Solusi Numerik Distribusi Tekanan dengan Persamaan Difusi Dua Dimensi pada Reservoir Panas Bumi Fasa Air Menggunakan Skema Crank-Nicholson

Mufarrih Ridhwan, Icih Sukarsih, Respita Wulan

Abstract


Penelitian dalam skripsi ini bertujuan untuk membuat model persamaan beda hingga skema Crank-Nicholson dari distribusi tekanan dengan persamaan difusi dua dimensi pada reservoir panas bumi fasa air. Penelitian sebelumnya yang dilakukan oleh Singarimbun (2012) mensimulasikan reservoir pada proses produksi dan injeksi fluida ke reservoir panas bumi fasa air. Model yang dipakai dalam penelitian ini adalah distribusi tekanan yang ditransformasi dari koordinat cartesius ke koordinat silinder polar, sebagai formasi tekanan pada kondisi unsteady-state (tidak tunak) dimana tekanan dipengaruhi oleh waktu. Kemudian diterapkan metode beda hingga skema Crank-Nicholson dan disederhanakan dengan cara diskritisasi persamaan beda hingga. Solusi numerik distribusi tekanan dengan persamaan difusi dua dimensi terbentuk dari skema Crank-Nicholson.

 

This research is aimed to create a model for pressure equation finite difference Crank-Nicholson scheme of distribution of pressure with two-dimensional diffussions equation in the geothermal reservoir water phase. Previous research conducted by Singarimbun (2012) simulates geothermal reservoir on the production process and fluid injection on water phase. The model in this study is developed by transforming from Cartesian coordinates to cylindrical polar coordinates, as the formation of pressure is in unsteady-state condition the pressure is affected by time. Thus, the diffussions model then applied Crank-Nicholson scheme and simplified by means of the finite difference discretization equation. Pressure distribution with a numerical solution of two-dimensional diffusion equation formed from the Crank-Nicholson scheme.


Keywords


mass balance equations, pressure distribution, coordinate cylindrical symmetry, the finite difference method, numerical solutions.

References


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Mercer, C. R., 1979, Water Resources Research. Geothermal reservoir simulation: 2. Numerical solution techniques for liquid- and vapor-dominated hydrothermal systems, 31-46.

Saptadji, N. M., 2009, Sekilas tentang Panas Bumi, Diktat Kuliah Prodi Megister Geothermal ITB.

Singarimbun, A. d., 2012, Internatioanal Journal of Energy and Environment. Estimation of Parameter Distribution and Injection Process in Geothermal Reservoir, Issue 6, volume 6,.




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