臺灣博碩士論文加值系統

地面儲存槽的洩漏，是土壤污染主要的污染源之一，發生滲漏後，部分揮發性有機物(volatile organic compound, VOC)會以非水相液體(NAPL)殘存在土壤中，若經過一段時間，氣相、液相、及吸附相的VOC會處於平衡狀態。若要整治受污染的土層，需先移除滲漏的儲存槽，隨後VOC將會在自然環境下逸散至大氣中，此自然揮發的過程，值得研究。VOC存在土壤中，可分為純VOC和以多種化合物組成的複合VOC兩類，常見的汽油儲存槽滲漏污染問題，則以複合VOC污染居多。在本文中，我們發展了一個數值模式，描述複合VOC殘存相的揮發鋒面移動及地表下莫耳分率的空間分布，在模式中，考慮於揮發鋒面及其上下三個區域，透過有限差分法及可移動格網，近似求解莫耳分率的分佈。此外，考慮單一VOC污染的問題，將複合VOC模式簡化為單VOC模式，利用Boltzmann’s transformation，求得單VOC模式的解析解。本文考慮六個污染案例，包括有無殘存相解之濃度分佈，以及不同土壤孔隙率、污染物、初始莫耳分率對揮發鋒面和莫耳分率分布之影響。藉由計算VOC揮發鋒面的位置和移動速度，本研究發展的模式，或可用來分析或評估受VOC污染的現地問題。

Leak of underground storage tank is one of major sources for the spill of volatile organic compound (VOC) entering unsaturated soil. Once leak occurs, some VOCs may present in soil as residual non-aqueous phase liquid (NAPL) phase. The gas, liquid, and absorbed phases of VOC may reach equilibrium after a period of time in the soil. To clean up the contaminated soil, the tank must be removed and the VOC can then evaporate to the atmosphere. It is of interest to investigate the natural evaporation of NAPL. There are two types of VOC contamination in soil. One is multi-component VOC while the other is single-component VOC. Multi-component VOC, composed of several VOC components, is often found in petroleum leaking problems. This study develops a two-component model describing the mole fraction distributions of VOCs and migration of evaporation front of the VOC in NAPL phase in a homogeneous soil system. The model considers three regions which are above, below, and at the front and is solved by the finite difference method with a moving grid approach. The model is also simplified to a single-component model which deals with a one-component VOC contamination and solved analytically by Boltzmann’s transformation. Six cases are considered including a comparison of the solutions for the cases with and without the presence of residual NAPL phase and the assessment for the influences of different soil porosity, chemicals, and initial mole fraction on the front location and mole fraction. Finally, analytical expressions for the depth and moving speed of the front are also developed for practical uses.

摘要 --------------------------------------------------------------------------------------------------------I
ABSTRACT ----------------------------------------------------------------------------------------------II
致謝--------------------------------------------------------------------------------------------------------IV
TABLE OF CONTENTS ------------------------------------------------------------------------------V
LIST OF TABLES ------------------------------------------------------------------------------------VII
LIST OF FIGURES ---------------------------------------------------------------------------------VIII
NOTATION ----------------------------------------------------------------------------------------------X
CHAPTER 1 INTRODUCTION ---------------------------------------------------------------------1
1.1. Background -----------------------------------------------------------------------------1
1.2. Literature Review ---------------------------------------------------------------------2
1.3. Objectives -------------------------------------------------------------------------------4
CHAPTER 2 METHEMATICAL MODEL --------------------------------------------------------6
2.1 Mathematical model: Two-component case --------------------------------------6
2.1.1 Below the evaporation front ----------------------------------------------9
2.1.2 Above the evaporation front --------------------------------------------10
2.1.3 At the evaporation front -------------------------------------------------11
2.1.4 Boundary and initial conditions ----------------------------------------11
2.2 The numerical method in solving the model -----------------------------------13
2.2.1 Finite difference approximation ----------------------------------------13
2.2.2 The solution procedure of the model ----------------------------------15
2.3 Simplified model: Single-component case ---------------------------------------16
2.3.1 Below the evaporation front --------------------------------------------16
2.3.2 Above the evaporation front --------------------------------------------16
2.3.3 At the evaporation front -------------------------------------------------17
2.3.4 The analytical solution of single-component model ----------------19
CHAPTER 3 RESULTS AND DISCUSSION ----------------------------------------------------22
3.1 Case 1: Different evaporation times in two models ----------------------------23
3.2 Case 2: Initial mole fraction --------------------------------------------------------24
3.3 Case 3: Soil porosity ------------------------------------------------------------------25
3.4 Case 4: Absence of the NAPL phase ----------------------------------------------26
3.5 Case 5: Different chemicals ---------------------------------------------------------27
3.6 Case 6: Effect of effective diffusion coefficient on moving speed of
evaporation front---------------------------------------------------------28
CHAPTER 4 CONCLUSIONS----------------------------------------------------------------------29
REFERENCES------------------------------------------------------------------------------------------32

Baehr, A. L., 1987. Selective transport of hydrocarbons in the unsaturated zone due to aqueous and vapor phase partitioning. Water Resour. Res. 23 (10), 1926-1938.
Caldwell, J., Kwan, Y.Y., 2003. On the perturbation method for the Stefan problem with time-dependent boundary conditions. Int. J. Heat Mass Transfer. 46, 1497–1501.
Cheng, T.F., 2000. Numerical analysis of nonlinear multiphase Stefan problem. Comput. Struct. 75, 225-233.
Carslaw, H. S., Jaeger, J. C., 1959. Conduction of heat in solids. 2nd ed., Clarendon, Oxford,
Corapcioglu, M.Y., Baehr, A.L., 1987. A compositional multiphase model for groundwater contamination by petroleum products. Water Resour. Res. 23(1), 191-200.
Crank, J., 1984. Free and moving boundary problems. Oxford Univ. Press, New York,
Falta, R. W., Javandel, I., Pruess, K., Witherspoon, P. A., 1989. Density-driven flow of gas in unsaturated zone due to evaporation of the volatile organic compounds. Water Resour. Res. 25(10), 2159-2169.
Feltham, D.L., Garside, J., 2001. Analytical and numerical solutions describing the inward solidification of a binary melt. Chem. Eng. Sci. 56, 2357-2370.
Fetter, C.W., 1993. Contaminant hydrogeology. Prentice Hall, New Jersey.
Hoier, C. K., Sonnenborg, T. O., Jensen, K. H., Kortegaard, C., Nasser, M. M., 2007. Experimental investigation of pneumatic soil vapor extraction. J. Cont. Hydrol. 89, 29-47.
Javierre, E., Vuik, F.J., Vermolen, S., Zwaag, van der, 2006. A comparison of numerical models for one-dimensional Stefan problems. J. Comput. Appl. Math. 192, 445-459.
Jury, W. A., Spencer, W. F., Farmer, W. J., 1983. Behavior assessment model for trace organics in soil: I. Model description. J. Environ. Qual. 12 (4), 558-564.
Jury, W., A., Russo, D., Streile, G., EL Abd H., 1990. Evaluation of volatilization by organic chemicals residing below the soil surface. Water Resour. Res. 26 (1), 13-20.
Lee, M.Z.C., Marchant, T.R., 2004. Microwave thawing of cylinders. Appl. Math. Modell. 28, 711–733.
Massmann, J., Farrier, D., 1992. Effects of atmospheric pressure on gas-transport in the vadose zone. Water Resour. Res, 28(3), 777-791.
Millongton, R. J., Quirk, J. M., 1961. Permeability of porous solids. Trans. Faraday Soc. 57, 1200-1207.
Naaktgeboren, C., 2007. The zero-phase Stefan problem. Int. J. Heat Mass Transfer. 50, 4614–4622.
Patnaik, S., Voller, V.R., Parker, G., Frascati, A., 2009. Morphology of a melt front under a condition of spatial varying latent heat. Int. Comm. Heat Mass Transfer. 36, 535–538.
Perry, R. H., Green, D.W., Maloney, J.Q., 1997. Perry’s chemical engineers’ handbook. 7th ed., McGraw-Hill, New York.
Pinder, G. F., Abriola, L. M., 1986. On the simulation of nonaqueous phase organic compounds in the subsurface. Water Resour. Res. 22 (9), 109S-119S.
Purlis, E., Salvadori, V.O., 2009. Bread baking as a moving boundary problem. Part 1: Mathematical modelling. J. Food Eng. 91, 428–433.
Purlis, E., Salvadori, V.O., 2009. Bread baking as a moving boundary problem. Part 2: Model validation and numerical simulation. J. Food Eng. 91, 434–442.
Quintard, M., Whitaker, S., 1995. The mass flux boundary condition at a moving fluid-fluid interface. Ind. Eng. Chem. Res. 34, 3508-3513.
Rattanadecho, S., 2006. Simulation of melting of ice in a porous media under multipleconstant temperature heat sources using a combined transfiniteinterpolation and PDE methods. Chem. Eng. Sci. 61, 4571–4581.
Sazhin, S.S., Krutitskii, P.A., Gusev, I.G., Heikal, M.R., 2010. Transient heating of an evaporating droplet. Int. J. Heat Mass Transfer. 53, 2826–2836.
Shoemaker, C. A., Culver, T. B., Lion, L. W., Peterson, M. G., 1990. Analytical models of the impact of two- phase sorption on subsurface transport of volatile chemicals. Water Resour. Res. 26 (4), 745-758.
Sleep, B. E., Sykes, J. F., 1989. Modeling the transport of volatile organics in variably saturated media. Water Resour. Res. 25 (1), 81-92.
Stefan, J., 1889. Sber. Akad. Wiss. Wien. 98, 473-484.
Stefan, J., 1889. Sber. Akad. Wiss. Wien. 98, 965-983.
Szimmat, J., 2002. Numierical simulation of solidification processes in enclosures. Heat and Mass Transfer. 38, 279-293.
Vazquez-Nava, E., Lawrence, C., Thermal dissolution of a spherical particle with a moving boundary. Heat Transfer Eng. 30(5), 416–426.
Yates, S. R., Papieri, S. K., Gao, F., Gan, J., 2000. Analytical solutions for the transport of volatile organic chemicals in unsaturated layered systems. Water Resour. Res. 36(8), 1993-2000.
Yeh, H. D., 1987. Theis' solution by nonlinear least-squares and finite- difference Newton's method, Ground Water. 25(6), 710-715.
Zaidel, J., Russo, D., 1994. Diffusive transport of organic vapors in the unsaturated zone with kinetically-controlled volatilization and dissolution: analytical model and analysis. J. of Contam. Hydro. 17, 145-165.
Zaidal, J., Zazovsky, A., 1999. Theoretical study of multicomponent soil vapor extraction: propagation of evaporation-condensation fronts. J. of Contam. Hydro. 37, 225-268.