Effective Stress Coefficient Research Articles

Topology optimization for metamaterials with negative thermal expansion coefficients using energy-based homogenization

Since the existing topology designs of negative thermal expansion metamaterials are primarily based on the asymptotic homogenization theory, this paper conducts a topology optimization method of negative thermal expansion metamaterials based on the computationally efficient energy-based homogenization for the first time. In this research, (1) a new effective thermal stress coefficient equation is pioneeringly proposed using energy-based homogenization frame, where its theoretical derivation process is presented as well as its effectiveness and computational efficiency are verified by comparative cases. Additionally, the matlab code is open-sourced for public learning. (2) A topology optimization design of both 2D and 3D metamaterials with negative thermal expansion properties is established innovatively with Discrete Material Optimization (DMO). Its advantages are illustrated compared with the convectional method and its results are validated by Finite Element Method simulations. The new methods have promising applications in the evaluation and optimization of thermal expansion properties of composites.

Deformation-related earth pressure within grid wall-pattern foundation under adjacent surcharge

This study investigated the deformation-dependent earth pressure evolution on the periphery of the grid wall-pattern foundation fully embedded into soft ground. The numerical modelling was performed using the embedded Modified Cam Clay Constitutive model in the FLAC3D software platform and numerical results were validated using centrifuge results. The induced effective vertical and horizontal stresses acquired from the numerical modelling were used to compute the corresponding deformation-dependent earth pressure at different buffer zone distances and surcharge loading. Thereafter, the parameters that influence the determination of the lateral displacement, induced effective vertical stress and deformation-dependent earth pressure coefficient were investigated using machine learning and genetic programming was used to establish the physical equations that could be used to estimate parameters for similar problems. Moreover, for the deformation-dependent earth pressure to be within Rankine's active and passive earth pressure the buffer zone distance/depth ratio should be 10% of the grid wall-pattern foundation embedment into the ground. Furthermore, it was also discovered that the structure fully embedded into the ground under adjacent loading cannot only be designed based on Rankine's active and passive earth pressure investigation on the periphery but the evaluation should be done within the entire location of the grid wall foundation.

Measurements of the Effective Stress Coefficient for Elastic Moduli of Sandstone in Quasi-Static Regime Using Semiconductor Strain Gauges.

Numerous experimental and theoretical studies undertaken to determine the effective stress coefficient for seismic velocities in rocks stem from the importance of this geomechanical parameter both for monitoring changes in rock saturation and pore pressure distribution in connection with reservoir production, and for overpressure prediction in reservoirs and formations from seismic data. The present work pursues a task to determine, in the framework of a low-frequency laboratory study, the dependence of the elastic moduli of n-decane-saturated sandstone on the relationship between pore and confining pressures. The study was conducted on a sandstone sample with high quartz and notable clay content in a quasi-static regime when a 100 mL tank filled with n-decane was directly connected to the pore space of the sample. The measurements were carried out at a seismic frequency of 2 Hz and strains, controlled by semiconductor strain gauges, not exceeding 10-6. The study was performed using a forced-oscillation laboratory apparatus utilizing the stress-strain relationship. The dynamic elastic moduli were measured in two sets of experiments: at constant pore pressures of 0, 1, and 5 MPa and differential pressure (defined as a difference between confining and pore pressures) that varied from 3 to 19 MPa; and at a constant confining pressure of 20 MPa and pore pressure that varied from 1 to 17 MP. It was shown that the elastic moduli obtained in the measurements were in good agreement with the Gassmann moduli calculated for the range of differential pressures used in our experiments, which corresponds to the effective stress coefficient equal to unity.

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone, surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions (UNEs). However, the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved, including the generation of complex fracture networks, reactivation of natural fractures and faults, and thermo-hydro-mechanical-chemical (THMC) coupling of radionuclide gas transport in the subsurface. In this study, we provide an experimental investigation of hydro-mechanical (HM) coupling among gas flow, stress states, rock deformation, and rock damage using a unique multi-physics triaxial direct shear rock testing system. The testing system also features redundant gas pressure and flow rate measurements, well suited for parameter uncertainty quantification. Using porous tuff and tight granite samples that are relevant to historic UNE tests, we measured the Biot effective stress coefficient, rock matrix gas permeability, and fracture gas permeability at a range of pore pressure and stress conditions. The Biot effective stress coefficient varies from 0.69 to 1 for the tuff, whose porosity averages 35.3% ± 0.7%, while this coefficient varies from 0.51 to 0.78 for the tight granite (porosity <1%, perhaps an underestimate). Matrix gas permeability is strongly correlated to effective stress for the granite, but not for the porous tuff. Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event: (1) The porous tuff shows apparent fracture dilation or compression upon stress changes, which does not necessarily change the gas permeability; (2) The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement; and (3) Hydromechanical coupling among stress states, rock damage, and gas flow appears to be stronger in tight granite than in porous tuff.

Pore Pressure in Montmorillonite During Frictional Sliding

AbstractEarth's shallow crust is pervasively breached by fractures and faults that are often filled with saturated clays such as montmorillonite. Pore pressure in montmorillonite is difficult to measure due to its extremely low permeability, resulting in large uncertainties in its friction, which, in turn, may impact our understanding on the mechanical behaviors of the shallow crust. This difficulty motivates us to investigate pore pressure in montmorillonite during frictional sliding. Here we provide a first order understanding on the evolution of pore pressure in montmorillonite during frictional sliding by combining experimental data with an analytical consolidation model. Our result shows large variations in pore pressure in montmorillonite during frictional sliding, which need correction for the evaluation of friction of montmorillonite. We re‐visit this problem with the measured stresses at the end of our slow loading experiments where the modeled pore pressure approaches zero and obtain a new relation that shows a significant cohesive strength. The new relation may be united with our modeled pore pressure with a Biot‐Willis effective stress coefficient of α ∼ 0.5. X‐ray powder diffraction analysis of our samples shows evidence that intense deformation occurred during the frictional sliding with strain‐hardening, consistent with the occurrence of shear localization in the clay matrix following extended frictional sliding (Tembe et al., 2010, https://doi.org/10.1029/2009JB006383). These results suggest that our new relation may represent a constitutive relation for an intensely sheared, saturated montmorillonite in frictional sliding. Our result also suggests that substantial cohesion may appear on some natural clay‐rich faults.

The impact of supercritical CO2 exposure time on the effective stress law for permeability in shale

Carbon dioxide (CO2) sequestration in shale formations is regarded as an effective approach for reducing CO2 emissions. Permeability is critical for CO2 geological sequestration as it impacts migration of CO2 in shale formations. The effective stress coefficient for permeability (χ) scales the relative influence of pore pressure on permeability compared to confining pressure. This study examined the changes in χ of dry and wet shale samples with different times of supercritical CO2 (ScCO2) exposure. The results suggest that, as ScCO2 exposure time increases from 0 to 40 days, the χ of dry shale increases from 0.8304 to 0.9563, and that of wet shale increases from 0.8379 to 1.0134. Wet shale exhibits a greater increase in χ than dry shale for the same exposure time. These changes in χ may result from CO2-shale interaction that converts smaller-sized pores in shale into larger-sized pores, based on nuclear magnetic resonance (NMR) measurements. Furthermore, the presence of water intensifies the response of shale to ScCO2, thereby enhancing this transformation. Our findings provide insights into the accurate prediction of shale permeability evolution during CO2 storage, and can assist in optimizing CO2 injection strategies as well as evaluating the potential for CO2 sequestration.

Laboratory Study of Effective Stress Coefficient for Saturated Claystone

Claystone is potentially the main rock formation for the deep geological disposal of high-level radioactive nuclear waste. A major factor that affects the deformation of the host medium is effective stress. Therefore, studying the effective stress principle of claystone is essential for a stability analysis of waste disposal facilities. Consolidated drained (CD) tests were carried out on claystone samples to study their effective stress principle in this paper. Firstly, two samples were saturated under a specified confining pressure and pore pressure for about one month. Secondly, the confining pressure and pore pressure were increased to a specified value simultaneously and then reverted to the previous stress state (the deformations of the samples were recorded during the whole process). Different incremental combinations of the confining pressure and pore pressure were tried at this step. Finally, the effective stress coefficients of the samples were obtained through a back analysis. Furthermore, some potential influencing factors (the neutral stress and loading rate) of the effective stress coefficient were also studied through additional tests. Some interesting results are worth mentioning: (1) the effective stress coefficient of claystone is close to one; (2) the neutral stress and loading rate may have little effect on the effective stress coefficient of claystone.

Experimental investigation on the effects of confining pressure and pore pressure on gas/water transport properties of COx argillite

As a preferred host rock for the disposal of high-level long-lived radioactive waste in France, Callovo-Oxfordian (COx) argillite inevitably undergoes gas and water intrusion during long-term sealing. In this study, a series of gas and water permeability tests have been performed on dry, partially saturated, and fully saturated COx argillite to investigate the effects of confining pressure and pore pressure on transport properties of this material. It is first found that gas permeability is very sensitive to the sample damage state for dry samples. Due to the presence of microcracks, the relationship between porosity and gas permeability is not evident, while the Klinkenberg effect is clearly observed in intact samples. Moreover, gas permeability of partially saturated samples is very sensitive to water saturation, especially for highly saturated samples. This indicates that the material has a good gas sealing capacity after the host rock is resaturated during the long-term sealing process. For both low- and highly saturated samples, confining pressure and gas pressure have very different effects on gas permeability of partially saturated argillite. Water permeability of argillite varies between 10−20–10−21 m2 (Kw), suggesting a good water-sealing capacity. The evolution of Kw is more sensitive to the change of pore pressure than to the change of confining pressure, indicating that the effective stress coefficient for water permeability is greater than 1. The intrinsic permeability of this low-permeable clayey rock is discussed at the end of this work.

Anisotropic Evolution of Effective Stress and Pore Pressure during Coalbed Methane Drainage

Summary The anisotropy and dynamic variation in permeability of gas-adsorbing coals have a significant influence on fluid flow behavior in the cleat system. The assumption of a constant anisotropy coefficient (the ratio between permeability components in orthogonal directions) has been traditionally made to simplify the seepage-stress coupling analytical model. In this approach, the pressure drop of the coalbed is separated into desorption and nondesorption areas. To evaluate the effective stress, pore pressure, permeability distribution, and variable anisotropy coefficient more accurately, analytical formulas were developed that consider elastic mechanics and methane sorption. The results show that the anisotropy coefficient can be dynamic when cleat compressibility anisotropy exists. Pressure contours are a set of ellipses that increase in eccentricity from the near-wellbore area to the pressure drop boundary, leading to corresponding anisotropy changes in effective stress and permeability. The gas desorption-related matrix shrinkage effect causes a discontinuous pressure drop gradient at the boundary between desorption and nondesorption areas, resulting in nonsmooth pressure drop curves. The pressure gradient difference changes with the radius of the desorption area and is nonisotropic, with the high-permeability direction showing a greater difference than the low-permeability direction. These results indicate that the dynamic anisotropy coefficient has a significant impact on coalbed drainage and extraction. Compared to previous mathematical models, which assumed permeability isotropy or constant anisotropy coefficient in cleat systems, the proposed model provides a more accurate method to evaluate pressure and permeability distribution.

The Hydro‐Mechanical Properties of Fracture Intersections: Pressure‐Dependant Permeability and Effective Stress Law

AbstractFluid flow through the brittle crust is primarily controlled by the capability of fracture networks to provide pathways for fluid transport. The dominant permeability orientation within fractured rock masses has been consistently correlated with the development of fracture intersections; an observation also made at the meso‐regional scale. Despite the importance attributed to fracture intersections in promoting fluid flow, the magnitude of their enhancement of fractured rock permeability has not yet been quantified. Here, we characterize the hydro‐mechanical properties of intersections in samples of Seljadalur Basalt by generating two orthogonal, tensile fractures produced by two separate loadings using a Brazilian test apparatus, and measuring their permeability as a function of hydrostatic pressure. We observe that intersecting fractures are significantly more permeable and less compliant than two independent macro‐fractures. We formulate a model for fracture intersection permeability as a function of pressure by adding the contributions of two independent fractures plus a tube‐like cavity with an effective elastic compressibility determined by its geometry. Permeability measurements during cyclic loading allowed determination of the effective stress coefficient (α in pe = pc − αpp) for fracture and intersection permeability. We observe a trend of lower αintersection values with respect to αfracture, which suggests that the channels controlling fluid flow have a higher aspect ratio (are more tubular) for the intersections relative to independent fractures. Our results suggest that fracture intersections play a critical role in maintaining permeability at depth, which has significant implications for the quantification and upscaling of fracture permeability toward reservoir‐scale simulations.

Wellbore cement fracture permeability as a function of confining stress and pore pressure

Cemented annulus fractures are a major leakage path in a wellbore system, and their permeability plays an important role in the behavior of fluid flow through a leaky wellbore. The permeability of these fractures is affected by changing conditions including the external stresses acting on the fracture and the fluid pressure within the fracture. Laboratory gas flow experiments were conducted in a triaxial cell to evaluate the permeability of a wellbore cement fracture under a wide range of confining stress and pore pressure conditions. For the first time, an effective stress law that considers the simultaneous effect of confining stress and pore pressure was defined for the wellbore cement fracture permeability. The results showed that the effective stress coefficient (λ) for permeability increased linearly with the Terzaghi effective stress (σ-p) with an average of λ=1 in the range of applied pressures. The relationship between the effective stress and fracture permeability was examined using two physical-based models widely used for rock fractures. The results from the experimental work were incorporated into numerical simulations to estimate the impact of effective stress on the interpreted hydraulic aperture and leakage behavior through a fractured annular cement. Accounting for effective stress-dependent permeability through the wellbore length significantly increased the leakage rate at the wellhead compared with the assumption of a constant cemented annulus permeability.

Effects of fracture filling ratio and confining stress on the equivalent effective stress coefficient of rocks containing a single fracture

Because fractures are ubiquitous in rock masses, the states of stress and fracture filling significantly impact the coupled hydromechanical behaviors of fractured rocks. Based on the effective stress principle of porous media , we developed a method to determine the equivalent effective stress coefficient of rocks containing a single fracture , and analyzed the impacts of fracture filling area ratio, confining stress, and pore pressure . Confining stress and pore pressure were applied sequentially onto rock specimens, and two bulk moduli were calculated based on the measured deformation during the loading process of confining stress and pore pressure. The equivalent effective stress coefficient was then determined as the ratio of the two bulk moduli. Our results show that the equivalent effective stress coefficient increases as the filling area ratio or confining stress decreases, or pore pressure increases. The difference in equivalent effective stress coefficient of specimens with two filling area ratios decreases as the confining stress increases. The effective stress coefficient of a single fracture is inherently considered to be the ratio of the nominal fracture surface occupied by water to the total fracture surface area. When the confining stress and filling ratio increases or the pore pressure decreases, the nominal fracture surface occupied by water decreases, resulting in the corresponding reduction of the equivalent effective stress coefficient. These results provide important insights into the coupled hydromechanical behaviors of fractured rocks.

A Review of Techniques for Measuring the Biot Coefficient and Other Effective Stress Parameters for Fluid-Saturated Rocks

Abstract Predicting the behavior of a saturated rock with variations in pore fluid pressure during geo-energy production and storage, deep geological disposal of nuclear wastes, etc. with skeletal mechanical behavior in the linear elastic range is carried out using the isothermal theory of poroelasticity that incorporates Biot's effective stress principle. For conditions that are not within linear elasticity, other effective stress coefficients are used. Several experimental methods for determining Biot's and other effective stress coefficients have been documented in the literature. The objective of this study is to review the fundamentals of these techniques, their advantages and disadvantages, and to include several case studies. Current techniques for Biot's coefficient are based on different premises: jacketed and unjacketed bulk moduli or compressibility values; volume changes of the bulk and pore fluid from a drained triaxial test on a saturated sample; isotropic-isochoric compression tests on a saturated sample; matching volumetric strains for dry and saturated samples; estimation of the Biot coefficient from other poroelastic parameters; and approximation of the jacketed bulk modulus from ultrasonic wave velocities and/or unjacketed bulk modulus from the mineralogical compositions. Other effective stress coefficients are based on matching failure envelopes for dry and saturated samples and variations of rock properties (such as volumetric strain, permeability, and ultrasonic wave velocities) with respect to confining stress and pore pressure. This article discusses variations in Biot's and other effective stress coefficients produced using the different techniques and how factors such as pore geometry, test conditions, stress path, and test temperature affect the coefficients.

Transient Green's functions of dislocations in transversely isotropic and layered poroelastic half-spaces

We derive, for the first time, the transient response (or Green's function, GF) induced by a general point dislocation in a transversely isotropic and layered poroelastic half-space where the contributions from the fluid dislocation and fluid-phase coupling effect are considered. The GF is expressed in terms of the powerful Fourier-Bessel series system of vector functions recently introduced (with the expansion coefficients being the novel dislocation Love numbers). The corresponding source functions, i.e. discontinuities across the source level, are derived, which show that 1) the fluid-phase creates a new type of source functions called fluid dislocation, and 2) it further contributes directly to the traditional solid horizontal tensile dislocation (or tensile-fracture) via the Biot effective stress coefficient. While the dual-variable and position (DVP) method is applied to take care of multilayers, the Talbot's method is employed to carry out the inverse Laplace transform, both showing excellent numerical stability, efficiency, and accuracy. Key features of these GFs are analyzed numerically. It is shown that 1) the poroelastic process is featured by some transient statuses, including drained and undrained limits; 2) while these two limits are sharply different when the dislocation source is a vertical strike-slip or horizontal tensile-fracture, they are the same when a vertical dip-slip or vertical tensile-fracture is in a homogeneous half-space; 3) in all the cases, there are temporal poroelastic deformations which are significantly different from these two limits; and 4) the fluid dislocation alone could significantly contribute to the poroelastic deformation at the earlier time history. These GFs provide the kernel functions in the corresponding boundary element formulation and the method of fundamental solutions, with potential applications in geomechanics and biomedical engineering.

Estimation of in situ stresses from PP-wave azimuthal seismic data in fracture-induced anisotropic media

Horizontally transverse isotropy (HTI) induced by vertical or subvertical aligned fractures is common for unconventional fractured porous shale oil or gas reservoirs. Compared with the unfractured rocks, the seismic response characteristics of PP-wave azimuthal amplitudes are usually disturbed by the fractures and the in situ stresses. Knowledge of fracture properties, as well as in situ stresses, is required to optimize horizontal well planning and hydraulic fracturing during production, and the seismic inversion for in situ stresses from the PP-wave azimuthal amplitude data in fracture-induced anisotropic media is an essential step. Using the linear-slip theory and the effective stress law, we derive the fluid-saturated effective elastic stiffness tensors parameterized by background elastic moduli, the effective stress coefficient of isotropic host rocks, fluid modulus, porosity, and fracture parameters based on the anisotropic Gassmann’s fluid substitution equation. Combining the perturbations in saturated stiffness tensors and scattering theory, we formulate the reflection coefficient equation of PP-wave data as a function of background porosity-related stress parameter and two (i.e., normal and shear) fracture weakness parameters. Following Bayes’ rule, we estimate the porosity-related stress parameter and fracture weaknesses using the inversion method of azimuthal Fourier coefficients. Finally, we compute the effective horizontal and vertical in situ stresses using the estimated elastic moduli, porosity-related stress parameter, and fracture weaknesses. Synthetic and real data sets demonstrate that our proposed inversion approach based on the derived reflection equation provides us another way to obtain reasonable estimates of in situ stresses in a complex-fractured porous shale reservoir.

Investigating poromechanical causes for hydraulic fracture complexity using a 3D coupled hydro-mechanical model

Hydraulic fracturing is widely used to increase permeability of tight deep geological formations for improving oil and gas production and enhance geothermal energy extraction. Prior studies often predicted simple planar or near planar hydraulic fractures even though these simple fractures do not adequately explain the measured data. Instead, it is likely that complex fracture networks are created. The phenomenon of hydraulic fracture branching that gives rise to complex fracture networks is poorly understood. In this study, we develop a numerical modeling tool, based on sequential coupling of solid solver HOSS and fluid solver PFLOTRAN, to investigate the mechanisms for hydraulic fracture branching. The spherocylindrical microplane constitutive model is implemented to model fracture growth in anisotropic rocks. We verify our coupled model using the KGD analytical solution. Using a set of simulations, we demonstrate that a hydraulic fracture can branch into lateral directions for certain in situ stress conditions if there are pre-existing permeable weak layers whose initial Biot effective stress coefficient is greater than that of the matrix. In addition, we investigate the effect of three-dimensional pre-existing geological discontinuities on the creation of complex fracture systems. Our results demonstrate that branched hydraulic fractures can be predicted if we account for (1) damage-dependent Biot effective stress coefficients and (2) pre-existing geologic discontinuities. This represents a 3D poromechanics mechanism for the creation of branched fracture networks where multiple fractures can propagate simultaneously in a dense parallel swarm.

The influence of confining stress and pore pressure on effective stress coefficient for permeability: A novel Discretized Clay Shell Model for clayey sandstone

The effective stress coefficient α determines the effective stress and dominates the permeability of rocks. This study proposes a novel theoretical model called the Discretized Clay Shell Model (DCSM) that modifies the Clay Shell Model (CSM) by incorporating the stress-dependent elastic modulus of clay into a discretized multi-layer clay domain to depict the relationship between α, pore pressure, and confining stress. The proposed model was successfully used to provide insights into the stress-dependent α of clayey sandstones. We found that α always decreased with increasing pore pressure and could decrease or increase with increasing confining stress. The modelling trends, which are also observed in the previous laboratory tests, can be well explained using two effects due to the heterogeneity of radial stress within clay domain, that is, the bulk and differential clay hardening effects. The bulk clay hardening effect generates a decreasing trend in α with increasing pore pressure, while the differential clay hardening effect competes with the bulk clay hardening effect and yields a reverse trend, that is, α first decreases with increasing confining stress and then decreases when the confining stress reaches a certain critical value. This study provides synthetic cases to quantify the influence of stress-dependent α evaluated by the DCSM on the evaluation of the permeability-depth relation. Based on the laboratory testing data, the calibrated parameters of the stress-dependent permeability model assuming α=1 are significantly overestimated, and the prediction model yields overestimated permeability up to three to four orders of magnitude. Meanwhile, the synthetic in-situ case shows that the predicted permeability could be underestimated by up to one third, and the errors due to laboratory analysis that neglect the stress dependency of α will propagate to and amplify the errors of prediction for the in-situ permeability-depth relation.

Experimental study on the effective stress law and permeability of damaged sandstone under true triaxial stress

The effective stress law and the permeability play a notable role in dealing with the gas-solid coupling problem of porous media . The key parameter to quantify the influence of pore pressure to effective stress is the effective stress coefficient α ij . However, current relevant researches are mainly focused on the pore elastic flow characteristics in the elastic stage or hydrostatic pressure under conventional triaxial stress state, which are difficult to reflect the actual formation stress condition. To this end, the present study was conducted to investigate the influence of induced damage on the effective stress coefficient and the permeability of sandstone under true triaxial stress. The results showed that the effective stress coefficient and the permeability were closely related to the damage evolution and fracture propagation . α ij exhibited obvious anisotropy, α 1 was larger than α 2 and α 3 , and α 3 > α 2 appeared in the horizontal direction. α ij increased with increasing the fracture density and opening, even greater than unity. Increasing the initial horizontal stress could reduce α ij under the damage state. The elastic modulus E ij also exerted anisotropy during loading, E 1 basically exhibited an increasing trend followed by a decrease as the axial strain increased, E 2 and E 3 were continue to degrade with increasing the axial strain. Loading the deviatoric stress could cause damage, which induced the initiation and propagation of microcracks , and in turn led to the nonlinear stress-strain relationship and volume expansion of the rock, so the permeability increased, and it had increased sharply before reaching the peak strength. Under the influence of σ 2 , α ij first increased and then decreased with increasing the intermediate principal stress coefficient b under the damage stage. The porosity effect also affected the relationship between α ij and the permeability related to the induced damage, and α ij revealed an increasing trend as the permeability increased. • Effective stress coefficient a ij increases with fracture growth, even beyond unity. • a ij and E ij exhibit anisotropy with loading. a 1 is the largest, and a 3 > a 2 . • Increasing the horizontal stress can reduce a ij related to the induced damage. • a ij first decreases and then increases with increasing b under the damage state. • a ij increases with the increase in permeability attributed to the induced damage.

Investigation of poloxamer cell protective ability via shear sensitive aggregates in stirred aerated bioreactor

Mammalian cell cultivation in bioreactors is widely practiced in the pharmaceutical industry for production of monoclonal antibodies, vaccines and other therapeutic products. During cell culture, ensuring homogeneity and oxygen transport to the cultivation broth is essential for survival and proper cell growth. Due to the lack of a cell wall, mammalian cells are prone to damage by the gas aeration. Common practice how to protect mammalian cells against hydrodynamic forces is usage of poloxamers – synthetic, water-soluble nonionic copolymers. However, poloxamers are never pure compounds and the distribution of molecular weight strongly depends on the production process. This may lead to the final product containing impurities, which may have a negative impact on the protectivity of cells. Therefore, it is of high importance to know whether a particular poloxamer can be used as a cell protective agent. In this paper, we extend the usability of our method based on shear sensitive poly(methyl methacrylate) (PMMA) aggregate probes to investigate the protective capability of poloxamers. Comparative study of three different poloxamers and their impact on maximum effective hydrodynamic stress (τmax) and mass transfer coefficient (kLa) is conducted in the bench-scale 3.5 L Minifors bioreactor.

Coupled Seepage Mechanics Model of Coal Containing Methane Based on Pore Structure Fractal Features

The paper applies fractal theory to the structure of fractal coal pores and calculates the fractal dimension and integrated fractal dimension for each pore section &gt;100 nm, 100 nm &gt; d &gt; 5.25 nm, and &lt;2 nm. In the experiment, we performed the full stress–strain-seepage experiment of methane-bearing coal, revealed the deformation–seepage characteristics of methane-bearing coal under load, and deduced the dynamic prediction mechanical model of methane-bearing coal permeability based on pore heterogeneity, followed by practical verification. The results show that the permeability change in methane-bearing coal is an external manifestation of coal pore deformation, and the two are closely related and affected by changes in the effective stress coefficient. The derived fractal-deformation-coupled methane permeability mechanics model based on coal pore heterogeneity has high accuracy, a general expression for the stress–strain-permeability model based on coal heterogeneity is given, and the fractal Langmuir model is verified to be highly accurate (&gt;0.9) and can be used for coal reservoir permeability prediction.