Spectrum Of Relaxation Times Research Articles

Finite element simulations of quartz crystal microbalances (QCM): from Sauerbrey to fractional viscoelasticity under water

2D finite element simulations are performed on QCM working in the thickness-shear mode and loaded with different homogeneous films. They include a purely elastic film, a viscoelastic Maxwellian liquid, viscoelastic-Voigt solid, and the fractional viscoelastic (power-law) version of each case. Unlike single-relaxation kind models, fractional viscoelasticity considers the relaxation-time spectrum often found in polymeric materials. The films are tested in air or covered with liquids of different viscosities. Two substrate thicknesses are tested: 100 nm and 500 nm, the latter being close to the condition that promotes the resonance of the adsorbed film. In all cases the simulations are compared with small-load approximation theory (SLA). The 100 nm films follow the theory closely, although significant deviations of the SLA are observed as the overtone number n increases, even in purely elastic films. We also show that it is possible to identify the viscoelastic ‘fingerprint’ of the 100 nm films in air using raw data and Sauerbrey’s equivalent thickness obtained with the QCM in the 3 < n < 13 range. These numerical data are validated by experimental measurements of crosslinked polydimethylsiloxane films with thicknesses ∼150 nm. In contrast, the 500 nm films deviate notoriously from the SLA, for all viscoelastic models and overtones, with the largest deviation observed in the elastic film. When a liquid layer covers the QCM without an adsorbed film, the only overtone that numerically reproduces the theoretical value is the fundamental, n = 1. For n > 1, strong coupling between the solid and liquid is detected, and the original vibration modes of the crystal are altered by the presence of the liquid. Finally, the numerical simulations suggest that it is possible to detect whether a viscoelastic film is formed under a liquid layer using only the information from n = 1. In these film/liquid systems we also observe the so-called missing-mass effect, although the theory and simulations exhibit different levels of impact of such effect when the liquid viscosity is high.

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Enhancing permeability estimation methods in Brazilian pre-salt complex carbonate reservoirs

Carbonate pre-salt reservoirs pose formidable challenges for formation evaluation and estimation of petrophysical properties such as rock flow capacity. The high complexity of the pore system and its textural heterogeneity often lead to poor predictions when using conventional formation evaluation methods. This paper discusses and tests the applicability of two approaches to calculate the absolute permeability curves for the carbonate reservoirs of the Barra Velha Formation in the Santos Basin, proposing a fine-tuned workflow for these complex rocks. In developing our workflow, we used data from a case study well, comprising a complete well log suite and two formation tests, and routine core analysis results (RCAL) in core plugs and sidewall cores. Our workflow consists of: (1) reinterpreting the nuclear magnetic resonance (NMR) log in vugular intervals by decomposing the transversal relaxation time spectra; (2) calculating the absolute permeability by the Timur–Coates model and adjusting the coefficients with the RCAL results from representative samples; (3) applying the Flow Zone Indicator (FZI) method for rock typing to optimally define Hydraulic Flow Units (HFU); (4) checking the consistency of HFUs regarding pore geometry and lithological characteristics; (5) evaluating the performance of the models against core data and formation tests. The predicted permeability curves performed well for the NMR and FZI models when compared to the RCAL data from representative samples, with mean absolute errors for the logarithm of permeabilities equal to 0.78 and 0.87, respectively. This represents an improvement of 15% and 5% when compared to the simplistic approach that uses a power law to relate porosity to permeability from RCAL. These curves also reasonably reproduce the results from the formation tests for the top part of the reservoir, where matrix porosity dominates the flow. However, the NMR and FZI permeability curves underestimate the test results at the bottom part of the reservoir, where karstic and fracture features dominate, demonstrating limitations in these permeability estimation methods for this specific scenario. From our observations, we propose several improvements to enhance the current methods for estimating absolute permeability in pre-salt carbonate reservoirs. In the case of the NMR approach, it is essential to consider the effects of mud invasion in vugs for the correct estimation of the proportions of free and irreducible fluids. In the FZI approach, optimization in defining the quantity and limits of hydraulic flow units is important, which shows that four units are sufficient to represent the reservoir interval.

Direct computations of viscoelastic moduli of biomolecular condensates.

Biomolecular condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model that leverages information regarding intra- and inter-chain contacts, which we extract from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations of phase separation. The key ingredient of the generalized Rouse model is a graph Laplacian that we compute from equilibrium MMC simulations. We compute two flavors of graph Laplacians, one based on a single-chain graph that accounts only for intra-chain contacts, and the other referred to as a collective graph that accounts for inter-chain interactions. Calculations based on the single-chain graph systematically overestimate the storage and loss moduli, whereas calculations based on the collective graph reproduce the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two graphs proves to be most accurate. In line with the theory of Rouse and contrary to recent assertions, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic vs dominantly viscous behaviors does not imply a single relaxation time. Instead, it is influenced by the totality of the relaxation modes. Hence, our analysis affirms that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain the relaxation time spectra that underlie the dynamics within condensates. This is of practical importance given advancements in passive and active microrheology measurements of condensate viscoelasticity.

Robust Recovery of Optimally Smoothed Polymer Relaxation Spectrum from Stress Relaxation Test Measurements.

The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods, different mechanisms are built-in to obtain a smooth enough and noise-robust relaxation spectrum model. The regularization of the original problem and/or limit of the set of admissible solutions are the most commonly used remedies. Here, the problem of determining an optimally smoothed continuous relaxation time spectrum is directly stated and solved for the first time, assuming that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. The relaxation time spectrum model that reproduces the relaxation modulus measurements and is the best smoothed in the class of continuous square-integrable functions is sought. Based on the Hilbert projection theorem, the best-smoothed relaxation spectrum model is found to be described by a finite sum of specific exponential-hyperbolic basis functions. For noise-corrupted measurements, a quadratic with respect to the Lagrange multipliers term is introduced into the Lagrangian functional of the model's best smoothing problem. As a result, a small model error of the relaxation modulus model is obtained, which increases the model's robustness. The necessary and sufficient optimality conditions are derived whose unique solution yields a direct analytical formula of the best-smoothed relaxation spectrum model. The related model of the relaxation modulus is given. A computational identification algorithm using the singular value decomposition is presented, which can be easily implemented in any computing environment. The approximation error, model smoothness, noise robustness, and identifiability of the polymer real spectrum are studied analytically. It is demonstrated by numerical studies that the algorithm proposed can be successfully applied for the identification of one- and two-mode Gaussian-like relaxation spectra. The applicability of this approach to determining the Baumgaertel, Schausberger, and Winter spectrum is also examined, and it is shown that it is well approximated for higher frequencies and, in particular, in the neighborhood of the local maximum. However, the comparison of the asymptotic properties of the best-smoothed spectrum model and the BSW model a priori excludes a good approximation of the spectrum in the close neighborhood of zero-relaxation time.

NMR transverse relaxation times and phase equilibria of methane hydrate in mesoporous alumina

The processes of formation (and decomposition) of methane hydrate from water adsorbed in the pores of spherical granules of mesoporous alumina (Al2O3) have been investigated using the low-field NMR spin–spin relaxation time (T2) and DSC methods. Analysis of the obtained data showed that changes observed in the relaxation time spectra represent a strong case in favor of the model envisaging hydrate growth in pore spaces without conspicuous water transfer through the volume content of the sample with mesoporous structure. As the supercooling strength of the liquid phase enhances, the size of the pores in which hydrate formation takes place decreases. At this, the size of the hydrate particles previously formed in larger pores tends to increase. Hydrate nucleation was shown to be followed by intensive and rapid hydrate formation in some parts of the alumina granules in the sample. The “skipping” mechanism of hydrate formation between granules remains unclear.

Pore Structure Characterization and Fractal Characteristics of Tight Limestone Based on Low-Temperature Nitrogen Adsorption and Nuclear Magnetic Resonance

Pore structure characterization and fractal analysis have great significance for understanding and evaluating tight limestone reservoirs. In this work, the pore structure of tight limestone, low-temperature nitrogen adsorption (LTNA), and low-field nuclear magnetic resonance (NMR) are characterized, and the fractal dimension of the pore structure of tight limestone is discussed based on LTNA and NMR data. The results indicate that the pores of tight limestone have H3 and H4 types, the pore size distribution (PSD) of the H3 type is a wave distribution ranging from 2 to 10 nm, and the PSD of the H4 type is a unimodal distribution ranging from 2 to 10 nm. The transverse relaxation time (T2) spectrum of tight limestone shows a single peak (DF), double peak (SF), and triple peak (TF), and the ranges for the T2 spectra for micropores, mesopores, and macropores are 0.1 to 10 ms, 10 to 100 ms, and greater than 100 ms, respectively. The LTNA fractal dimension of tight limestone (DL) ranges between 2.4446 and 2.7688, with an average of 2.5729, and the NMR fractal dimensions of micropores (DNMR1), mesopores (DNMR2), and macropores (DNMR3) are distributed between 0.3744 and 1.1293, 2.4263 and 2.9395, and 2.6582 and 2.9989, respectively. Moreover, there is a negative correlation between DL and average pore radius, a positive correlation between DL and specific surface area, and a positive correlation between DNMR2 and DNMR3 and micropore content, while DNMR2 and DNMR3 are negatively correlated with the content of mesopores and macropores.

Comparison of viscoelastic flows in two- and three-dimensional serpentine channels.

Polymer solutions in the dilute regime play a significant role in industrial applications. Due to the intricate rheological properties of these highly viscoelastic fluids, especially in complex flow geometries, a thorough numerical analysis of their flow dynamics is imperative. In this research, we present a numerical investigation of purely elastic instability occurring in two- and three-dimensional serpentine channels under conditions where fluid inertia is negligible and across a broad spectrum of polymer relaxation times. Our findings reveal a strong qualitative agreement between the existing experimental results obtained from dilute solutions of flexible polymers in microfluidic devices and the numerical simulations conducted in two and three dimensions using the Oldroyd-B model. Spatial flow observations and statistical analysis of temporal flow features indicate that this purely elastic turbulent flow exhibits nonhomogeneous, non-Gaussian, and anisotropic characteristics across all scales. Additionally, our comparison of two- and three-dimensional simulations demonstrates that the elastic instability is primarily driven by the curvature of the streamlines induced by the flow geometry, rather than the weak secondary flow in the azimuthal direction. Therefore, our two-dimensional numerical simulations successfully replicate, at least qualitatively, the features observed in three-dimensional experiments. Furthermore, spectral analysis suggests that, in comparison to elastic turbulence in the dilute regime, the range of scales for the excited fluctuations is narrower.

A method for determining the spectral relaxation functions of polymers under single stretching of micro samples

The principles of designing products made of the latest complex-structured polymer composite materials necessitate the need to take into account the large-scale structural effects determined by processes at the supramolecular and molecular levels of the polymer: relaxation, kinetic (breaking and recombination of chemical bonds), recrystallization of supramolecular structures, etc. The development of these processes is described by relaxation functions, which, in turn, can be calculated using the functions of relaxation time spectra. The purpose of the work was to develop a specialized equipment for testing micro-samples with a variable working part for uniaxial stretching along with the experimental technique and computational algorithms for processing the obtained measurement data, and experimental approbation of the developed approach to determining spectral relaxation functions. A method is proposed for estimating relaxation functions not at fixed stress levels within linear elasticity, at secant points of deformation diagrams, at fixed values of the linear elasticity modulus, but within an extended range of the sample deformation up to pre-rupture states. A set of test equipment designed for tensile tests of micro-samples with a thickness of the working part of 0.2 – 1.2 mm has been developed. The tooling can be installed on modern high-precision breaking machines. Tensile tests of polyethylene terephthalate micro-samples with a thickness of 50 and 175 μm were carried out taking into account the scale factor. A tensile test of micro-samples that are technologically stabilized by paper frames of a special shape is described. Diagrams illustrating the kinetics of changes in the spectral relaxation functions of oriented polyethylene terephthalate (PET) are constructed proceeding from the data of testing micro-samples with a constant strain rate. A method for using these diagrams in calculations of empirical relaxation time spectra is described. The results of testing micro-samples of polyethylene terephthalate are presented. Illustrative deformation diagrams of the studied polymer samples and calculated diagrams of functions of relaxation time spectra calculated according to the described method are given.

A Method to Identify Pore Fluids in Heterogeneous Conglomerate Reservoirs Using a Nuclear Magnetic Resonance Log with Oil-Based Mud Invasion

Summary Nuclear magnetic resonance (NMR) logging has been extensively utilized for identifying pore fluids in recent years. However, after oil-based mud (OBM) invasion, OBM filtrate partially takes the place of the original fluid in the reservoir and the morphology of the NMR T2 (transverse relaxation time) spectrum changes. OBM invasion makes it difficult to identify the formation fluid using routine NMR fluid identification methods. In this study, we took heterogeneous conglomerate formation in the northwestern Junggar Basin as a case study and carried out core experiments under four conditions (viz., water-saturated, OBM displacing water, oil-saturated, and OBM displacing oil) and simulated the states of OBM invasion into water and hydrocarbon-bearing formation. Comparative analysis finds that when the OBM invades the water layer, the movable peak of the T2 spectrum primarily reflects the bulk relaxation characteristics of OBM filtrate, whereas when the OBM invades into the oil layer, the T2 spectrum may exhibit a three-peak distribution, where the first peak mainly indicates irreducible water, the second peak reflects OBM filtrate, and the third peak primarily reflects nondisplaced oil. To facilitate fluid identification, two T2 cutoffs are adopted to divide the T2 spectrum into three segments, and combined with the T2 geometric average, a fluid identification factor (ifluid) is proposed. Finally, identification criteria for reservoir type are established on the NMR logging and drillstem test data. The field application verifies the reliability of the proposed methods. These methods realize the identification of oil layers under OBM drilling and guide the subsequent production and development of oil reservoirs.

Fine quantitative characterization of high-H2S gas reservoirs under the influence of liquid sulfur deposition and adsorption

In order to clarify the influence of liquid sulfur deposition and adsorption to high-H2S gas reservoirs, three types of natural cores with typical carbonate pore structures were selected for high-temperature and high-pressure core displacement experiments. Fine quantitative characterization of the cores in three steady states (original, after sulfur injection, and after gas flooding) was carried out using the nuclear magnetic resonance (NMR) transverse relaxation time spectrum and imaging, X-ray computer tomography (CT) of full-diameter cores, basic physical property testing, and field emission scanning electron microscopy imaging. The loss of pore volume caused by sulfur deposition and adsorption mainly comes from the medium and large pores with sizes bigger than 1 000 μm. Liquid sulfur has a stronger adsorption and deposition ability in smaller pore spaces, and causes greater damage to reservoirs with poor original pore structures. The pore structure of the three types of carbonate reservoirs shows multiple fractal characteristics. The worse the pore structure, the greater the change of internal pore distribution caused by liquid sulfur deposition and adsorption, and the stronger the heterogeneity. Liquid sulfur deposition and adsorption change the pore size distribution, pore connectivity, and heterogeneity of the rock, which further changes the physical properties of the reservoir. After sulfur injection and gas flooding, the permeability of Type I reservoirs with good physical properties decreased by 16%, and that of Types II and III reservoirs with poor physical properties decreased by 90% or more, suggesting an extremely high damage. This indicates that the worse the initial physical properties, the greater the damage of liquid sulfur deposition and adsorption. Liquid sulfur is adsorbed and deposited in different types of pore space in the forms of flocculence, cobweb, or retinitis, causing different changes in the pore structure and physical property of the reservoir.

Drug-induced transitions from micelles to vesicles in ionic surfactant solutions

Surfactant solutions play key roles in scientific research and technological applications. Here we investigated solutions that combined an ionic surfactant, Cetylpyridinium Chloride (CPyCl), with a non-steroidal, anti-inflammatory drug, Sodium Diclofenac (Diclo). The study covered a wide range of compositions and utilized both rheology and cryogenic-Electron Microscopy (cryo-EM). The solutions were prepared at three different concentrations of CPyCl: 5.0 mM, 16.7 mM and 33.0 mM, and we maintained the ratio of surfactant to salt, R=CPyCl/Diclo, within the range of 0.24<R<1.2. Linear viscoelasticity was measured at 25°C. The use of dilute solutions allowed for detailed cryo-EM imaging. By tracking the evolution of the zero-frequency viscosity as a function of Diclo concentration, we identified distinct regions of different rheological responses. The correlation between frequency sweep data and cryo-EM images enabled us to link these regions to specific morphological transitions ranging from spherical micelles to long and entangled wormlike micelles, to branched networks and, eventually, to perforated vesicles. For some systems, we were able to measure the complete spectrum of relaxation times, including the shortest characteristic Rouse time at high frequencies, previously only achieved by Diffusive Wave Spectroscopy. The use of existing models to evaluate the relevant important microstructural parameters such as entanglement, contour, and persistence lengths allowed us to establish a clear correlation between the microstructural parameters derived through rheology and the insights from the cryo-EM analysis.

Influence of High-Frequency Ultrasonic Vibration Load on Pore-Fracture Structure in Hard Rock: A Study Based on 3D Reconstruction Technology.

Rock fracture is a macroscopic fracturing process resulting from the initiation and propagation of microscopic cracks. Therefore, it is crucial to comprehend the damage and fracture mechanism of rock under ultrasonic vibration by investigating the evolutionary pattern of the meso-pore fracture structure in response to high-frequency vibrational loads, as explored in this study. Standard red sandstone samples with a diameter of 50 mm and height of 100 mm were subjected to ultrasonic high-frequency vibration tests. NMR and CT scans were conducted on the rock samples at different stages of ultrasonic vibration excitation to obtain the corresponding transverse relaxation time (T2) spectra and CT scan images for each layer. The NMR test results revealed that smaller pores formed within the rock under high-frequency vibration loads, with a noticeable expansion observed in micropores. Three-dimensional reconstruction analysis based on two-dimensional CT images demonstrated an increase in pore count by 145.56%, 122.67%, and 98.87%, respectively, for the upper, middle, and lower parts of the rock after 120 s of ultrasonic vibration excitation; furthermore, the maximum pore volume increased by 239.42%, 109.16%, and 18.99%, respectively, for these regions during this period as well. These findings contribute towards a deeper understanding regarding the mechanisms underlying rock fragmentation when exposed to high-frequency vibrational loads.

Nanosecond solvation dynamics in a polymer electrolyte for lithium batteries.

Solvation dynamics critically affect charge transport. Spectroscopic experiments and computer simulations show that these dynamics in aqueous systems occur on a picosecond timescale. In the case of organic electrolytes, however, conflicting values ranging from 1 to several 100 picoseconds have been reported. We resolve this conflict by studying mixtures of an organic polymer and a lithium salt. Lithium ions coordinate with multiple polymer chains, resulting in temporary crosslinks. Relaxation of these crosslinks, detected by quasielastic neutron scattering, are directly related to solvation dynamics. Simulations reveal a broad spectrum of relaxation times. The average timescale for solvation dynamics in both experiment and simulation is one nanosecond. We present the direct measurement of ultraslow dynamics of solvation shell break-up in an electrolyte.

Long-Term Viscoelastic Behavior of Polyisobutylene Sealants before and after Thermal Stabilization.

Polyisobutylene (PIB) is commonly used as a primary sealant in multi-layer insulating glazing elements, where temperatures often exceed 100 °C. At such conditions, PIB undergoes structural changes, causing different relaxation dynamics and leading to decreased lifetime of the material. Understanding thermal behavior is therefore imperative for achieving effective insulation of these materials for long-term use in insulating application. The present study was focused on the temperature dependence of viscoelastic behavior of two commercially available polyisobutylene (PIB) materials, which are commonly used as primary sealants for energy-efficient multi-layer glazing units. The long-term viscoelastic behavior of the materials before and after thermal treatment at high temperatures was studied by using time-temperature superposition (tTS). Van-Gurp-Palmen plots were obtained directly from experimental data and enabled the study of thermally induced changes, while the relaxation time spectra were calculated from master curves and enabled the calculation of molecular weight distribution. The results showed that, after thermal treatment, the structure of PIB materials changes from linear to branched, while the molecular weight distributions transition from monomodal to bimodal. The untreated samples exhibited viscous-like behavior, while the thermally stabilized samples exhibited solid-like behavior, extending the material response for ~6 decades towards a longer timescale. Moreover, the presented results can be directly used to simulate the mechanical responses of the sealants using currently available FEM software packages to predict their functional and structural lifetime.

Structural Relaxation, Rejuvenation and Plasticity of Metallic Glasses: Microscopic Details from Anelastic Relaxation Spectra

The lack of periodicity and long-range order poses significant challenges in explaining and modeling the properties of metallic glasses. Conventional modeling of nonexponential relaxation with stretched exponents leads to inconsistencies and rarely offers information on microscopic properties. Instead, using quasi-static anelastic relaxation, we have obtained relaxation-time spectra over &gt;10 orders of magnitude of time for several metallic glasses. The spectra enable us to examine in microscopic detail the distribution of shear transformation zones and their properties. They reveal an atomically-quantized hierarchy of shear transformation zones, providing insights into the effect of structural relaxation and rejuvenation, the origin of plasticity and the mechanisms of the alpha and beta relaxation.

Designing a swimming rheometer to measure the linear and non-linear properties of a viscoelastic fluid

At low Reynolds numbers, “swirlers” – swimmers with an axisymmetric “head” and “tail” counterrotating about the axis of symmetry – generate no net propulsion in a Newtonian fluid as a consequence of the “scallop theorem”. Viscoelasticity in the suspending fluid breaks the time-reversibility and allows swirlers to propel themselves, with the swim speed being a function of swimmer geometry, fluid elasticity, and swimming gait. Using analytical theory and numerical simulations, we study the unsteady motion of a freely-suspended self-propelled swirler though viscoelastic fluids described by the Giesekus model, allowing for general axisymmetric geometry and time-dependent tail rotation rate. We show the steady swim speed can be calculated for general arbitrary axisymmetric geometries at low Deborah number via the reciprocal theorem and the solution of two Newtonian flow problems. In this “weak flow” limit, we analytically determine the swim speed and its dependence on the parameters of the Giesekus fluid which in turn are related to the primary and secondary normal stress coefficients Ψ1 and Ψ2. Furthermore, at low De, we derive the unsteady swim speed as a function of a specified unsteady tail rotation rate and the material properties of the suspending fluid. We show that for a particular tail rotation rate, the unsteady swim speed can be analyzed to recover the spectrum of fluid relaxation times, analogous to small-amplitude oscillatory shear measurements on a benchtop rheometer. This study expands upon the design space for a “swimming rheometer” by increasing its functionality to make and interpret rheological measurements.

Study of pore-throat structure characteristics and fluid mobility of Chang 7 tight sandstone reservoir in Jiyuan area, Ordos Basin

Abstract Quantitative studies of the pore-throat structure (PTS) characteristics of tight sandstone reservoirs and their effects on fluid mobility were proposed to accurately evaluate reservoir quality and predict sweet spots for tight oil exploration. This study conducted high-pressure mercury injection (HPMI) and nuclear magnetic resonance (NMR) experiments on 14 tight sandstone samples from the Chang 7 member of the Yanchang Formation in the Jiyuan area of the Ordos Basin. The HPMI was combined with the piecewise fitting method to transform the NMR movable fluid transverse relaxation time (T 2) spectrum and quantitatively characterize the PTS characteristics and the full pore-throat size distribution (PSD). Then, movable fluid effective porosity (MFEP) was proposed to quantitatively evaluate the fluid mobility of tight sandstone reservoirs and systematically elucidate its main controlling factors. The results showed that the PTS could be divided into four types (I, II, III, and IV), which showed gradual decreases in average pore-throat radius (R a), continuous increases in the total fractal dimension (D t), and successive deterioration of reservoir fluid mobility and percolation capacity. Moreover, the full PSD (0.001–10 μm) showed unimodal and multi-fractal characteristics. According to the Swanson parameter (r apex), the reservoir space types can be divided into small and large pore-throat and the corresponding fractal dimension has a relationship where D 1 &lt; D 2. Large pore-throat had higher permeability contribution and pore-throat heterogeneity but a lower development degree and MFEP than small pore-throat, which had a relatively uniform and regular PSD and represented the primary location of movable fluids. Moreover, the development degree and heterogeneity of small pore throat controlled the flowability of reservoir fluids. MFEP can overcome the constraints of tiny throats and clay minerals on movable fluid, quantify the movable fluid content occupying the effective reservoir space, and accurately evaluate the reservoir fluid mobility. The combination and development of various pore-throat sizes and types in tight sandstone reservoirs results in different PTS characteristics, whereas differences in the mineral composition and content of reservoirs aggravate PTS heterogeneity, which is the main factor controlling the fluid mobility.

Fast permeability estimation using NMR well logging data log-normal decomposition

Nuclear magnetic resonance (NMR) well logging and NMR core analysis provide a non-invasive approach to a fast reservoir rock pore structures evaluation. The NMR data is presented as a time distribution called transverse relaxation time spectrum (T2 spectrum) and, with proper adjustment, the area under the T2 distribution curve is directly related to the porosity of the reservoir rock. Based on the assumption that immovable and free fluid are present in pores of different sizes, NMR well logging and core analysis use these differences to characterize the fluids found inside the rock pores. In this way, a fixed T2 value can be selected as a cutoff. The amplitudes of the T2 spectrum that have their T2 coordinates below this fixed value are related to the fluids that are in the small pores (immovable fluids), and those that have their T2 coordinates above this value are related to the large pores (free or movable fluids). This T2 value is called T2cutoff and can be estimated in a laboratory with NMR data acquisition on water-saturated core samples. This is done by comparing the NMR acquisition data from a plug fully saturated with water with the NMR acquisition data taken from the same partially saturated plug. In this work, a new method to estimate the pore size distribution, a variable T2cutoff curve, and the Timur–Coates permeability curve of the formation along the reservoir rock is presented. The method is based on the decomposition in log-normal components of the T2 spectra of NMR well logging and on the permeability and porosity of plugs, measured in a laboratory.

Effectiveness of DPD Simulations to Predict the Dynamics of Polymer Chains in Solutions at Equilibrium and Steady Shear Flows

AbstractThe suitability of dissipative particle dynamics simulations is investigated to predict the dynamics of polymer chains in dilute polymer solutions. The authors find that the predictions depend on the value of the repulsive parameter for bead‐bead pairwise interactions used in the DPD simulations (aij). For all systems, the chain sizes and the relaxation time spectrum are analyzed. For aij = 0, theta solvent behaviour is obtained, whereas the dynamics at equilibrium agrees well with the predictions of the Zimm model. For higher values of aij, the static properties of the chain show good solvent behaviour. However, the scaling laws for the chain dynamics at equilibrium show wide variations, with consistent results obtained only at an intermediate value of aij = 25. At higher values of the repulsive parameter (aij ⩾ 25), the simulations are also able to predict the abrupt cut‐off in the relaxation spectrum, which has been observed earlier in experiments of dilute solutions. To verify further, the chain dynamics in shear flow using DPD simulations is studied. Specifically, the variation of the chain is analysed stretch and end‐over‐end tumbling with shear rates. Overall, the trends obtained from DPD simulations agree well with those observed in earlier BD simulations.