Numerical and experimental investigation of convective drying in unsaturated porous media with bound water

The heat and mass transfer in an unsaturated wet cylindrical porous bed packed with quartz particles was investigated theoretically for relatively low convective drying rates. Local thermodynamic equilibrium was assumed in the mathematical model describing the multi-phase flow in the unsaturated porous media using the energy and mass conservation equations to describe the heat and mass transfer during the drying. The drying model included convection and capillary transport of the free water, diffusion of bound water, and convection and diffusion of the gas. The numerical results indicated that the drying process could be divided into three periods, the temperature rise period, the constant drying rate period and the decreasing drying rate period. The numerical results agreed well with the experimental data verifying that the mathematical model can evaluate the drying performance of porous media for low drying rates. The effects of drying conditions such as the ambient temperature, the relative humidity, and the velocity of the drying air, on the drying process were evaluated by numerical solution.     

A Study of Microscale Gas Trapping Using Etched Silicon Micromodels

Immobilization and trapping of carbon dioxide (CO₂) enhances the security of geological storage. Trapping mechanisms have been characterized in four groups: structural, residual, dissolution, and mineralization. While structural trapping acts immediately when injection starts and is well investigated, the contribution of residual and dissolution trapping increases over storage time and these contributions need to be better understood for better predictions. This paper focuses on an experimental pore-scale investigation of residual and capillary trapping. CO₂?Cwater imbibition experiments were conducted in micromodels whose homogenous pore space is geometrically and topologically similar to Berea sandstone. Microvisual data, photographs and video footage, describes the trapping mechanism and, especially, the disconnection and shrinkage of the CO₂ phase. Results show that depending on the flow rate of the imbibing water different trapping mechanisms are observed. Lower flow rates, comparable to the trailing edge of a CO₂ plume, lead to more snap-off events and greater trapped residual saturation, whereas rates comparable to the near wellbore area during enhanced sequestration showed displacement of gas bubbles and greater dissolution that ultimately leads to very low or zero gas saturations. Furthermore, complete dissolution events showed that homogenous as well as heterogeneous dissolution occurs. Whereas the latter is subdivided into microbubble formation and dissolution on crevices or pore roughness, the former occurs without the influence of pore walls. Based on the observations we suggest that the type of rock and its roughness as well as the fines present at the CO₂ brine interface are important factors determining the dissolution mechanism.     

A Non-isothermal Pore Network Drying Model with Gravity Effect

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid–gas interface through temperature-dependent equilibrium vapor pressure and surface tension as well as the phase change enthalpy (in evaporation and condensation). The interfacial effects due to capillary forces and gravity are combined in an invasion potential; viscous forces are neglected. Simulation results show stabilized invasion patterns and finite drying front width by the influence of gravity.     

储层含水条件下致密砂岩/页岩无机质纳米孔隙气相渗透率模型

页岩及致密砂岩储层富含纳米级孔隙,且储层条件下页岩孔隙(尤其无机质孔隙)及致密砂岩孔隙普遍含水,因此含水条件下纳米孔隙气体的流动能力的评价对这两类气藏的产能分析及生产预测具有重要意义.本文首先基于纳米孔隙内液态水及汽态水热力学平衡理论,量化了储层孔隙含水饱和度分布特征;进一步在纳米孔隙单相气体传质理论的基础上,考虑了孔隙含水饱和度对气体流动的影响;最终建立了含水饱和度与气相渗透率的关系曲线. 基于本文岩心孔隙分布特征,计算结果表明:储层含水饱和度对气体流动能力的影响不容忽视,在储层含水饱和度20%的情况下,气相流动能力与干燥情况相比将降低约10%;在含水饱和度40% 的情况下,气相流动能力将降低约20%.      

Dependence of Pore-to-Core Up-scaled Reaction Rate on Flow Rate in Porous Media

Due to inherent heterogeneities in structure, mineral placement and fluid velocity in rock, bulk reaction rates realized during reactive flow through porous media may differ significantly from that predicted by laboratory-measured rate laws. In particular, rate laws determined in batch reactor experiments do not capture any of the flow dependence that will be experienced in the porous medium. Based on network flow model simulations of anorthite and kaolinite reactions in two sandstone pore networks under acidic conditions commensurate with CO₂ sequestration, we compute up-scaled reaction rates at the core scale and investigate the dependence of the observed reaction rates on flow rate. For the anorthite reaction which, under these acidic conditions is far from equilibrium and dominated by pH, we find a power law dependence of reaction rate on flow rate. For the kaolinite reaction, which is near equilibrium, a more complex dependence emerges, with the up-scaled rate tending to rapidly increasing net precipitation at low-flow rates, then reversing and tending toward net dissolution at high-flow rates.     

多孔介质在压力梯度作用下的热质耦合数值模拟

多孔介质干燥导致热质耦合传输过程。本文基于连续介质力学的宏观尺度,对多孔介质的热、湿和气三者耦合迁移进行数值模拟,研究压力梯度对热质传输的影响。多孔介质传质机理主要为水汽和空气的对流和扩散传输、吸附水在含湿量梯度作用下的自由扩散和其在温度梯度即Soret效应驱动下的流动。采用Galerkin加权余量的有限元方法,提出了...     

Internal Heating Effect and Enhancement of Drying of Ceramics by Microwave Heating with Dynamic Control

The effectiveness of internal heating for enhancing the drying of molded ceramics is evaluated by both modeling and experiments. In the theoretical analysis, three dimensional drying-induced strain–stress are modeled, and the numerical solutions show that the internal heating generates lower internal stress than continuous convective heating or intermittent convective heating. Microwave drying is examined experimentally to study the effect of internal heating on the drying behavior of a wet sample of a kaolin slab. The drying behavior is compared among three modes: microwave heating, hot air heating and radiation heating. The transient behavior of temperatures in microwave drying is quite different from conventional drying by external heating. In particular, the temperature of the slab drops once in the progress of drying. This phenomenon cannot be predicted adequately by a simple model of one-dimensional heat conduction and moisture diffusion accompanied with an internal heat generation rate given as a linear function of the moisture content. It should be noted that the temperature behavior takes place due to the combined interactions with internal evaporation of moisture by rise in internal vapor pressure and shift of impedance or interference in the applicator. Microwave heating with a constant power above 100 W results in sample breakage due to the internal vapor pressure. However, if the power is dynamically controlled so as to maintain the temperature less than the boiling point of water, the drying succeeds without any crack generation until completion with a significantly faster drying rate than drying in convective heating or in the oven.     

Mixing of Stably Stratified Gases in Subsurface Reservoirs: A Comparison of Diffusion Models

Numerical simulations of the mixing of carbon dioxide (CO₂) and methane (CH₄) in a gravitationally stable configuration have been carried out using the multicomponent flow and transport simulator TOUGH2/EOS7C. The purpose of the simulations is to compare and test the appropriateness of the advective–diffusive model (ADM) relative to the more accurate dusty-gas model (DGM). The configuration is relevant to carbon sequestration in depleted natural gas reservoirs, where injected CO₂ will migrate to low levels of the reservoir by buoyancy flow. Once a gravitationally stable configuration is attained, mixing will continue on a longer time scale by molecular diffusion. However, diffusive mixing of real gas components CO₂ and CH₄ can give rise to pressure gradients that can induce pressurization and flow that may affect the mixing process. Understanding this coupled response of diffusion and flow to concentration gradients is important for predicting mixing times in stratified gas reservoirs used for carbon sequestration. Motivated by prior studies that have shown that the ADM and DGM deviate from one another in low permeability systems, we have compared the ADM and DGM for the case of permeability equal to 10^–15 m² and 10^–18 m². At representative reservoir conditions of 40 bar and 40°C, gas transport by advection and diffusion using the ADM is slightly overpredicted for permeability equal to 10^–15 m², and substantially overpredicted for permeability equal to 10^–18 m² compared to DGM predictions. This result suggests that gas reservoirs with permeabilities larger than approximately 10^–15 m² can be adequately simulated using the ADM. For simulations of gas transport in the cap rock, or other very low permeability layers, the DGM is recommended.     

In-Situ Capillary Trapping of CO<Subscript>2</Subscript> by Co-Injection

Co-injection of water with CO₂ is an effective scheme to control initial gas saturation in porous media. A fractional flow rate of water of approximately 5–10% is sufficient to reduce initial gas saturations. After water injection following the co-injection, most of the gas injected in the porous media is trapped by capillarity with a low fractional volume of migrating gas. In this study, we first derive an analytical model to predict the gas saturation levels for co-injection with water. The initial gas saturation is controlled by the fractional flow ratio in the co-injection process. Next, we experimentally investigate the effect of initial gas saturation on residual gas saturation at capillary trapping by co-injecting gas and water followed by pure water injection, using a water and nitrogen system at room temperature. Depending on relative permeability, initial gas saturation is reduced by co-injection of water. If the initial saturation in the Berea sandstone core is controlled at 20–40%, most of the gas is trapped by capillarity, and less than 20% of the gas with respect to the injected gas volume is migrated by water injection. In the packed bed of Toyoura standard sand, the initial gas saturation is approximately 20% for a wide range of gas with a fractional flow rate from 0.50 to 0.95. The residual gas saturation for these conditions is approximately 15%. Less than approximately 25% of the gas migrates by water injection. The amount of water required for co-injection systems is estimated on the basis of the analytical model and experimental results.     

Pore-Network Modeling of Isothermal Drying in Porous Media

In this paper we present numerical results obtained with a pore-network model for the drying of porous media that accounts for various processes at the pore scale. These include mass transfer by advection and diffusion in the gas phase, viscous flow in the liquid and gas phases and capillary effects at the liquid--gas interface. We extend our work by studying the effect of capillarity-induced flow in macroscopic liquid films that form at the pore walls as the liquid--gas interface recedes. A mathematical model that accounts for the effect of films on the drying rates and phase distribution patterns is presented. It is shown that film flow is a major transport mechanism in the drying of porous materials, its effect being dominant when capillarity controls the process, which is the case in typical applications.     

Stability of two-layer fluid flow

The problem of two-layer convective flow of viscous incompressible fluids in a horizontal channel with solid walls in the presence of evaporation is considered in the Oberbeck–Boussinesq approximation assuming that the interface is an undeformable thermocapillary surface and taking into account the Dufour effect in the upper layer which is a mixture of gas and liquid vapor. The effects of longitudinal temperature gradients at the boundaries of the channel and the thicknesses of the layer on the flow pattern and the evaporation rate are studied under conditions of specified gas flow and the absence of vapor flow on the upper boundary of the channel. It is shown that the long-wavelength asymptotics for the decrement is determined from the flow characteristics, the longwavelength perturbations occurring in the system decay monotonically, and the thermal instability mechanism is not potentially the most dangerous.     

Laboratory Experiments on Environmental Friendly Means to Improve Coalbed Methane Production by Carbon Dioxide/Flue Gas Injection

Scaled in situ laboratory core flooding experiments with CO₂, N₂ and flue gas were carried out on coal in an experimental high P,T device. These experiments will be able to give an insight into the design of the injection system, management, control of the operations and the efficiency of an ECBM project. Although the experience gained by the oil industry represents a valuable starting point, several problems are still to be studied and solved before CO₂ improved deep coalbed methane production may be operationally feasible. These are all related to the heterogeneous nature of the pore structure of coal, and in particular to the presence of fractures. More specifically, a number of questions need to be addressed, e.g. what are the conditions under which the fluid in the micro pores of the coal is displaced by the CO₂ in the presence of competitive adsorption; what is the role of compositional heterogeneity and fracture anisotropy of coal for the injection design and the efficiency of the sequestration in relation to the swelling and shrinkage characteristics of coal; how does the mobile and the immobile water in the coal affect the exchange process. These questions can be answered by means of downscaled laboratory experiments that are capable of accurately describing the coupled process of multiphase flow, competitive adsorption and geo-mechanics. The laboratory conditions have been simulated to match pressure and temperature at depths of 800 to 1,000 m. Under those conditions the injected CO₂ remains supercritical. Upto now, the results show that dewatering will be an essential step for successful ECBM combined with a CO₂ sequestration process.     

Laboratory Flow Experiments for Visualizing Carbon Dioxide-Induced,Density-Driven Brine Convection

Injection of carbon dioxide (CO₂) into saline aquifers confined by low- permeability cap rock will result in a layer of CO₂ overlying the brine. Dissolution of CO₂ into the brine increases the brine density, resulting in an unstable situation in which more-dense brine overlies less-dense brine. This gravitational instability could give rise to density-driven convection of the fluid, which is a favorable process of practical interest for CO₂ storage security because it accelerates the transfer of buoyant CO₂ into the aqueous phase, where it is no longer subject to an upward buoyant drive. Laboratory flow visualization tests in transparent Hele-Shaw cells have been performed to elucidate the processes and rates of this CO₂ solute-driven convection (CSC). Upon introduction of CO₂ into the system, a layer of CO₂-laden brine forms at the CO₂-water interface. Subsequently, small convective fingers form, which coalesce, broaden, and penetrate into the test cell. Images and time-series data of finger lengths and wavelengths are presented. Observed CO₂ uptake of the convection system indicates that the CO₂ dissolution rate is approximately constant for each test and is far greater than expected for a diffusion-only scenario. Numerical simulations of our system show good agreement with the experiments for onset time of convection and advancement of convective fingers. There are differences as well, the most prominent being the absence of cell-scale convection in the numerical simulations. This cell-scale convection observed in the experiments may be an artifact of a small temperature gradient induced by the cell illumination.     

Modeling of Rocks and Cement Alteration due to CO<Subscript>2</Subscript> Injection in an Exploited Gas Reservoir

The injection of CO₂ in exploited natural gas reservoirs as a means to reduce greenhouse gas (GHG) emissions is highly attractive as it takes place in well-known geological structures of proven integrity with respect to gas leakage. The injection of a reactive gas such as CO₂ puts emphasis on the possible alteration of reservoir and caprock formations and especially of the wells’ cement sheaths induced by the modification of chemical equilibria. Such studies are important for injectivity assurance, wellbore integrity, and risk assessment required for CO₂ sequestration site qualification. Within a R&D project funded by Eni, we set up a numerical model to investigate the rock–cement alterations driven by the injection of CO₂ into a depleted sweet natural gas pool. The simulations are performed with the TOUGHREACT simulator (Xu et al. in Comput Geosci 32:145–165, 2006) coupled to the TMGAS EOS module (Battistelli and Marcolini in Int J Greenh Gas Control 3:481–493, 2009) developed for the TOUGH2 family of reservoir simulators (Pruess et al. in TOUGH2 User’s Guide, Version 2.0, 1999). On the basis of field data, the system is considered in isothermal (50°C) and isobaric (128.5 bar) conditions. The effects of the evolving reservoir gas composition are taken into account before, during, and after CO₂ injection. Fully water-saturated conditions were assumed for the cement sheath and caprock domains. The gas phase does not flow by advection from the reservoir into the interacting domains so that molecular diffusion in the aqueous phase is the most important process controlling the mass transport occurring in the system under study.     

Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO<Subscript>2</Subscript> Sequestration

Dissolution of CO₂ into brine causes the density of the mixture to increase. The density gradient induces natural convection in the liquid phase, which is a favorable process of practical interest for CO₂ storage. Correct estimation of the dissolution rate is important because the time scale for dissolution corresponds to the time scale over which free phase CO₂ has a chance to leak out. However, for this estimation, the challenging simulation on the basis of convection–diffusion equation must be done. In this study, pseudo-diffusion coefficient is introduced which accounts for the rate of mass transferring by both convection and diffusion mechanisms. Experimental tests in fluid continuum and porous media were performed to measure the real rate of dissolution of CO₂ into water during the time. The pseudo diffusion coefficient of CO₂ into water was evaluated by the theory of pressure decay and this coefficient is used as a key parameter to quantify the natural convection and its effect on mass transfer of CO₂. For each experiment, fraction of ultimate dissolution is calculated from measured pressure data and the results are compared with predicted values from analytical solution. Measured CO₂ mass transfer rate from experiments are in reasonable agreement with values calculated from diffusion equation performed on the basis of pseudo-diffusion coefficient. It is suggested that solving diffusion equation with pseudo diffusion coefficient herein could be used as a simple and rapid tool to calculate the rate of mass transfer of CO₂ in CCS projects.     

Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Effects of nanoparticles mean diameter on the particle migration and thermo-hydraulic behavior of laminar mixed convection of a nanofluid in an inclined tube

Laminar mixed convection of a nanofluid consisting of Al₂O₃ and water through an inclined tube has been investigated numerically. As mathematical model two-phase mixture model has been adopted, thus three dimensional elliptical governing equations have been solved to understand the flow behavior at different Re–Gr combinations. Control volume technique is used for discretization of the governing equations. For the convective and diffusive terms the second order upwind method was used while the SIMPLEC procedure was adopted for the velocity–pressure coupling. For different nanoparticle mean diameters and tube inclinations thermo-fluid parameters such as secondary flow, axial velocity profiles, nanoparticles distribution at the tube cross section, axial evolution of peripheral average convective heat transfer coefficient and pressure drop along the tube, have been presented and discussed. Maximum enhancement on the heat transfer coefficient is seen at tube inclination of 45°.     

Numerical Simulation Studies of the Long-term Evolution of a CO<Subscript>2</Subscript> Plume in a Saline Aquifer with a Sloping Caprock

We have used the TOUGH2-MP/ECO2N code to perform numerical simulation studies of the long-term behavior of CO₂ stored in an aquifer with a sloping caprock. This problem is of great practical interest, and is very challenging due to the importance of multi-scale processes. We find that the mechanism of plume advance is different from what is seen in a forced immiscible displacement, such as gas injection into a water-saturated medium. Instead of pushing the water forward, the plume advances because the vertical pressure gradients within the plume are smaller than hydrostatic, causing the groundwater column to collapse ahead of the plume tip. Increased resistance to vertical flow of aqueous phase in anisotropic media leads to reduced speed of up-dip plume advancement. Vertical equilibrium models that ignore effects of vertical flow will overpredict the speed of plume advancement. The CO₂ plume becomes thinner as it advances, but the speed of advancement remains constant over the entire simulation period of up to 400 years, with migration distances of more than 80 km. Our simulations include dissolution of CO₂ into the aqueous phase and associated density increase, and molecular diffusion. However, no convection develops in the aqueous phase because it is suppressed by the relatively coarse (sub-) horizontal gridding required in a regional-scale model. A first crude sub-grid-scale model was developed to represent convective enhancement of CO₂ dissolution. This process is found to greatly reduce the thickness of the CO₂ plume, but, for the parameters used in our simulations, does not affect the speed of plume advancement.     

Diffusion properties of aqueous slurries in evaporative spray drying of copper (II) chloride dihydrate

This study examines the evaporative heat transfer and diffusive mass transfer of a droplet of CuCl₂ solution. The validation of a new predictive model involves comparisons with experimental data from previous studies of different fluids based on non-dimensional analysis. The study provides new insight about the effects of different concentrations of water on the CuCl₂ slurry drying at low to moderate air temperatures. Predictive correlations of heat and mass transfer are developed for the aqueous solution, subject to various drying conditions. The analysis is performed for moist air in contact with a sprayed aqueous solution of copper (II) chloride dihydrate [CuCl₂·(2H₂O)]. Results are presented and discussed for the drying processes.     

Thermo-gravitational convection in a continuous optical discharge

The relative importance of such processes as the free convective motion of the gas, the absorption of the laser radiation and radiative heat transfer is discussed. The burning of a continuous optical discharge under experimental conditions [6] is theoretically investigated. The two-dimensional problem of the convective motion of the gas in an optical discharge burning in a vertical CO₂ laser beam inside a cylindrical chamber is solved. The principal characteristics of thermogravitational convection of the radiating air under conditions of local thermodynamic equilibrium at atmospheric pressure are studied on the temperature interval from 300 to 20 000°K.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 124–129, July–August, 1989.