Browsing by Subject "Viscoelasticity"

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A MEMS dynamic mechanical analyzer for in situ viscoelastic characterization of 3D printed nanostructures
(2020-05-11) Cayll, David Richard; Cullinan, Michael
Cellular, metamaterial structures with sub-micron features have shown the ability to become excellent energy absorbing materials for impact mitigation due to the enhanced mechanical properties of materials at the nanoscale. However, in order to optimize the design of these energy absorbing metamaterial structures we need to be able to measure the dynamic properties of the sub-micron features such as storage and loss moduli and the loss factor. Therefore, at-scale testing is required to capture the scale, temperature, and strain rate dependent material properties of these nanoscale materials. This thesis presents the design, fabrication, and calibration of a MEMS-based dynamic mechanical analyzer (DMA) that can be directly integrated with the two-photon lithography (TPL) process commonly used to fabricate metamaterial structures with nanoscale features. The MEMS-based DMA consists of a chevron style thermal actuator used to generate a tensile load on the structure and two differential capacitive sensors on each side of the structure used to measure load and displacement. This design demonstrated 1.5 ± 0.75 nm displacement resolution and 104 ± 52 nN load resolution, respectively. Dynamic mechanical analysis was successfully conducted on a single nanowire feature printed between the load and displacement stages of the MEMS device with testing frequencies ranging between 0.01 – 10 Hz and testing temperatures ranging between 22°C - 47°C. These initial tests on an exemplar TPL part demonstrate that the printed nanowire behaves as a viscoelastic material wherein the transition from glassy to viscous behavior has already set in at the room temperature.
AFM-based microrheology of biological cells : correlation of local viscoelasticity and motility
(2003-08) Park, Soyeun, 1970-; Shih, Chih-Kang; Käs, Josef A.
Local viscoelasticity of a cell is important in understanding the extension of the lamellipodium, which contributes to the cell’s motility. It has been a challenge to accurately measure viscoelastic properties of a thin sample such as the lamellipodium of a cell (<1000 nm) due to the strong substrate effects and high stresses (>1 kPa). We account for the substrate effects by applying the two advanced models – the Chen and Tu models. The tightly regulated elastic moduli shown in the lamellipodium of fibroblasts manifestly display the successful adoption of these two models. In addition, these models provide the local Poisson ratio and adhesive state of a cell: the regions near the lamellipodium are well adhered while the regions further back to the main body are non-adhered. Our AFM technique successfully illuminates the heterogeneous nature of the cytoskeleton over the entire regions of the cell. By extending these models to the frequency-dependent microrheology technique, we decompose the elastic moduli into the loss and the storage moduli. Our AFM microrheology technique distinctly differentiates the malignantly transformed fibroblasts from the normal fibroblasts: the malignantly transformed fibroblasts display a decrease in viscoelastic moduli of the lamellipodium. Considering that motilities as well as viscoelastic properties of cells are induced by cytoskeletal changes, we focus our attention to illuminating on the cell’s protrusive mechanism correlated with the viscoelastic properties. To do this, we quantify the parameters of cell’s motility by analyzing time-lapsed phase contrast images. The resulting data show an increase in the motile activity caused by malignant transformation. In conclusion, these results are combined to suggest the correlation between the enhanced motility and the decrease in viscoelastic moduli. This conclusion is successfully explained by considering the microscopic model of the cell motility, i.e ‘Elastic Brownian Ratchet’ (Mogilner et al., 1996). It is understood that the lack of actin cross-linking proteins observed in malignantly transformed fibroblasts causes a cell to be softer and more motile. An increase in thermal fluctuations of softer cells can expedite the intercalation of G-actin that leads the cell’s protrusive motility.
Analysis of the Influence of Viscoelasticity in Curl Development in SLS
(2002) Jamal, N.M.; Dalgarno, K.W.
Curl in selectively laser sintered parts arises mainly from thermal distortion of parts within the build volume during processing. This results in nominally flat surfaces which lie horizontally in the part bed becoming warped. This paper reports on the use of finite element techniques to model curl development in polymer materials, and in particular on the influence of viscoelasticity on how curl develops. The development of time-dependent material models is reported, and the results of the implementation of these models presented, together with a comparison of the results with experimental data.
Development of a computational method for inverting dynamic moduli of multilayer systems with applications to flexible pavements
(2014-08) Xu, Qinwu; Prozzi, Jorge Alberto
Most existing computational methods for inverting material properties of multilayer systems have focused primarily on elastic properties of materials or a static approach. Typically, they are based on a two-stage approach: (I) modeling structural responses with a computer program, and (II) estimating layer properties mathematically using the response outputs determined in stage I without interactions with the governing state partial-differential-equation (PDE) of stage I. This two-stage approach may not be accurate and efficient enough for inverting larger scale model parameters. The objective of this research was to develop a computational method to invert dynamic moduli of multilayer systems with applications to flexible pavements under falling weight deflectometer (FWD) tests, thereby advancing existing methods and fostering understanding of material behaviors. This research first developed a finite-element and Newton-Raphson method to invert layer elastic moduli using FWD data. The model improved the moduli seeds estimation and achieved a satisfactory accuracy based on Monte Carlo simulations, addressing the common back-calculation issue of no unique solutions. Consequently, a time-domain finite-element method was developed to simulate dynamic-viscoelastic responses of the multilayer systems under loading pulses. Simulation results demonstrated that the dynamic-viscoelastic-damping-coupled model could emulate structural responses more accurately, thereby advancing existing simulation approaches. By using the dynamic-viscoelastic-response model as one computation module, this research led to the development of a PDE-constrained Lagrangian optimization method to invert dynamic moduli and viscoelastic properties of multilayer systems. The Lagrangian function was used as an objective function, with a regularization term and governing-state PDE constraint. Both the first-order (gradient) and second-order variation (Hessian matrix) of the Lagrangian were computed to satisfy necessary and sufficient optimality conditions, and Armijo rule was modified to determine a stable step length. The developed method improved computation speed significantly, and it is superior for large-scale inverse problems. The model was implemented for evaluating flexible pavements under FWD tests and for inverting the master curve of dynamic moduli of the asphalt layer. Independent computer coding was developed for all numerical methods. The computational methods developed may also be applied to other multilayer systems, such as tissues and sandwich structures at different time and length scales.
Durability of adhesive joints between concrete and FRP reinforcement in aggressive environments
(2004) Park, Soojae; Liechti, K. M.
The durability of the bondline between concrete and its fiber-reinforced polymer reinforcement was characterized at various temperature and humidity levels. The bondline consisted of an epoxy primer, an epoxy putty and an epoxy saturant. In principle, fracture could occur anywhere in this bondline, but attention was focused on the concrete/primer interface in this study because preliminary experiments indicated that this was the dominant failure mechanism. The initial part of the constitutive modeling of the epoxy primer was conducted using linear viscoelastic experiments. Confined compression experiments determined two linear material functions simultaneously. Because this was a relatively new experiment, the results were validated by conducting bulk compliance experiments. The viscoelastic region of the bulk modulus was as wide as that of the tensile and shear relaxation moduli. This result contradicts previous conceptions but is agreement with some other recent observations. Thermal and hygral expansions were also measured and used in a hybrid nonlinear viscoelastic constitutive model. The hybrid model captured the hygrothermal nonlinear viscoelastic deformation of the epoxy primer. This model is a combination of Schapery’s model and Popelar’s shear modified free volume model. Torsion tests were conducted and used to calibrate the distortional parameters in the free volume model. Tension experiments were performed at four different temperature and humidity levels and were used to calibrate the dilatational, thermal and hygral parameters in the hybrid model. The linear and hygrothermal nonlinear viscoelastic constitutive models were used in the analysis of time-dependent interfacial fracture between concrete and epoxy primer. A generalized time-dependent J integral was used as a fracture parameter for characterizing the time-dependent interfacial fracture. This was used instead of the strain energy release rate and the stress intensity factor because of the nonlinear viscoelastic deformation of the primer. Schapery’s pseudo stress model was calibrated using tension data at various temperature and humidity levels because it is required for the generalized J integral. An instrumented wedge test was conducted in order to determine the interfacial fracture energy at several loading rates and various temperature and humidity levels. The crack length was measured as a function of wedge speeds during steady state crack growth. The generalized J integral and cohesive zone size or failure zone size were computed using finite element analyses that incorporated the pseudo stress model. The pseudo stress model, cohesive zone size and the generalized J integral were all used to compute the work input into the failure zone, which was then equated to the fracture energy. The loading rate, temperature and humidity level all affected the fracture energy, which decreased with increasing temperature and humidity levels.
Effect of moisture on mixed-mode TSR on a glass/epoxy interface
(2017-12) Ferreira Vieira de Mattos, Daniel; Liechti, K. M.; Huang, Rui; Rodin, Gregory J; Ravi-Chandar, Krishnaswa; Bonnecaze, Roger T
The understanding of interfacial failure in adhesively bonded structures is important for several sectors including transportation and infrastructure. This problem has motivated studies for several decades. Adhesives are polymeric and, as such, present time, temperature, strain rate and moisture dependence. The effect of moisture on interfacial adhesion and fracture is still an open problem and demands a deep multi-disciplinary study considering nonlinear viscoelasticity, fracture mechanics, diffusion, chemistry and surface science. This is justified through the mechanisms through which moisture can affect interfacial adhesion. The presence of moisture can degrade the interface integrity. The absorbed moisture also modifies the mechanical properties of the bulk adhesive as well as its interactions with substrates, which introduces changes in the response of the adhesively bonded structure as it is subjected to an external load. An additional complication for interfacial cracks constrained to grow along the interface is that crack growth is governed by the tensile and shear stresses at the interface as well as the interfacial interactions (adhesion energy, strength and range) embodied in traction separation relations and giving rise to the term mixed-mode fracture. This research investigates the effect of moisture on interfacial fracture for different mode-mixes. The content is developed in four parts. First, the adhesive is experimentally characterized via the following tests: mechanical loading, water diffusion, thermal and hygral expansion. These results introduce the second part: a nonlinear viscoelastic model calibrated considering all those measured properties. This model captures the effect of time, temperature, strain rate and moisture on the mechanical behavior of the adhesive. The third part deals with the fracture behavior of a glass/epoxy interface over a range of mode-mixes and moisture conditions. This is complemented by analyses including optical profile measurements of the fractured surfaces and extraction of traction and separation relations and toughness. Finally, a significant emphasis was placed on the numerical analysis which was required for each of the three components outlined above.
Efficient frequency response analysis of structures with viscoelastic materials
(2006) Swenson, Eric Dexter; Bennighof, Jeffrey K.
Extreme energy absorption : the design, modeling, and testing of negative stiffness metamaterial inclusions
(2013-08) Klatt, Timothy Daniel; Seepersad, Carolyn; Haberman, Michael R. (Michael Richard), 1977-
A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes, et al., Nature, 410, pp. 565-567, (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The nonlinear multiscale model is then utilized in a set-based hierarchical design approach to explore the design space over a wide range of inclusion geometries. Finally, prototype NS inclusions are fabricated using an additive manufacturing technique and tested to determine quasi-static inclusion stiffness which is compared with analytical predictions.
Linear and nonlinear poroviscoelasticity, and fracture properties of gelatin-based hydrogels
(2022-08-08) Chen, Si (Ph. D. in engineering mechanics); Ravi-Chandar, K.; Huang, Rui; Landis, Chad M.; Lu, Nanshu; Keitz, Benjamin
Hydrogels are polymer networks embedded in a solvent which is usually predominantly water. Due to the solvent diffusion and rearrangement of the polymer network, hydrogels exhibit poroelastic and viscoelastic behaviors. The two behaviors are usually coupled and may influence other mechanical properties, such as fracture. While there is much work on modeling and simulation of poroelasticity, viscoelasticity, and fracture, there is still a need for more experimental work that explores the response of the material and the calibration of the material response. In this dissertation, three large suites of experiments were performed under nonhomogeneous conditions to characterize the linear and nonlinear poroelasticity, viscoelasticity, and fracture in gelatin-based hydrogels. First, the poroelasticity of gelatin-based hydrogel of two different compositions is examined through drying and swelling experiments, achieved by adjusting the humidity levels in an environmentally controlled enclosure. The deformation of the specimens was quantified through Digital Image Correlation. The experimental measurements were compared with the simulations based on the Finite Element Method (FEM) implemented on the public domain code FEniCS, to provide a way to calibrate the material parameters both for linear and nonlinear poroelasticity. Second, the coupled poroelastic and viscoelastic behaviors of hydrogels were explored through simultaneous swelling/drying and creep experiments also in a controlled environment. This work showed that the decomposition of the volumetric and isochoric deformation provides a way to separate the poroelastic and viscoelastic behaviors. According to the experimental results, the volumetric deformation was dominated by water diffusion, and isochoric deformation was influenced by both viscoelasticity and poroelasticity. A nonlinear poroviscoelastic theory was developed based on a two-potential formulation under a thermodynamic framework, that successfully captured the coupled power-law creep and swelling/drying behaviors. Finally, the fracture behavior of hydrogels was explored under various conditions through poroelastic diffusion and viscoelastic creep. The viscoelastic J-like integral based on Schapery's theory was calculated from the measured displacement field and served as a characteristic parameter for crack growth in quasi-steady conditions. To further explore the poroelastic influence on the crack tip, fracture tests of immersed-crack-tip conditions were performed, which showed that water diffusion decreased the fracture energy.
New discovery to reduce residual oil saturation by polymer flooding
(2017-05) Erincik, Mehmet Zeki; Pope, G. A.; Balhoff, Matthew T.
Eight coreflood experiments were conducted to investigate the effect of aqueous hydrolyzed polyacrylamide (HPAM) polymer solutions on residual oil saturation in sandstone cores. Seven of the experiments were conducted in high-permeability (~1500 mD) Bentheimer sandstones, six of the cores were saturated with a viscous oil (~120 cp), and one core was saturated with a light (10 cp) oil. The eighth experiment was performed in a Berea sandstone core using the light oil. Experiments #6 to 8 were done by Pengpeng Qi. These experiments are included in this thesis to provide more complete and convincing results. All experiments were first saturated with brine, flooded with oil to reach initial oil saturation, and then waterflooded with brine to zero oil cut. For experiments with viscous oil, a viscous glycerin solution was injected after the waterflood until the oil cut was zero. FP 3630S polymer was used in the seven Bentheimer coreflood experiments and FP 3330S polymer was used in the Berea coreflood experiment. The polymer solutions in low salinity brine had a high relaxation time. Additional hydrolysis of the polymers was done to further increase the relaxation time. The coreflood experiments were designed to maximize the effect of viscoelasticity on the residual oil saturation by flooding the cores at a high Deborah number, N [subscript De], which ranged from 30-300. The low-salinity polymer floods were followed by a second polymer flood with a similar viscosity, but higher salinity (viscosity was controlled by increasing polymer concentration). The higher salinity resulted in a much lower polymer relaxation time than the first polymer in low salinity brine, and therefore a lower N [subscript De] for the coreflood. Two of the experiments included additional polymer floods by alternating between the low and high salinity polymer solutions. The original objective of this work was to investigate the effect of polymer elasticity (measured by the dimensionless Deborah number, N [subscript De]) on residual oil saturation. The polymer flooding experiments were designed to keep the capillary number less than the capillary number of the preceding glycerin floods as well as less than the critical capillary number to avoid a reduction in the residual oil saturation caused by a high capillary number. Early in this experimental study, a surprising and remarkable discovery was made that completely changed the direction of the research. The residual oil saturation following the high-salinity polymer floods was reduced to remarkably low values. All eight experiments showed that the low-salinity polymer floods with high Deborah numbers resulted in additional oil recovery. The average reduction in oil saturation was ~10% for the seven Bentheimer corefloods, including the one with light oil (4%). There was a (weak) correlation indicating lower residual oil saturations with increasing N [subscript De] consistent with the observations by Qi et al. (2017). The most surprising observation and discovery was that the residual oil saturation decreased between 4 and 21% with an average reduction of 11% when high-salinity polymer solution was injected following the low-salinity polymer flood with the same viscosity and at the same or similar flow rates. The total reduction in residual oil saturation from both polymer floods was 21% below the residual oil saturation of the glycerin floods with the same viscosity. The lowest residual oil saturation in these experiments was only 7%. This is a truly remarkable result considering the interfacial tension between the polymer solution and oil is about the same as between water and oil. Additional measurements are needed to understand the mechanisms e.g. wettability measurements before and after the polymer floods in low and high salinity brines.
Physical characterization of bacterial biofilm polymer networks to determine the role of mechanics in infection and treatment
(2018-11-29) Kovach, Kristin N.; Gordon, Vernita Diane; Florin, Ernst-Ludwig; Marder, Michael P; Smyth, Hugh D; Lynd, Nathaniel
Biofilms are communities of microorganisms that produce a matrix of extracellular polymers to surround and protect themselves from external forces in their environment. This communal lifestyle is incredibly beneficial for microorganism survival. Characterization of the mechanical properties of biofilms is a vital and understudied component of fully understanding these biological systems. In this dissertation, we break down the mechanical response of the Pseudomonas aeruginosa biofilm by its constituent polymers. These bacteria produce unique polymers to resist a variety of stresses. In the first part of this dissertation, using oscillatory bulk rheology, we characterize the viscoelasticity of biofilm polymer networks. Using genetically manipulated lab strains of P. aeruginosa, we isolate the mechanical response of each polymer by analyzing biofilms comprised primarily of one type of polymer. We find that the polymers have unique mechanical properties: some increase the yield strain and others increase elastic modulus. In strains of P. aeruginosa isolated from chronic infections, we find that the bacteria evolve to increase production of polymers that maximize the energy required to yield the matrix. In the second part of this dissertation, we work to mechanically compromise each of the polymers in the matrix. By attacking different matrix components, we learn more about the structural properties that give rise to mechanical properties as well as identify the most promising therapeutic treatments to break down biofilm infections. We find that specific enzymes are useful for decreasing yield strain of biofilms and increasing the diffusivity of the matrix. Decrease in yield strain means that biofilms will take less deformation before losing mechanical integrity, and the increase in matrix diffusivity means that current treatments such as antibiotics are more effective as the antibiotics can more easily reach the bacteria in the matrix to effectively kill them. This dissertation treats biofilms as polymer networks, divorcing the analysis from biological responses, in an attempt to well-characterize the understudied mechanical properties of biofilms. By approaching these systems from a physical standpoint, we are able to learn more about biofilms by breaking the mechanical response into constituent components, as well as learn about how enzymatic treatments alter biofilm properties.
Plane nonlinear shear waves in relaxing media
(2019-08) Cormack, John Michael Napier; Hamilton, Mark F.; Downer, Michael C; Haberman, Michael R; Spratt, Kyle S; Wilson, Preston S
This dissertation investigates plane nonlinear shear wave motion in a material that possesses a single relaxation mechanism. Derivations that employ three common yet separate descriptions of viscoelasticity are followed to arrive at the same mathematical model for a nonlinear and relaxing medium. The model is then used to obtain a single wave equation for linearly polarized particle motion, and two coupled wave equations for elliptically polarized particle motion. The resulting wave equations account for cubic nonlinearity and viscoelasticity in the form of a single relaxation mechanism. Progressive wave solutions are obtained from a Burgers-type evolution equation, thereby illustrating competition between nonlinearity and viscoelasticity in the wave motion. Energy loss due to relaxation is found insufficient to prevent the occurrence of multivalued solutions of the evolution equation when the wave amplitude is sufficiently large, thus indicating that the model is lacking essential physics in those cases. Multivalued solutions are prevented by employing weak shock theory in the obtained analytical solution for a step shock, or by introducing shear viscosity when solving the evolution equation numerically. A coordinate transformation is employed that allows simulation of waveform evolution up to and beyond the point of waveform overturning, which permits determination of the parameter space in which multivalued solutions exist. The analysis is also applied to nonlinear shear waves in media characterized by attenuation that is proportional to frequency raised to some power. Finally, standing nonlinear shear waves are investigated by developing an augmented Duffing equation that describes the nonlinear response of a shear wave resonator near its lowest resonance. Both linearly and elliptically polarized motions are described with analytical implicit solutions of the augmented Duffing equation.
Short timescale Brownian motion and applications
(2015-08) Mo, Jianyong; Raizen, Mark G.; Downer, Mike; Fiete, Gregory A; Bengtson, Roger D; Kumar, Pawan
This dissertation details our experiments and numerical calculations on short timescale Brownian motion and its applications. We test the Maxwell-Boltzmann distribution using micrometer-sized spheres in liquids at room temperature. In addition to that, we use Brownian particles as probes to study boundary effects imposed by a solid wall, viscoelasticities of complex fluids, slippage at solid-fluid interfaces, and fluid compressibility. The experiments presented in this dissertation relies on the use of tightly focused laser beams to both contain and probe the Brownian motion of microspheres in fluids. A dielectric sphere near the focus of a laser beam scatters some of the incident photons in a direction which depends on the particle's position. Changes in the particle's position are encoded in the spatial distribution of the scattered beam, which can be measured with high sensitivity. It is important to emphasize that the Brownian motion in this dissertation is exclusive for translational Brownian motion. We have reported shot-noise limited measurements of the instantaneous velocity distribution of a Brownian particle. Our system consists of a single micron-sized glass sphere held in an optical tweezer in a liquid in equilibrium at room temperature. We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and a modified energy equipartition theorem that account for the kinetic energy of the liquid displaced by the particle. Our measurements con rm the distribution over a dynamic range of more than six orders of magnitude in count-rate and five standard deviations in velocity. We have reported high-bandwidth, comprehensive measurements of Brownian motion of an optically trapped micrometer-sized silica sphere in water near an approximately at wall. At short distances, we observe anisotropic Brownian motion with respect to the wall. We find that surface confinement not only occurs in the long time scale diffusive regime but also in the short time scale ballistic regime, and the velocity autocorrelation function of the Brownian particle decays faster than that of particle in a bulk fluid. Furthermore, at low frequencies the thermal force loses its color due to the reflected flow from the no-slip boundary. The power spectrum of the thermal force on the particle near a no-slip boundary becomes at at low frequencies. We have numerically studied Brownian motion of a microsphere in complex fluids. We show that Brownian motion of immersed particles can be dramatically affected by the viscoelastic properties of the host fluids. Thus, this fact can be used to extract the properties of complex fluids via observing the motion of the embedded particles. This will be followed by two experimental demonstrations of obtaining the viscosities of water and acetone. We also study Brownian motion with partial and full slip boundary conditions both on the surface of a sphere and a boundary. We show that the motion of particles can be significantly altered by the boundary condition of fluid flow on a solid surface. We suggest that this fact can be used to measure the slippage, namely the slip length. Lastly, I will discuss the efforts to study fluid compressibility and nonequilibrium physics using a short duration pulsed laser. We expect to increase the postion sensitivity from current 10⁻¹⁵ m/[square root of Hz] to about 10⁻¹⁹ m/[ square root of Hz] by using a pulsed laser with a peak power of 10^8 W. With such a high position sensitivity, we expect to be able to resolve the compressibility of fluids. We will also discuss a few future experiments studying non-equilibrium physics.
The effect of polymer viscoelasticity on residual oil saturation
(2018-06-13) Qi, Pengpeng; Balhoff, Matthew T.; Pope, Gary A,; Mohanty, Kishore; Delshad, Mojdeh; Johnston, Keith P.
Water-based polymers are often used to improve oil recovery by increasing sweep efficiency. However, recent laboratory and field work have suggested these polymers, which are often viscoelastic, may also reduce residual oil saturation. The objective of this work is to investigate the effect of viscoelastic polymers on residual oil saturation in sandstones and identify conditions and mechanisms for the improved recovery. Sandstones (Bentheimer and Berea) were saturated with either high viscosity (120cp) or low viscosity oil (10cp) and then waterflooded to residual oil saturation using either brine only or brine followed by an inelastic Newtonian fluid (diluted glycerin). These floods were followed by injection of a viscoelastic polymer, hydrolyzed polyacrylamide (HPAM). To maximize the polymer solutions relaxation time, polymer solutions were often hydrolyzed at a high pH condition (pH>10) and 70°C oven for 3-5 days, and they were neutralized with HCl before injections. Significant reduction in residual oil was observed for all core floods when the polymer had significant elasticity (determined by the dimensionless Deborah number, N [subscript De]). An average residual oil reduction of 11% OOIP was found during HPAM polymer floods for N [subscript De] of 1 to 400. HPAM floods with very low elasticity (N [subscript De] <0.6) did not result in observable reduction in residual oil saturation. Relaxation times of polymers with hydrolysis increased by a factor 2-3 without changing much in polymer viscosity at polymer equivalent shear rate (20-30s⁻¹), and neutralization with HCl does not reduce polymer relaxation time. Capillary numbers from the viscoelastic polymer floods were well controlled, which indicates that viscoelastic polymer can reduce residual oil saturation. Results from CT scans further support these observations. A correlation between Deborah number and normalized residual oil saturation reduction was developed (an Elastic Desaturation Curve, EDC) based on the core flood experiments, and this correlation was successfully implemented into UTCHEM, a chemical flooding reservoir simulator. Viscoelastic models (EDC and relaxation time model) were validated with the core flood results, and they were also applied on a reservoir model based on Oilfield. It was found an additional 3-4%OOIP was recovered from polymer viscoelasticity. Finally, microfluidic experiments were performed with Newtonian fluids and polymers with low and high elasticities to study the fundamental oil recovery mechanisms. It was observed that trapped residual oil can oscillate upstream a constriction when flooded by viscoelastic polymer, but not inelastic fluids. These pore scale observations may partially explain the improved recovery in the core scale experiments.
Various applications of discontinuous Petrov-Galerkin (DPG) finite element methods
(2018-06-25) Fuentes, Federico, Ph. D.; Demkowicz, Leszek; Babuska, Ivo M.; Caffarelli, Luis A.; Hughes, Thomas J. R.; Oden, J. Tinsley; Wilder, Aleta
Discontinuous Petrov-Galerkin (DPG) finite element methods have garnered significant attention since they were originally introduced. They discretize variational formulations with broken (discontinuous) test spaces and are crafted to be numerically stable by implicitly computing a near-optimal discrete test space as a function of a discrete trial space. Moreover, they are completely general in the sense that they can be applied to a variety of variational formulations, including non-conventional ones that involve non-symmetric functional settings, such as ultraweak variational formulations. In most cases, these properties have been harnessed to develop numerical methods that provide robust control of relevant equation parameters, like in convection-diffusion problems and other singularly perturbed problems. In this work, other features of DPG methods are systematically exploited and applied to different problems. More specifically, the versatility of DPG methods is elucidated by utilizing the underlying methodology to discretize four distinct variational formulations of the equations of linear elasticity. By taking advantage of interface variables inherent to DPG discretizations, an approach to coupling different variational formulations within the same domain is described and used to solve interesting problems. Moreover, the convenient algebraic structure in DPG methods is harnessed to develop a new family of numerical methods called discrete least-squares (DLS) finite element methods. These involve solving, with improved conditioning properties, a discrete least-squares problem associated with an overdetermined rectangular system of equations, instead of directly solving the usual square systems. Their utility is demonstrated with illustrative examples. Additionally, high-order polygonal DPG (PolyDPG) methods are devised by using the intrinsic discontinuities present in ultraweak formulations. The resulting methods can handle heavily distorted non-convex polygonal elements and discontinuous material properties. A polygonal adaptive strategy was also proposed and compared with standard techniques. Lastly, the natural high-order residual-based a posteriori error estimator ingrained within DPG methods was further applied to problems of physical relevance, like the validation of dynamic mechanical analysis (DMA) calibration experiments of viscoelastic materials, and the modeling of form-wound medium-voltage stator coils sitting inside large electric machinery.