基岩含水层水平井流的若干问题
|
摘要
近年来水平井由于其在许多领域的应用较垂直井优越得多,因此在地下工程、海底工程和石油工程、污染物修复、水文地质工程中得到了广泛的应用和研究。其中,在矿山开采和隧道工程中,经常要遇到巷道/隧道的涌水问题,此类问题时水平井问题的一个分支。另外基岩及裂隙岩体在自然界中广泛分布,受自重应力的影响,其渗透性随着深度的增加呈负指数减小的趋势。因此,基岩裂隙地区含水层中巷道/隧道涌水问题的研究在实际工程中具有重要的理论指导意义。针对此类问题,前人已经做了一定的研究,提出了围岩中水平隧道涌水的渗流模型及其解析解和数值解。并分析了隧道涌水量与隧道埋深的关系以及多个不同深度隧道之间的叠加效应,讨论了隧道围岩双层水位问题。但是前人的研究中缺少有关隔水边界如何影响巷道/隧道涌水的论述。另外,前人在对比渗透性随深度呈负指数增长的非均质含水层和均质含水层方面的研究也不是很充足。
本文将在考虑围岩渗透性随深度呈负指数变化的情况下,建立隔水边界附近地下水从各向异性围岩向水平隧道涌水的渗流模型,并利用解析解和数值解进行求解和演算。在渗透系数随深度呈负指数变化的非均质各向异性二维稳定流问题中,对于顶部为定水头边界侧面为铅直隔水边界的情况进行解析解求解。对于侧面为其他角度隔水边界的情况利用有限元法,结合MATLAB提取单元和节点数据,并应用VB编程计算进行求解。对于上面为隔水边界,侧面为定水头边界补给的情况,同样利用有限元法进行求解计算。并分析各个参数对涌水量,水位分布以及峰值涌水深度的影响。进而揭示涌水问题的本质规律进一步从动力学角度探讨隧道涌水规律。另外,本文对比了渗透性随深度呈负指数增长的非均质含水层褐渗透系数保持不变的均质含水层中水平井的涌水问题。最后本文利用雅砻江锦屏二级水电站的实测数据,利用两种数学模型进行渗透参数的反演。
Just for its advantages, horizontal well technology and its research has been widely adopted in fields of underground engineering, submarine engineering, petroleum exploitation, pollutants repairing and hydrogeology engineering. Both tunnels and drainage roadway can be treated as horizontal well. Tunnels gushing and drainage roadway gushing problem is common in mining exploring and always bring in significant loss. Rock aquifer with the dept-dependent exponential decrease of hydraulic conductivity is widely distributed in nature. Therefore the research of tunnel and drainage roadway which located in rock aquifer possesses practical and theoretical guidance significance. Previous have done some research about tunnels gushing and drainage roadway gushing problem. And solutions are obtained for predicting tunnel water inflows and water head for the commonly observed case of an exponential decrease of hydraulic conductivity with depth in isotropic jointed rock mass. However, there is no research about how non-flow boundary influence the tunnel water inflows. What’s more, the comparison between rock aquifer with the dept- exponential decrease of hydraulic conductivity and homogeneous rock aquifer is not sufficient.
According to the angle between the constant water head boundary and non-flow boundary, analytical solution and finite-element solution are presented respectively. Effects of tunnel depth, non-flow and constant water head boundary boundary distance on predicted water inflow are discussed. For the finite-element solution, MATLAB is adopted for mesh and VB is used for calculation. Analyzing is given to the tunnel water inflows, depth of peak water inflows and enormous difference between the up and down water head. What’s more a comparison about tunnel water inflow is given between heterogeneous and homogeneous rock aquifer. At last, two kinds of mathematical model are applied into Yalongjiang Secondary Hydropower Station, and hydraulic conductivity is obtained according to tunnel water inflow date.
本文将在考虑围岩渗透性随深度呈负指数变化的情况下,建立隔水边界附近地下水从各向异性围岩向水平隧道涌水的渗流模型,并利用解析解和数值解进行求解和演算。在渗透系数随深度呈负指数变化的非均质各向异性二维稳定流问题中,对于顶部为定水头边界侧面为铅直隔水边界的情况进行解析解求解。对于侧面为其他角度隔水边界的情况利用有限元法,结合MATLAB提取单元和节点数据,并应用VB编程计算进行求解。对于上面为隔水边界,侧面为定水头边界补给的情况,同样利用有限元法进行求解计算。并分析各个参数对涌水量,水位分布以及峰值涌水深度的影响。进而揭示涌水问题的本质规律进一步从动力学角度探讨隧道涌水规律。另外,本文对比了渗透性随深度呈负指数增长的非均质含水层褐渗透系数保持不变的均质含水层中水平井的涌水问题。最后本文利用雅砻江锦屏二级水电站的实测数据,利用两种数学模型进行渗透参数的反演。
Just for its advantages, horizontal well technology and its research has been widely adopted in fields of underground engineering, submarine engineering, petroleum exploitation, pollutants repairing and hydrogeology engineering. Both tunnels and drainage roadway can be treated as horizontal well. Tunnels gushing and drainage roadway gushing problem is common in mining exploring and always bring in significant loss. Rock aquifer with the dept-dependent exponential decrease of hydraulic conductivity is widely distributed in nature. Therefore the research of tunnel and drainage roadway which located in rock aquifer possesses practical and theoretical guidance significance. Previous have done some research about tunnels gushing and drainage roadway gushing problem. And solutions are obtained for predicting tunnel water inflows and water head for the commonly observed case of an exponential decrease of hydraulic conductivity with depth in isotropic jointed rock mass. However, there is no research about how non-flow boundary influence the tunnel water inflows. What’s more, the comparison between rock aquifer with the dept- exponential decrease of hydraulic conductivity and homogeneous rock aquifer is not sufficient.
According to the angle between the constant water head boundary and non-flow boundary, analytical solution and finite-element solution are presented respectively. Effects of tunnel depth, non-flow and constant water head boundary boundary distance on predicted water inflow are discussed. For the finite-element solution, MATLAB is adopted for mesh and VB is used for calculation. Analyzing is given to the tunnel water inflows, depth of peak water inflows and enormous difference between the up and down water head. What’s more a comparison about tunnel water inflow is given between heterogeneous and homogeneous rock aquifer. At last, two kinds of mathematical model are applied into Yalongjiang Secondary Hydropower Station, and hydraulic conductivity is obtained according to tunnel water inflow date.
引文
[1]陈崇希,唐仲华.地下水流动问题数值方法.武汉:中国地质大学出版社,1994
[2]陈崇希,林敏.地下水动力学.武汉:中国地质大学出版社,1999
[3]杜强,康永尚,万力,等.渗透性参数非均质特征的研究进展.地学前缘,1996,3(1-2):182-190
[4]蒋小伟,万力等.基于压水试验数据的砂泥岩裂隙岩体渗透结构分析.自然科学进展,2008, 18(3):355-360
[5]李保珠,李锋,薛传东,等.有限元法在涌水量预测中的应用.矿业工程,2003,1(5):55-58
[6]李茂芳.水文地质压水试验.北京:水利电力出版社,1987,87
[7]梁昆淼.数学物理方法.北京:高等教育出版社,1998
[8]胡伏生.岩溶充水矿床涌水量垂向变化规律研究[博士学位论文].北京:中国地质大学(北京),1997
[9]胡伏生,万力,田开铭,等.渗透系数衰减时矿坑涌水量与开采深度的关系.煤田地质与勘查,1998 (2):37-41
[10]陆君安.偏微粉方程的MATLAB解法.武汉:武汉大学出版社,2001
[11]田开铭,万力.各向异性裂隙介质渗透性的研究与评价.北京:学苑出版社,1989
[12]万力,李定方,李吉庆.三维裂隙网络的多边形单元渗流模型.水利水运科学研究,1993,6(4):347-353
[13]王纯祥,蒋宇静,江崎哲郎,等.复杂条件下长大隧道涌水预测及其对环境影响评价。岩石力学与工程学报,2008,27(12):2411-2417
[14]王恩志.岩体裂隙的网络分析及渗流模型.岩石力学与工程学报,1993,12(3):214-221
[15]王建秀,杨立中,何静.深埋隧道涌水量数值计算中的试算流量法.岩石力学与工程学报,2002,21(12):1176–1780.
[16]王建秀,朱合华,叶为民.隧道涌水量的预测及其工程应用.岩石力学与工程学报,2004,23(7):1150–1153
[17]王媛,秦峰,李东田.南水北调西线工程区地下径流模型、岩体透水性及隧洞涌水量预测.岩石力学与工程学报,2005,24(20):3673-3678
[18]徐国锋,杨建锋,陈侃福.台缙高速公路苍岭隧道水文地质勘察与涌水量预测.岩石力学与工程学报,2005,24(2),5531-5535
[19]薛禹群,谢春红.水文地质学的数值法.北京:煤炭工业出版社,1980
[20]薛禹群,朱学愚,吴吉春,等.地下水动力学.北京:地质出版社,1997
[21]于开宁.砂岩岩体渗透性评价及特征[博士学位论文].北京:中国地质大学,2003
[22]詹红兵,万军伟,水资源和环境工程中水平井研究简介.地球科学-中国地质大学学报,2003,28(5),511-516
[23]朱大力,李秋枫.预测隧道涌水量的方法.工程勘察,2004,4:18-22,32.
[24] Antonellin M,Aydin A.Effect of faulting on fluid flow in porous sandstones:petrophysical properties . AAPG,1994,78(3):355-377
[25] Carlsson A,Olsson T.Hydraulic properties of swedish crystalline rocks:hydraulic conductivuty and its relation to depth. Bulletin of the Geological Institutions of the University of Uppsala, New Series, 1978, 7:71-84
[26] Cleveland T G. Recovery performance for vertical and horizontal wells using semianalytical simulation.Ground Water, 1994, 32(1): 103-107
[27] David N. Jenkins, John K. Prentice.Theory for aquifer test analysis in fractured rocks under linear (nonradial) flow conditions.Ground Water. 20(1), 1982: 12-21
[28] Daviau F, Mouronval G, Bourdarot G, et al. Pressure analysis for horizontal wells. SPE formation Evaluation, 1988,3: 716-724
[29] Environmental Protection Agency (EPA). Manual alternative methods for fluid delivery and recovery .EPA/625/r-94/003,1994
[30] Falta R W. Analytical solutions for gas-flow due to gas injection and extraction from horizontal wells .Ground Water. 1995. 33(2): 235-246
[31] Freeze R. A., and J.A. Cherry. Groundwater. Englewood Cliffs, New Jerscy: Prentice-Hall Inc,1979
[32] Gale J E,Rouleau A,Witherspoon P A. Hydrogeologic characteristics of a fractured Granite. AWRC Conference Groundwater in Fractured Rock. Canberra: AWRC Conference, 1982. 95-108.
[33] Goode P A,Thambynayagam R K M. Pressure drawdown and buildup analysis of horizontal wells in anisotropic media.SPE Formation Evaluation,1987,2(4): 683-697
[34] Goodman,Moye D G,Van Schalkwyk A,et al. Groundwater inflows during tunnel driving.Engineering Geology,1965,2(2):39-56
[35] Hantush M S,Papadopulos I S.Flow of ground water to collector wells.Proc Am Soc Civil Engrs .J Hydraulics Division, 1962, HY5: 221-244
[36] Hunt B, Massmann J W. Vapor flow to trench in leaky aquifer .J Envir Engr, 2000, 126:375-380
[37] Joshi S D. Augmentation of well productivity with slant and horizontal wells. J of Petroleum Tech, 1988, 40(6): 729-739
[38] Kawecki M W. Transient flow to a horizontal water well .Ground Water,2000,38(6): 842-850
[39] Kompani-Zare, M., Zhan, H., and Samani, N., Analytical study of capture zone of a horizontal well in a confined aquifer, Journal of Hydrology, 2005. 307(1-4), 48-59
[40] Kuchuk F J, Goode P A, Wilkinson D J, et al. Pressure transient behavior of horizontal wells with and without gas cap or aquifer .SPE Formation evaluation, 1991, 6: 86-94
[41] Langseth, DE,Hydraulic Performance of Horizontal Wells IN: Superfund '90. Proceedings of the 11th National Conference, 1990. 398-408.
[42] Lee C H, Farmer I. Fluid Flow in Discontinuous Rocks.London: Chapman& Hall, 1993
[43] Lei, F Z. 1999. An Analytical Solution for Steady Flow into a Tunnel. Ground Water 37(1): 23-26,1999
[44] Long. C.S, Gilmour. P, Witherspoon. P. A model for steady fluid flow in random three-dimensional networks of disk-chaped fractures.Water Resources Research, 1985, 21(8): 1105-1115
[45] Louis C. Rock hydraulics[A]. L Muller Rock mechanics.Vienna:Springer-Verlag,1974, 299-387
[46] Maurer W C. Recent advances in horizontal drilling.J Canadian Pet Technol, 1995,34:25-33
[47] Mela K. and Louie J.N. Correlation Length and Fractal Dimension Interpretation From Seismic Date Using Variograms and Power Spectra.GEOPHYSICS,2001, 66(5):1372-1378
[48] Michael Tarshish , Combined Mathematical Model of Flow in an Aquifer-Horizontal Well System.1992 Ground Water 30(6):931-935
[49] Morgan J H. Horizontal drilling applications of petroleum technologies for environmental purposes.Ground Water Mon Rev, 1992, 12(2):98-102
[50] Murdoch L C. Transient analyses of an interceptor trench.Water Resour Res,1994,30(11): 3023-3031
[51] Nueman S P. Trends Prospects and Challenges in Quantifying Flow and Transport through Fractured Rocks. Hydrogeology Journal, 2005,13(1):124-147
[52] Ozkan E, Raghavan R, Joshi S D. Horizontal-well Pressure analysis.SPE Formation Evaluation, 1989, 4: 567-575
[53] Park E, Zhan H. Hydraulics of a finite-diameter horizontal well with wellbore storage and skineffect.Adv Water Resources, 2002, 25(4): 389-400
[54] Penmatcha V R,Arbabi s,Aziz K.Effect of pressure drop in horizontal wells and optimum well length[A]. Proceedings of the 1997 SPE production operations sysposium.Oklahoma:Soc Pet Eng, 1997
[55] Philippe Renard, Approximate discharge for constant head test with recharging boundary. Ground Water 2005,43( 3):439-442
[56] Plummer C R, Nelson J D, Zumwalt G S. Horizontal and vertical well comparison for in situ air sparging .Ground Water Monitoring and Eemediation, 1997, 17(1): 91-96
[57] Polubarinova-Kochina P. Theory of Groundwater Movement,(Translated from Russian by J.M.Roger de Wiest). Princeton University press. NJ,1962.
[58] Sawyer C S, Lieuallen-Dulam K K. Productivity comparison of horizontal and vertical ground water remediation well scenarios . Ground Water, 1998, 36(1): 98-103
[59] Seines K,Lieu S C,Haug B T.Troll horizontal well tests demonstrate large production potential from thin oil zones.SPE Reservoir Engineering, 1994, 9(2):133-139
[60] Snow D T.Hydraulic character of fractured metamorphic rocks of the front range and implications of the rocky mountain Arsenal Well. Colorado School of Mines Quarterly, 1968, 63(1): 167-199
[61] Zekai Sen, Aquifer Test Analysis in Fractured Rocks with Linear Flow Pattern.Ground Water,24(1), 1986: 72-78
[62] Zhan H. Analytical study of capture time to a horizontal well .J Hydrol, 1999, 217: 46-54
[63] Zhan H, Cao J. Analytical and semi-analytical solutions of horizontal well capture times under no-flow and constant-head boundaries .Adv Water Resources, 2000, 23(8): 835-848
[64] Zhan H, Park E. Vapor flow to horizontal wells in unsaturated zones.Soil Sci Soc Am J, 2002, 66(3): 710-721
[65] Zhang.L L,Franklin A. Prediction of water flow into rock tunnels:an analytical solutionassuming an hydraulic conductivity gradient.Int J Rock Mech Min Sci Geomech Abstr,1993,30(1):37-46
[2]陈崇希,林敏.地下水动力学.武汉:中国地质大学出版社,1999
[3]杜强,康永尚,万力,等.渗透性参数非均质特征的研究进展.地学前缘,1996,3(1-2):182-190
[4]蒋小伟,万力等.基于压水试验数据的砂泥岩裂隙岩体渗透结构分析.自然科学进展,2008, 18(3):355-360
[5]李保珠,李锋,薛传东,等.有限元法在涌水量预测中的应用.矿业工程,2003,1(5):55-58
[6]李茂芳.水文地质压水试验.北京:水利电力出版社,1987,87
[7]梁昆淼.数学物理方法.北京:高等教育出版社,1998
[8]胡伏生.岩溶充水矿床涌水量垂向变化规律研究[博士学位论文].北京:中国地质大学(北京),1997
[9]胡伏生,万力,田开铭,等.渗透系数衰减时矿坑涌水量与开采深度的关系.煤田地质与勘查,1998 (2):37-41
[10]陆君安.偏微粉方程的MATLAB解法.武汉:武汉大学出版社,2001
[11]田开铭,万力.各向异性裂隙介质渗透性的研究与评价.北京:学苑出版社,1989
[12]万力,李定方,李吉庆.三维裂隙网络的多边形单元渗流模型.水利水运科学研究,1993,6(4):347-353
[13]王纯祥,蒋宇静,江崎哲郎,等.复杂条件下长大隧道涌水预测及其对环境影响评价。岩石力学与工程学报,2008,27(12):2411-2417
[14]王恩志.岩体裂隙的网络分析及渗流模型.岩石力学与工程学报,1993,12(3):214-221
[15]王建秀,杨立中,何静.深埋隧道涌水量数值计算中的试算流量法.岩石力学与工程学报,2002,21(12):1176–1780.
[16]王建秀,朱合华,叶为民.隧道涌水量的预测及其工程应用.岩石力学与工程学报,2004,23(7):1150–1153
[17]王媛,秦峰,李东田.南水北调西线工程区地下径流模型、岩体透水性及隧洞涌水量预测.岩石力学与工程学报,2005,24(20):3673-3678
[18]徐国锋,杨建锋,陈侃福.台缙高速公路苍岭隧道水文地质勘察与涌水量预测.岩石力学与工程学报,2005,24(2),5531-5535
[19]薛禹群,谢春红.水文地质学的数值法.北京:煤炭工业出版社,1980
[20]薛禹群,朱学愚,吴吉春,等.地下水动力学.北京:地质出版社,1997
[21]于开宁.砂岩岩体渗透性评价及特征[博士学位论文].北京:中国地质大学,2003
[22]詹红兵,万军伟,水资源和环境工程中水平井研究简介.地球科学-中国地质大学学报,2003,28(5),511-516
[23]朱大力,李秋枫.预测隧道涌水量的方法.工程勘察,2004,4:18-22,32.
[24] Antonellin M,Aydin A.Effect of faulting on fluid flow in porous sandstones:petrophysical properties . AAPG,1994,78(3):355-377
[25] Carlsson A,Olsson T.Hydraulic properties of swedish crystalline rocks:hydraulic conductivuty and its relation to depth. Bulletin of the Geological Institutions of the University of Uppsala, New Series, 1978, 7:71-84
[26] Cleveland T G. Recovery performance for vertical and horizontal wells using semianalytical simulation.Ground Water, 1994, 32(1): 103-107
[27] David N. Jenkins, John K. Prentice.Theory for aquifer test analysis in fractured rocks under linear (nonradial) flow conditions.Ground Water. 20(1), 1982: 12-21
[28] Daviau F, Mouronval G, Bourdarot G, et al. Pressure analysis for horizontal wells. SPE formation Evaluation, 1988,3: 716-724
[29] Environmental Protection Agency (EPA). Manual alternative methods for fluid delivery and recovery .EPA/625/r-94/003,1994
[30] Falta R W. Analytical solutions for gas-flow due to gas injection and extraction from horizontal wells .Ground Water. 1995. 33(2): 235-246
[31] Freeze R. A., and J.A. Cherry. Groundwater. Englewood Cliffs, New Jerscy: Prentice-Hall Inc,1979
[32] Gale J E,Rouleau A,Witherspoon P A. Hydrogeologic characteristics of a fractured Granite. AWRC Conference Groundwater in Fractured Rock. Canberra: AWRC Conference, 1982. 95-108.
[33] Goode P A,Thambynayagam R K M. Pressure drawdown and buildup analysis of horizontal wells in anisotropic media.SPE Formation Evaluation,1987,2(4): 683-697
[34] Goodman,Moye D G,Van Schalkwyk A,et al. Groundwater inflows during tunnel driving.Engineering Geology,1965,2(2):39-56
[35] Hantush M S,Papadopulos I S.Flow of ground water to collector wells.Proc Am Soc Civil Engrs .J Hydraulics Division, 1962, HY5: 221-244
[36] Hunt B, Massmann J W. Vapor flow to trench in leaky aquifer .J Envir Engr, 2000, 126:375-380
[37] Joshi S D. Augmentation of well productivity with slant and horizontal wells. J of Petroleum Tech, 1988, 40(6): 729-739
[38] Kawecki M W. Transient flow to a horizontal water well .Ground Water,2000,38(6): 842-850
[39] Kompani-Zare, M., Zhan, H., and Samani, N., Analytical study of capture zone of a horizontal well in a confined aquifer, Journal of Hydrology, 2005. 307(1-4), 48-59
[40] Kuchuk F J, Goode P A, Wilkinson D J, et al. Pressure transient behavior of horizontal wells with and without gas cap or aquifer .SPE Formation evaluation, 1991, 6: 86-94
[41] Langseth, DE,Hydraulic Performance of Horizontal Wells IN: Superfund '90. Proceedings of the 11th National Conference, 1990. 398-408.
[42] Lee C H, Farmer I. Fluid Flow in Discontinuous Rocks.London: Chapman& Hall, 1993
[43] Lei, F Z. 1999. An Analytical Solution for Steady Flow into a Tunnel. Ground Water 37(1): 23-26,1999
[44] Long. C.S, Gilmour. P, Witherspoon. P. A model for steady fluid flow in random three-dimensional networks of disk-chaped fractures.Water Resources Research, 1985, 21(8): 1105-1115
[45] Louis C. Rock hydraulics[A]. L Muller Rock mechanics.Vienna:Springer-Verlag,1974, 299-387
[46] Maurer W C. Recent advances in horizontal drilling.J Canadian Pet Technol, 1995,34:25-33
[47] Mela K. and Louie J.N. Correlation Length and Fractal Dimension Interpretation From Seismic Date Using Variograms and Power Spectra.GEOPHYSICS,2001, 66(5):1372-1378
[48] Michael Tarshish , Combined Mathematical Model of Flow in an Aquifer-Horizontal Well System.1992 Ground Water 30(6):931-935
[49] Morgan J H. Horizontal drilling applications of petroleum technologies for environmental purposes.Ground Water Mon Rev, 1992, 12(2):98-102
[50] Murdoch L C. Transient analyses of an interceptor trench.Water Resour Res,1994,30(11): 3023-3031
[51] Nueman S P. Trends Prospects and Challenges in Quantifying Flow and Transport through Fractured Rocks. Hydrogeology Journal, 2005,13(1):124-147
[52] Ozkan E, Raghavan R, Joshi S D. Horizontal-well Pressure analysis.SPE Formation Evaluation, 1989, 4: 567-575
[53] Park E, Zhan H. Hydraulics of a finite-diameter horizontal well with wellbore storage and skineffect.Adv Water Resources, 2002, 25(4): 389-400
[54] Penmatcha V R,Arbabi s,Aziz K.Effect of pressure drop in horizontal wells and optimum well length[A]. Proceedings of the 1997 SPE production operations sysposium.Oklahoma:Soc Pet Eng, 1997
[55] Philippe Renard, Approximate discharge for constant head test with recharging boundary. Ground Water 2005,43( 3):439-442
[56] Plummer C R, Nelson J D, Zumwalt G S. Horizontal and vertical well comparison for in situ air sparging .Ground Water Monitoring and Eemediation, 1997, 17(1): 91-96
[57] Polubarinova-Kochina P. Theory of Groundwater Movement,(Translated from Russian by J.M.Roger de Wiest). Princeton University press. NJ,1962.
[58] Sawyer C S, Lieuallen-Dulam K K. Productivity comparison of horizontal and vertical ground water remediation well scenarios . Ground Water, 1998, 36(1): 98-103
[59] Seines K,Lieu S C,Haug B T.Troll horizontal well tests demonstrate large production potential from thin oil zones.SPE Reservoir Engineering, 1994, 9(2):133-139
[60] Snow D T.Hydraulic character of fractured metamorphic rocks of the front range and implications of the rocky mountain Arsenal Well. Colorado School of Mines Quarterly, 1968, 63(1): 167-199
[61] Zekai Sen, Aquifer Test Analysis in Fractured Rocks with Linear Flow Pattern.Ground Water,24(1), 1986: 72-78
[62] Zhan H. Analytical study of capture time to a horizontal well .J Hydrol, 1999, 217: 46-54
[63] Zhan H, Cao J. Analytical and semi-analytical solutions of horizontal well capture times under no-flow and constant-head boundaries .Adv Water Resources, 2000, 23(8): 835-848
[64] Zhan H, Park E. Vapor flow to horizontal wells in unsaturated zones.Soil Sci Soc Am J, 2002, 66(3): 710-721
[65] Zhang.L L,Franklin A. Prediction of water flow into rock tunnels:an analytical solutionassuming an hydraulic conductivity gradient.Int J Rock Mech Min Sci Geomech Abstr,1993,30(1):37-46
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |