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有限地層之壓力反應行為 ( 卡式座標 )

有限地層之壓力反應行為 ( 卡式座標 ). 報告人：吳珉豪. 中華民國 101 年 7 月. 大綱. 卡式座標 (Cartesian System) 理論基礎 解析法 - 利用形狀因子 (C A ) 計算 有限地層 壓力 反應 曲線. 卡式座標 (Cartesian System ) 理論基礎 -1. Closed system ( Earlougher , 1977) Dimensionless pressure drop p D

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有限地層之壓力反應行為 ( 卡式座標 )

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  1. 有限地層之壓力反應行為(卡式座標) 報告人：吳珉豪 中華民國101年7月

  2. 大綱 卡式座標(Cartesian System) • 理論基礎 • 解析法-利用形狀因子(CA)計算有限地層壓力反應曲線

  3. 卡式座標(Cartesian System)理論基礎-1 Closed system (Earlougher, 1977) Dimensionless pressure drop pD • All closed reservoirs systems have transient behavior (tDA> 0.000025) • At long time the system reaches pseudosteady state

  4. 卡式座標(Cartesian System)理論基礎-2 Dimensionless time, tD(Based on wellbore radius) Dimensionless time, tDA(Based on drainage area)

  5. 卡式座標(Cartesian System)理論基礎-3 John Lee (1982) • “Use Infinite-System Solution With Less Than 1% Error for tDA < ” This means that the time in hours is calculate from • Time required for the pseudosteady state “Less Than 1% Error for tDA > ” • Time required for the pseudosteady state equation to be exact “Exact for tDA > ”

  6. 卡式座標(Cartesian System)理論基礎-4 • For a well in the center of a closed square, CA is 30.8828.

  7. 卡式座標-地層設計 • 卡式地層之面積等同於圓柱地層之面積。 • 圓柱座標半徑re=100 ft等面積對應之卡式座標正方形長度為L=177.24ft。 • 而圓柱座標半徑re=50 ft等面積對應之卡式座標正方形長度為L=88.62ft。 L re

  8. 解析解-無因次壓力隨無因次時間變化(pD-tD plot) L=177.24 ft L=88.62 ft

  9. 解析解-無因次壓力隨無因次時間變化 (pD-tDAplot) L=177.24 ft L=88.62 ft

  10. Homework • 有限地層之壓力反應曲線(pD-tD) in log-log Scale Less Than 1% Error for tDA（reD=1000） Exact for tDA（reD=1000） • 有限地層之壓力反應曲線(pD-tDA) in log-log Scale reD=1000 • Additional homework(林再興老師指派) • 台灣中油在南海探勘油氣歷史 • Deadline：7/5

  11. 報告結束

  12. 大綱 • 理論基礎 圓柱座標(Radial System) • Introduction to van Everdingen and Hust Solution • Analytical solution of infiniteradial system constant rate at inner boundary • Analytical solution of finite radial system with closed boundary, constant rate at inner boundary

  13. 理論基礎-1 Physical laws used • (1) Continuity equations (Mass balances) • (2) Flow laws (Darcy’s law) Assumptions • (1)Slightly compressible liquid(微可壓縮) • (2)1-D Radial flow(徑向) • (3)Isothermal flow(等溫) • (4)Single phase flow(單相) • (5)Pressure gradient→0()(壓力梯度趨近於零) • (6)Rock-fluid properties = const.(流體性質為常數)

  14. 理論基礎-2 • Diffusivity Equation • Dimensionless Diffusivity Equation

  15. 理論基礎-3 Infinite cylindrical reservoir van Everdingen and Hurst (1949) • 井底流壓隨時間變化之解析方程式

  16. van Everdingen and Hurst solution

  17. 理論基礎-4 Infinite cylindrical reservoir with line-source well Assumption: Ei(Exponential Integral) Solution to the diffusivity equation is

  18. 理論基礎-5 Log approximation solution Log approximation (Line Source, rD=1)

  19. 理論基礎-6 • Constant Rate at Inner Boundary, No Flow Across Outer Boundary • Dimensionless pressure is function of dimensionless time, dimensionless radius and dimensionless external radius

  20. 理論基礎-7 Table-1 infinite-acting reservoirpD(John Lee, 1982) Transient state • 1.For tD< 0.01, pD can be approximated by the relation (John Lee, 1982) • 2. For tD< 0.25reD2Table-1 use valid for finite reservoirs(John Lee, 1982) • 3. For 0.25reD2 > tD > 100, table-1 can be extended by use of the equation(John Lee, 1982)

  21. 理論基礎-8 Pseudo steady state • When tD > 0.25reD2 , pressure reached the pseudo steady state and pD can be calculated from: (John Lee, 1982) Pseudo steady Transient

  22. 地層參數設定與操作條件設定

  23. 地層示意圖 qo= 1 (STB/day) Outer Boundary Oil Reservoir co = 2E-6 (psi-1) cw= 2.6E-6(psi-1) μo= 13.2 (cp) μw= 1 (cp) k = 300 (md) ϕ = 0.2 cf= 5.6E-6 (psi-1) h=672 (ft) rw=0.25 (ft) re=10 (ft), 50(ft),and 100(ft)

  24. 解析法-有限地層與無限地層之壓力曲線圖 reD=200 reD=40 reD=400

  25. 解析法-transition zonebehavior reD=200 reD=40 reD=400

  26. Homework • 無限地層之壓力反應曲線(pD-tD) in log-log Scale • 有限地層之壓力反應曲線(pD-tD) in log-log Scale • reD=1000

  27. 大綱 圓柱座標(Radial System) • Introduction to dat. file • Output the result • Matching the analytical solution and numerical Solution

  28. 地層參數設定與操作條件設定

  29. Introduction to DAT file 檔案的標題(Title) 輸出、輸入使用現場單位(Field Unit)

  30. Introduction to DAT file 座標系統為Radial, 網格為1211 井口半徑 K方向為向下增加 網格頂部深度 IJK方向網格設計

  31. Introduction to DAT file I方向網格設計，共十二格

  32. Introduction to DAT file 孔隙率 Porosity 岩石壓縮度 Rock Compressibility 岩石壓縮度參考壓力Reference pressure for the rock compressibility 滲透率(Permeability)

  33. Introduction to DAT file 油-水模型 壓力區間 溶解油氣比、油的地層體積因子、氣體膨脹因子、油黏滯度與氣體黏滯度

  34. Introduction to DAT file 油、氣、水密度 CO為油的壓縮度； CVO為0代表油的黏滯度不隨壓力改變 BWI為水的地層體積因子； CW為水的壓縮度； REFPW水的地層體積因子參考壓力； VWI為水的黏滯度； CVW為0代表油的田滯度不隨壓力改變

  35. Introduction to DAT file 為油水相對滲透率

  36. Introduction to DAT file 計算結果是由網格中心位置取值 起泡點的壓力 (Bubble Point) 參考壓力(REFPRES)； 參考深度(REFDEPTH) 油水界面深度(DWOC)； 參考深度

  37. Introduction to DAT file 數值計算收斂條件 (略)

  38. Introduction to DAT file 計算起始日期 此處為注入井(INJECTOR)；注入成分為Oil。 也可更改為PRODUCER進行生產 井口名稱Oil-Well 注入(或生產)條件為1STB 井口半徑、幾何形狀、井口比例以及膚表因子 穿孔區間與全貫穿

  39. Run Simulation Run Immediately 將Dat拖曳到IMEX

  40. Output Result 將IRF拖曳到Results Graph

  41. Output Result 選擇井底流壓(pwf)隨時間變化 點選左上角之圖示

  42. Output Result

  43. Output Result 輸出到EXCEL 將壓力與時間複製貼上於現有EXCEL

  44. Output Result 將壓力與時間複製貼上。 須注意模擬器設定的時間單位為(day)

  45. Simulation Result

  46. Matching the Analytical Solution and Numerical Solution

  47. Homework • 利用模擬器設計地層大小(reD=1000)並將得到結果利用公式計算壓力反應曲線。 • 將上述結果與前一次作業之解析解進行比對(放在同一張圖上) • 更改參數(如:產率、滲透率…等)，觀察曲線變化。

  48. Hint • k [=] md; h [=] ft; p [=] psi; q [=] STB/day; μ [=] cp; B [=] RB/STB • k [=] md; t [=] hr; ct[=] psi-1; φ [=] %; rw[=] ft

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