### 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 |
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Title of host publication | Advanced Materials, Structures and Mechanical Engineering |

Editors | H.M. Song, H.K. Son, Jong Wan Hu |

Publisher | Trans Tech Publications Ltd |

Pages | 959-973 |

Number of pages | 15 |

ISBN (Electronic) | 9783038352549 |

DOIs | |

Publication status | Published - Jan 1 2014 |

Event | 2014 International Conference on Advanced Materials, Structures and Mechanical Engineering, ICAMSME 2014 - Incheon, Korea, Republic of Duration: May 3 2014 → May 4 2014 |

### Publication series

Name | Advanced Materials Research |
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Volume | 1025-1026 |

ISSN (Print) | 1022-6680 |

ISSN (Electronic) | 1662-8985 |

### Other

Other | 2014 International Conference on Advanced Materials, Structures and Mechanical Engineering, ICAMSME 2014 |
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Country | Korea, Republic of |

City | Incheon |

Period | 5/3/14 → 5/4/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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

T3 - Advanced Materials Research

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 -