单裂隙流-固耦合渗流的试验研究

通过对较大尺寸的单裂隙岩体试块进行不同侧面加载的渗流试验,在实验室里开展了单裂隙流 固耦合渗流研究,模拟核废料贮藏库的围岩自由面的最危险部位的渗流量 应力耦合状态。分析了裂隙岩体渗流与应力的耦合机理,获得了几种典型情况下的试验数据,并拟合出不同应力条件下单裂隙岩体渗流量与应力间数学经验公式。从而说明并非任一方向的应力增加都能使渗流量减小,而是裂隙岩体的渗流量随着双向压应力的增加而减少,随着平行于裂隙面方向的单向压应力的增加而增加。缝隙开度虽然随着法向应力的增加而逐渐减小,但最终不可能完全闭合,所以,此时流量不可能为零。同时,在试验过程中还通过闭环控制来实现被加载面的均匀受力,这为大尺寸岩体试验提供了一种很好的加载方法。     

A New Analytical Formulation for Interwell Finite-Step Tracer Injection Tests in Reservoirs

Analytical models to describe tracer transport in reservoirs commonly set conditions either on the tracer concentration or the tracer flow at the injection border. Here a different formulation based on tracer sources is presented. This approach avoids some of the physical inconsistencies that can be found when setting conditions on the tracer concentration. The case of a tracer injected as a finite-step in an infinite one-dimensional homogeneous reservoir with a uniform flow is considered. The solution is analytically obtained. The results are confronted against the two common boundary cases. The new approach predicts slightly delayed and broader pulses. The tracer breakthrough curves differences can be large for small Peclet numbers. These differences weakly reduce by increasing the injection period. The new approach contains tracer injection elements that can make it suitable to describe real conditions found in reservoir tracer tests.     

New Considerations on Analytical Solutions Employed in Tracer Flow Modeling

A methodology commonly used to obtain analytical and semi-analytical solutions to describe spike and finite-step tracer injection tests is discussed. In these cases, solutions to the diffusion–convection equation are derived from the solution of a different problem, namely the continuous injection of a tracer. Within this procedure, spike injection results from the time derivative of this solution, and finite-step injection from the superposition of two solutions shifted in time. In this paper we show that although this methodology is mathematically correct, attention should be paid to the properties of the solutions. Their boundary conditions may not represent physically acceptable situations, since these conditions are inherited from a different problem. The application of the methodology to a simple one-dimensional case of a tracer pulse diffusing in a homogeneous, semi-infinite reservoir shows serious problems regarding boundary conditions and mass conservation. These problems has not probably been found before since tracer breakthrough curves are not very sensitive to them. However, the problems clearly show up when the tracer distribution in space is analyzed. We conclude that the traditional methodology should not be employed. Equations should be solved imposing the specific boundary and initial conditions corresponding to the original system under consideration.     

Role of Molecular Diffusion in Contaminant Migration and Recovery in an Alluvial Aquifer System

Highly-resolved simulations and flow and transport in an alluvial system at the Lawrence Livermore National Laboratory (LLNL) site explore the role of diffusion in the migration and recovery of a conservative solute. Heterogeneity is resolved to the hydrofacies scale with a discretization of 10.0, 5.0 and 0.5m in the strike, dip and vertical directions of the alluvial-fan system. Transport simulations rely on recently developed random-walk techniques that accurately account for local dispersion processes at interfaces between materials with contrasting hydraulic and transport properties. Solute migration and recovery by pump and treat are shown to be highly sensitive to magnitude of effective diffusion coefficient. Further, transport appears significantly more sensitive to the diffusion coefficient than to local-scale dispersion processes represented by a dispersivity coefficient. Predicted hold back of solute mass near source locations during ambient migration and pump-and-treat remediation is consistent with observations at LLNL, and reminiscent of observations at the MADE site of Columbus Air Force Base, Mississippi. Results confirm the important role of diffusion in low-conductivity materials and, consequently, its impact on efficacy of pump-and-treat and other remedial technologies. In a typical alluvial system on a decadal time scale this process is, in part, fundamentally nonreversible because the average thickness of low-K hydrofacies is considerably greater than the mean-square length of penetration of the solute plume.     

Comparison of Observations from a Laboratory Model with Stochastic Theory: Initial Analysis of Hydraulic and Tracer Experiments

Hydraulic and tracer tests were conducted in a flow cell containing a mixture of sediments designed to mimic a two-dimensional, log-normally distributed, second-order stationary, exponentially correlated random conductivity field. With 60 integral scales in the direction of mean flow and 25 integral scales perpendicular to this direction, behavior of flow and transport in the interior of the flow cell can be compared directly with stochastic solutions for flow and transport. Using 144 piezometers and 361 platinum electrodes, the distribution of hydraulic head and the concentrations of an ionic tracer could be monitored in substantial detail. The present discussion presents the details of the experimental equipment. Results and initial analysis of hydraulic measurements and characterization of a two-dimensional tracer plume are also presented. Analysis using first-order hydraulic theory shows that the flow through the medium was consistent with an effective conductivity equal to the geometric mean of the conductivity distribution. Further, the semivariogram of head increments as observed in the experimental results was consistent with the semivariogram predicted by theory. The chemical transport experiments are here compared with the early solutions presented by Dagan (1984, 1987). The observed rate of longitudinal spread of two tracer plumes was slightly less than that predicted using this theory. Further, the spread in the transverse dimension was observed to decline from the initial plume dimensions and then remain constant or increase slightly, but at a rate lower than predicted by the theory. The difference between the hydraulic and transport results is believed to be related to the fact that the hydraulic results were averaged over a very large portion of the flow cell such that ergodic conditions could be assumed. In contrast, the initial geometry of the plume covered only approximately five integral scales in the transverse direction such that the validity of the assumption of ergodic conditions must be questioned in the analysis of results for the chemical transport.     

Moving Boundary Problem for Diffusion Release of Drug from a Cylinder Polymeric Matrix

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Diffusion of macromolecular solutions in the turbulent boundary layer of a cylindrical pipe

This paper presents a model for the evolution of a transversal concentration profile of a macromolecular solution (PEO) injected into a cylindrical pipe at turbulent flow conditions (R 40000). This model, based on the diffusion of a scalar quantity emitted by two diametrically opposed point sinks, proves to be in good agreement with the experimental data. C concentration - C _w wall concentration - C _i initial concentration before injection - x downstream distance from the slot - y normal distance from the wall - characteristic height of diffusion, i.e. the value ofg at whichC/C _w = 0.5 - n characteristic exponent - R radius of pipe - D diameter of pipe - a, b constants - L _m mixing length, i.e. the value ofx at whichC _w /C _i =Q _i /Q _T - Q _i flow rate of injection - Q _T flow rate - f, g annex functions - n ₀ maximal value ofn     

Stationary Transverse Diffusion in a Horizontal Porous Medium Boundary-Layer Flow with Concentration-Dependent Fluid Density and Viscosity

Stable transport of high-concentrated solute is considered in horizontal boundary-layer flows above a wall of constant concentration. Mixing is accomplished by advection and molecular diffusion only. The utilized boundary-layer approximation allows to investigate the exclusive influence of gravity on vertical diffusion. The hydrodynamic dispersion mechanism was disregarded in the present study which confines its applicabilty to flows with small molecular Péclet numbers. A linear variability of both the fluid's density and viscosity with changing concentration is taken into account as well as the complete set of mass-fraction based balance equations. Steady-state concentration and velocity distributions above the horizontal wall have been obtained using the series truncation method which recently had proven successful to solve the corresponding problem using the Boussinesq assumption. The impact of the latter on these distributions is discussed by what has been additionally-facilitated by the existence of an exact analytical solution for the simpler Boussinesq case. Whereas no density variability influence exists with use of the Boussinesq assumption the complete system of mass-fraction based equations predicts opposing effects of density and viscosity differences between oncoming and near-wall fluids on concentration distributions. Larger density differences narrow the transition zone between both fluids, larger viscosity differences widen it. Thus, a compensation of both effects can be observed for individual fluids and for certain regions of the flow field.     

塔河油田超埋深碳酸盐岩油藏基质的力学试验研究

碳酸盐岩油气藏在全球范围内分布广泛,其中30%以上为缝洞型碳酸盐岩油气藏。在我国缝洞型油藏占已探明的碳酸盐岩油藏储量的2/3,是今后增储的主要领域。为准确揭示碳酸盐岩油藏基质的力学特性,本文以塔河油田奥陶系油藏地层为研究背景,通过现场深孔钻井取样得到埋深达5300~6200m的碳酸盐岩油藏基质岩样,并通过力学试验首次获得超埋深碳酸盐岩油藏基质的弹模、泊松比、抗压强度、抗拉强度、粘聚力、内摩擦角等力学参数,借助电镜扫描试验揭示出超埋深碳酸盐岩的微细观破裂机制。该项研究成果可为分析碳酸盐岩油藏溶洞的垮塌破坏机理提供有效的试验参数。     

An analysis of species separation in a thermogravitational column filled with a porous medium

In the past, the analysis of species separation in a thermogravitational column filled with porous media has been based on strong dependency of thermal and molecular diffusion to dispersion. In this work, we suggest an alternative and show that the dispersion effect is negligible for the conditions in a packed hermogravitational column and that compositional dependency of the thermal diffusion should be accounted for.     

Gravity Affected Lateral Dispersion and Diffusion in a Stationary Horizontal Porous Medium Shear Flow

Transport of dissolved species by a carrier fluid in a porous medium comprises advection and diffusion/dispersion processes. Hydrodynamic dispersion is commonly characterized by an empirical relationship, in which the dispersion mechanism is described by contributions of molecular diffusion and mechanical dispersion expressed as a function of the molecular Peclét number. Mathematically these two phenomena are modeled by a constant diffusion coefficient and by velocity dependent dispersion coefficients, respectively. Here, the commonly utilized Bear--Scheidegger dispersion model of linear proportionality between mechanical dispersion and velocity, and the more complicated Bear--Bachmat model derived on a streamtube array model porous medium and better describing observed dispersion coefficients in the moderate molecular Peclét number range, will be considered. Analyzing the mixing flow of two parallelly flowing confluent fluids with different concentrations of a dissolved species within the frames of boundary layer theory one has to deal with transverse mixing only. With the Boussinesq approximation being adopted approximate analytical solutions of the corresponding boundary layer system of equations show that there is no effect of density coupling on concentration distributions across the mixing layer in the pure molecular diffusion regime case. With the Peclét number of the oncoming flow growing beyond unity, density coupling has an increasing influence on the mixing zone. When the Peclét number grows further this influence is successively reduced until its disappearance in the pure mechanical dispersion regime.     

Modeling of Heat and Mass Transfer in a Fractured Porous Medium

While fractured formations are possibly the most important contributors to the production of oil worldwide, modeling fractured formations with rigorous treatments has eluded reservoir engineers in the past. To date, one of the most commonly used fractured reservoir models remains the one that was suggested by Warren and Root nearly four decades ago. In this paper, a new model for fractures embedded in a porous medium is proposed. The model considers the Navier-Stokes equation in the fracture (channel flow) while using the Brinkman equation for the porous medium. Unlike the previous approach, the proposed model does not require the assumption of orthogonality of the fractures (sugar cube assumption) nor does it impose incorrect boundary conditions for the interface between the fracture and the porous medium. Also, the transfer coefficient between the fracture and matrix interface does not need to be specified, unlike the cases for which Darcy's law is used. In order to demonstrate the usefulness of the approach, a two-dimensional model of a fractured formation is developed and numerical simulation runs conducted.

The proposed model is derived through a series of finite element modeling runs for various cases using the Navier-Stokes equation in the channel while maintaining the Brinkman equation in the porous medium. Various cases studied include different fracture orientations, fracture frequencies, and thermal and solutal constraints. The usefulness of the proposed model in modeling complex formations is discussed. Finally, a series of numerical runs also provided validity of the proposed model for the cases in which thermal and solutal effects are important. Such a study of double diffusive phenomena, coupled with forced convection, in the context of fractured formations has not been reported before.     

Prediction of interwell tracer flow behaviour in heterogeneous reservoirs

A new numerical approach has been developed for predicting the interwell tracer flow behaviour in heterogeneous porous media typical of water and oil reservoirs. This approach uses a mixed finite-element method with triangular elements to predict pressure and velocity fields, and a novel random walk model to simulate the tracer transport through the reservoir, and to perdict the concentration response at the production well. The mixed finite-element method solves the pressure and velocity simultaneously imposing suitable boundary conditions for both pressure and velocity, which allows the solution of the tracer velocity to be more accurate and to conserve mass more precisely than a standard finite-element method. The random walk model can reflect the tracer flow behaviour directly by tracking the movement of particles representing the tracer input volume.The technique has been validated by comparing the predicted results with analytical solutions of tracer concentration response for a homogeneous five-spot pattern, and with published experimentally observed tracer fronts at breakthrough for homogeneous and three heterogeneous cases of five-spot pattern. Good agreement has been achieved for all cases. The model presented in this paper is general, and can therefore be applied to drive patterns other than the five-spot pattern, and for different types of heterogeneities; it can also include effects such as longitudinal and transverse dispersion and adsorption.     

Numerical Simulation of Thermal and Concentration Natural Convection in a Porous Cavity in the Presence of an Opposing Flow

Two-dimensional steady-state thermal concentration convection in a rectangular porous cavity is simulated numerically. The temperature and concentration gradients are horizontal and the buoyancy forces act either in the same or in opposite directions. The flow through the porous medium is described by the Darcy-Brinkman or Forchheimer equations. The SIMPLER numerical algorithm based on the finite volume approach is used for solving the problem in the velocity-pressure variables.Numerous series of calculations were carried out over the range Ra _t =3·10⁶ and 3·10⁷, 10^-6 < Da < 1, 1 < N < 20, Le=10 and 100, where Ra, Da, Le, and N are the Rayleigh, Darcy, and Lewis numbers and the buoyancy ratio, respectively. It is shown that the main effect of the presence of the porous medium is to reduce the heat and mass transfer and attenuate the flow field with decrease in permeability. For a certain combination of the Ra, Le, and N numbers the flow has a multicellular structure. The mean Nusselt and Sherwood numbers are presented as functions of the governing parameters.     

Analysis of a second‐order upwind method for the simulation of solute transport in 2D shallow water flow

A two‐dimensional model for the simulation of solute transport by convection and diffusion into shallow water flow over variable bottom is presented. It is based on a finite volume method over triangular unstructured grids. A first‐order upwind technique, a second order in space and time and an extended first‐order method are applied to solve the non‐diffusive terms in both the flow and solute equations and a centred implicit discretization is applied to the diffusion terms. The stability constraints are studied and the form to avoid oscillatory results in the solute concentration in the presence of complex flow situations is detailed. Some comparisons are carried out in order to show the performance in terms of accuracy of the different options. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental study of heat and mass transfer from a horizontal cylinder in downward air-water mist flow with blockage effect

An experimental study was made on convective heat and mass transfer from a horizontal heated cylinder in a downward flow of air-water mist at a blockage ratio of 0.4. The measured local heat transfer coefficients agree fairly well with the authors' numerical solutions obtained previously for the front surface of a cylinder over the ranges mass flow ratio 0–4.5×10⁻², a temperature difference between the cylinder and air 10–43 K, gas Reynolds number (7.9–23)×10³, Rosin-Rammler size parameter 105–168 μm, and dispersion parameter 3.4–3.7. Heat transfer augmentation, two-pahse to single-phase of greater than 19 was attained at the forward stagnation point. For heat transfer in the rear part of the cylinder, an empirical formula is derived by taking into account the dimensionless governing variables, that is, coolant-feed and evaporation parameters.     

Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.