

start

Figure 2: The flowchartof the algorithmof DCPA

Procedure (steps of the study):

The data used for DCPA is Kamojang field (steam dominated type of reservoir), i.e. production rate of KMJ-11 well (Sri,2011) is:

start

read ln(Q), ln(q/Q)

and ln(t) data

drawing ln(q/Q) vs ln(Q)

chart

drawing ln(q/Q) vs ln (t)

chart

get a

0

and a

1

constants

get b

0

and b

1

constants

write a

0

, a

1

, b

0

and b

1

finish

start

read t, a

0

, a

1

, b

0

and b

1

data

calculate q

i

, , q and q

d

drawing q vs t and q

d

vs t charts

result

finish

Excel

Month ton/hour

From the natural logarithm of QD and Q chart (Figure 3) we can determine the a0 and a1

constants, and from the natural logarithm of QDand t chart (Figure 4) we can determine

the b0and b1constants.

Decline cumulative production analysis ,

KMJ 11 Well, Jan.-Oct. 1996

Figure 3: Natural logarithm of decline cumulative production (QD) and cumulative

y = -1.0191x - 3E-05 R² = 0.99999

-2.5 -2 -1.5 -1 -0.5 0

0 0.5 1 1.5 2 2.5

ln (q/Q)

ln (t)

Decline cumulative production analysis,

KMJ-11 Well, Jan. - Oct. 1996

Figure 4: Natural logarithm of decline cumulative production (QD) and production time

(t).

Substitution a0, a1, b0, and b1to Eqn. (10) and (11), to calculate initial rate (Qi) and decline

exponent , and then we get the production rate – time equation:

ton/hour.

The Result

The DCPA algorithm has been written and executed. Plotting the calculated production rate versus time has been done. Figure 5 shows the decline production curve obtained with the DCPA (blue line) plot very close the production rate data KMJ-11 well (yellow square).

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Figure 5: Matching curve between the DCPA (calculated) and the decline production (measurement data) of KMJ-11 Well, and production rate forecast KMJ 11 Well, Kamojang

Geothermal Field, West Jawa, Indonesia

Conclusion

The DCPA algorithm has been made in this research, with the possibility to use as a toll for production forecasting for the dominated steam as well as the liquid dominated of geothermal wells.

It is expected that the following research can be continued by using the recent data measurement of KMJ 11, and other wells in Kamojang Geothermal Field; before continuing in applying the DPCA in Liquid Dominated wells.

Reference

H.A. Davilla Jose, 2017, Applying Decline Cumulative Production Analysis (DCPA) to Geothermal Resources,Proceedings, 42nd _{Workshop on Geothermal Reservoir Engineering,}

Stanford University, Stanford, California. SGP-TR-212.

Erwin Kreyszig, 2011,Advanced Engineering Mathematics, John Willey & Sons, inc., USA.

George B. Arfken, 2005, Mathematical Methods for Physicists, sixth ed., Elsevier Academic Press.

Imam Fachruddin, 2010,Pengantar Fortran 90, DepartemenFisika, Universitas Indonesia.

SayogiSudarman, M. Boedihardi, Kris Pudyastuti, Bardan, 1995, Kamojang Geothermal Field 10 Year Operation Experience. World Geothermal Congress, Florence, 1995.