Application and Derivation of Material Balance Equation for Abnormally Pressured Gas Condensate Reservoirs with Gas Recharge Capacity and Water Influx
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摘要: 物质平衡法是计算气藏地质储量、水侵量、补给气量的有效方法之一.具有补给气的异常高压有水凝析气藏是气藏开发中最复杂的类型之一, 兼具异常高压气藏、凝析气藏和补给气的边底水气藏的特性.综合考虑开发过程中的凝析油析出, 岩石、束缚水和凝析油弹性膨胀, 水相挥发, 凝析气相中水蒸气增多, 水溶气溢出, 边底水的推进及外来气补给等复杂物理现象, 根据物质平衡原理, 推导了具有补给气的异常高压有水凝析气藏物质平衡方程, 并运用相对海明距离及关联度理论, 以驱动指数均方差、比拟压力与采出程度偏差指数和综合目标函数为分析因素, 分析了各组合方案贴近程度及相似程度, 挑选最佳组合方案并确定出地质储量、补给气量及水侵量, 同时计算了水体倍数.实例计算表明: 中国西北某凝析气藏地质储量为66.80×108 m3, 如果忽略凝析油, 计算地质储量偏大, 误差高达91.77%, 其次是水侵、弹性膨胀和气侵的影响, 误差分别为75.75%、23.95%和12.87%, 而溢出水溶气为2.69%与水蒸气为1.65%, 影响较小, 但也不可忽略.Abstract: Material balance equation is an effective approach to estimate the OGIP, water influx, and gas recharge capacity in condensate gas reservoirs. The condensate gas reservoir with gas recharge capacity, abnormally high pressure, and edge and bottom water-drive is one of the most complicated reservoirs which include the features of condensate gas, pressure-dependent parameters and water influx. In this study, a new material balance equation for this reservoir was derived which considering retrograde condensation, the expansion of rock, bounded water and condensate oil, the phase change of vapor and dissolved gas, water and gas influx. The theories of Haiming Distance and relevance is used to analyze the mean square error of drive index, deviation index between pseudo pressure ratio and recovery, and generalized objective function. Based on the analysis of relative similarity degree and closeness coefficient, we chose the optimization scheme, and calculated the OGIP, gas recharge, water influx, and the aquifer volume. Based on the case study in condensate gas reservoir in Northwest China, a calculated reserve is 66.80×108 m3. We investigated and analyzed the parameters sensitivity by calculating the errors in the assumption of those parameters not included. The error of reserve estimation is up to 91.77% if oil condensate is not considered. Other parameters also have some effect such as water influx, the expansion and gas recharge. Respectively, the errors are 75.75%, 23.95% and 12.87%. The effect of gas escape from the dissolution and vapor is not significant but cannot be neglected, the errors are 2.69% of escaped gas and 1.65% of vapor.
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图 1 具有补给气的异常高压有水凝析气藏物理模型
Fig. 1. Schematic view of overpressured condensate gas reservoir with gas and water recharge
图 2 累积补给气量与累积水侵量变化曲线
Fig. 2. Relations of cumulative gas recharge and water influx versus cumulative gas production
图 3 各驱动指数随地层压力变化曲线
Fig. 3. Relations of each drive index versus average reservoir pressure
表 1 某异常高压有水凝析气藏历年生产动态数据
Table 1. Production data of an overpressured condensate gas reservoir with gas and water recharge
时间 Gp(108 m3) Wp(104 m3) p(MPa) z(无因次) p/z(MPa) 1992-05-05 1.151 785 87 0.131 8 57.21 1.331 42.99 1993-05-05 2.126 046 64 0.224 1 57.13 1.330 42.96 1994-05-05 3.154 868 49 0.353 7 56.89 1.327 42.87 1995-05-05 3.598 907 41 0.417 3 56.75 1.325 42.82 1996-05-05 3.885 874 76 0.445 8 56.64 1.324 42.78 1997-05-05 5.337 316 62 0.645 5 56.46 1.322 42.71 1998-05-05 6.851 595 73 0.866 2 56.23 1.319 42.63 1999-05-05 8.004 122 27 0.939 1 56.04 1.317 42.56 2000-05-05 8.875 949 43 0.968 0 55.87 1.315 42.50 2001-05-05 9.590 680 61 0.991 7 55.62 1.312 42.40 2002-05-05 10.809 073 08 1.119 8 55.21 1.307 42.25 2003-05-05 12.077 439 45 1.196 5 54.91 1.302 42.18 2004-05-05 13.317 895 74 1.279 8 54.65 1.300 42.04 2005-05-05 14.412 627 56 1.383 3 54.53 1.298 42.00 2006-05-05 17.921 065 70 1.691 5 53.06 1.281 41.41 2007-05-05 24.213 451 08 1.873 8 50.11 1.256 39.90 2008-05-05 31.114 022 74 2.160 2 48.01 1.232 38.96 2009-05-05 39.002 150 12 2.774 4 47.15 1.208 38.02 
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表 2 某异常高压有水凝析气藏流体特征参数
Table 2. Characteristic parameters of the fluid in the example reservoir
时间 Bg(无因次) Bw(无因次) yw(104m3/104m3) Rsw(104m3/104m3) So 1992-05-05 0.008 528 1.003 627 0.005 435 5.600 0.000 1993-05-05 0.008 545 1.003 620 0.005 447 5.593 0.000 1994-05-05 0.008 560 1.003 582 0.005 479 5.578 0.000 1995-05-05 0.008 582 1.003 560 0.005 496 5.568 0.000 1996-05-05 0.008 585 1.003 555 0.005 513 5.554 0.000 1997-05-05 0.008 600 1.003 536 0.005 548 5.542 0.000 1998-05-05 0.008 629 1.003 520 0.005 580 5.528 0.000 1999-05-05 0.008 640 1.003 491 0.005 600 5.516 0.000 2000-05-05 0.008 651 1.003 455 0.005 633 5.496 0.000 2001-05-05 0.008 680 1.003 418 0.005 663 5.468 0.000 2002-05-05 0.008 703 1.003 373 0.005 740 5.432 0.000 2003-05-05 0.008 726 1.003 320 0.005 840 5.388 0.004 2004-05-05 0.008 740 1.003 291 0.005 880 5.364 0.008 2005-05-05 0.008 746 1.003 273 0.005 905 5.350 0.009 2006-05-05 0.008 836 1.003 091 0.006 200 5.170 0.022 2007-05-05 0.008 951 1.002 727 0.006 770 4.880 0.040 2008-05-05 0.009 040 1.002 350 0.007 450 4.570 0.061 2009-05-05 0.009 093 1.002 055 0.008 243 4.275 0.074
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表 3 前10个最佳组合方案各项计算指标
Table 3. Index list of the top 10 optimal combination programs
G(108 m3) Gc(108m3) We(104m3) δ β γ di ωi 优选顺序 66.800 2.298 1 016.25 0.680 0 0.002 9 0.682 9 0.632 0 0.654 0 1 66.980 2.297 1 015.93 0.681 5 0.005 1 0.686 6 0.633 1 0.652 5 2 67.600 2.254 1 015.38 0.693 3 0.006 5 0.699 8 0.634 3 0.651 0 3 67.610 2.245 1 015.78 0.693 5 0.004 1 0.697 6 0.637 3 0.647 2 4 67.870 2.227 1 015.13 0.701 2 0.006 2 0.707 4 0.640 2 0.642 3 5 68.110 2.230 1 015.06 0.710 0 0.007 7 0.717 7 0.641 0 0.636 4 6 68.110 2.221 1 015.07 0.705 8 0.006 9 0.712 7 0.642 9 0.631 0 7 68.500 2.199 1 014.78 0.727 1 0.007 7 0.734 8 0.643 7 0.627 8 8 68.850 2.183 1 014.40 0.745 3 0.009 5 0.754 8 0.644 5 0.626 9 9 69.280 2.163 1 014.38 0.771 2 0.010 1 0.781 3 0.645 5 0.624 8 10
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表 4 地质储量计算结果
Table 4. Caculated results of estimated OGIP
影响因素 新模型 凝析油 水蒸气 溢出水溶气 气侵量 水侵量 弹性膨胀量 地质储量(108 m3) 66.80 128.11 67.96 68.62 75.45 117.42 82.83 误差(%) 0.00 91.77 1.65 2.69 12.87 75.75 23.95
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表 5 不同模型的影响因素
Table 5. Considering influence factors of different models
考虑因素项 反凝析 水蒸气 溢出水溶气 气侵量 水侵量 弹性膨胀量 新模型 √ √ √ √ √ √ Fetkovich et al., 1998 夏静等, 2007 √ 刘道杰等, 2011 √ √ √ 王星等，2010 √ √ 李骞等，2010 √ √ 马永祥，1997 √ √ 陈玉祥等，2005 √ √
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表 7 水体能量计算结果
Table 7. Calculated water influx
时间 p(MPa) We (104m3) (Cw+Cf)Δp (无因次) Vpw (104m3) 水体倍数(无因次) 1992-05-05 57.21 0.00 0.000 357 0.00 0.000 1993-05-05 57.13 0.04 0.000 617 64.86 0.011 1994-05-05 56.89 0.18 0.001 396 128.96 0.023 1995-05-05 56.75 0.31 0.001 850 167.55 0.029 1996-05-05 56.64 0.41 0.002 207 185.75 0.033 1997-05-05 56.46 0.63 0.002 792 225.68 0.040 1998-05-05 56.23 1.09 0.003 538 307.51 0.054 1999-05-05 56.04 14.00 0.004 155 3 369.53 0.592 2000-05-05 55.87 22.00 0.004 707 4 674.19 0.822 2001-05-05 55.62 30.00 0.005 518 5 436.56 0.956 2002-05-05 55.21 59.00 0.006 849 8 614.32 1.514 2003-05-05 54.91 89.00 0.007 823 11 376.91 2.000 2004-05-05 54.65 111.00 0.008 667 12 807.47 2.251 2005-05-05 54.53 120.00 0.009 056 13 250.39 2.329 2006-05-05 53.06 228.00 0.013 828 16 488.33 2.898 2007-05-05 50.11 507.00 0.023 404 21 663.28 3.808 2008-05-05 48.01 930.00 0.030 220 30 774.06 5.410 2009-05-05 47.15 1 016.25 0.033 012 30 807.15 5.416
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