Experimental and Numerical Study of Gel Particles Movement and Deposition in Porous Media After Polymer Flooding

Gel particle, a promising conformance control technology, is recently applying to after-polymer-flooding reservoirs by reusing the remaining polymer in porous media. However, there is no available numerical model which is useful for simulating the conformance control. A series of lab experiments are conducted to explore the main characters of gel particles movements after polymer flooding. Four main mechanisms, namely, swelling, synergy with remaining polymer, shear breaking, and deformation migration, are recognized and described by mathematical formulas. Based on the physical experiments, a numerical model is established to simulate gel particles propagation after polymer flooding. In particular, gel particles are treated as an additional component in aqueous phase. The interaction between the particle gels and the remaining polymer is simplified by aqueous viscosity relationship and particle gel grain size variation. Two transport forms, plugging and deformation migration, are embodied in the model, and the local pressure gradient controls which form the propagation belongs to. The retention of particle gels will cause pore volume decrease and therefore reduce the permeability of thief zones to bypassing water to less swept zones. An iterative method is employed to decouple the gel particle profile control model, which is robust and fairly time-saving. In particular, the flow model is numerically solved by the IMPSAT method and the gel particles continuity equation is explicitly solved by using an operator splitting technique. The newly developed model is validated by history matching results of 1D experiments and actual application case. The results suggest that the presented model is helpful to optimize parameters for profile control for gel particle profile control technology.     

The effect of moisture-induced swelling on the absorption capacity of transversely isotropic elastic polymer–matrix composites

The interaction between humid air and transversely isotropic fiber-reinforced composites with swelling polymeric matrix is considered. A model is proposed for the water saturation level in a polymer when stresses are applied, that uses directly obtainable material parameters only. In a composite, the reinforcements modify the water uptake of the polymer matrix because of the internal stresses that are induced by its restricted swelling, and this effect is evaluated. As a consequence of the coupling between stresses and absorption capacity, the sorption isotherm of a composite is ruled by the (non-linear) Langmuir equation when the unreinforced matrix obeys the (linear) Henry’s law.     

Numerical prediction of extrudate swell of branched polymer melts

This paper is concerned with the numerical prediction of the extrudate swell behaviour of branched polymer melts in a planar configuration. The multi-mode extended pom-pom (XPP) model is used to describe the polymer dynamics. A second-order operator-integration-factor splitting scheme is used for the temporal discretisation of the problem, whilst a spectral element scheme is used in space. The free surface is evolved in a Lagrangian manner using the third-order conditionally stable Adams–Bashforth method. A thorough mesh convergence study is performed with respect to the temporal and spatial discretisation parameters. The influence of the nature of the discrete relaxation spectrum on the swelling ratio and as an indicator of polydispersity is investigated. The predictions of numerical simulations are also compared with a selection of experimental results from the literature. The parameters in the XPP model are determined from rheological data. Good agreement is obtained for branched low-density polyethylenes. The ability to model a melt with a high molecular weight tail using a discrete relaxation spectrum for which the largest relaxation time is isolated from the others is also investigated.     

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels. At a low temperature, uncrosslinked PNIPAM can be dissolved in water and form a homogenous liquid solution. When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer. Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel. When the temperature is changed, the hydrogel undergoes a phase transition: the amount of water in the hydrogel in equilibrium changes with temperature discontinuously. While the aqueous solution is a liquid and cannot sustain any nonhydrostatic stress in equilibrium, the hydrogel is a solid and can sustain nonhydrostatic stress in equilibrium. The nonhydrostatic stress can markedly affect various aspects of the phase transition in the hydrogel. We adopt the Flory-Rehner model, and show that the interaction parameter as a function of temperature and concentration obtained from the PNIPAM-water solution can be used to analyze diverse phenomena associated with the phase transition of the PNIPAM hydrogel. We analyze free swelling, uniaxially and biaxially constrained swelling of a hydrogel, swelling of a core-shell structure, and coexistent phases in a rod. The analysis is related to available experimental observations. Also outlined is a general theory of coexistent phases undergoing inhomogeneous deformation.     

A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels

An elastomeric gel is a cross-linked polymer network swollen with a solvent, and certain gels can undergo large reversible volume changes as they are cycled about a critical temperature. We have developed a continuum-level theory to describe the coupled mechanical deformation, fluid permeation, and heat transfer of such thermally responsive gels. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. We have numerically implemented our theory in a finite element program. We show that our theory is capable of simulating swelling, squeezing of fluid by applied mechanical forces, and thermally responsive swelling/de-swelling of such materials.     

A chemo-electro-mechanical model for simulation of responsive deformation of glucose-sensitive hydrogels with the effect of enzyme catalysis

A multi-effect-coupling glucose-stimulus (MECglu) model is developed and solved numerically for the swelling behavior of soft smart hydrogels responding to changes in the environmental glucose concentration. The model considers the effect of the glucose oxidation reaction catalyzed by enzymes including glucose oxidase and catalase. It is composed of the Nernst-Planck equation for the mobile species in the solvent, the Poisson equation for the electric potential, and a nonlinear mechanical equation for the large deformations of the hydrogel that arise due to the conversion of chemical energy to mechanical. Based on the theory of the chemo-electro-mechanical-coupled fields, the formulation of the fixed charge groups bound onto the cross-linked polymer network is associated with the change of the ambient solution pH. The MECglu model is validated by comparison between the steady-state computation and experimental equilibrium swelling curves, and good agreement is obtained. A parameter study is then conducted by steady-state simulations to ascertain the impact of various solvent parameters on the responsive swelling behavior of the hydrogel. One key parameter is the glucose concentration, which is varied within the range of practical physiological glucose concentrations from 0 to 16.5 mM (300 mg/ml) to support the design and optimization of an insulin delivery system based on a glucose-sensitive hydrogel with immobilized glucose oxidase and catalase. The influence of oxygen and glucose concentrations in the solvent is then further studied for the distributive profiles of reacting and diffusive species concentrations, the electric potential, the displacement, as well as the swelling ratio of the glucose-sensitive hydrogel.     

温度梯度对热致型形状记忆聚合物板力学性能的影响

形状记忆聚合物作为一种新型的智能材料,由于质量轻、成本低以及变形回复率大等优势,已经在航空、医学等领域得到广泛应用。当前对于热致型形状记忆聚合物力学行为的研究,大都集中在整体变温的情况下,随着应用环境的越来越广泛,温度梯度对材料力学性能的影响效果越发重要。本文在均匀应力的假设下,给出材料在不同初始和传热条件下的温度梯度分布情况,结合传热学和热致型形状记忆聚合物相变理论本构模型,分别讨论了不同温度梯度对存储应变、弹性模量等力学性能的影响,通过理论分析和实验数据对比验证了模型正确性。本文研究可为不同导热情况下,对热致型形状记忆聚合物力学行为监测提供思路,也为形状记忆聚合物的进一步工程应用提供理论依据。     

考虑微观变形特征的水凝胶均匀和非均匀溶胀分析及其影响参数研究

本文给出考虑微观变形的水凝胶溶胀的分析模型,该模型假设构成聚合物网络的单链受到由于周围链的作用而产生类似圆管状的约束,并且认为每个单链变形与网络变形之间存在非仿射关系.利用该模型分析了凝胶在自由溶胀情形,预拉伸凝胶单一方向溶胀情形以及具有刚性核的球形凝胶溶胀至平衡状态情形的变形特征.研究表明,对于自由溶胀的均匀变形情形...     

Influence of microstructural parameters on mechanical behavior of polymer gels

The swelling deformation behavior of polymer gels is often described in terms of the Flory–Rehner framework, in which the Flory–Rehner free energy function is based on the simplest affine network model, does not take entanglements into account. However, the real polymer networks have many chain entanglements. In this paper, a new hybrid free energy function composed of the Edwards–Vilgis slip-link model and the Flory–Huggins solution theory is presented for the prediction of the influence of chain entanglements on mechanical behavior of gels. The simulation results of mechanical behavior in free swelling, uniaxial extension, biaxial constraint and simple shear are presented. It is shown that in the nonentangled state, this new hybrid free energy function reduces to the Flory–Rehner free energy function; in the entangled state, the influence of entanglements on the mechanical behavior of gels is significant, the more entangled networks exhibit higher stress.     

Rheological behavior of a semi-crystalline polymer during isothermal crystallization

The theological behavior of a molten semi-crystalline polymer, namely, a high density polyethylene (HDPE), was investigated during isothermal crystallization from the melt, using dynamic oscillatory experiments at 1 tad/s in a parallel plates rheometer. The theological results were compared with those obtained from differential scanning calorimetry in the same conditions. During the crystallization, the molten and crystallizing polymer provides a useful model for filled polymers, the crystalline phase being the filler and the liquid phase being the matrix. In most cases, the filler can be considered to be spherical shaped (spherulites). Owing to the amorphous phase linking liquid and crystallites, the adhesion between matrix and filler in this system is perfect. The filler content increases continuously during the crystallization. This model might be used to test laws relating the theological parameters to the volume fraction of filler. Problems related to the rheometry for such systems are discussed and the key parameters insuring reproducibility and accuracy in the measurements are pointed out. The relative sensitivity of the various theological parameters (storage and loss moduli, loss angle) to structural changes of the liquid has been out forward. Some preliminary equations relating the variation of these parameters to the volume fraction of filler, through the use of simple fractal exponents have been derived and discussed in comparison with laws provided by various authors.     

Continuum theory of swelling material surfaces with applications to thermo-responsive gel membranes and surface mass transport

Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk materials, such as the properties of spreading and absorption of liquids. In particular, polymer gel membranes experience swelling or shrinking when their solvent content change, and the non-homogeneous swelling field may be exploited to control their shape. Here, we develop a theory of swelling material surfaces to model polymer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. We also specialize the theory to thermo-responsive gels, which are made of polymers that change their affinity with a solvent when temperature varies.     

Numerical Modelling of Swelling Pressure in Unsaturated Expansive Elasto-Plastic Porous Media

The focus of this work is to provide a new concept for accessing the swelling stress in expansive porous media, especially in highly compacted bentonite. The key to the new approach is the simulation with a chemical swelling model of an infinitesimal volume change followed by a back compaction Process. Free extension is allowed in the first step, to calculate the interlayer porosity change (micro) and the induced volume change potential (macro). The object-oriented FEM simulator GeoSys/RockFlow allows the combination of different processes. The hydro-mechanic/chemical (H²M/C) model takes into consideration two phase flow and deformation, as well as chemical swelling effects. The negative displacements on each boundary after the free extension simulation are taken as Dirichlet boundary conditions of the back compaction problem. The deformation step is simulated in the context of elasto-plasticity using the modified Cam-Clay model. The stresses obtained by back compaction represent the swelling pressure. A 2D example of compacted bentonite is analyzed with the new H²M/C model.     

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate. The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length. The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic tim...     

Freezing around a finite heat sink immersed in an infinite phase change medium

Freezing around a spherical heat sink immersed in an infinite phase change medium — a free boundary problem involving growth and decay of the free boundary — is analysed here. A one-dimensional conduction model is formulated and the resulting partial differential equations are solved by finite difference methods. The energy discharged from the phase change medium during the heat transfer process is analysed for latent heat thermal energy storage applications. Results are presented for a wide range of parameters that are encountered in energy storage devices. The cases of slab/cylindrical heat sink are reexamined for a range of parameters not covered by the earlier investigators     

Solvent uptake and cavitation

This paper offers a treatment for investigating the role of the interplay between mechanics and the absorption of a swelling agent on the equilibrium and cavitation of a spherical specimen. This treatment is then applied, within the context of the classical theory of swelling of a rubber by a liquid, to establish, among other things, necessary conditions for the existence of multiphase equilibria and the occurrence of cavitation. These conditions involve the parameters entering the theory, namely the number c_S of polymer chains per unit reference volume, the volume υ occupied by a swelling-agent molecule, and the Flory-Huggins interaction parameter χ.     

Non-isothermal kinetics of a moving phase boundary

In this paper we derive an explicit formula for a kinetic relation governing the motion of a phase boundary in a bilinear thermoelastic material capable of undergoing solid-solid phase transitions. To obtain the relation, we study traveling wave solutions of a regularized problem that includes viscosity, heat conduction and convective heat exchange with an ambient medium. Both inertia and latent heat of transformation are taken into account. We investigate the effect of material parameters on the kinetic relation and show that in a certain range of parameters the driving force becomes a non-monotone function of the interface velocity. The model also predicts a nonzero resistance to phase boundary motion, part of which is caused by the thermal trapping. Received: November 15, 2001 / Published online September 4, 2002 RID="*" ID="*" e-mail: annav@math.pitt.edu Communicated by Lev Truskinovsky, Minneapolis     

A thermo-mechanically coupled field model for shape memory alloys

The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations.     

A coupled theory of fluid permeation and large deformations for elastomeric materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.