周期性海潮和气压波动引起的地下水流和气流的解析研究
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摘要
本文定量研究了海潮效应和气压效应对非饱和带土壤孔隙中的气流和承压含水层井孔水位波动的影响。文章采用解析的方法，将从动力学方程出发，通过复平面的分离变量法，得到了方程精确的解析解，并结合计算机技术对解析解和各个模型参数之间的关系进行敏感性分析，同时为含水系统水文地质参数的求取提供了一种高效、便捷和经济的途径。
地下气流的研究在土壤气相抽提（Soil Vapor Extraction）技术中发挥着重要的作用，如去除非饱和带土壤中的挥发性有机化合物（VOCs），量化污染物自然衰减效率等。文章第三章阐述了海潮和地表气压波动引起的非饱和带的气流，改进了前人的数值半解析解，推导得到了精确的解析解，大大节约了计算时间，同时，引入一个假想实例，基于拟牛顿算法和非线性的最小二乘拟合原理，反求得到了上层非饱和带的空气渗透率和有效孔隙度。此外，由于气温白天高晚间低的周期性变化，大气压也会呈现周期性波动；这种波动会导致透气性土壤地表进行“呼吸”，本文引入一个“地表呼吸量”的概念，并对这一物理量对模型各参数的依赖性进行了定量分析。分析发现，当地下水位和气压波动具有相同的频率和同量级的振幅时，单独考虑其中一种波动和同时考虑两者波动将在地表产生同一量级的气流量。特别地，当同时考虑两者波动时，气流量随着上层非饱和带的渗透率和下层潜水含水层的孔隙度的增大而增大，而随着波动两者的相位差、波动频率和上层非饱和带的厚度的增大而减小。当上层非饱和带的空气渗透率减小10倍时，气流量可瞬时衰减为0，而当两者波动的相位差由π变到0时，气流量将减小4到5倍。
承压含水层井孔水位的气压效应作为地下水微动态的重要组成部分，在地震预测预报系统中发挥着重要的作用。文中第四章首次定量研究了井孔储存效应对气压波动引起的承压含水层井水水位波动的抑制和滞后效应，建立了相应的数学模型，并推出了其解析解，给出了承压含水层井孔水位波动与气压波动的定量关系。我们发现，随着井径的增大或者含水层水力扩散系数的减小，气压波动引起的井水水位的波动减弱。当井径无穷大或含水层水力扩散系数无穷小时，井水水位不再随气压波动；反之，当井径无限小或含水层水力扩散系数无穷大时，井水水位则正好以反相位随气压波动，且井水水位波动幅度和气压波动幅度之比刚好为气压效应系数。随后，引入具体算例，定量分析了井水水位随井半径变化的情况。最后，结合曹妃甸地区具体观测数据，提供了含水层水文地质参数求取的一种新方法与新思路。
Subsurface airflow and groundwater flow can beinduced by a variety of driving forces,such asprecipitation,artificial rechargeorpumping, theeffects of barometric pressurefluctuations andtidal fluctuations, earth tides andearthquakes. In this paper, we focus ondriving forces of the effects of barometric pressure fluctuations and tidal fluctuations on thegroundwater flow and subsurface airflow, which play a vital role in obtaininghydrogeological parameters.
A study onsubsurface airflow is of high importance in quantifying the effectiveness ofnatural attenuation of volatile organic compounds (VOCs) or in determining the need ofengineering systems (e.g., soil vapor extraction of VOCs).In chapter3, we present a newanalytical solution for describing the subsurface airflow induced by barometric pressure andgroundwater head fluctuations. The solution improves a previously-published semi-analyticalsolution into a fully-explicit expression and can save much computation efforts when it wasused to estimate the soil permeability and porosity, which was demonstrated by a hypotheticalexample. If the groundwater head and barometric pressurefluctuations have the samefrequency and the same order of magnitude for the amplitudes, each or the combination ofboth fluctuations will generate the air exchange volumes of the same order of magnitudethrough the ground surface. Particularly, the air exchange volume caused by the combinedfluctuations increases with the upper layer’s permeability, lower layer’s porosity, anddecreases with the phase difference between these two fluctuations, fluctuation frequency,and the upper layer’s thickness. The air exchange volume may decrease quickly to zeroessentially when the upper layer’s permeability decreases tenfold, and decrease fourfold tofivefold when the phase difference decreases from π to zero.
In chapter4, we first considered quantitatively the well storage effect on the barometricpressure fluctuation--induced water level fluctuation in a well screened in a single confinedaquifer. The mathematical model for the system is given, and an analytical solution to themodel is derived. The quantitative dependency of the well water level variation on the modelparameters such as the well radius, the hydraulic diffusivity of the aquifer, and the barometricpressure fluctuation is discussed. It is found that the fluctuation of the water level in thewell becomes weak as the well radius increases and/or the aquifer’s hydraulic diffusivitydecreases. When the well radius tends to infinity or the hydraulic diffusivity tends to zero,water level in well will no longer fluctuate with barometric pressure fluctuation. On the other hand, when the well radius tends to zero or the hydraulic diffusivity tends to infinity, thewater level in well will fluctuate with the barometric pressure fluctuation in an inverse phase(i.e., phase shift=π), and the ratio of the well water level fluctuation amplitude to thebarometric pressure fluctuation amplitude equals the barometric efficiency.At last,observation data in Caofeidian area are used as a case study to obtain hydrogeologicalparameters.
地下气流的研究在土壤气相抽提（Soil Vapor Extraction）技术中发挥着重要的作用，如去除非饱和带土壤中的挥发性有机化合物（VOCs），量化污染物自然衰减效率等。文章第三章阐述了海潮和地表气压波动引起的非饱和带的气流，改进了前人的数值半解析解，推导得到了精确的解析解，大大节约了计算时间，同时，引入一个假想实例，基于拟牛顿算法和非线性的最小二乘拟合原理，反求得到了上层非饱和带的空气渗透率和有效孔隙度。此外，由于气温白天高晚间低的周期性变化，大气压也会呈现周期性波动；这种波动会导致透气性土壤地表进行“呼吸”，本文引入一个“地表呼吸量”的概念，并对这一物理量对模型各参数的依赖性进行了定量分析。分析发现，当地下水位和气压波动具有相同的频率和同量级的振幅时，单独考虑其中一种波动和同时考虑两者波动将在地表产生同一量级的气流量。特别地，当同时考虑两者波动时，气流量随着上层非饱和带的渗透率和下层潜水含水层的孔隙度的增大而增大，而随着波动两者的相位差、波动频率和上层非饱和带的厚度的增大而减小。当上层非饱和带的空气渗透率减小10倍时，气流量可瞬时衰减为0，而当两者波动的相位差由π变到0时，气流量将减小4到5倍。
承压含水层井孔水位的气压效应作为地下水微动态的重要组成部分，在地震预测预报系统中发挥着重要的作用。文中第四章首次定量研究了井孔储存效应对气压波动引起的承压含水层井水水位波动的抑制和滞后效应，建立了相应的数学模型，并推出了其解析解，给出了承压含水层井孔水位波动与气压波动的定量关系。我们发现，随着井径的增大或者含水层水力扩散系数的减小，气压波动引起的井水水位的波动减弱。当井径无穷大或含水层水力扩散系数无穷小时，井水水位不再随气压波动；反之，当井径无限小或含水层水力扩散系数无穷大时，井水水位则正好以反相位随气压波动，且井水水位波动幅度和气压波动幅度之比刚好为气压效应系数。随后，引入具体算例，定量分析了井水水位随井半径变化的情况。最后，结合曹妃甸地区具体观测数据，提供了含水层水文地质参数求取的一种新方法与新思路。
Subsurface airflow and groundwater flow can beinduced by a variety of driving forces,such asprecipitation,artificial rechargeorpumping, theeffects of barometric pressurefluctuations andtidal fluctuations, earth tides andearthquakes. In this paper, we focus ondriving forces of the effects of barometric pressure fluctuations and tidal fluctuations on thegroundwater flow and subsurface airflow, which play a vital role in obtaininghydrogeological parameters.
A study onsubsurface airflow is of high importance in quantifying the effectiveness ofnatural attenuation of volatile organic compounds (VOCs) or in determining the need ofengineering systems (e.g., soil vapor extraction of VOCs).In chapter3, we present a newanalytical solution for describing the subsurface airflow induced by barometric pressure andgroundwater head fluctuations. The solution improves a previously-published semi-analyticalsolution into a fully-explicit expression and can save much computation efforts when it wasused to estimate the soil permeability and porosity, which was demonstrated by a hypotheticalexample. If the groundwater head and barometric pressurefluctuations have the samefrequency and the same order of magnitude for the amplitudes, each or the combination ofboth fluctuations will generate the air exchange volumes of the same order of magnitudethrough the ground surface. Particularly, the air exchange volume caused by the combinedfluctuations increases with the upper layer’s permeability, lower layer’s porosity, anddecreases with the phase difference between these two fluctuations, fluctuation frequency,and the upper layer’s thickness. The air exchange volume may decrease quickly to zeroessentially when the upper layer’s permeability decreases tenfold, and decrease fourfold tofivefold when the phase difference decreases from π to zero.
In chapter4, we first considered quantitatively the well storage effect on the barometricpressure fluctuation--induced water level fluctuation in a well screened in a single confinedaquifer. The mathematical model for the system is given, and an analytical solution to themodel is derived. The quantitative dependency of the well water level variation on the modelparameters such as the well radius, the hydraulic diffusivity of the aquifer, and the barometricpressure fluctuation is discussed. It is found that the fluctuation of the water level in thewell becomes weak as the well radius increases and/or the aquifer’s hydraulic diffusivitydecreases. When the well radius tends to infinity or the hydraulic diffusivity tends to zero,water level in well will no longer fluctuate with barometric pressure fluctuation. On the other hand, when the well radius tends to zero or the hydraulic diffusivity tends to infinity, thewater level in well will fluctuate with the barometric pressure fluctuation in an inverse phase(i.e., phase shift=π), and the ratio of the well water level fluctuation amplitude to thebarometric pressure fluctuation amplitude equals the barometric efficiency.At last,observation data in Caofeidian area are used as a case study to obtain hydrogeologicalparameters.
引文
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Bear J. Hydraulics of ground water. Jerusalem: McGraw-Hill Inc..1979
Bredehoeft, J. D.. Response of well-aquifer systems to earth tides. J. Grophys. Res.,72,1967.3075~3087
Buckingham, E.. Contributions to our knowledge of the aeration of soils.Bull.25, Soils Bur.,U.S. Dep. Of Agric., Washington D.C..1904
Carrera, J., and S. P. Neuman. Estimation of aquifer parameters under transient and steadystate conditions:1. Maximum likelihood method incorporating prior information.WaterResour. Res.,22(2),1986.199~210
Carrera, J., and S. P. Neuman. Estimation of aquifer parameters under transient and steadystate conditions:3. Uniqueness, stability, and solution algorithms.Water Resour.Res.,22(2),1986.211~227
Fetter, C. W..Applied Hydrogeology, Prentice-Hall.Englewood Cliffs N. J.,1994
Hsieh, P. A., J. D. Bredehoeft, and J. M. Farr. Determination of Aquifer Transmissivity fromEarth Tide Analysis.Water Resour. Res.,1987,23(10),1824~1832
Jacob, C. E..The flow of water in an elastic artesian aquifer.Eos Trans. AGU,21,1940,574~586
Jacob, C. E. Flowof ground-water. In Engineering Hydraulics.Rouse H.(ed.). Wiley: NewYork.1950
Jeng, D. S., X. Mao, P. Enot, D. A. Barry, and L. Li. Spring-neap tide-induced beach watertable fluctuations in a sloping coastal aquifer.Water Resour. Res.,2005,41:(7)W07026,doi:10.1029/2005WR003945
Jiao, J. J., and H. L. Li. Breathing of coastal vadose zone induced by sea levelfluctuations.Geophys Res Lett,2004,31(11):L11502, doi:10.1029/2004GL019572
Kamp, G. V., and J. E. Gale.Theory of earth tide and barometric effects in porous formationswith compressible grains.Water Resour. Res.,1983,19,538~544
Li, H. L., and Q. C. Yang. A least-squares penalty method algorithm for inverse problems ofsteady-state aquifer models.Adv. Water Resour.,2000,23(8),867-880
Li, H. L., and J. J. Jiao. One-dimensional airflow in unsaturated zone induced by periodicwater table fluctuation.Water Resour. Res.,2005,41(4):W04007, doi:10.1029/2004WR003916
Li, H. L., L. Li, L. David, C. B. Michel, and L. Guanyi. Modeling tidal signals enhanced by asubmarine spring in a coastal confined aquifer extending under the sea.Adv. WaterResour.,2007,30,1046~1052
Li, J., H. B. Zhan, G. H. Huang, and K. H. You. Tide-induced airflow in a two-layered coastalland with atmospheric pressure fluctuations.Adv. Water Resour.,2011, doi:10.1016/j.advwaters.2011.02.014
Li, L., and D. A. Barry. Wave-induced beach groundwater flow.Adv. Water Resour.,2000,23(4),325-337
Li, L., D. A. Barry, F. Stagnitti, J. Y. Parlange, and D. S. Jeng. Beach water table fluctuationsdue to spring-neap tides: moving boundary effects.Adv. Water Resour.,2000,23(8),817-824
Li, H., G. Li, J. Cheng, and M. C. Boufadel.Tide-induced head fluctuations in a confinedaquifer with sedimentcovering its outlet at the sea floor.Water Resour. Res.,2007,43,W03404, doi:10.1029/2005WR004724
Lu, N.. Time-series analysis for determining vertical air permeability in unsaturated zones.J.Geotech Geoenviron,1999,125(1),69~77
Nielsen, P.. Tidal Dynamics of the Water-Table in Beaches.Water Resour. Res.,1990,26(9),2127~2134
Rojstaczer, S.. Determination of Fluid-Flow Properties from the Response of Water Levels inWells to Atmospheric Loading.Water Resour. Res.,1988,24(11),1927~1938
Shan, C., R. W. Falta, and I. Javandel. Analytical Solutions for Steady-State Gas-Flow to aSoil Vapor Extraction Well.Water Resour. Res.,1992,28(4),1105~1120
Shan, C.. Analytical Solutions for Determining Vertical Air Permeability in UnsaturatedSoils.Water Resour. Res.,1995,31(9),2193~2200
Stallman, R. W.. Flow in the zone of areation.Adv. Hydrosci.,1967,4,151~195
Stallman, R. W., and E. P. Weeks. The use of atmospherically induced gas-pressurefluctuations for computing hydraulic conductivity of the unsaturated zone(abstract).Geol. Soc. Am. Abstr. Programs, part7, p.213,1969
Szilagyi, J.. Vadose zone influences on aquifer parameter estimates of saturated-zonehydraulic theory.J. Hydrol.,2004,286(1-4),78~86, doi:10.1016/j.hydrol.2003.09.009
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