Numerical simulation of convective flows in a soil during the evaporation of water containing a dissolved admixture

The concentration profile is investigated for a solution that saturates a low-permeability soil. The simulation results showed the presence of three flow regimes. The salt accumulated near the phase transition boundary increases the solution density and may lead to the development of natural concentration-induced convection which interacts with the rising flow (forced convection). The stability threshold of the forced flow and the effect on it of natural convection that arises are determined. It is shown that at intense flow to the evaporation surface the admixture concentration increases at this boundary rapidly and reaches the saturation concentration. In this case, the admixture precipitates. In the slow evaporation regime the admixture diffuses from the high-concentration region, which prevents the development of convective flow.     

Two-Valued Solutions in the Problem of Salt Precipitation during Groundwater Evaporation

The problem of the evaporation of groundwater containing a dissolved admixture is studied. It is shown that in the salt precipitation regime the solution is nonunique. At critical parameter values the solutions merge and in a certain region the solution of the problem disappears. The nonexistence of a solution corresponds to clogging of the pore space with precipitated salt.     

Laboratory Investigation of LNAPL Migration in Double-Porosity Soil Under Fractured Condition Using Digital Image Analysis

Gas production from shale gas reservoirs plays a significant role in satisfying increasing energy demands. Compared with conventional sandstone and carbonate reservoirs, shale gas reservoirs are characterized by extremely low porosity, ultra-low permeability and high clay content. Slip flow, diffusion, adsorption and desorption are the primary gas transport processes in shale matrix, while Darcy flow is restricted to fractures. Understanding methane diffusion and adsorption, and gas flow and equilibrium in the low-permeability matrix of shale is crucial for shale formation evaluation and for predicting gas production. Modeling of diffusion in low-permeability shale rocks requires use of the Dusty gas model (DGM) rather than Fick’s law. The DGM is incorporated in the TOUGH2 module EOS7C-ECBM, a modified version of EOS7C that simulates multicomponent gas mixture transport in porous media. Also included in EOS7C-ECBM is the extended Langmuir model for adsorption and desorption of gases. In this study, a column shale model was constructed to simulate methane diffusion and adsorption through shale rocks. The process of binary \(\hbox {CH}_{4}{-}\hbox {N}_{2}\) diffusion and adsorption was analyzed. A sensitivity study was performed to investigate the effects of pressure, temperature and permeability on diffusion and adsorption in shale rocks. The results show that methane gas diffusion and adsorption in shale is a slow process of dynamic equilibrium, which can be illustrated by the slope of a curve in \(\hbox {CH}_{4}\) mass variation. The amount of adsorption increases with the pressure increase at the low pressure, and the mass change by gas diffusion will decrease due to the decrease in the compressibility factor of the gas. With the elevated temperature, the gas molecules move faster and then the greater gas diffusion rates make the process duration shorter. The gas diffusion rate decreases with the permeability decrease, and there is a limit of gas diffusion if the permeability is less than \(1.0\,\times \,10^{-15}\, \hbox { m}^{2}\). The results can provide insights for a better understanding of methane diffusion and adsorption in the shale rocks so as to optimize gas production performance of shale gas reservoirs.     

Injection of a salt solution into a geothermal reservoir saturated with superheated vapor

The injection of water containing a dissolved admixture into a high-temperature geothermal reservoir saturated with superheated vapor is considered. Behind the evaporation front on which the admixture precipitates a dissolution front separating regions with the initial concentration and with the concentration of the saturated solution coexisting with the solid salt phase is formed. It is found that the self-similar solution of the problem with two moving boundaries is two-valued. With variation of the parameters and the initial and boundary conditions the solutions may approach each other and at certain critical values merge. In the supercritical region the self-similar solution does not exist. The non-existence of a solution can be interpreted as the filling of the pores with precipitated salt and the cessation of the phase motion.     

Estimation of Dynamic Relative Permeability and Capillary Pressure from Countercurrent Imbibition Experiments

Direct laboratory measurements of in situ water-phase saturation history are used to estimate relative permeability and capillary pressure functions. The magnitude of so-called nonequilibrium effects during spontaneous imbibition is quantified and, if significant, these effects are incorporated within the estimation technique. The primary constraint employed is that curves must increase or decrease monotonically; otherwise, no predetermined functionality is assumed. The technique is demonstrated using water saturation profile histories obtained for diatomite (a low-permeability and high-porosity rock). Results indicate that nonequilibrium effects detected at laboratory scale in low-permeability rocks influence the estimation of unsteady-state relative permeability and capillary pressure.     

Determination of Salt Diffusion Coefficient in Brick: Analytical Methods

This paper presents an investigation into salt diffusion in new, fully saturated brick under isothermal conditions. A commonly used experiment methodology, diffusion cell method, is adopted. The analytical and numerical solutions are obtained. The analytical solution is simple and straightforward, which determines temporally salt concentrations in the monitored chamber. It enables us to estimate salt diffusion coefficients in a fast and accurate way.     

Accumulation and Precipitation of Salts during Groundwater Evaporation and Flow

A mathematical model for the precipitation of dissolved salts during groundwater evaporation is proposed. An asymptotic solution of the problem is obtained for a specified flow law. It is shown that there are two different regimes of solute precipitation which are determined by the evaporation front velocity and the groundwater flow rate. The dependence of the precipitated salt mass on the soil surface temperature, the atmospheric humidity, the initial solute concentration and the filtration rate is illustrated.     

Water Injection into a Low-Permeability Rock - 1 Hydrofracture Growth

In this paper, we model water injection through a growing vertical hydrofracture penetrating a low-permeability reservoir. The results are useful in oilfield waterflood applications and in liquid waste disposal through reinjection. Using Duhamel's principle, we extend the Gordeyev and Entov (1997) self-similar 2D solution of pressure diffusion from a growing fracture to the case of variable injection pressure. The flow of water injected into a low-permeability rock is almost perpendicular to the fracture for a time sufficiently long to be of practical interest. We revisit Carter's model of 1D fluid injection (Howard and Fast, 1957) and extend it to the case of variable injection pressure. We express the cumulative injection through the injection pressure and effective fracture area. Maintaining fluid injection above a reasonable minimal value leads inevitably to fracture growth regardless of the injector design and the injection policy. The average rate of fracture growth can be predicted from early injection. A smart injection controller that can prevent rapid fracture growth is needed.     

Longitudinal diffusion of solid particle admixture in a flow through a tube

The propagation of solid particle admixture in a flow through a flat channel is studied.The processes of diffusion and convective transfer as well as solid particle deposition due to gravity result in varying admixture concentration both in depth and longtitudinally.The study of admixture longitudinal distribution is of great interest in a lot of applications, therefore this paper gives the derivation of longitudinal diffusion equation for a mean cross-section admixture concentration.The equation contains three effective parameters; i.e. convective tranfer velocity, longitudinal diffusion coefficient and particle deposition time. These parameters integrally reflect local processes of matter transfer as well as momentum.The proposed model is specific and differs from Taylor equation for longitudinal diffusion, since the fact of particle deposition and adhesion is taken into account. As a result of particle deposition a sediment layer is formed on the channel bottom which increases in thickness with time. To describe this process balance conditions for the whole flow mass and admixture mass on sediment sediment surface are formulated and a condition for matter movement towards the channel bottom is derived that is different from zero due to particle adhesion.     

层状盐岩力学特性研究进展

盐岩具有孔隙度低,渗透率小,损伤自恢复和塑性变形能力大等特性.本文着眼于深部盐岩能源地下储备,在简要介绍国内外盐岩力学特性研究现状基础上,着重综述了近期关于层状沉积型盐岩工程力学特性研究的进展.层状盐岩压缩试验表明泥质硬石膏夹层对盐岩体的变形和破坏特性有明显的影响,揭示了复合岩体的变形和破坏机制;层状盐岩流变试验表明层状盐岩的蠕变主要由盐岩层控制,硬夹层的存在对溶腔围岩的长期蠕变起到抑制作用;为了深入了解界面的力学特性,开展了层状盐岩直接剪切试验、间接拉伸试验和界面微观分析试验,试验表明层状盐岩体中盐岩夹层界面具有较强的黏结力,这十分有利于盐岩溶腔的密闭性和稳定性;针对特殊的层状岩体提出了复合岩体Cosserat介质扩展本构模型,并应用于层状盐岩构造中能源储库稳定性分析中.最后指出了层状盐岩工程力学特性研究中值得关注的几个重点研究方向.      

Numerical Modeling of Salt Transport and Precipitation in Non-Isothermal Partially Saturated Porous Media Considering Kinetics of Salt Phase Changes

Water and salts strongly influence the durability of porous materials. One of the most adverse phenomena which is related to the salt and moisture presence in the pore system of building materials is salt crystallization. The process is associated with the supersaturation ratio. The salt phase change kinetics is taken into account during the modeling of coupled moisture, salt, and heat transport. To solve the set of governing, differential equations the finite element and the finite difference methods are used. Three different rate laws are assumed in modeling the salt phase change. The drying, cooling, and warming of the cement mortar sample, during which the salt phase change occurs, have been simulated using the developed software. The changes of salt concentration in the pore solution and the amount of precipitated salt due to variation of boundary conditions are presented and discussed. The results obtained in the numerical simulation assuming the first, second, and fourth order rate low indicate that the higher order of the rate law the longer time delay between the change of boundary conditions and the salt precipitation. Such an analysis might be very useful during the determination of the material parameters by solving the inverse problem.     

A semi-analytic solution of a wellbore in a non-isothermal low-permeability porous medium under non-hydrostatic stresses

The transient stress, displacement, pore pressure and temperature fields around a wellbore in a thermo-poro-elastic (THM) medium subject to non-hydrostatic remote stresses are analyzed under non-isothermal plane-strain conditions. The linear THM model proposed by Coussy (1989) is adopted in the analysis with a focus on thermal effects in low-permeability saturated rocks, characterized by a latent heat associated with local changes of fluid mass content. Non-dimensionalized parameters are identified by reformulating the fully-coupled governing equations and boundary conditions. The wellbore problem is simplified by decomposing it into axisymmetric and deviatoric loading cases. The corresponding analytical solutions are obtained in Laplace space. The inverse Laplace transforms are performed numerically to find the time-dependent distributions of field variables in the rock mass around the wellbore. These numerical results show that although the pore pressure diffusion has little influence on temperature and stress, temperature changes can strongly affect the pore pressure and stress around the wellbore. The temperature change can lead to changes in near-well stresses and the resulting significant change in wellbore breakdown pressure illustrates the importance of considering the THM coupling.     

Influence of precipitation on the Portevin-Le Chatelier effect in Al-Mg alloys

In the alloy with solute content higher than the limiting solubility, the solute atoms that have failed to dissolve will precipitate from the solid solution and form precipitations. In this study, the Portevin-Le Chatelier (PLC) effects in annealed 5456 and 5052 aluminum alloys with different precipitation contents have been investigated under different applied strain rates. The results suggest that precipitations have significant effect on the PLC effect and the more the precipitations are, the greater the influence is. Furthermore, the solute diffusion is pipe diffusion in 5052 alloy with lower precipitation content. However, for 5456 alloy with higher precipitation content, the diffusion is no longer the case but more complex.     

Characteristics of Salt-Precipitation and the Associated Pressure Build-Up during CO<Subscript>2</Subscript> Storage in Saline Aquifers

Mitigation and control of borehole pressure at the bottom of an injection well is directly related to the effective management of well injectivity during geologic carbon sequestration activity. Researchers have generally accepted the idea that high rates of CO₂ injection into low permeability strata results in increased bottom-hole pressure in a well. However, the results of this study suggested that this is not always the case, due to the occurrence of localized salt precipitation adjacent to the injection well. A series of numerical simulations indicated that in some cases, a low rate of CO₂ injection into high permeability formation induced greater pressure build-up. This occurred because of the different types of salt precipitation pattern controlled by buoyancy-driven CO₂ plume migration. The first type is non-localized salt precipitation, which is characterized by uniform salt precipitation within the dry-out zone. The second type, localized salt precipitation, is characterized by an abnormally high level of salt precipitation at the dry-out front. This localized salt precipitation acts as a barrier that hampers the propagation of both CO₂ and pressure to the far field as well as counter-flowing brine migration toward the injection well. These dynamic processes caused a drastic pressure build-up in the well, which decreased injectivity. By modeling a series of test cases, it was found that low-rate CO₂ injection into high permeability formation was likely to cause localized salt precipitation. Sensitivity studies revealed that brine salinity linearly affected the level of salt precipitation, and that vertical permeability enhanced the buoyancy effect which increased the growth of the salt barrier. The porosity also affected both the level of localized salt precipitation and dry-out zone extension depending on injection rates. High temperature injected CO₂ promoted the vertical movement of the CO₂ plume, which accelerated localized salt precipitation, but at the same time caused a decrease in the density of the injected CO₂. The combination of these two effects eventually decreased bottomhole pressure. Considering the injectivity degradation, a method is proposed for decreasing the pressure build-up and increasing injectivity by assigning a ‘skin zone’ that represents a local region with a transmissivity different from that of the surrounding aquifer.     

Stagnation Points as Loci of Solute Concentration Extrema at the Evaporative Surface of a Random Porous Medium

Transport in Porous Media - Evaporation of a saline solution from a porous medium often leads to the precipitation of salt at the surface of the porous medium. It is commonly observed that the...     

An Analytical Solution and Nonlinear Regression Analysis for Sandface Temperature Transient Data in the Presence of a Near-Wellbore Damaged Zone

Throughout this study, we present a dual-continuum model of transport of the natural gas in shale formations. The model includes several physical mechanisms such as diffusion, adsorption and rock stress sensitivity. The slippage has a clear effect in the low-permeability formations which can be described by the apparent permeability. The adsorption mechanism has been modeled by the Langmuir isotherm. The porosity-stress model has been used to describe stress state of the rocks. The thermodynamics deviation factor is calculated using the equation of state of Peng–Robinson. The governing differential system has been solved numerically using the mixed finite element method (MFEM). The stability of the MFEM has been investigated theoretically and numerically. A semi-implicit scheme is employed to solve the two coupled pressure equations, while the thermodynamic calculations are conducted explicitly. Moreover, numerical experiments are performed under the corresponding physical parameters of the model. Some represented results are shown in graphs including the rates of production as well as the pressures and the apparent permeability profiles.

     

Fresh water injection into a geothermal reservoir which contains superheated vapor and solid phase salt

A mathematical model is proposed for the process with two unknown phase transition interfaces. At the leading interface, evaporation occurs and a salt precipitates. The interface that moves at a lower velocity is a dissolution surface. In the isothermal approximation the self-similar solution is obtained. It is shown that fresh water injection may lead to solid precipitate transfer from one region to another, substantially increasing the precipitate content behind the evaporation front. This significantly decreases permeability and, hence, the flow velocity through permeable rocks. With approaching the critical parameter region the branches of the obtained two-valued self-similar solution also approach and at critical values merge, which corresponds to the disappearance of the solution. The non-existence of the self-similar solution can be interpreted as the filling of the pores with salt precipitate and the flow arrest in the geothermal reservoir.     

Polytypic transformations of aluminum hydroxide: A mechanistic investigation

The diffusion of ammonia vapors into a solution of aluminum nitrate or ferric nitrate results in the precipitation of their respective hydroxides and oxyhydroxides. Polymorphic phase formation of aluminum hydroxide is controlled by the rate of crystallization. The PXRD patterns of products obtained via vapor phase diffusion revealed that poorly ordered aluminum hydroxide is formed during the initial stages of crystallization. After 8 days, the formation of the bayerite phase of aluminum hydroxide was observed. Upon prolonged exposure to ammonia vapors, bayerite was transformed into gibbsite. The infrared spectrum of the product confirmed the presence of different polytypic phases of aluminum hydroxide. The results demonstrated that the crystal structure of metal hydroxides is controlled by the rate of crystallization, nature of the metal ion, site selectivity and specificity and preparative conditions.     

Monitoring of Pollutant Diffusion into Clay Liners by Electrical Methods

A non-destructive test was carried out on a liner material—sand bentonite mixture (SB) with a continuous concentration diffusion of NaCl electrolyte. The work reported studied the spacio-temporal variation of the electrical conductivity $\sigma ^{*}_{\mathrm{s}}$ (z, t) in a diffusion soil column with different heights. A relationship between the interstitial pore fluid concentration of SB and the electrical conductivity of the solution has been established by mixing and compacting samples of sand bentonite with NaCl electrolytes at different concentrations. Electrical conductivity of compacted specimens was measured with a two-electrode cell. The conductivity measurements were used to quantify the pore fluid concentration and effective diffusion coefficient of SB liners. It is concluded here that the electrical conductivity of compacted specimens depends mainly on the salt concentration in the pore fluid and it could be used to measure ionic movement through liners during diffusion. The experimental diffusion coefficient reached theoretical diffusion coefficient when sample height is equal to 40 cm.     

Convection in a rotating medium above a thermally inhomogeneous horizontal surface

The linear stationary problem of convection in a medium rotating about a vertical axis above a thermally inhomogeneous horizontal surface is theoretically investigated. Attention is mainly focused on the case of a homogeneous medium, but certain stratification effects and especially the convection characteristics in binary mixtures (for example, in saline sea water) are also considered. When the rotation is rapid (large Taylor numbers) the convective cells are strongly elongated in the vertical direction, though they also contain a thin Ekman boundary layer. The importance of the boundary conditions on the horizontal surface (in parallel with the no-slip conditions, more general conditions that may follow from the quadratic turbulent friction model are considered) is shown. In the case of binary mixtures, the differential diffusion and rotation effects may together result in the appearance of “induced salt fingers”, the deep penetration of convection into an arbitrarily stably stratified medium. The convective motions may then have a considerable effect on the background vertical temperature and admixture distributions. Attention is drawn to an original manifestation of the analogy between the rotation and stratification effects: in a non-rotating, stably stratified medium, near a thermally inhomogeneous vertical surface, the convection also penetrates deep into the medium, but in the horizontal direction, so that, when the coordinate system is rotated through 90°, the solution coincides with the case of a rotating non-stratified fluid considered here.