A model of hindered solute transport in a poroelastic shale

1994 ◽  
Vol 445 (1925) ◽  
pp. 679-692 ◽  
Keyword(s):  
Pore Pressure ◽  
Direct Effect ◽  
Swelling Pressure ◽  
Solute Concentration ◽  
Solute Diffusion ◽  
Permeable Membrane ◽  
Coupled Diffusion ◽  
Final Steady State ◽  
Thermodynamic Pressure ◽  
Osmotic Pressure Difference

Theories for the transport of solvent and solute through an imperfect semi-permeable membrane are used as the basis for a model of transport through shale. The flow of solute is reduced, relative to that of solvent, by a transmission coefficient λ ≼ 1. In this model, it is assumed that the chemical composition of the pore fluid has no direct effect upon the swelling of the shale, other than via the thermodynamic pressure p . Invasion is governed by a pair of coupled diffusion equations. There is an initial, rapid diffusion of pressure, leading to a swelling pressure (1-λ) RT ∆ x / V w , where RT ∆ x / V w is the van’t Hoff osmotic pressure difference due to a change in solute mole fraction ∆ x . A subsequent slow diffu­sion process, dominated by diffusion of the solute, then occurs. A change in solute concentration has been assumed to have no direct effect upon the rock, and ultimately has no effect upon the pore pressure and stress. Nevertheless, imperfect exclusion of solute can lead to transient changes in pore pressure which might destabilize the shale before the final steady state is achieved. This is demonstrated by a poroelastic analysis of pressure and solute diffusion into rock surrounding a wellbore.

Laboratory assessment of semi-permeable properties of a natural sodium bentonite

2018 ◽  
Vol 55 (11) ◽  
pp. 1611-1631 ◽  
Author(s):  
Andrea Dominijanni ◽  
Nicolò Guarena ◽  
Mario Manassero
Keyword(s):  
Mechanistic Model ◽  
Effective Diffusion ◽  
Swelling Pressure ◽  
Solute Concentration ◽  
Transport Processes ◽  
Laboratory Assessment ◽  
Sodium Bentonite ◽  
Clay Particles ◽  
Chemical Osmosis ◽  
Multi Stage

The relevance of the semi-permeable properties of bentonites, which affect both their transport processes and mechanical behaviour, has been assessed through the experimental determination of three parameters: the reflection coefficient, ω; the osmotic effective diffusion coefficient, [Formula: see text]; and the swell coefficient, ϖ. Two multi-stage tests were conducted on a natural sodium bentonite, while varying both the specimen void ratio, e, and the solute concentration, cs, of the equilibrium sodium chloride (NaCl) solutions. The measured phenomenological parameters were interpreted through a mechanistic model, in which the electric charge of clay particles is taken into account via a single material parameter, [Formula: see text], referred to as the “solid charge coefficient”. A constant value of [Formula: see text] = 110 mmol/L was found to provide an accurate interpretation of the experimental data, at least within the investigated range of bentonite void ratios (3.33 ≤ e ≤ 4.18) and NaCl concentrations of the external bulk solutions (5 ≤ cs ≤ 90 mmol/L). The results support the hypothesis that both chemical osmosis and swelling pressure are macroscopic manifestations of the same interactions, which occur at the microscopic scale between the clay particles and the ions contained in the pore solution, and that both of them can be modelled through a single theoretical framework.

Coherency Strain Energy in any Crystal System: Applications to in Situ Observations of Cigm in Calcite

1990 ◽  
Vol 205 ◽  
Author(s):  
R.S. May ◽  
B. Evans
Keyword(s):  
Driving Force ◽  
Migration Rate ◽  
Strain Energy ◽  
Solute Concentration ◽  
Coherency Strain ◽  
Solute Diffusion ◽  
Boundary Orientation ◽  
In Situ Observations ◽  
And Migration

AbstractIn situ observations of CIGM in CaCO3 bicrystals with a SrCO3 solute source were made. The change in boundary orientation and migration rate were compared with solute concentration. The liquid film model for coherency strain Induced migration was generalized to any non-cubic system and applied to CaCO3-SrCO3. The coherent layer was modeled as a thin film on an infinite half-space. The strain energy was found from solution of the Hooke's law expressions transformed to the appropriate coordinate system. For triclinic or monoclinic films the strain tensor was found by an eigenvector decomposition of the transformation matrix that defined the lattice parameter change with composition. High anisotropy of Vegard's law constants for CaCO3-SrCO3 caused (111) to have the lowest coherency strain per unit solute. Surfaces perpendicular to (111) in coherent equilibria were predicted to have half the solute concentration and three times the migration driving force of those perpendicular to (111). However, no correlation between solute concentration and boundary orientation was observed. Ambiguous and contradictory evidence for a relationship between solute concentration, boundary orientation, and migration rate was found. The self-stress state of a grain boundary in a solute diffusion field may be better modelled as hydrostatic rather than plane stress. Hydrostatic compression may interact with the boundary excess volume and cause a PV driving force for migration. Predictions based on coherent equilibrium at a surface have not been tested for that geometry in calcite; they should be tested before they are applied to grain boundaries.

scholarly journals Forward Osmosis Membrane Technology in Wastewater Treatment

2021 ◽  
Author(s):  
Deniz Şahin
Keyword(s):  
Wastewater Treatment ◽  
Forward Osmosis ◽  
Solute Concentration ◽  
Membrane Technology ◽  
Membrane Process ◽  
Water And Wastewater Treatment ◽  
Concentration Difference ◽  
Permeable Membrane ◽  
Treatment Processes ◽  
Space Requirements

In recent times, membrane technology has proven to be a more favorable option in wastewater treatment processes. Membrane technologies are more advantageous than conventional technologies such as efficiency, space requirements, energy, quality of permeate, and technical skills requirements. The forward osmosis (FO) membrane process has been widely applied as one of the promising technologies in water and wastewater treatment. Forward osmosis uses the osmotic pressure difference induced by the solute concentration difference between the feed and draw solutions. The proces requires a semi-permeable membrane which has comparable rejection range in size of pollutants (1 nm and below). This chapter reviews the application of FO membrane process in wastewater treatment. It considers the advantages and the disadvantages of this process.

Two-Dimensional Pore Pressure Distribution Model to Evaluate Effects of Shale Semipermeable Membrane Characteristics

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Jia Wei ◽  
Yuanfang Cheng ◽  
Chuanliang Yan
Keyword(s):  
Diffusion Coefficient ◽  
Pressure Distribution ◽  
Pore Pressure ◽  
Effective Diffusion Coefficient ◽  
Early Stage ◽  
Drilling Fluid ◽  
Effective Diffusion ◽  
Solute Diffusion ◽  
Sensitivity Analyses ◽  
Distribution Model

During the drilling of shale formations, drilling fluids can intrude into the wellbore, raise the pore pressure, and lead to wellbore instability. Based on the thermodynamic theory, a new model was established to calculate pore pressure. The model considers the effects of solute diffusion and solution convection and conducts sensitivity analyses. The results show that the drilling fluid activity significantly affects the pore pressure distribution. The pore pressure under high drilling fluid activity will increase rapidly in the early stage. Low drilling fluid activity can effectively suppress the growth of pore pressure. And a low effective diffusion coefficient of solute and a high membrane efficiency also help to reduce pore pressure. Therefore, reducing drilling fluid activity should be conducted in priority in drilling fluid design. Lowering its solute effective diffusion coefficient and increasing its viscosity can also be considered as auxiliary methods.

scholarly journals The near-wellbore pressure calculation model incorporating thermochemical effect

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 623-630
Author(s):  
Zhiqiang Tang ◽  
Qian Li ◽  
Hu Yin
Keyword(s):  
Pore Pressure ◽  
Drilling Fluid ◽  
Solute Concentration ◽  
Calculation Model ◽  
Hydraulic Pressure ◽  
Fluid Temperature ◽  
Wellbore Instability ◽  
Wellbore Pressure ◽  
Pressure Calculation ◽  
Tight Formation

The potential difference of hydraulic pressure, solute concentration and temperature between the drilling fluid and the formation fluid can induce the flow of solvent and cause changes in the pore pressure during drilling a tight formation, which may result in wellbore instability. According to the continuity equation of fluid, the pore pressure calculation model considering the effect of thermochemical coupling is established and the solution of the pore pressure in the Laplace domain is given. Using this model, the effects of the temperature, solute concentration and viscosity of drilling fluid on the pore pressure around the wellbore are simulated. The results show that, when the wellbore pressure is higher than the formation pressure and the solute concentration of the drilling fluid is larger than that of the formation fluid, the near-wellbore pore pressure will decrease first and then increase during drilling a tight formation, and increasing the drilling fluid temperature will decrease the pore pressure. Increasing the solute concentration of the drilling fluid can inhibit the increase of the pore pressure.

Continuum and atomistic models of strongly coupled diffusion, stress, and solute concentration

2011 ◽  
Vol 196 (1) ◽  
pp. 361-370 ◽  
Author(s):  
Hamed Haftbaradaran ◽  
Jun Song ◽  
W.A. Curtin ◽  
Huajian Gao
Keyword(s):  
Solute Concentration ◽  
Strongly Coupled ◽  
Coupled Diffusion ◽  
Atomistic Models ◽  
Diffusion Stress

scholarly journals Changes in the plasmodesma structure and permeability at the bundle sheath and mesophyll interface during the maize C4 leaf development

2020 ◽  
Author(s):  
Peng Gao ◽  
Baijuan Du ◽  
Pinghua Li ◽  
Byung-Ho Kang
Keyword(s):  
Cell Wall ◽  
Organic Acids ◽  
Molecular Diffusion ◽  
C4 Photosynthesis ◽  
Solute Concentration ◽  
Bundle Sheath ◽  
Solute Diffusion ◽  
Cell Wall Modification ◽  
Maize Leaf ◽  
Kranz Anatomy

AbstractPlasmodesmata are intercellular channels that facilitate molecular diffusion between neighboring plant cells. The development and functions of plasmodesmata are controlled by multiple intra- and intercellular signaling pathways. Plasmodesmata are critical for dual-cell C4 photosynthesis in maize because plasmodesmata at the mesophyll and bundle sheath interface mediate exchange of CO2-carrying organic acids. We examined developmental profiles of plasmodesmata and chloroplasts in the maize leaf from young cells in the base to mature cell in the tip using microscopy approaches. Young mesophyll and bundle sheath cells in the leaf base had proplastids, and their plasmodesmata were simple, devoid of cytoplasmic sleeves. In maturing cells where Kranz anatomy and dimorphic chloroplasts were evident, we observed extensive remodeling of plasmodesmata that included acquisition of an electron-dense ring on the mesophyll side and cytoplasmic sleeves on the bundle sheath side. Interestingly, the changes in plasmodesmata involved a drop in symplastic dye mobility and suberin accumulation in the cell wall, implying a more stringent mesophyll-bundle sheath transport. We compared kinetics of the plasmodesmata and the cell wall modification in wildtype leaves with leaves from ppdk and dct2 mutants with defective C4 pathways. Plasmodesmata development, symplastic transport inhibition, and cell wall suberization were accelerated in the mutant lines, probably due to the aberrant C4 cycle. Transcriptomic analyses of the mutants confirmed the expedited changes in the cell wall. Our results suggest that a regulatory machinery at the mesophyll-bundle sheath boundary suppresses erroneous flux of C4 metabolites in the maize leaf.Significance StatementPlasmodesmata in the maize Kranz anatomy mediate the exchange of organic acids between mesophyll and bundle sheath. Since solute diffusion through plasmodesmata is governed by solute concentration gradients, a balanced distribution of C4 metabolites is critical for concentration of CO2 in the bundle sheath. Plasmodesmata bridging the mesophyll and bundle sheath cytoplasm have a cylindrical cavity, which can facilitate molecular movements, and a valve-like attachment. Construction of the sophisticated plasmodesmata was linked to C4 photosynthesis, and plasmodesmata assembly finished more rapidly in maize mutants with defective C4 pathways than in wild-type plants. These results suggest that the specialized plasmodesmata contribute to controlled transport of C4 metabolites.

Analysis of Chemo-Poro-Thermo-Mechanical Effects on Wellbore Strengthening

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Jia Li ◽  
Zhengsong Qiu ◽  
Hanyi Zhong ◽  
Xin Zhao ◽  
Weian Huang
Keyword(s):  
Heat Conduction ◽  
Pore Pressure ◽  
Thermal Convection ◽  
Drilling Fluid ◽  
Solute Concentration ◽  
Fracture Aperture ◽  
Strengthening Effect ◽  
Coupled Models ◽  
Fracture Width ◽  
Wellbore Strengthening

Abstract The application of wellbore strengthening treatment has less effect on shale formations. Several numerical studies were developed to describe the mechanism, which promoted the development of wellbore strengthening theory. Previous studies explored the mechanism mainly by considering the seepage flow. Therefore, multi-field coupled models were established to analyze the solute transmission, thermal convection, and heat conduction on wellbore strengthening by introducing the theory of multi-field coupling into physical model. First, the fracture width distribution and wellbore tangential stress were investigated to research the interaction of thermal and chemical effects with different gradients. Then, the concrete mechanism of temperature and solute concentration gradient was analyzed based on the distribution of pore pressure and stress field. Results show that the prediction of hoop stress and fracture aperture may not be accurate without considering the influence of solute transfer, thermal convection, and heat conduction, because stress state is mainly affected by temperature field and the pore pressure varies greatly under different chemical gradients. Additionally, the lower temperature and larger solute concentration improve the wellbore strengthening effect of drilling fluid.

Processes Related to the Water Uptake by EUROBITUM Bituminised Radioactive Waste: Theoretical Considerations and First Experimental Results

2008 ◽  
Vol 1107 ◽  
Author(s):  
An Mariën ◽  
Steven Smets ◽  
Xiangling Li ◽  
Elie Valcke
Keyword(s):  
Radioactive Waste ◽  
Water Uptake ◽  
Swelling Pressure ◽  
Management Program ◽  
Constant Volume ◽  
Constant Stress ◽  
Stress Tests ◽  
Permeable Membrane ◽  
Boom Clay ◽  
Clay Formation

AbstractAccording to the present Belgian radioactive waste management program, Eurobitum bituminised radioactive waste will be disposed of in a geologically stable underground clay formation. The Boom Clay is studied as a potential host formation because of its low diffusion and high retention properties towards radionuclides. The presence of the radioactive waste should not disturb these properties. Due to the presence of hygroscopic salts (25 to 30 weight% NaNO3), Eurobitum will take up pore water which will result in a swelling and possibly in a very high swelling pressure. First scoping calculations suggest that the swelling pressure exerted to Boom Clay should remain below 7 to 8 MPa to avoid the formation of fractures. If the bitumen in EUROBITUM behaved like a perfect semi-permeable membrane and if no swelling were allowed after the dissolution of NaNO3 into a saturated solution of 10.8 M, osmotic pressures of ∼50 MPa could be attained. To better understand the interaction between the swelling Eurobitum and the host formation, coupled hydro-chemical-mechanical constitutive laws for Eurobitum have to be developed. To this purpose, water uptake tests under constant volume (‘confined’) and constant stress (‘semi-confined’) conditions are being performed. After ∼2 years of hydration of small inactive Eurobitum samples in constant volume conditions, the swelling pressure has raised to ∼12 MPa. The volume of samples that can swell against counter pressures of 2.2, 3.3, or 4.4 MPa (constant stress tests) increased with ∼5 to 11 volume%, independently of the applied counter pressure. Approximately 10 weight% of the initial NaNO3 content has been leached.

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