Dispersion and Chemical Reactions in Porous Media

The effect of chemical reactions on the process of admixture transport by a flow through a porous medium is considered. On the basis of a number of examples it is shown that the dispersion coefficient depends on the chemical reaction rate constant.     

Simultaneous Measurement of Effective Chemical Shrinkage and Modulus Evolutions During Polymerization

A novel method is proposed to simultaneously measure the effective chemical shrinkage and modulus evolutions of advanced polymers during polymerization. The method utilizes glass fiber Bragg grating (FBG) sensors. They are embedded in two uncured cylindrical polymer specimens with different configurations and the Bragg wavelength (BW) shifts are continuously documented during the polymerization process. A theoretical relationship is derived between the BW shifts and the evolution properties, and an inverse numerical procedure to determine the properties from the BW shifts is established. Extensive numerical analyses are conducted to provide general guidelines for selecting an optimum combination of the two specimen configurations. The method is implemented for a high-temperature curing thermosetting polymer. Validity of the proposed method is corroborated by two independent verification experiments: a self-consistency test to verify the measurement accuracy of raw data and a warpage measurement test of a bi-material strip to verify the accuracy of evolution properties.     

A Comparative Study of Gas Flooding and Foam-Assisted Chemical Flooding in Bentheimer Sandstones

Transport in Porous Media - A laboratory study of principal immiscible gas flooding schemes is reported. Very well-controlled experiments on continuous gas injection, water-alternating-gas (WAG)...     

Numerical and Experimental Evaluation of Dispersion Coefficient for Resin Transfer Modeling

Resin transfer molding (RTM) is a composite manufacturing process. A preformed fiber is placed in a closed mold and a viscous resin is injected into the mold. In this article, a model is developed to predict the flow pattern, extent of reaction, and temperature change during the filling and curing in a thin rectangular mold. A numerical simulation is presented to predict the free surface and its interactions with heat transfer and cure for flow of a shear-thinning resin through the preformed fiber.To simulate this process, using local thermal equilibrium assumption, it is essential to include the thermal dispersion term in energy equation. The best method to achieve this result is experimental simulation and preparing proportionate system at simple conditions without curing. By comparison of recorded temperature values (using installed instruments at various locations), and the corresponding results from numerical solution for different estimated values of dispersion coefficient, this coefficient has been evaluated based on the best matching estimate. The results show that, to simulate composite manufacturing process by RTM method, the effect of dispersion term in energy equation shall not be neglected.     

Diffusion of Tracer in Altered Tonalite: Experiments and Simulations with Heterogeneous Distribution of Porosity

Numerical time-domain-diffusion simulations were used for studying the diffusion behavior of tracer molecules in rock matrix with homogeneous and heterogeneous porosity. As the heterogeneous sample in these simulations, a 3D tomographic image of altered tonalite was used, in which the mineral components and the pores resolved by X-ray microtomography were represented by their respective intragranular porosities determined previously by the ¹⁴C-PMMA method. The apparent diffusion coefficient of a tracer in altered tonalite was determined experimentally, and was then used in the simulations. In the altered tonalite analyzed, inclusion of heterogeneity in the porosity increased the diffusion coefficient by 16 %. Altered and pristine feldspar was the main mineral component in the sample (72 %), and it also provided the dominant contribution to tracer diffusion, explaining alone 52 % of the diffusion coefficient. The large pores resolved by microtomography (6 %) and altered and pristine mica (22 %) gave an equal contribution to the diffusion coefficient. The simulation method applied was also validated by comparing the results to both an analytical and a numerical solution to the diffusion equation in a homogenous medium. In addition, the method was compared to discrete-time random-walk simulations in the case of randomly placed overlapping spheres.     

考虑转速影响的滚珠丝杠副摩擦系数计算与试验研究

针对目前滚珠丝杠副摩擦系数选取多以轴承经验值为依据的现状,基于滚珠丝杠副的结构特点建立滚珠与滚道的运动学及动力学模型,得到滚珠丝杠副摩擦系数与预紧力及摩擦力矩之间的关系,并推导出滚珠丝杠副摩擦系数计算公式.通过新型设计的预紧力可调机构可实现对双螺母滚珠丝杠副预紧力的任意加载与实时监测.利用该机构,结合摩擦力矩测量系统便可实现对滚珠丝杠副摩擦力矩和预紧力的直接测量,从而计算不同预紧力和转速下的实际摩擦系数.由于测量系统转速限制,试验在转速400 r/min以下的低速条件进行,最终得到摩擦系数随转速与预紧力的变化规律,并给出了滚珠丝杠副低速下摩擦系数的选用范围.通过试验得到合理的滚珠丝杠副摩擦系数取值对今后研究其摩擦特性有着重要的意义.     

Dispersion Phenomena in Thermal Diffusion and Modelling of Thermogravitational Experiments in Porous Media

In a TIPM paper published in 1992, the authors presented a simple model of thermogravitational diffusion in packed columns (TPC). Though qualitatively in agreement with the experimental results, this model exhibited a systematic discrepancy with respect to the magnitude of the permeability of maximum separation in the TPC experiments. Here, the results of a re-examination of the classical phenomenology of irreversible thermodynamics in porous media, applied to TPC, are described. Through the interpretation of additional TPC experiments, we show that the effective thermal diffusion coefficient in TPC includes a dependency upon the fluid velocity. This dependency is consistent with a nonlinear extension of irreversible thermodynamics, and the model so amended accounts for a correct re-interpretation of the experiments.     

Computation of the Longitudinal and Transverse Dispersion Coefficient in an Adsorbing Porous Medium Using Homogenization

This article compares for the first time, local longitudinal and transverse dispersion coefficients obtained by homogenization with experimental data of dispersion coefficients in porous media, using the correct porosity dependence. It is shown that the longitudinal dispersion coefficient can be reasonably represented by a simple periodic unit cell (PUC), which consists of a single sphere in a cube. We present a slightly modified and simplified approach to derive the homogenized equations, which emphasizes physical aspects of homogenization. Subsequently, we give full dimensional expressions for the dispersion tensor based on a comparison with the convective dispersion equation used for contaminant transport, inclusive the correct dependence on porosity. For the PUC of choice, the dispersion relations are identical to the relations obtained for periodic media. We show that commercial finite element software can be readily used to compute longitudinal and transverse dispersion coefficients in 2D and 3D. The 3D results are for the first time obtained at relevant Peclet numbers. There is good agreement for longitudinal dispersion. The computed transverse dispersion coefficients for a single sphere in a cube are much too low. The effect of adsorption on the dispersion coefficient is also studied. Adsorption does not affect the transverse dispersion coefficient. However, adsorption enhances the longitudinal dispersion coefficient in agreement with an analysis of homogenization applied to Taylor dispersion discussed in the literature.     

考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型

基于三维分形理论,建立了考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型,并且考虑了微凸体的弹性变形、弹塑性变形和完全塑性变形. 通过该模型,分析了摩擦系数、分形维数、分形粗糙度和接触载荷对热接触热导的影响. 研究结果表明:接触热导随着摩擦系数和分形粗糙度的增大而减小,随着分形维数和接触载荷的增大而增大. 该研究为开展接合面的热传递提供了一定的理论基础.      

Using Resampling Residuals for Estimating Confidence Intervals of the Effective Viscosity and Forchheimer Coefficient

Determination of parameters characterizing flows in porous media is a complex inverse problem. It is especially difficult to determine confidence intervals of such parameters. In this note, we develop a method based on utilization of bootstrapping in order to find confidence intervals of model parameters, which are determined by minimizing the discrepancy between model predictions and published experimental results. The discrepancy is characterized by the objective function defined as the sum of squared residuals in the points where experimental measurements are taken. A residual is defined as the difference between the experimentally measured value and the model prediction of this value. We utilized bootstrapping to generate surrogate experimental data by randomly resampling residuals and then adding them back to model predictions. The model parameters that give the best fit with a large number of surrogate data were then determined. By analyzing the histograms of best-fit parameter values, we were able to find confidence intervals for these parameters. We utilized the developed method to determine confidence intervals for the effective viscosity and Forchheimer coefficient.     

Effective Parameter Interpretation and Extrapolation of Dispersion Simulations by Means of a Simple Two-Velocity Model

The investigation of dispersion by microscopic simulations yields a lot of detailed information. To identify characteristic behaviours, it is useful to condense this information into a few effective parameters, which describe the transport process in the model geometry on a larger scale. For this purpose, a very simple two-velocity model has been developed, which models the transition from reversible to irreversible spreading of a tracer volume. It is shown that this model is very similar to Taylor–Aris dispersion and that it is quite suitable to approximate the time dependence of dispersion. The model is applied to characterize the effect of dead end pores on dispersion with a single correlation parameter. Up to Péclet numbers of about 500, 'hold-up'-dispersion similar to Taylor–Aris-dispersion is found. The simulations have been performed by the lattice Bhatnagar–Gross–Krook (BGK) method, which is a particular type of cellular automata and therefore allows an easy implementation of complicated geometries. The fully irreversible asymptotic dispersion is reached in an exponential process, the parameters of which can be identified by the two-velocity model after the mixing has noticeably begun. These are used to extrapolate the process which reduces the computational effort by about one order of magnitude.     

接触式机械密封端面摩擦系数影响因素分析与试验

通过理论模拟计算和试验,研究并分析工作参数和端面形貌分形参数对接触式机械密封端面摩擦系数的影响.依据接触式机械密封端面摩擦系数分形模型,并考虑端面摩擦系数与端面平均温度的相互耦合关系,通过模拟计算,对B104a-70型机械密封端面摩擦系数的影响因素进行分析.计算结果表明,端面摩擦系数随着弹簧比压的增大而增大,随着密封流体压力的增大而减小;当转速较小时,端面摩擦系数随着转速的增大而增大,当转速增大到一定数值后,端面摩擦系数则随着转速的增大而略有减小;端面摩擦系数随着软质环端面分形维数的增大和特征尺度系数的减小而增大,且端面越光滑增大的幅度越大.通过在不同的弹簧比压、密封流体压力和转速下的试验对理论计算结果进行了验证,试验密封流体为15℃清水.结果表明:随着弹簧比压、密封流体压力及转速的变化,摩擦系数理论计算值与试验值的变化规律相同;当转速和密封流体压力均较小时,最大相对误差为21.74%;而当转速达到正常工作转速2 900 r/min时,最大相对误差为5.08%.     

Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer

In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.     

Numerical Simulation of the Tube Flow of a Mixture with Chemical Reactions and Condensation

The results of calculating a model of a direct-flow chemical vapor-deposition reactor are presented. The phase- formation stages are considered over a wide time range. This makes it possible to identify different flow structures in which interference between the heat and mass transfer and chemical condensation processes occurs.     

Transport,Dilution, and Dispersion of Contaminant in a Leaky Karst Conduit

Often the water flowing in a solution conduit is a combination of contaminated water entering at sinkholes and cleaner water released from the limestone matrix. The concentration of contaminants flowing in a conduit is reduced by this dilution and also by longitudinal conduit dispersion. This article seeks to quantify relative importance of these two mechanisms. Water entering the conduit from the matrix causes the conduit flow speed to increase with distance. This in turn causes the strength of dispersion to increase in the downstream direction. The breakthrough curve at a spring, resulting from transport, dilution, and dispersion, has been obtained for the initial-value problem using a modification of the standard Green’s function approach, employing characteristic curves. The predicted breakthrough curves are skewed, with a rapid rise and slow decay. This feature does not result from the ordinary advection–dispersion model. Applying the new model to a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida yields a value of dispersivity at 400 m. It is concluded that variable dispersion provides a possible explanation for the skewness and tailing that are often observed in spring breakthrough curves. It is demonstrated that the new model, in conjunction with the measured spring breakthrough curve, can extract the parameters of the conduit and flow.     

Propagation,Dispersion, and Localization of Elastic Waves in Low-Symmetric Anisotropic Waveguides

The results of a theoretical investigation into ultrasonic linear normal wavefields in anisotropic three-dimensional bodies with mechanical orthorhombic symmetry are presented. A detailed study is made of the dispersion dependencies for higher normal wave modes in a single-layered orthorhombic plate-type waveguide. Moreover, the distribution of complex branches corresponding to the edge standing wave modes is studied and their role in the transformation of the entire spectrum upon a change in the travel direction in the waveguide plane is analyzed. A new type of localization of the higher modes of high-frequency short-range normal waves in a crystal layer is described. An efficient method is developed for studying the spectrum of ultrasonic normal waves in a circular cylindrical waveguide made of an orthorhombic monocrystal     

Algebraic-Delay Differential Systems, State-Dependent Delay, and Temporal Order of Reactions

Systems of the form

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.     

Simultaneous extension, inflation, and shear of a cylindrical tube

Summary Rivlin's solution [1] of the title problem for Mooney materials is generalized by dropping the assumption that the hydrostatic pressure is a function of the radial distance only. Due to this generalization the normal tractions over the cylindrical surfaces are not constant as in the previous solution but vary linearly along the axis of the tube. Further, the longitudinal forces per unit length of the deformed tube, over the cylindrical surfaces, are no longer equal. Solutions for a solid cylinder are then deduced from the general solution. The effect of self-weight on the solutions is briefly dealt with.