溶质在土壤中运动的微观机理及其在滴灌施肥中的应用
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摘要
干旱缺水是影响我国农业可持续发展的主要因素，滴灌作为先进的节水灌溉技术在我国已得到了大面积推广应用。与此同时，有关随水施肥也成为现代节水农业研究的一项重要内容，水分与肥料等溶质与土壤的物理化学反应直接影响到作物对水分、肥料的高效安全利用。本文采用理论模拟和室内外试验研究相结合的方法，重点研究了溶质在土壤孔隙运动的微观机理，提出了改进的溶质运移模拟模型，在此基础上模拟了不同溶质在土壤中的运移，并通过室内滴灌条件下水氮分布试验，应用上述模型模拟了滴灌条件下水分及氮素运移。取得主要结论如下：(1)对溶质在土壤孔隙中微观机理研究表明，对土壤孔隙内水盐运动的直接模拟可以提高对宏观尺度下模型的模拟可靠性。本文假定介质为各向均匀、所有孔隙全部连通；水分在土壤孔隙中的运动处于层流，水分与土壤固体颗粒的边界设为不可滑动边界，并用碰撞-弹回法处理，利用lattice Boltzmann方法模拟流体及溶质在土壤孔隙内的运动和扩散，计算了溶质在宏观尺度下的时空分布，确定了宏观尺度下溶质从非正常弥散向正常弥散的转换过程和时间。模拟结果表明，水分在孔隙内的流速分布并不均匀，流体主要是沿几个流体通道运动，这种运动特征导致了溶质运移偏离正常弥散方程所描述的迁移过程，而且溶质浓度的空间分布具有持续的拖尾现象。改进的CTRW模型能更真实地描述溶质的运移规律。(2)研究了溶质非费克弥散现象的空间分数维对流—弥散模型，表明了空间分数维对流—弥散方程是描述溶质在含有大孔隙土壤中运移的一种有效模型。文献中的空间分数维对流弥散方程中的分数维是由Riemann-Liouville方程定义的，只适用于溶质在无限含水层的运动，模型在模拟溶质在土壤内的运移时存在一定的物理缺陷。为克服这一缺陷，本文利用Caputo定义的分数维导数定义了一个分数维弥散通量，基于质量守恒原理建立了一种新的分数维对流弥散方程，并提出了求解该方程的一种有限体数值法。除此之外，本文还研究了不同边界条件对溶质运移的影响。(3)吸附性溶质在土壤中运移的模拟研究表明，吸附性溶质的迁移与描述惰性溶质的迁移类似，也是由迁移距离概率函数和完成每一步迁移所需时间的概率密度函数来描述的。本文假定惰性溶质和吸附性溶质的迁移距离函数分布式相同，而迁移所需的时间概率分布函数不同。考虑到大部分田间土壤具有很强的空间变异性，本文利用带有拖尾的概率幂函数来描述迁移时间的概率密度分布，把CTRW模型简化为时间分数维对流—弥散模型。以质量守恒为基础，本文提出了求解该方程的有限体积法。通过对三种不同的吸附性溶质运移的模拟计算表明，分数维对流—弥散方程比经典的对流—弥散模型能更好地解释溶质穿透曲线中长长的拖尾现象，试验值与模拟值有良好的相关性，表明了时间分数维对流—弥散方程中的参数与土壤孔隙水流速无关。(4)通过滴灌同步施肥(相同流量和灌水量、不同硝态氮浓度)条件下根际土壤水氮室内土槽试验，测定了土壤水分和硝态氮的时空分布。结果表明：土壤水分分布均表现为地表湿润区以滴头为中心向四周扩散，停灌后上下层土壤水势梯度随径向距离的增加而逐渐减小。高浓度处理土壤硝态氮表现为随径向距离的增加逐渐减小，硝态氮的含量与径向距离及土层深度成反比；低浓度处理土壤硝态氮随径向距离及土层深度增加先增大后减小，在深度分布上表现为开口向左的抛物线分布，并随着时间的推移各处理相同径向距离土壤硝态氮含量的差异均逐渐减少。(5)对滴灌条件下水分运动进行了模拟研究。为准确描述土壤含水量在不同土质的界面上是不连续的、提高Richards方程数值解的稳定性，本文以土壤水基质势作为模拟变量，采用混合的Richards’方程，利用一种截距式Newton方法来处理重力项，把Picard法的一阶收敛提高到收敛速度介于一阶与二阶之间，使最终产生的线性方程组的矩阵是对角占优的，从而保证在非线性迭代过程中的解不出现振荡，加快了非线性迭代的收敛，提高模拟土壤水分的效率。(6)模拟研究了滴灌条件下的硝态氮运移。实验采用回填土，土壤中无明显大的孔隙，模型中溶质的迁移距离用正态分布表示。根据质量守恒原理，提出了一种描述滴灌条件下氮素运移的CTRW模型，并提出了求解该CTRW模型的数值解法。结果表明，与常规的两区模型相比，改进后的CTRW模型能更好地模拟溶质在土壤中的运动过程。水和化学物质在土壤中的运动主要是由土壤中孔隙的非均匀性决定的。图像技术的发展和计算物理的提高，为进一步研究土壤中的水盐运动机理和提高模拟可靠性提供了技术手段。CTRW模型可以弥补传统对流—弥散方程的不足，能够更准确的模拟滴灌条件下土壤水肥的运动，本文正是研究孔隙尺度下非饱和土壤中的水盐运动规律模拟方向的的一个尝试，但限于土壤本身的空间变异性及试验时间的有限、滴灌条件取样的困难、计算参数的测试选取等试验条件，对肥分的研究又仅限于硝态氮，模拟结果虽基本反映了实验中水分和硝态氮的运动情况，但仍存在一定的误差，今后尚须继续研究。
The shortage of fresh water is a main factor that hampers sustainable agricultural development in China, and drip-irrigation, as an advanced irrigation technology, has been widely applied in China. At the meantime, drip fertigation has also received increasingly attention in modern agriculture in which the reaction between water, soil and the soil solution affects the use of soil nutrients by plants. The objective of this thesis is to use a combination of numerical modeling and experiments to investigate the fundamentals of solute transport in pore space of soil with a view to improve modeling at macroscopic scales, which can be used to investigate the movement of nutrients under drip fertigation. The main conclusions of this thesis are:
(1) Assuming that water flow is laminar and that the medium is homogenous and all pores in it are hydraulically connected, water flow and solute transport in the pore scale were simulated using the lattice Boltzmann method by treating the water-solid interface as non-slip boundary. The result reveals that water flow is mainly concentrated along a few channels. As a result, the movement of tracers is anomalous, which cannot be accurately described by the classical advection-dispersion equation. Comparing the results with the continuous time random walk (CTRW) reveals that the solute movement is well described by CTRW with a modified exponentially distributed transition time.
(2) A spatial fractional advection-dispersion equation model (FADE) is investigated, which is shown to be an effective model to simulate solute movement in natural soils with big pores. The FADE currently available in literature is based on Riemann-Lioville equation, limiting its application to infinite domains. A modified method based on the Caputo derivatives is presented to overcome this problem. A finite volume approach is given to numerically solve the modified FADE and its associated boundaries. The model is then compared with experimental data, and the results show good agreement.
(3) Study on the movement of adsorptive solute reveals that its movement can be simulated using the similar framework as for non-adsorptive solute, using a probability distribution function to describe the distance between the pore and the time it takes a solute particle to move from one pore to another. The difference between the adsorptive and non-adsorptive solutes is the time for solute particle to move one pore to another. Given the inherent heterogeneity of natural soils, this thesis used a power-law function to describe the time it takes the adsorptive solute to move from one pore to another, making the CTRW model into a time-fractional advection-dispersion equation. Based on the principle of mass balance, a finite volume method is proposed to solve the equation and then compares it with experimental data. The results indicate that the model accurately captures the persistent long tails in the breakthrough curves, and that the transport parameters are independent of water flow rate.
(4) Experimental study of the movement of nitrate under drip fertigation was carried out in the tank filled with sandy soil. The measurement of water content and nitrate concentration reveals the water content is symmetrical vertically around the emitter and after the termination irrigation, the gradient of the water potential changes. Also, the peak nitrate concentration is affected applied nitration concentration, decreasing with the distance from the emitter as the applied concentration increases.
(5) A two-dimensional model is proposed to simulate the movement of water in soil under drip irrigation. To accurately describe water movement in heterogeneous soil and variably saturated condition, the mixed-form Richards' equation was used. To improve the convergence of the numerical model, a chord Newton method was used to solve the gravity term so as to make the final matrix diagonally dominant. This stabilizes the solution, thereby increasing the convergence rate.
(6) Using the above models for both water flow and solute transport, the nitrate movement under the drip irrigation is modeled. Since the experiments were conducted using repacked soil, there are no obvious big pores. I thus used the time-fractional CTRW model to simulate nitrate movement in which the distance between the adjacent pores is assumed to be normally distributed. Comparing with the commonly used the mobile-immobile model, the proposed model improves the description of the solute movement in soils. Comparison of the model with experiment shows fair agreement.
The movement of water and solute in soil is dictated by the pore geometry. The advent and development of imaging technology and computer power over the last two decades has made it feasible to investigate pore-scale water and solute movement. The CTRW model presented in this paper can overcome some limitations of the commonly used advection-dispersion model, and is used in this work to investigate nutrient transport under drip fertigation. However, due to the restriction of experiments, such as the difficulty of sampling, this work is restricted to nitrate. The simulations show similar trend as the measurements, but this is still some discrepancy. Further research is needed.
The shortage of fresh water is a main factor that hampers sustainable agricultural development in China, and drip-irrigation, as an advanced irrigation technology, has been widely applied in China. At the meantime, drip fertigation has also received increasingly attention in modern agriculture in which the reaction between water, soil and the soil solution affects the use of soil nutrients by plants. The objective of this thesis is to use a combination of numerical modeling and experiments to investigate the fundamentals of solute transport in pore space of soil with a view to improve modeling at macroscopic scales, which can be used to investigate the movement of nutrients under drip fertigation. The main conclusions of this thesis are:
(1) Assuming that water flow is laminar and that the medium is homogenous and all pores in it are hydraulically connected, water flow and solute transport in the pore scale were simulated using the lattice Boltzmann method by treating the water-solid interface as non-slip boundary. The result reveals that water flow is mainly concentrated along a few channels. As a result, the movement of tracers is anomalous, which cannot be accurately described by the classical advection-dispersion equation. Comparing the results with the continuous time random walk (CTRW) reveals that the solute movement is well described by CTRW with a modified exponentially distributed transition time.
(2) A spatial fractional advection-dispersion equation model (FADE) is investigated, which is shown to be an effective model to simulate solute movement in natural soils with big pores. The FADE currently available in literature is based on Riemann-Lioville equation, limiting its application to infinite domains. A modified method based on the Caputo derivatives is presented to overcome this problem. A finite volume approach is given to numerically solve the modified FADE and its associated boundaries. The model is then compared with experimental data, and the results show good agreement.
(3) Study on the movement of adsorptive solute reveals that its movement can be simulated using the similar framework as for non-adsorptive solute, using a probability distribution function to describe the distance between the pore and the time it takes a solute particle to move from one pore to another. The difference between the adsorptive and non-adsorptive solutes is the time for solute particle to move one pore to another. Given the inherent heterogeneity of natural soils, this thesis used a power-law function to describe the time it takes the adsorptive solute to move from one pore to another, making the CTRW model into a time-fractional advection-dispersion equation. Based on the principle of mass balance, a finite volume method is proposed to solve the equation and then compares it with experimental data. The results indicate that the model accurately captures the persistent long tails in the breakthrough curves, and that the transport parameters are independent of water flow rate.
(4) Experimental study of the movement of nitrate under drip fertigation was carried out in the tank filled with sandy soil. The measurement of water content and nitrate concentration reveals the water content is symmetrical vertically around the emitter and after the termination irrigation, the gradient of the water potential changes. Also, the peak nitrate concentration is affected applied nitration concentration, decreasing with the distance from the emitter as the applied concentration increases.
(5) A two-dimensional model is proposed to simulate the movement of water in soil under drip irrigation. To accurately describe water movement in heterogeneous soil and variably saturated condition, the mixed-form Richards' equation was used. To improve the convergence of the numerical model, a chord Newton method was used to solve the gravity term so as to make the final matrix diagonally dominant. This stabilizes the solution, thereby increasing the convergence rate.
(6) Using the above models for both water flow and solute transport, the nitrate movement under the drip irrigation is modeled. Since the experiments were conducted using repacked soil, there are no obvious big pores. I thus used the time-fractional CTRW model to simulate nitrate movement in which the distance between the adjacent pores is assumed to be normally distributed. Comparing with the commonly used the mobile-immobile model, the proposed model improves the description of the solute movement in soils. Comparison of the model with experiment shows fair agreement.
The movement of water and solute in soil is dictated by the pore geometry. The advent and development of imaging technology and computer power over the last two decades has made it feasible to investigate pore-scale water and solute movement. The CTRW model presented in this paper can overcome some limitations of the commonly used advection-dispersion model, and is used in this work to investigate nutrient transport under drip fertigation. However, due to the restriction of experiments, such as the difficulty of sampling, this work is restricted to nitrate. The simulations show similar trend as the measurements, but this is still some discrepancy. Further research is needed.
引文
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