Lattice Boltzmann simulation of solute transport in a single rough fracture

In this study, the lattice Boltzmann method （LBM） was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves （BTCs） for continuous injection sources in rough fractures were analyzed and discussed with different Reynolds numbers （Re）. The results show that the rough frac~＇e wall leads to a large fluid velocity gradient across the aperture. Consequently, there is a broad distribution of the immobile region along the rough fracture wall. This distribution of the immobile region is very sensitive to the Re and fracture geometry, and the immobile region is enlarged with the increase of Re and roughness. The concentration of the solute front in the mobile region increases with the Re. Furthermore, the Re and roughness have significant effects on BTCs, and the slow solute molecule exchange between the mobile and immobile regions results in a long breakthrough tail for the rough fracture. This study also demonstrates that the developed LBM can be effective in studying the solute transport in a rough fracture.     

NUMERICAL STUDY OF NON-AQUEOUS PHASE LIQUID TRANSPORT IN A SINGLE FILLED FRACTURE BY LATTICE BOLTZMANN METHOD

In this article,the Non-Aqueous Phase Liquid(NAPL)transport in the single filled fracture was studied with the Shan-Chen multi-component multiphase Lattice Boltzmann Method(LBM)with special consideration of wettability effects.With the help of the model,the contact angle of the non-wetting phase and wetting phase interface at a solid wall could be adjusted.By considering a set of appropriate boundary conditions,the fractured conductivity was investigated in condition that the NAPL blocks the channels in the single filled fracture.In order to study the wettability effects on the NAPL transport,a constant driving force was introduced in the Shan-Chen multi-component multiphase LBM.Flow regimes with different wettabilities were discussed.Simulated results show that the LBM is a very instrumental method for simulating and studying the immiscible multiphase flow problems in single filled fracture.     

Revisit of advection-dispersion equation model with velocity-dependent dispersion in capturing tracer dynamics in single empty fractures

An accurate quantification of the contaminant transport through fractured media is critical for dealing with water-quality related scientific and engineering issues, where the dispersion coefficient is an important and elusive parameter for the solute transport modeling. Many previous studies show that the dispersion coefficient(D) in the standard advection-dispersion equation(ADE) model can be approximated by D=av~λ(where a is the dispersivity), a formula to be revisited systematically in this study by laboratory experiments and model analysis. First, a series of tracer transport experiments in single empty fractures are conducted in cases of different hydraulic gradients. Second, the tracer breakthrough curves are determined by simulations based on the ADE model, to obtain the dispersion coefficients corresponding to various fracture roughnesses and flow velocities. A varying trend of λ is analyzed under different flow conditions. Results show that although the standard ADE model cannot be used to characterize the late-time tailing of the tracer BTCs, likely due to the solute retention, this simple model can simulate most of the solute mass dynamics moving through fractures and may therefore provide information for estimating the dispersion in parsimonious models appropriate for the non-Fickian transport. The following three conclusions are drawn:(1) the peak of the breakthrough curves comes earlier with increasing the roughness, according to the ADE simulation,(2) the value of λ generally decreases as the relative roughness of the fracture increases,(3) the value of λ is approximately equal to 2.0 when the dispersion is dominated by the molecular diffusion in the smooth fracture.     

A simplified dynamic method for field capacity estimation and its parameter analysis

This paper presents a simplified dynamic method based on the definition of field capacity. Two soil hydraulic characteristics models, the Brooks-Corey （BC） model and the van Genuchten （vG） model, and four soil data groups were used in this study. The relative drainage rate, which is a unique parameter and independent of the soil type in the simplified dynamic method, was analyzed using the pressure-based method with a matric potential of -1/3 bar and the flux-based method with a drainage flux of 0.005 cm/d. As a result, the relative drainage rate of the simplified dynamic method was determined to be 3% per day. This was verified by the similar field capacity results estimated with the three methods for most soils suitable for cultivating plants. In addition, the drainage time calculated with the simplified dynamic method was two to three days, which agrees with the classical definition of field capacity. We recommend the simplified dynamic method with a relative drainage rate of 3% per day due to its simple application and clearly physically-based concept.     

COUPLING DISTINCT AND CONTINUOUS MEDIUM MODEL FOR FLOW ANALYSIS IN A FRACTURED ROCK MASS AND ITS APPLICATION

Fractures in a rock mass can be divided into dominant fracture system and network fracture system. An approach for the analysis of three dimensional ground water flow in a fractured rock mass is presented, in which flow in the dominant fracture system is described by a distinct medium model while flow in the network fracture system plus rock matrices (if considered) is described by a continuous medium model, and the two models are coupled by hydraulic head and flux. The coupling model facilitates to calculate one-by-one the fluid flow in the dominant fractures which are functioned as the major water transmission conduits, and it avoids unnecessary calculating fluid flow in individual network fractures which are numerous in number. In this way, the method can be applied to a large-sized calculation domain. In addition, a method of using network geometry data to calculate its equivalent porous permeability is presented in the paper, and the model implementation of water source and sink such as the pumping     

Motion and deformation of immiscible droplet in plane Poiseuille flow at low Reynolds number

Droplet migration in plane Poiseuille flow is numerically investigated with a dissipative particle dynamics method.The single droplet deformation in the channel flow is first studied to verify the current method and the physical model.The effect of the viscosity ratio between the droplet and the solvent and the effect of the confinement are systematically investigated.The droplet is in an off-centerline equilibrium position with a specific selection of the parameters.A large viscosity ratio makes the droplet locate in a near-wall equilibrium position,and a large capillary number makes the droplet migrate to the near-centerline region of the channel.For the droplet migration at the same Capillary number,there is a critical width of the channel,which is less than twice of the droplet diameter,and the droplet will only migrate to the channel centerline if the width is less than this critical value.     

Lagrangian methods for water transport processes in a long-narrow bay- Xiangshan Bay,China

A better understanding of water transport processes is highly desirable for the exploitation of the ocean resources and the protection of the ocean ecological system. In this paper, the Lagrangian methods are used to study the water transport processes in Xiangshan Bay in China, a typical semi-closed and narrow-shaped bay with complex coastline and topography. A high-resolution 3-D hydrodynamic model is developed and verified, and the results from the model agree well with the field data. Based on the hydrodynamic model, the Lagrangian residual current is computed by using the particle tracking method. A concept based on the dynamical systems theory, the Lagrangian coherent structures （LCSs）, is introduced to uncover the underlying structures which act as the transport barriers in the flow. The finite-time Lyapunov exponent （FTLE） fields are computed from the hydrodynamic model results to extract the LCSs. The results indicate that the LCSs act as the internal structures of the Lagrangian residual current and the Lagrangian residual current displays the residual current speed and direction of different water regimes separated by the LCSs. The water masses with different transport characteristics can be identified and their exchange ability with other water masses can be estimated by combining the Lagrangian particle tracking with the LCSs methods. The comprehensive applications of these Lagrangian methods reveal the underlying structures and the inhomogeneous characteristics of the water transport in Xiangshan Bay.     

Modeling atrazine transport in soil columns with HYDRUS-1D

Both physical and chemical processes affect the fate and transport of herbicides. It is useful to simulate these processes with computer programs to predict solute movement. Simulations were run with HYDRUS-1D to identify the sorption and degradation parameters of atrazine through calibration from the breakthrough curves (BTCs). Data from undisturbed and disturbed soil column experiments were compared and analyzed using the dual-porosity model. The study results show that the values of dispersivity are slightly lower in disturbed columns, suggesting that the more heterogeneous the structure is, the higher the dispersivity. Sorption parameters also show slight variability, which is attributed to the differences in soil properties, experimental conditions and methods, or other ecological factors. For both of the columns, the degradation rates were similar. Potassium bromide was used as a conservative non-reactive tracer to characterize the water movement in columns. Atrazine BTCs exhibited significant tailing and asymmetry, indicating non-equilibrium sorption during solute transport. The dual-porosity model was verified to best fit the BTCs of the column experiments. Greater or lesser concentration of atrazine spreading to the bottom of the columns indicated risk of groundwater contamination. Overall, HYDRUS-1D successfully simulated the atrazine transport in soil columns.     

TRANSVERSE MIXING IN A TRAPEZOIDAL COMPOUND OPEN CHANNEL

Transverse mixing characteristics of solute in the open channel flow can provide useful information for river environmental management. The lateral mixing coefficient is a crucial parameter for reproducing the transverse mixing either by numerical simulation or by analytical prediction. Since the solute mixing can be greatly affected by the lateral variations in water depth, mixing coefficient should be determined in each sub-section （i.e., the main channel, side slope and flood plain） separately. In this article, the transverse mixing in a symmetric trapezoidal compound channel was studied based on laboratory measurement of longitudinal and transverse velocity components and lateral distribution of solute concentration. The lateral mixing coefficient was estimated by adopting different Schmidt numbers in different sub-sections divided according to the developing trend of the eddy viscosity, and finally a piecewise linear profile of mixing coefficient was adopted to analytically predict the transverse solute concentration. The comparison between the analytically predicted data and the measuring solute concentration proved that this is an effective way to estimate the lateral mixing in the open channel flow with lateral variations in water depth,     

SECOND-ORDER DRIFT FORCES AND MOMENTS BETWEEN TWO SUBMERGED BODIES IN WAVES ON 3D METHOD

Two near field methods, namely the integral method and differential method, were presented for giving second-order mean drift forces and moments between two fixed submerged bodies in regular waves. For the integral method, with a series of mathematical manipulations, second order drift forces and moments could be easily expressed by distributed sources which could be calculated by source distribution techniques with the assumption that the amplitude of ship motions are small on the basis of the linear 3D frequency theory. For the differential method, drift forces and moments could be expressed by the derivative of velocity potential with respect to space coordinate. Because two bodies would behaveas a single body while the clearance is very large, the numerical results of one sphere in such case were given and compared with analytical results of a single sphere which does not involve the effect of free surface. When submerged depth becomes enough large, a good agreement can be reached. Then the integral method was used to predict the second order drift forces and moments of two submerged spheres and spheroids with a small lateral separation distance in waves compared with the numerical results obtained by the differential method and they agree well. By comparison, it indicates the interaction effects between two submerged bodies have a profound influence on the drift forces and moments. In this paper, the forward speed effect on submerged spheres was also considered.     

SOLUTE TRANSPORT IN NATURAL FRACTURES BASED ON DIGITAL IMAGE TECHNOLOGY

A method of fracture boundary extraction was developed using the Gaussian template and Canny boundary detection on the basis of the collected digital images of natural fractures. The roughness and apertures of the fractures were briefly discussed from the point of view of digital image analysis. The extracted fractured image was translated into a lattice image which can be directly used in numerical simulation. The lattice Boltzmann and modified moment propagation mixed method was then applied to the simulation of solute transport in a natural single fracture, and this mixed method could take the advantages of the lattice Boltzmann method in dealing with complex physical boundaries. The obtained concentrations was fitted with the CXTFIT2.1 code and compared with the results obtained with the commercial software Feflow. The comparison indicates that the simulation using the mixed method is sound.     

Modelling of solute transport in a filled fracture: Effects of heterogeneity of filled medium

In this paper, the developed lattice Boltzmann method(LBM) is used to model the solute transport in a filled fracture under a heterogeneous advective velocity field. The results of the developed LBM in modelling the solute transport are compared with the published experimental data. The numerically derived BTCs indicate that the distribution of the filled medium in the fracture has a significant effect on the characteristics of the BTCs, even with the same porosity. The heterogeneity of the filled medium is responsible not only for the heterogeneous advective velocity field but also for the early arrival and long tails of the BTCs. The long tailings of the BTCs increase their length with the increase of the duration of the input pulse. Furthermore, the BTCs obtained from the LBM simulations are well consistent with the two-region model(TRM). The fitting results show that the fractional mobile region varies with the distribution of the filled medium. The long tailings of the BTCs increase their length with the increase of the immobile region while the concentration peak value increases with the increase of the mobile region.     

INCOMPRESSIBLE MULTI-RELAXATION-TIME LATTICE BOLTZMANN MODEL IN 3-D SPACE

Multi-Relaxation-Time Lattice Boltzmann Method(MRT LBM) is of better numerical stability and has attracted more and more research interests.The previous MRT LBM included artificial compressible effects.To overcome the disadvantage,an incompressible MRT LBM has been proposed in two dimensions recently.In this article,we present incompressible MRT LBMs in 3-D space,with example of nineteen-velocity.The equilibria in momentum space are derived from an earlier incompressible Lattice Bhatnagar-Gross-Krook(LBGK) ...     

LATTICE BOLTZMANN METHOD WITH DOUBLE MESHES

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＩｎｒｅｃｅｎｔ ｙｅａｒｓ ,ｔｈｅｏｒｙａｎｄａｐｐｌｉｃａｔｉｏｎｓｏｆＬａｔｔｉｃｅＢｏｌｔｚｍａｎｎｍｅｔｈｏｄ (ＬＢＭ )ｈａｖｅｍａｄｅｒａｐｉｄ ｐｒｏｇｒｅｓｓ ,ｍａｋｉｎｇＬＢＭｃｏｍｐｅｔｉｔｉｖｅｔｏｔｈｅｃｏｎｖｅｎｔｉｏｎａｌａｐｐｒｏａｃｈｅｓｉｎＣｏｍｐｕｔａｔｉｏｎａｌＦｌｕｉｄＤｙｎａｍｉｃｓ (ＣＦＤ )ａｎｄａｎａｌｔｅｒｎａｔｉｖｅｗａｙｔｏｓｉｍｕ ｌａｔｅｔｈｅｆｌｕｉｄｆｌｅｌｄ[1] .ＴｈｅｋｅｙｉｄｅａｂｅｈｉｎｄＬＢＭｉｓｔｈ…     

LABORATORY EXPERIMENTS ON SOLUTE TRANSPORT IN A PARTIAL TRANSFIXION SINGLE FRACTURE

In the study of solute transport in rough single fracture,the contact area is an important factor.The single fracture is defined as two categories in this article:the full transfixion single fracture and the partial transfixion single fracture.The purpose of this article is to research how the contact area affects the solute transport in partial transfixion single fracture.The contact area is generalized as square blocks with three sizes,and contact rate is variable,a series of experiments for solute transp...     

Three-dimensional analysis of spreading and mixing of miscible compound in heterogeneous variable-aperture fracture

As mass transport mechanisms,the spreading and mixing(dilution) processes of miscible contaminated compounds are fundamental to understanding reactive transport behaviors and transverse dispersion.In this study,the spreading and dilution processes of a miscible contaminated compound in a three-dimensional self-affine rough fracture were simulated with the coupled lattice Boltzmann method(LBM).Moment analysis and the Shannon entropy(dilution index) were employed to analyze the spreading and mixing processes,respectively.The corresponding results showed that the spreading process was anisotropic due to the heterogeneous aperture distribution.A compound was transported faster in a large aperture region than in a small aperture region due to the occurrence of preferential flow.Both the spreading and mixing processes were highly dependent on the fluid flow velocity and molecular diffusion.The calculated results of the dilution index showed that increasing the fluid flow velocity and molecular diffusion coefficient led to a higher increasing rate of the dilution index.     

NUMERICAL STUDY OF WALL WETTABILITIES AND TOPOGRAPHY ON DRAG REDUCTION EFFECT IN MICRO-CHANNEL FLOW BY LATTICE BOLTZMANN METHOD

The dynamics of two-phase flows with a constant driving force inside a micro-channel is studied by using the Lattice Boltzmann Method (LBM) and the Shan-Chen multiphase model in this article. Flow regimes under different wall wettabilities and over smooth and grooved geometric surfaces are investigated. It is found that flow behaviors are strongly affected by the wall wettability and topography. Our results show that the LBM is efficient and accurate, and has very good application prospect in the study of drag reduction of microscopic seepage of reservoir.     

NUMERICAL STUDY OF THE RELATIONSHIP BETWEEN APPARENT SLIP LENGTH AND CONTACT ANGLE BY LATTICE BOLTZMANN METHOD

The apparent slip between solid wall and liquid is studied by using the Lattice Boltzmann Method (LBM) and theShan-Chen multiphase model in this paper. With a no-slip bounce-back scheme applied to the interface, flow regimes under differentwall wettabilities are investigated. Because of the wall wettability, liquid apparent slip is observed. Slip lengths for different wallwettabilities are found to collapse nearly onto a single curve as a function of the static contact angle, and thereby a relationshipbetween apparent slip length and contact angle is suggested. Our results also show that the wall wettability leads to the formation of alow-density layer between solid wall and liquid, which produced apparent slip in the micro-scale.