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 E_i(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 E_i(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.

• Periodical: Advanced Materials Research (Volumes 1025-1026)
• Pages: 959-973
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1025-1026.959
• Online since: September 2014
• Authors: Alamta Singarimbun*, Yasuhiro Fujimitsu, Mitra Djamal, Rezkia Dewi Andajani
• Keywords: Picard-McLaurin Iteration, Pressure Transient, Trapezoid Integration, Well Testing

References

[1] Bedrikovetsky and B.P. Peter: Well Testing Analysis Theoretical Foundation: Presentation Slide, The University of Adelaide (2008).

[2] J. Kuchuk, F.M. Onur and F. Hollander: Dev. Petrol. Sci. Vol. 57 (2010).

[3] T.A. Blasingame: Petroleum Engineering 620 Course Notes: Fluid Flow in Petroleum Reservoir Flow Solutions Lecture 3- Linear Flow Solutions Infinite Acting and Finite Acting Case, Texas A&M University/College of Engineering (1994).

[4] M. Abramowitz and I.A. Stegun: Handbook of Mathematical Functions with Formula, Graphs, and Mathematical Tables, United States Department of Commerce Luther H. Hodges, Secretary- National Bureau of Standards (1972).

[5] M.A. Grant, I.G. Donaldson and P.F. Bixley: Geothermal Reservoir Engineering, United State (1982), in press.

[6] D.L. Katz and R.L. Lee: Natural Gas Engineering Production and Storage (International Edition 1990) , McGraw Hill, United State (1990).

[7] J. Sochacki and E.G. Parker: Abstr. Appl. Anal. Vol. 05, No. 01 (2000), p.47.

[8] Information on http: /www. peacesoftware. de/einigewerte/calc_dampf. php5.

[9] P.A. Witherspoon and T.N. Narashimban: Result of Reservoir Evaluation Test, East Mesa Geothermal Field, Lawrence Berkeley Laboratory University of California (1976).