Zhifang Zhou

Experimental investigation of contaminant migration in filled fracture

Experiment equipments involved in the single tube fracture and double tube fracture models are designed to research the characteristics of groundwater flow and solute transport in filled fracture. During the experiment, the state of groundwater flow can be characterized as linear flow, and satisfies Darcy’s law. Therefore, based on the pipe flow of hydraulics and Darcy’s law, the flow rate and water flow velocity can be calculated. Also, dispersion parameters were calculated with the fitting of observed data and analytical solution in the single tube fracture model. Furthermore, effects of some factors on solute transport are involved in the double tube fracture model, and length of branch fracture, particles’ diameter and flow rate in water inlet have been discussed. Results show that the arrival time of concentration peak value in the single tube fracture model is faster than that in the double tube fracture model, and two concentration peak values exist in the double tube fracture model. Arrival time of concentration peak value is faster with the increase of branch fracture length. Furthermore, if the branch fracture is longer, arrival time of the first concentration peak value is faster, while arrival time of the second concentration peak value is slower, relative to short branch fracture.

A Joint Analytic Method for Estimating Aquitard Hydraulic Parameters.

The vertical hydraulic conductivity (Kv ), elastic (Sske ), and inelastic (Sskv ) skeletal specific storage of aquitards are three of the most critical parameters in land subsidence investigations. Two new analytic methods are proposed to estimate the three parameters. The first analytic method is based on a new concept of delay time ratio for estimating Kv and Sske of an aquitard subject to long-term stable, cyclic hydraulic head changes at boundaries. The second analytic method estimates the Sskv of the aquitard subject to linearly declining hydraulic heads at boundaries. Both methods are based on analytical solutions for flow within the aquitard, and they are jointly employed to obtain the three parameter estimates. This joint analytic method is applied to estimate the Kv , Sske , and Sskv of a 34.54-m thick aquitard for which the deformation progress has been recorded by an extensometer located in Shanghai, China. The estimated results are then calibrated by PEST (Doherty 2005), a parameter estimation code coupled with a one-dimensional aquitard-drainage model. The Kv and Sske estimated by the joint analytic method are quite close to those estimated via inverse modeling and performed much better in simulating elastic deformation than the estimates obtained from the stress-strain diagram method of Ye and Xue (2005). The newly proposed joint analytic method is an effective tool that provides reasonable initial values for calibrating land subsidence models.

An analytical solution for leakage rate and depletion of aquitard influenced by the delayed yield phenomenon

Delayed yield phenomenon (DYP) occurs when the drawdown of an aquitard is no longer in equilibrium owing to previous changes in the level of water in adjacent aquifers. In this study, an analytical solution to determine the distribution of the drawdown at any time and at any point in an aquitard, in which the water level was not in equilibrium at the initial time, and the water level of the aquifers immediately above and below the aquitard was time dependent was developed. The analytical solution for the flow rate at any time and location was presented based on variations in drawdown in the aquitard. In addition, the effects of the DYP on the leakage rate and depletion of the aquitard were studied. Subsequent comparison of the proposed analytical and numerical solutions revealed that they were in good agreement. The results of this study will be useful to future studies of groundwater flow and environmental problems, such as water budgets, rising sea levels, solute transport, heat conduction and ground subsidence.

Roughness scale dependence of the relationship between tracer longitudinal dispersion and Peclet number in variable-aperture fractures

The relationship between the longitudinal dispersion (DL) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the DL and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the DL from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the DL and Pe revealed that the longitudinal dispersivity αL increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of αL and the secondary roughness played a significant role in enhancing the αL. As the Taylor dispersion mechanism dominated, the αL was insensitive to the influence of multiscale roughness in variable‐aperture fractures.

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA) technique. The pore-scale model was developed by coupling the Navier-Stoke equation (NSE) and advection-diffusion equation with reaction (ADER). Eddies were captured in the self-affine fracture due to the increasing Reynolds number and the sudden expansion of aperture. The flux-weighted breakthrough curves (BTCs) of reaction product showed the typical non-Fickian characteristics (i.e., “early arrival” and “heavy tail”). It was found that the reactant was involved in eddies and then reacted inside the eddy-controlled domain. Consequently, eddies played a significant role in delaying the mass exchange process between the eddy-controlled domain and the main flow channel, which resulted in the “heavy tail” in BTCs. As the Reynolds number increased, the breakthrough time increased while the concentration peaks of BTCs decreased. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the degree of reactant mixing. The results showed that the quantification of dilution for nonreaction transport was in good agreement with the outcomes of mixing-induced reaction transport. The high Reynolds number and Peclet number had a negative influence on the mixing process at the early time whereas they led to the enhanced mixing process at the late time.

Experimental investigation of solute transport in unsaturated fractured rock

An experiment is designed to perform tracer tests in an unsaturated fractured rock with a horizontal fracture. Data from an intact and an artificial sandstone sample was collected and used to discuss the effect of the fracture on tracer migration. The delay time of the tracer in the fracture was further determined in terms of the fracture aperture involved. An alternative electrical conductivity (or electrical resistance) method was developed to measure the change in the tracer concentration with time and space. The method causes no disturbance to the flow and concentration fields, and is convenient to use. The test results show the fluctuations in the tracer concentrations and there were 2–3 peak values of concentration in the monitored sections related to the heterogeneity of the water content and pore distribution. Also, the fracture was found to delay migration of the tracer before it is filled with the tracer solution and quicken the velocity of migration afterwards. This results in accumulation of the tracer near the fracture. Furthermore, the delay time of the tracer increases with fracture aperture in a nonlinear manner.

Scale effect and value criterion of the permeability of the interlayer staggered zones in the basalt of Jinsha River basin, China

The hydrogeological characteristics of structural planes are different to those of the associated bedrock. The permeability, and therefore hydraulic conductivity (K), of a structural plane can be significantly different at different scales. The interlayer staggered zones in the Emeishan Basalt of early Late Permian were studied; this formation is located in the Baihetan hydropower project area in Jinsha River Basin, China. The seepage flow distribution of a solid model and two generalized models (A and B) were computed using COMSOL. The K values of the interlayer staggered zones for all three models were calculated by both simulation and analytical methods. The results show that the calculated K results of the generalized models can reflect the variation trend of permeability in each section of the solid model, and the approximate analytical calculation of K can be taken into account in the calculation of K in the generalized models instead of that found by simulation. Further studies are needed to investigate permeability variation in the interlayer staggered zones under the condition of different scales, considering the scaling variation in each section of an interlayer staggered zone. The permeability of each section of an interlayer staggered zone presents a certain degree of dispersivity at small scales; however, the permeability values tends to converge to a similar value as the scale of each section increases. The regularity of each section of the interlayer staggered zones under the condition of different scales can provide a scientific basis for reasonable selection of different engineering options.RésuméLes caractéristiques hydrogéologiques de plans structuraux sont différentes de celles de la formation au sein de laquelle ils sont interstratifiés. La perméabilité (ou conductivité hydraulique K) d’un plan structural peut-être significativement différente à diverses échelles. Les zones intercoulées décalées du basalte Emeishan du début du Permien Terminal ont été étudiées; cette formation se situe dans la zone du projet hydroélectrique de Baihetan dans le bassin de la rivière Jinsha, Chine. La distribution des flux de suintement issue d’un modèle solide et de deux modèles généralisés (A et B) a été calculée en utilisant COMSOL. Les valeurs de K des zones intercoulées décalées ont été calculées pour les trois modèles à la fois par des méthodes de simulation numérique et des méthodes analytiques. Les résultats montrent que les K calculées avec les modèles généralisés peuvent bien refléter la tendance de variation de la perméabilité dans chaque partie du modèle solide; ils montrent aussi que le calcul analytique approché de K peut être pris en compte pour le calcul de K dans les modèles généralisés à la place des valeurs trouvées par simulation numérique. Des études complémentaires sont nécessaires pour étudier la variation de la perméabilité dans les zones intercoulées décalées pour différentes conditions d’échelle, en considérant la variation d’échelle dans chaque partie d’une zone intercoulée dispersée. La perméabilité de chaque partie d’une zone intercoulée dispersée présente une certaine dispersion aux petites échelles; cependant, les valeurs de perméabilité tendent à converger vers une valeur similaire lorsque l’échelle de chaque partie augmente. La régularité de chaque partie des zones intercoulées décalées, sous différentes conditions d’échelles, peut fournir une base scientifique pour la sélection raisonnable de différentes options d’ingénierie.ResumenLas características hidrogeológicas de los planos estructurales son diferentes a las de la roca madre asociada. La permeabilidad, y por lo tanto la conductividad hidráulica (K), de un plano estructural puede ser significativamente diferente en distintas escalas. Se estudiaron las zonas intercaladas entre las capas en el basalto Emeishan de principios del Pérmico tardío; esta formación se encuentra en el área del proyecto hidroeléctrico de Baihetan en la cuenca del río Jinsha, China. La distribución del flujo de filtración de un modelo sólido y dos modelos generalizados (A y B) se calcularon utilizando COMSOL. Los valores de K de las zonas intercaladas entre las capas para los tres modelos se calcularon mediante métodos de simulación y analíticos. Los resultados muestran que los resultados K calculados de los modelos generalizados pueden reflejar la tendencia de variación de la permeabilidad en cada sección del modelo sólido, y el cálculo analítico aproximado de K se puede tener en cuenta en el cálculo de K en los modelos generalizados en lugar de aquellos que se encuentra por simulación. Se necesitan más estudios para investigar la variación de la permeabilidad en las zonas intercaladas entre las capas bajo la condición de diferentes escalas, considerando la variación de escala en cada sección de una zona intercalada entre capas. La permeabilidad de cada sección de una zona intercalada entre capas presenta un cierto grado de dispersividad a escalas pequeñas; sin embargo, los valores de permeabilidad tienden a converger a un valor similar a medida que aumenta la escala de cada sección. La regularidad de cada sección de las zonas intercaladas entre capas bajo la condición de diferentes escalas puede proporcionar una base científica para la selección razonable de diferentes opciones de ingeniería.摘要结构面的水文地质特征与相关基岩的水文地质特征不同。结构面的渗透率以及水力传导率(K)在不同尺度上会大不相同。研究了晚二叠世早期峨眉山玄武岩互层交错带;这个地层位于中国金沙江流域白鹤滩水电项目区。利用COMSOL计算了实体模型和两个概化模型的渗流分布。通过模拟和解析方法计算了所有三个模型互层交错带的K值。结果显示,概化模型计算的K结果可反映出实体模型每个截面的渗透率变化趋势,在概化模型中计算k可考虑k的大概解析计算结果,而不用模拟中发现的结果。鉴于互层交错带每个截面的尺度变化,需要进行进一步的研究来调查不同尺度条件下互层交错带的渗透率变化。互层交错带每个截面的渗透率在小尺度上展现出一定程度的弥散性,然而,随着每个截面尺度的增加,渗透率值趋于收敛成类似的值。在不同尺度条件下,互层交错带每个截面的规律性可为不同工程的合理选择提供科学依据。ResumoAs características hidrogeológicas de planos estruturais são diferentes daquelas associadas ao acamamento. A permeabilidade, e consequentemente a condutividade hidráulica (K), de um plano estrutural pode ser significativamente diferente em diferentes escalas. Foram estudadas as zonas intracamadas intercaladas no Basalto de Permiano Tardio inicial de Emeishan; esta formação está localizada na área hidrelétrica de Baihetan na Bacia do Rio Jinsha, China. A distribuição de fluxo de infiltração de um modelo sólido e dois outros modelos generalizados (A e B) foram gerados usando COMSOL. Os valores de K das zonas intracamadas intercaladas para os três modelos foram calculados usando ambos os métodos: simulação e analítico. Os resultados mostram que os K calculados dos modelos generalizados podem refletir a variação de tendência da permeabilidade em cada seção do modelo sólido, e a aproximação de cálculo analítico do K pode ser levado em consideração no cálculo de K em modelos generalizados ao invés do encontrado por simulação. São necessários estudos mais aprofundados para a investigação da variação de permeabilidade das zonas intracamadas intercaladas sob a condição de diferentes escalas, considerando a variação de escala em cada seção de uma zona intracamada intercalada. A permeabilidade de cada seção de uma zona intracamada intercalada apresenta certo grau de dispersão em escalas pequenas; no entanto, os valores de permeabilidade tendem a convergir para um valor similar na medida em que a escala de cada seção aumenta. A regularidade de cada seção de zonas intracamadas intercaladas sob a condição de diferentes escalas pode proporcionar uma base científica para uma seleção razoável de opções no campo da engenharia.

Investigation of the hydraulic connection between the upper storage reservoir and the underground powerhouse in the Hongping Pumped Storage Hydroelectric Powerstation

Field tracer tests in fractured rocks were performed to investigate the hydraulic connection between the upper storage reservoir and the underground powerhouse in the Hongping Pumped Hydroelectric Storage Powerstation (HPHSP). Data from tracer measurement points indicated the appearance of multiple peak values during the course of tracer migration, which revealed multiple water pathways in fractured aquifers owing to the development and intersection of fractures and faults. Also, complex hydrogeological structural systems were proposed according to geological data from borehole logs and outcrops seen in the exploration adit. These structures revealed the different permeability and strong heterogeneity of the fractured media and can, therefore, explain the existence of a concentrated water-conducting passage from the upper storage reservoir to the underground powerhouse. Multiple peak values in the field tests were examined using a laboratory cross-fracture experiment involving tracer migration and numerical simulation based on transition probability. According to the observed data and the numerical results, the laboratory model and simulation method can capture the characteristics of groundwater flow and tracer migration in fractured rocks.

Contaminant transport in a small deformation aquitard affected by the delayed drainage phenomenon

This paper presents a formulation accounting for the effect of Delayed Drainage Phenomenon (DDP) on the breakthrough of contaminant flux in an aquitard, by considering the movement of soil particles, porosity variation, hydraulic head variation and transient flow during the consolidation. The water flow equation in an aquitard was based on the Terzaghis consolidation theory, and the contaminant transport equation was derived on the basis of the mass balance law. Two cases were used to illustrate the effect of DDP on the contaminant transport in an aquitard of small deformation. It is found that the breakthrough time of contaminant in an aquitard is very long, which is mainly ascribed to the low permeability of aquitard and sorption of soil particles. It is also found that the increase of depletion, which is in general induced by the increase of thickness and specific storativity, and the decrease of hydraulic conductivity, enhance the impact of DDP on the contaminant transport in an aquitard. A larger delay index (τ0) of DDP gives a greater Delay Breakthrough Time (DBT) of solute transport in an aquitard, which controls the difference of the breakthrough time of contaminant transport in aquitards with and without the occurrence of DDP. For the cases where advection plays a dominant role during the process of solute transport, τ0 is almost linearly correlated with DBT, and the ratio of DBT over the breakthrough time without consideration of DDP also approximately shows a linear relationship with the ratio of specific storativity to porosity, given a fixed drawdown in the adjacent aquifer with the sorption being ignored.

Solution methods of hydraulic conductivity in low permeable saturated soil during liquid releasing

Solution methods of hydrogeological parameters in saturated zones for certain geological behaviors have been presented in many studies. Traditional solution methods of hydrogeological parameters, such as hydraulic conductivity and storage coefficient, were acquired by in situ hydrogeological experiment or seepage control equations. However, those two methods obtain a constant value of hydrogeological parameters which is not very suitable in practical cases. This study assumes that hydrogeological parameters to be a variable value because the properties of soil were changed during liquid releasing. An analytical solution for liquid releasing from saturated soil was deduced based on the existing seepage control equation, and the analytical value of hydrogeological parameters was obtained. Moreover, analytical expression for hydraulic conductivity was developed, and variable hydraulic conductivity was gained by analyzing flow quantity during seepage. Different calculation methods were used to get constant and variable conductivity coefficient, respectively. A laboratorial test model of saturated soil under designed conditions was also established to verify the analytical solutions of both constant and variable parameters by fitting the calculated value and measured value curve. Seepage tests and case studies showed that variable hydraulic conductivity value presents higher agreement with the measured data for flux versus time than constant hydraulic conductivity. In order to prove the fact that variable parameter is more reasonable in real cases, we also conducted a group of comparative tests by rising and falling the hydraulic head of seepage model in three periods. Three different hydraulic conductivities were obtained, and then they were substituted to seepage equation for the sake of curve fitting. The correlation coefficient between measured flow versus time curve (obtained from hydraulic conductivity vs. time curve) and calculated flow versus time curve is higher than flow versus time obtained from hydraulic conductivity versus periods. Solution methods suggested in this paper are generally applicable to problems involving the hydraulic conductivity, specific storage and other related hydrogeological parameters calculation of low permeable saturated soil.