Mixing of miscible shear-thinning fluids in a lid-driven cavity

The concentration and velocity fields of two refractive index matched miscible shear-thinning fluids in a lid-driven cavity were investigated by using planar laser-induced fluorescence and particle image velocimetry,as well by computational fluid dynamics.Quantitative analyses show that the results obtained by flow simulations with the species transport model are in good agreement with the experimental results.The effects of different parameters were studied by using the intensity of segregation.For two fluids with the same rheological parameters,the relative amounts of liquids H_(1)/H and the power-law index n dominate the mixing process while the Reynolds number Re plays a marginal role.As for two fluids with density difference,buoyancy has significant influence on the mixing process.The dimensionless group Ar/Re(redefined such as to include shear thinning behavior)is proposed for assessing the effect of buoyancy and rheological properties on the mixing of miscible shear-thinning fluids.

A MIXED FINITE ELEMENT AND CHARACTERISTIC MIXED FINITE ELEMENT FOR INCOMPRESSIBLE MISCIBLE DARCY-FORCHHEIMER DISPLACEMENT AND NUMERICAL ANALYSIS

In this paper a mixed finite element-characteristic mixed finite element method is discussed to simulate an incompressible miscible Darcy-Forchheimer problem.The flow equation is solved by a mixed finite element and the approximation accuracy of Darch-Forchheimer velocity is improved one order.The concentration equation is solved by the method of mixed finite element,where the convection is discretized along the characteristic direction and the diffusion is discretized by the zero-order mixed finite element method.The characteristics can confirm strong stability at sharp fronts and avoids numerical dispersion and nonphysical oscillation.In actual computations the characteristics adopts a large time step without any loss of accuracy.The scalar unknowns and its adjoint vector function are obtained simultaneously and the law of mass conservation holds in every element by the zero-order mixed finite element discretization of diffusion flux.In order to derive the optimal 3/2-order error estimate in L^(2) norm,a post-processing technique is included in the approximation to the scalar unknowns.Numerical experiments are illustrated finally to validate theoretical analysis and efficiency.This method can be used to solve such an important problem.

APPLICATION OF SUPERCONVERGENCE TO A MODEL FOR COMPRESSIBLE MISCIBLE DISPLACEMENT

A modification of a finite element method of Douglas and Roberts for approximating the solution of the equations describing compressible miscible displacement in a porous medium is proposed and analyzed. The pressure is treated by a parabolic mixed finite element method using a Raviart-Thomas space of index rover a quasiregular partition, An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. A simple computational procedure allows the superconvergence property of the fluid velocity to be retained in our total algorithm.

SUPERCONVERGENCE OF THE FULL-DISCRETE F.E.M. FOR COMPRESSIBLE MISCIBLE DISPLACEMENT: THE FULL TENSOR CASE

An efficient time stepping procedure is proposed to treat the system describing compressible miscible displacement in a porous medium by employing a mixed finite element method to approximate the pressure and the fluid velocity and a standard Galerkin method to approximate the concentration. An extension of the Darcy velocity along Gauss lines is used in the evaluation of the coefficients in the Galerkin procedure for the concentration. These results show that the total algorithm has the superconvergence property of the fluid velocity.

Oxidization characteristics and thermal miscible flooding of high pressure air injection in light oil reservoirs

Physical modeling,numerical simulation and field case analysis were carried out to find out the subsurface thermal oxidation state,thermal oxidation front characteristics and production dynamic characteristics of high pressure air injection thermal oxidation miscible flooding technology.The lighter the composition and the lower the viscosity of the crude oil,the lower the fuel consumption and the combustion temperature are.The thermal oxidation front of light oil and volatile oil can advance stably,and a medium-temperature thermal oxidation stable displacement state can be formed in the light oil reservoir under high pressure conditions.With strong thermal gasification and distillation,light oil and volatile oil are likely to form a single phase zone of gasification and distillation with thermal flue gas at the high-temperature and high-pressure heat front,finally,an air-injection thermal miscible front.In light oil reservoirs,the development process of high-pressure air-injection thermal miscible flooding can be divided into three stages:boosting pressure stage,low gas-oil ratio and high-efficiency stable production stage and high gas-oil ratio production stage.Approximately 70%of crude oil is produced during the boosting pressure stage and low gas-oil ratio high-efficiency and stable production stage.

APPROXIMATION OF THE CONCENTRATION BY A VISCOSITY SPLITTING METHOD FOR TWO-PHASE MISCIBLE DISPLACEMENT PROBLEM

The miscible displacement of one incompressible fluid by another in a porous medium is considered in this paper. The concentration is split in a first-order hyberbolic equation and a homogeneous parabolic equation within each lime step. The pressure and Us velocity field is computed by a mixed finite element method. Optimal order estimates are derived for the no diffusion case and the diffusion case.

A simulation approach: Miscible carbon dioxide injection in a carbonate reservoir

The purpose of this study is to optimize the existing carbon dioxide （CO2） flood in deep dolomite formations by improving oil sweep efficiency of miscible CO2 floods and enhancing the conformance control. A full compositional simulation model using a detailed geologic characterization was built to optimize the injection pattern. The model is a quarter of an inverted nine-spot and covers 20 acres of field formation. Geologic description was used to construct the simulation grids. The simulation layers represent actual flow units and resemble the large variation of reservoir properties. History match was performed to validate the model. Several sensitivity runs were made to improve the CO2 sweep efficiency and increase the oil recovery. Finally, the optimum CO2 injection rate for dolomite formations was determined approximately. Simulation results also indicate that a water-alternating-gas （WAG） ratio of 1：1 along with an ultimate CO2 slug of 100% hydrocarbon pore volume （HCPV） will allow an incremental oil recovery of 18%. The additional recovery increases to 34% if a polymer is injected as a conformance control agent during the course of the WAG process at a ratio of 1：1. According to the results, a pattern reconfiguration change from the nine spot to staggered line drive would represent an incremental oil recovery of 26%.

FINITE ELEMENT SIMULATIONS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT WITH MOLECULAR DISPERSION IN POROUS MEDIA

We consider a nonlinear parabolic system describing compressible miscibledisplacement in a porous medium [5]. Continuous time and discrete time Galerkinmethods are introduced to approximate the solution and optimal H^1 error estimatesare obtained. One contribution of this paper is a demonstration of how moleculardispersion can be handled.

MISCIBLE PRECIPITATES IN V-Ti-N MICROALLOYED STEELS

The characteristics and the formation of the miscible particles in V-Ti-N microalloyed steels were studied.It was found that the vanadium to form V-Ti miscible particles starts to precipi- tate after pouring and cooling to temperature below 11 50℃ by means of the epitaxial precipi- tation on the pre-existing titanium nitrides.The vanadium content in the particles is markedly influenced by the cooling rate after solidification.

Miscibility of light oil and flue gas under thermal action

The miscibility of flue gas and different types of light oils is investigated through slender-tube miscible displacement experiment at high temperature and high pressure.Under the conditions of high temperature and high pressure,the miscible displacement of flue gas and light oil is possible.At the same temperature,there is a linear relationship between oil displacement efficiency and pressure.At the same pressure,the oil displacement efficiency increases gently and then rapidly to more than 90% to achieve miscible displacement with the increase of temperature.The rapid increase of oil displacement efficiency is closely related to the process that the light components of oil transit in phase state due to distillation with the rise of temperature.Moreover,at the same pressure,the lighter the oil,the lower the minimum miscibility temperature between flue gas and oil,which allows easier miscibility and ultimately better performance of thermal miscible flooding by air injection.The miscibility between flue gas and light oil at high temperature and high pressure is more typically characterized by phase transition at high temperature in supercritical state,and it is different from the contact extraction miscibility of CO_(2) under conventional high pressure conditions.

Averaged Dynamics of Fluids near the Oscillating Interface in a Hele-Shaw Cell

The steady flow in a Hele-Shaw cell filled with fluids with a high viscosity contrast in the presence of fluid oscillations is experimentally studied.The control of oscillatory dynamics of multiphase systems with interfaces is a challenging technological problem.We consider miscible(water and glycerol)and immiscible(water and high-viscosity silicone oil PMS-1000)fluids under subsonic oscillations perpendicular to the interface.Observations show that the interface shape depends on the amplitude and frequency of oscillations.The interface is undisturbed only in the absence of oscillations.Under small amplitudes,the interface between water and glycerol widens due to mixing.When the critical amplitude is reached,the interface becomes unstable to the fingering instability:Aqueous fingers penetrate the high-viscosity glycerol and induce intensive mixing of miscible fluids and associated decay of the instability.After the disappearance of the fingers,the interface takes a U-shape in the central part of the cell.A similar effect is observed for immiscible fluids:The oscillating interface tends to bend to the side of a high-viscosity fluid.Again,when the critical amplitude is reached,the fingering instability arises at the convex interface.This paper focuses on the causes of bending of the initially undisturbed interface between miscible or immiscible fluids.For this purpose,we measure the steady flow velocity near the interface and in the bulk of a high-viscosity fluid using Particle Image Velocimetry(PIV).

CHARACTERISTIC FINITE DIFFERENCE METHODS FOR POSITIVE SEMIDEFINITE PROBLEM OF TWO-PHASE(OIL AND WATER)MISCIBLE FLOW IN POROUS MEDIA

Numerical simulation of two-phase (oil and water) miscible flow in porousmedia is the mathematical foundation in energy problems. For a two-dimensional posi-tive problem, Douglas put forward the well-known characteristic finite difference method.However, for numerical analysis there exist difficulties. They assumed that the problem isperiodic and the diffusion matrix of the concentration equation was positive definite. Butin many practical situations the diffusion matrixes are only positive semidefinite. In thispaper, we put forward a kind of characteristic finite difference schemes and obtain optimalorder estimates in l2 norm for the error in the approximation assumptions.

A priori error analysis of a discontinuous Galerkin approximation for a kind of compressible miscible displacement problems

A kind of compressible miscible displacement problems which include molecular diffusion and dispersion in porous media are investigated.A symmetric interior penalty discontinuous Galerkin (SIPG) method is applied to the coupled system of flow and transport.Using the induction hypotheses instead of the cut-off operator and the interpolation projection properties,a priori hp error estimates are presented.The error bounds in L2(H1) norm for concentration and in L∞(L2) norm for velocity are optimal in h and suboptimal in p with a loss of power 1/2.

FINITE ELEMENT METHOD FOR INCOMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

Under the assumptions of nonlinear finite element and △t=o(h),Ewing and Wheeler discussed a Galerkin method for the single phase incompressible miscible displacement of one fluid by another in porous media.In the present paper we give a finite element scheme which weakens the △t=o(h)-restriction to △t=o(h~ε),0<ε≤1/2.Furthermore,this scheme is suitable for both linear element and nonlinear element.We also derive the optimal approximation estimates for concentration c,its gradient ▽c and the gradient ▽p of the pressure p.

Machine learning with active pharmaceutical ingredient/polymer interaction mechanism:Prediction for complex phase behaviors of pharmaceuticals and formulations

The high throughput prediction of the thermodynamic phase behavior of active pharmaceutical ingredients(APIs)with pharmaceutically relevant excipients remains a major scientific challenge in the screening of pharmaceutical formulations.In this work,a developed machine-learning model efficiently predicts the solubility of APIs in polymers by learning the phase equilibrium principle and using a few molecular descriptors.Under the few-shot learning framework,thermodynamic theory(perturbed-chain statistical associating fluid theory)was used for data augmentation,and computational chemistry was applied for molecular descriptors'screening.The results showed that the developed machine-learning model can predict the API-polymer phase diagram accurately,broaden the solubility data of APIs in polymers,and reproduce the relationship between API solubility and the interaction mechanisms between API and polymer successfully,which provided efficient guidance for the development of pharmaceutical formulations.

A CHARACTERISTIC MIXED FINITE ELEMENT TWO-GRID METHOD FOR COMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEM

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium.The concentration equation is treated by a mixed finite element method with characteristics(CMFEM)and the pressure equation is treated by a parabolic mixed finite element method(PMFEM).Two-grid algorithm is considered to linearize nonlinear coupled system of two parabolic partial differential equations.Moreover,the L q error estimates are conducted for the pressure,Darcy velocity and concentration variables in the two-grid solutions.Both theoretical analysis and numerical experiments are presented to show that the two-grid algorithm is very effective.

ON THE APPROXIMATION OF INCOMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEMS IN POROUS MEDIA BY MIXED AND STANDARD FINITE VOLUME ELEMENT METHODS

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations,the pressure–velocity equation and the concentration equation.In this paper,we present a mixed finite volume element method(FVEM)for the approximation of the pressure–velocity equation and a standard FVEM for the concentration equation.A priori error estimates in L^(∞)(L^(2))are derived for velocity,pressure and concentration.Numerical results are presented to substantiate the validity of the theoretical results.

A Posteriori Error Estimates of a Combined Mixed Finite Element and Discontinuous Galerkin Method for a Kind of Compressible Miscible Displacement Problems

Akind of compressiblemiscible displacement problemswhich includemolecular diffusion and dispersion in porous media are investigated.The mixed finite element method is applied to the flow equation,and the transport one is solved by the symmetric interior penalty discontinuous Galerkin method.Based on a duality argument,employing projection estimates and approximation properties,a posteriori residual-type hp error estimates for the coupled system are presented,which is often used for guiding adaptivity.Comparing with the error analysis carried out by Yang(Int.J.Numer.Meth.Fluids,65(7)(2011),pp.781-797),the current work is more complicated and challenging.

Development of minimum tie line length method for determination of minimum miscible pressure in gas injection process

Gas injection process is a very important technology in enhanced oil recovery.Minimum miscible pressure is one of the key parameters in gas injection processes.Various experimental methods such as slim tube are used to measure MMP.These methods are costly and time consuming.Recently computational methods are used in order to achieve a cost-effective and reliable technique to evaluate MMP.In this work,a new methodology has been proposed for determination of MMP using the minimum tie line length method.A real mixing cell model was developed to estimate the MMP,MME and key tie lines.This method is simple,robust,and faster than conventional one-dimensional simulation of slim tube.The new mixing cells method can accurately determine the whole key tie lines to a shift,regardless of the number of injection gas and reservoir fluid components.Unlike other methods of mixing cells,this method automatically corrects dispersion by additional contacts to achieve the low variation domain of tie line slope.Also,the determination and implementation of the minimum miscibility enrichment are investigated.

INTERDIFFUSION KINETICS OF MISCIBLE POLYMER/POLYMER LAMINATES INVESTIGATED BY ATOMIC FORCE MICROSCOPY

The miscibility of poly（vinyl chloride）/poly（n-butyl methacrylate） （PVC/PnBMA） blend and the interdiffusion kinetics of PVC/PnBMA laminates have been investigated by differential scanning calorimetry （DSC） and atomic force microscopy （AFM）, respectively. This blend exhibited a lower critical solution temperature behavior. Below 120 ℃, DSC results showed each blend with different PVC contents exhibited only a single glass transition temperature which increased with PVC content, indicating that PVC and PnBMA were miscible. After PVC/PnBMA laminates were annealed at different temperature for different time, a smooth cross-section across interface was prepared by ultramicrotoming. Combined with topography and phase images of tapping mode AFM, the relative concentration profile, interface width and the relationship between interface width and annealing time could be obtained. In a regime of rubbery/rubbery interdiffusion, the diffusion obeyed a typical Fickian Case-I behavior where the interface width was proportional to the square root of annealing time. The mutual diffusion coefficient was in good agreement with that obtained from DSC and positron annihilation lifetime spectroscopy. However, in the regime of glassy/rubbery interdiffusion, the diffusion followed a typical Case-II behavior where the interface width was proportional to annealing time. These results imply that AFM is a reliable and powerful tool for the investigation of polymer/polymer interdiffusion at a level of polymer chain size.