# Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration

Alamta Singarimbun, Yasuhiro Fujimitsu, Mitra Djamal, Rezkia Dewi Andajani

Research output: Chapter in Book/Report/Conference proceedingConference contribution

### Abstract

Exploitation of geothermal resource results the decrease of fluid pressure in geothermal reservoir. In production process, the analysis of reservoir condition is made by observing the pressure state. When the fluid is pumped into the reservoir, the value of pressure varies with time which is called as transient state. The plot of pressure versus time will create a curve with a certain slope. From the graph of the pressure the reservoir condition can be analyzed. The solution of the pressure transient is identified as exponential integral equation Ei(x). When the input to the function is really small for example at x < 0.01, the equation will form an asymptotic curve. Analytical solution involves logarithm natural and Euler constant (γ). In this paper we try to approach the solution of exponential integral equation by numerical integration. The objective of this study is to make a numerical model of the pressure change in a geothermal reservoir and to compare the result between numerical method and analytic. There are two methods used in this study, first is Picard- McLaurin iteration to solve the ordinary differential equations (ODE), and the second is trapezoidal integration to calculate the function of Ei(x). The modeling shows that the result of the calculation with the numerical method matched with the analytic with the range of error between 0.0008 to 4.5 % for drawdown test and 0.19 to 7.7 % for buildup test.

Original language English Advanced Materials, Structures and Mechanical Engineering H.M. Song, H.K. Son, Jong Wan Hu Trans Tech Publications Ltd 959-973 15 9783038352549 https://doi.org/10.4028/www.scientific.net/AMR.1025-1026.959 Published - Jan 1 2014 2014 International Conference on Advanced Materials, Structures and Mechanical Engineering, ICAMSME 2014 - Incheon, Korea, Republic ofDuration: May 3 2014 → May 4 2014

### Publication series

Name Advanced Materials Research 1025-1026 1022-6680 1662-8985

### Other

Other 2014 International Conference on Advanced Materials, Structures and Mechanical Engineering, ICAMSME 2014 Korea, Republic of Incheon 5/3/14 → 5/4/14

### Fingerprint

Integral equations
Numerical methods
Fluids
Ordinary differential equations
Numerical models

### All Science Journal Classification (ASJC) codes

• Engineering(all)

### Cite this

Singarimbun, A., Fujimitsu, Y., Djamal, M., & Andajani, R. D. (2014). Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration. In H. M. Song, H. K. Son, & J. W. Hu (Eds.), Advanced Materials, Structures and Mechanical Engineering (pp. 959-973). (Advanced Materials Research; Vol. 1025-1026). Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/AMR.1025-1026.959

Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration. / Singarimbun, Alamta; Fujimitsu, Yasuhiro; Djamal, Mitra; Andajani, Rezkia Dewi.

Advanced Materials, Structures and Mechanical Engineering. ed. / H.M. Song; H.K. Son; Jong Wan Hu. Trans Tech Publications Ltd, 2014. p. 959-973 (Advanced Materials Research; Vol. 1025-1026).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Singarimbun, A, Fujimitsu, Y, Djamal, M & Andajani, RD 2014, Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration. in HM Song, HK Son & JW Hu (eds), Advanced Materials, Structures and Mechanical Engineering. Advanced Materials Research, vol. 1025-1026, Trans Tech Publications Ltd, pp. 959-973, 2014 International Conference on Advanced Materials, Structures and Mechanical Engineering, ICAMSME 2014, Incheon, Korea, Republic of, 5/3/14. https://doi.org/10.4028/www.scientific.net/AMR.1025-1026.959
Singarimbun A, Fujimitsu Y, Djamal M, Andajani RD. Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration. In Song HM, Son HK, Hu JW, editors, Advanced Materials, Structures and Mechanical Engineering. Trans Tech Publications Ltd. 2014. p. 959-973. (Advanced Materials Research). https://doi.org/10.4028/www.scientific.net/AMR.1025-1026.959
Singarimbun, Alamta ; Fujimitsu, Yasuhiro ; Djamal, Mitra ; Andajani, Rezkia Dewi. / Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration. Advanced Materials, Structures and Mechanical Engineering. editor / H.M. Song ; H.K. Son ; Jong Wan Hu. Trans Tech Publications Ltd, 2014. pp. 959-973 (Advanced Materials Research).
title = "Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration",
abstract = "Exploitation of geothermal resource results the decrease of fluid pressure in geothermal reservoir. In production process, the analysis of reservoir condition is made by observing the pressure state. When the fluid is pumped into the reservoir, the value of pressure varies with time which is called as transient state. The plot of pressure versus time will create a curve with a certain slope. From the graph of the pressure the reservoir condition can be analyzed. The solution of the pressure transient is identified as exponential integral equation Ei(x). When the input to the function is really small for example at x < 0.01, the equation will form an asymptotic curve. Analytical solution involves logarithm natural and Euler constant (γ). In this paper we try to approach the solution of exponential integral equation by numerical integration. The objective of this study is to make a numerical model of the pressure change in a geothermal reservoir and to compare the result between numerical method and analytic. There are two methods used in this study, first is Picard- McLaurin iteration to solve the ordinary differential equations (ODE), and the second is trapezoidal integration to calculate the function of Ei(x). The modeling shows that the result of the calculation with the numerical method matched with the analytic with the range of error between 0.0008 to 4.5 {\%} for drawdown test and 0.19 to 7.7 {\%} for buildup test.",
author = "Alamta Singarimbun and Yasuhiro Fujimitsu and Mitra Djamal and Andajani, {Rezkia Dewi}",
year = "2014",
month = "1",
day = "1",
doi = "10.4028/www.scientific.net/AMR.1025-1026.959",
language = "English",
publisher = "Trans Tech Publications Ltd",
pages = "959--973",
editor = "H.M. Song and H.K. Son and Hu, {Jong Wan}",
booktitle = "Advanced Materials, Structures and Mechanical Engineering",

}

TY - GEN

T1 - Pressure transient modeling in geothermal reservoir by using Picard-Mclaurin iteration

AU - Singarimbun, Alamta

AU - Fujimitsu, Yasuhiro

AU - Djamal, Mitra

AU - Andajani, Rezkia Dewi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Exploitation of geothermal resource results the decrease of fluid pressure in geothermal reservoir. In production process, the analysis of reservoir condition is made by observing the pressure state. When the fluid is pumped into the reservoir, the value of pressure varies with time which is called as transient state. The plot of pressure versus time will create a curve with a certain slope. From the graph of the pressure the reservoir condition can be analyzed. The solution of the pressure transient is identified as exponential integral equation Ei(x). When the input to the function is really small for example at x < 0.01, the equation will form an asymptotic curve. Analytical solution involves logarithm natural and Euler constant (γ). In this paper we try to approach the solution of exponential integral equation by numerical integration. The objective of this study is to make a numerical model of the pressure change in a geothermal reservoir and to compare the result between numerical method and analytic. There are two methods used in this study, first is Picard- McLaurin iteration to solve the ordinary differential equations (ODE), and the second is trapezoidal integration to calculate the function of Ei(x). The modeling shows that the result of the calculation with the numerical method matched with the analytic with the range of error between 0.0008 to 4.5 % for drawdown test and 0.19 to 7.7 % for buildup test.

AB - Exploitation of geothermal resource results the decrease of fluid pressure in geothermal reservoir. In production process, the analysis of reservoir condition is made by observing the pressure state. When the fluid is pumped into the reservoir, the value of pressure varies with time which is called as transient state. The plot of pressure versus time will create a curve with a certain slope. From the graph of the pressure the reservoir condition can be analyzed. The solution of the pressure transient is identified as exponential integral equation Ei(x). When the input to the function is really small for example at x < 0.01, the equation will form an asymptotic curve. Analytical solution involves logarithm natural and Euler constant (γ). In this paper we try to approach the solution of exponential integral equation by numerical integration. The objective of this study is to make a numerical model of the pressure change in a geothermal reservoir and to compare the result between numerical method and analytic. There are two methods used in this study, first is Picard- McLaurin iteration to solve the ordinary differential equations (ODE), and the second is trapezoidal integration to calculate the function of Ei(x). The modeling shows that the result of the calculation with the numerical method matched with the analytic with the range of error between 0.0008 to 4.5 % for drawdown test and 0.19 to 7.7 % for buildup test.

UR - http://www.scopus.com/inward/record.url?scp=84913597031&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84913597031&partnerID=8YFLogxK

U2 - 10.4028/www.scientific.net/AMR.1025-1026.959

DO - 10.4028/www.scientific.net/AMR.1025-1026.959

M3 - Conference contribution

AN - SCOPUS:84913597031

SP - 959

EP - 973

BT - Advanced Materials, Structures and Mechanical Engineering

A2 - Song, H.M.

A2 - Son, H.K.

A2 - Hu, Jong Wan

PB - Trans Tech Publications Ltd

ER -