Fluid Transport Model Research Articles

Visualized analysis of microscale rock mechanism research: A bibliometric data mining approach

Rock mechanics is an indispensable discipline in diverse sectors, from resource retrieval to disaster mitigation. Diving deeper into this field, particularly into microscale rock mechanics, offers strategic insights and potential advancements for rock engineering practice. The objective of this research is to map the scientific production tied to microscale rock mechanics to date. In doing so, we perform a bibliometric analysis to look over and discuss the performance of the related literature. The conceptual fabric of microscale rock mechanics research, constituted by four central themes, was revealed and visualized through a text mining analysis. These areas include (1) modeling and simulation of fluid flow and transport within porous media, (2) characterizing fracture and failure in rocks, (3) understanding the deformation mechanism in response to geological processes, and (4) studying the mechanical properties of rocks subjected to extreme conditions. Lastly, an upcoming research agenda for microscale rock mechanics was proposed, centered on addressing three identified research gaps: (I) the integration of geological processes to characterize mineral properties, (II) the augmentation of fracture predictions achieved through multiscale modeling of rock heterogeneity, and (III) the exploitation of Artificial Intelligence technologies for anticipating complex fracturing scenarios. This comprehensive approach promises to enrich our understanding of rock mechanics and its applications.

Influence of pore length non-uniformity on transport properties of random nanopore networks

The modeling of fluid transport in nanoporous materials has long attracted attention because of the numerous industrial applications of such materials, particularly in membrane-based separations, and others such as adsorptive gas separation and storage, catalysis, and the emerging area of nanofluidics. While effective medium theory has been widely used in modelling this transport, a critical approximation that all pores have the same length is commonly made, whose adequacy is unknown. Here we apply effective medium theory to a randomly overlapping capillary model having an inherent pore length distribution related to the pore radius distribution, and compare the network transport properties with those of the commonly used uniform pore length random network. We find that the consideration of nonuniform pore length distribution leads to significantly higher effective diffusivity and lower associated apparent tortuosity, mediated by the lower mean pore length of large pores due to their higher probability of overlap. The decrease in pore length with an increase in pore radius and the competing effects of adsorption and diffusion, lead to more complex behaviour of the transport properties with variation in temperature and relative standard deviation of the pore radius distribution. Our results clearly demonstrate the importance of considering nonuniformity of pore length, as the conventional uniform pore length approximation leads to significantly different and therefore misleading results.

Inhomogeneous Fluid Transport Modeling in Dual-Scale Porous Media Considering Fluid-Solid Interactions.

Dynamics of fluid transport in ultratight reservoirs such as organic-rich shales differ from those in high-permeable reservoirs due to the complex nature of fluid transport and fluid-solid interaction in nanopores. We present a multiphase multicomponent transport model for primary production and gas injection in shale, considering the dual-scale porosity and intricate fluid-solid interactions. The pore space in the shale matrix is divided into macropores and nanopores based on pore size distribution. We employ density functional theory (DFT) to account for fluid-solid interactions and to compute the inhomogeneous fluid density distribution and phase behavior within a dual-scale matrix. The calculated fluid thermodynamic properties and transmissibility values are then integrated into the multiphase multicomponent transport model grounded in Maxwell-Stefan theory to simulate primary oil production from and gas injection into organic-rich shales. Our findings highlight DFT's adeptness in detailing the complex fluid inhomogeneities within nanopores─a critical concept that a cubic equation of state does not capture. Fluids within pores are categorized into confined and bulk states, restricted by a threshold pore width of 30 nm. Different compositions of fluid mixtures are observed in macropores and nanopores: heavier hydrocarbon components preferentially accumulate in nanopores due to their strong fluid-solid interactions. We utilize the developed model to simulate hydrocarbon production from an organic-rich shale matrix as well as CO2 injection into the matrix. During primary hydrocarbon production, strong fluid-solid interactions in nanopores impede the mobility of heavy components in the near-wall region, leading to their confinement. Consequently, heavy components mostly remain within the nanopores in the shale matrix during primary hydrocarbon production. During the CO2 injection process, the injected CO2 alters fluid composition within macropores and nanopores, promoting fluid redistribution. Injected CO2 engages in competitive fluid-solid interactions against intermediate hydrocarbons, successfully displacing a considerable number of these hydrocarbons from the nanopores.

Ti/Te effects on transport in EAST low q95 plasmas

Enhanced confinement is observed in EAST low q95 ( q95<3.5 ) plasmas with the temperature ratio ( Ti/Te ) increasing. A statistically significant positive correlation between H98y2 and Ti/Te has been established. Increased Ti triggerd by Neutral Beam Injection in experiments maintaining constant Te leads initially to an improved Ti/Te ratio, which subsequently mitigates heat transport in the ion channel. The Trapped Gyro–Landau Fluid transport model was applied to analyse the dependence of the turbulent transport on Ti/Te . Simulation results demonstrate that the Ion Temperature Gradient mode is stabilized in high Ti/Te plasma, with ion flux results from predictive modelling further validating this effect. These findings corroborate the Weiland model and complement one another. This study contributes to a deeper understanding of how the dimensionless parameter Ti/Te influences plasma transport, and helps demonstrate the feasibility of operations under the low q95 condition required for the ITER-inductive scenario in the new Ti/Te regime.

Pore scale modeling of fluid transport in complex reservoirs: Multi-scale digital rock construction, flow experiments and simulation methods

Pore scale modeling of fluid transport in complex reservoirs: Multi-scale digital rock construction, flow experiments and simulation methods

New Lie Symmetries and Exact Solutions of a Mathematical Model Describing Solute Transport in Poroelastic Materials

A one-dimensional model for fluid and solute transport in poroelastic materials (PEMs) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary cases, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated, and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

A source-to-surface model of heat and fluid transport in the Taupō Rift, New Zealand

We construct 2-D numerical models of bulk heat and water transport from the mid-crust (10 km depth) to the surface in a 20 km-wide continental rift, based on observations from the Taupō Rift in the central Taupō Volcanic Zone (TVZ) of New Zealand.The model represents a simplified geological setting with two low-permeability basement-like rock-types, the first defining the margins of the rift and the second a distinct ‘rifted basement’. The rift is overlain with a 2 km-thick, 20 km-wide layer of shallow volcanic infill. At the base of model there is a 10 km-deep heat source (the ‘hotplate’) with a specified TVZ-like heat flux of 0.77 Wm−2 and a ‘target’ average hotplate temperature of 700o to 900 °C, required to maintain the low melt fractions at ∼10 km depth inferred from geophysics.Parameterising the permeability of the rifted basement is a key part of the paper as it enables both the heat flux boundary condition and a temperature constraint to be satisfied at the hotplate. More generally, it allows the flexibility to control the depth of temperature contours which represent proxies for geophysical measurements. It is described as a power-law for log10(horizontal component of permeability, kh) with specified values of kh at two depths and a power law exponent as free parameters. Viable models which satisfy all constraints for the hydrothermal system beneath the TVZ rift have a power-law exponent less than ∼0.4, shallow (2 km deep) kh's of 10–14.0 to 10–13.0 m2, and deep (10 km) kh‘s <10–16.5 m2. The vertical component of the rifted basement permeability, kv, is ten times higher than kh.A generic feature of the models is that irregular, unsteady convection occurs in the upper ∼5 km of the rift. This results in temporal and spatial fluctuations in heat and fluid flow which are interpreted as high-temperature TVZ-like geothermal systems which have temperatures of ca. 300 °C at 2 km depth. Over the nominal simulation time of 3 Myr, approximately 40% of the geothermal systems are clustered within ∼2 km of the rift margins, with the remainder distributed roughly uniformly across the rift. Between the geothermal systems cool recharge from the surface occurs, with temperatures as low as 50 °C occurring at 5 km depth. The models successfully match temperature proxies for the depths of maximum seismicity (450 °C) and shallowest partial melt (> 700 °C) inferred from geophysical observations.Heat transport within the rift is dominated by convection. This is true even at 10 km depth, at the base of the geothermal systems, where kh in the rifted basement approaches 10−17 m2. In this situation, the relatively large value of vertical permeability kv, ∼ 10−16 m2, allows convection to occur. Conductive heat transport dominates in regions ∼1 km in vertical extent immediately above the hotplate and between the geothermal systems.The vigour of the hydrothermal systems is controlled by the permeability of the shallow volcanics, through which all cold surface recharge and hot outflows of fluid occur. Models with low permeability for the shallow volcanics produce longer lasting and higher temperature geothermal systems, and those with high permeability produce fewer and cooler geothermal systems.

Multiscale modelling of fluid transport in vascular tumours subjected to electrophoresis anticancer therapies

Electrophoresis facilitated cancer treatment has demonstrated experimental efficacy in enhancing drug delivery within vascularised tumours. However, the lack of realistic mathematical models with direct measurements in the context of electrochemotherapy poses a challenge. We investigate the impact of an applied electric potential on the flow of Darcian-type fluid occurring in two distinct phases: the tumour and healthy regions. We employ the asymptotic homogenisation technique, assuming that the macroscale of the tumour domain is larger than the microscale characterised by vessel heterogeneities. We retain information about the microstructure by encoding information in the homogenised coefficients. We take into account both vascularisation and the microscale variations of the leading order and fine scale electric potential. The resulting effective differential problem reads as a Darcy-type system of PDEs, where the flow is driven by an effective source. The novel model can be used to predict the effect of an applied electric field on cancerous biological tissues, paving a new way of improving current electrochemotherapy protocols.

Design and field-scale demonstration of the buoyant-kill process for restoring integrity of wells with sustained casing pressure

Sustained Casing Pressure (SCP) is the persistent casinghead pressure resulting from the well’s annular integrity loss and migration of gas above the leaking cement sheath. Downhole—intervention methods for SCP removal employ workover rigs to access and plug off the leaking annulus at depth from within the well. The inexpensive rig-less method of Buoyant Kill involves surface injection of immiscible heavy fluid at the casinghead into the well’s annulus to replace the annular fluid column above the gas-leaking cement and stop gas migration. Laboratory and pilot-size testing have shown feasibility of the method. Presented here, is a field-scale demonstration experiment conducted in a pressurized 2750-foot well with water displaced by an immiscible brominated organic fluid over 20-h long operation. Discussed is experimental design supported by fluid selection study, benchtop and pilot tests, and fluid transport model. Also analyzed is the process performance and operational problems. The results confirm feasibility of the Buoyant Kill technique for SCP removal. The overall change of the wellhead and downhole pressures follows the expected patterns indicating partial removal of the simulated SCP. The removal is incomplete due to pumping pressure pulses and wellhead pressure variations resulting in some emulsification of the two fluids and partial loss of the injection fluid into the overflow. The results show that wellhead pressure control and injection pump operation are critical for successful SCP removal using the Buoyant Kill technique.

Recent advancements of CFD and heat transfer studies in pyrolysis: A review

There is a pressing need to process the solid waste by using pyrolysis technology due to its uniqueness to produce various solid, liquid and gaseous products. However, further understanding of pyrolysis process is needed. Most importantly, the role of computational fluid dynamics (CFD) in pyrolysis is to be thoroughly investigated. In recent times, there has been significant progress in the research works aligned with evaluating the role of CFD in biomass pyrolysis. Hence, the current review manuscript focusses the current state of the art in the application of CFD tools to multi-scale biomass pyrolysis systems. Modeling of fluid and heat transport in conventional pyrolysis reactors, microwave-assisted pyrolysis reactors, and solar-assisted pyrolysis reactors for the conversion of biomass have been critically analyzed. The theoretical basis and the practical applicability of the CFD models to efficiently emulate and predict the overall complexity of pyrolysis process for the multi-scale and multi-phase nature of biomass have been discussed. However, the validity and accuracy of the CFD models needs to be enhanced. In the future directions, the steps for expanding the applicability of these theoretical and computational models have been outlined. This review would provide detailed understanding of CFD role in pyrolysis process conducted in various reactor systems.

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow.

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations uses lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, acute respiratory distress syndrome (ARDS), hypoalbuminemia, and effects of PEEP. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Clinically useful solution forms are provided allowing calculation of interstitial fluid pressure, crossflows, and critical capillary pressures. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature. That creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow provides an explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium is self-clearing.

The Revised Starling Hypothesis: Modeling the impact of the glycocalyx on vascular refilling during ultrafiltration in humans

The glycocalyx lines systemic capillaries and influences the distribution of osmotic forces across the capillary between the intravascular and interstitial compartments. By creating a pericapillary space between the capillary and the interstitium with a low osmotic pressure, the predicted and measured water flux at the distal end of systemic capillaries is outward under physiological conditions – contrary to the prediction of the traditional Starling model of capillary fluid transport. This has led to a ‘revised’ Starling model in which the predicted the movement of water from the capillary into the interstitium is consistently outward, and the return of water from the interstitial compartment necessary to maintain intravascular volume occurs nearly exclusively through the lymphatic system. We developed a methematicl model of the revised Starling Hypothesis that is applicable to the whole body in the special circumstance of hemodialysis, where the contributions of renal function to blood volume regulation may be ignored, and the total input and output of water and solutes are controlled and measured as part of the process of hemodialysis. We created a revised, two compartment (vascular+interstitial space), Starling model using the quantitative model of Facchini et al. (Microvasc. Res. 94:52-63, 2014) that describes capillary transport through the glycocalyx (albeit as normalized dimensionless values). We modelled the return of interstitial water to the vascular space through lymphatic flow based on the interstitial pressure (Possenti et al., Micro. Vasc. Res. 122:101-110, 2019), and we estimated the interstitial pressure based upon the formulation of Chapple et al. (Comp. Meth, and Prog. In Biomed. 41: 33-54,1993). We used the two-compartment model (intravascular and extravascular spaces) developed by de los Reyes et al. (J. Theoret. Biol. 390:146-155, 2016) to analyze transcapillary fluxes based on the traditional Starling model, and we embedded the description of fluxes across glycocalyx developed by Facchini et al. to decribe the fluxes of solutes and water across the glycocalyx and peri-glycocalyx/sub-capillary space and added control of lymphatic function within this two-compartment model to create a revised Starling model. The traditional and revised models were evaluated using data from periods of ultrafiltration in which the hematocrit (Crit-line), body weight and measured fluid input or ultrafiltrate removed were measured, and we compared the predicted fluxes of solvent and solutes across the capillary and through the lymphatic system between the traditional and revised Starling models. The two models lead to dramatically different predictions—all of the fluid transported out of the capillary must come back via the lymphatics according to the revised Starling model. This places vital importance upon the lymphatic flow during vascular refilling when blood volume is reduced and must be repleted to maintain stable cardiac function. Partially funded by the Renal Research Institute This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Modeling and numerical simulation of non-Newtonian arterial blood flow for mild to severe stenosis

The fundamental cause of coronary heart disease is thought to be atherosclerosis. Blood flow in arteries under plaque formation is widely studied using both experimental and theoretical methods in literature. This paper presents a comprehensive study on the mathematical modelling and numerical simulation of non-Newtonian blood flow in an idealized stenosed artery. Non-Newtonian behavior of blood flow is assumed by Casson and Quemada fluid models. An analysis is performed for four forms of stenosis, 50%, 60%, 70%, and 80%, which are defined by a narrowing of the artery's diameter. The mathematical model for non-Newtonian fluid transport is presented in the form of highly nonlinear coupled partial differential equations. A finite-volume approach is used to solve the system of equations numerically. The solutions are obtained using a hybrid mesh with hexahedron and tetrahedron control volumes. Numerical solutions are validated first with experimental results from the literature for a Newtonian fluid, and then the results are extended to non-Newtonian fluid models. It can be observed that the non-Newtonian nature of the fluid model influences flow dynamics and is a significant aspect to consider for arteries with small diameter. The velocity and pressure drop rise as the degree of stenosis develops. Wall shear is substantially larger in stenotic passages and severity of stenosis is directly related with this increasing behavior.

A Double-Permeability Poroelasticity Model for Fluid Transport in a Biological Tissue

A Double-Permeability Poroelasticity Model for Fluid Transport in a Biological Tissue

An in silico approach to understanding the interaction between cardiovascular and pulmonary lymphatic dysfunction.

The lung is extremely sensitive to interstitial fluid balance, yet the role of pulmonary lymphatics in lung fluid homeostasis and its interaction with cardiovascular pressures is poorly understood. In health, there is a fine balance between fluid extravasated from the pulmonary capillaries into the interstitium and the return of fluid to the circulation via the lymphatic vessels. This balance is maintained by an extremely interdependent system governed by pressures in the fluids (air and blood) and tissue (interstitium), lung motion during breathing, and the permeability of the tissues. Chronic elevation in left atrial pressure (LAP) due to left heart disease increases the capillary blood pressure. The consequent fluid accumulation in the delicate lung tissue increases its weight, decreases its compliance, and impairs gas exchange. This interdependent system is difficult, if not impossible, to study experimentally. Computational modeling provides a unique perspective to analyze fluid movement in the cardiopulmonary vasculature in health and disease. We have developed an initial in silico model of pulmonary lymphatic function using an anatomically structured model to represent ventilation and perfusion and underlying biophysical laws governing fluid transfer at the interstitium. This novel model was tested against increased LAP and noncardiogenic effects (increased permeability). The model returned physiologically reasonable values for all applications, predicting pulmonary edema when LAP reached 25 mmHg and with increased permeability.NEW & NOTEWORTHY This model presents a novel approach to understanding the interaction between cardiac dysfunction and pulmonary lymphatic function, using anatomically structured models and biophysical equations to estimate regional variation in fluid transport from blood to interstitial and lymphatic flux. This fluid transport model brings together advanced models of ventilation, perfusion, and lung mechanics to produce a detailed model of fluid transport in health and various altered pathological conditions.

The role of surface forces in environment-enhanced cracking of brittle solids

Fracture initiation and propagation in brittle materials is promoted in surface-reactive (sorptive) environments, a phenomenon known as subcritical crack growth (SCG). Laboratory measured crack-propagation velocity vs. stress intensity factor relationships typically exhibit highly nonlinear, multi-stage characteristics that are sensitive to environmental factors such as adsorbate concentration and temperature. For practical purposes, empirical relationships (e.g., a power law) have been used to describe this complex phenomenon. However, how the overall SCG behavior emerges from the underlying fundamental processes near the crack tip, such as the interaction of the crack surfaces separated by only a few nanometers and mass transport within the nano-confined space, is still not well understood. This paper develops a mechanistic, surface-force-based fracture theory (SFFT) which integrates surface force models, fluid transport models, and linear elastic fracture mechanics to quantitatively explain the multi-stage characteristics of SCG in brittle solids. A numerical model is developed based on SFFT and solved through an implicit partitioned scheme for efficiency and modularity. The results are validated by Wiederhorn's data on crack propagation in soda-lime glasses at a wide range of relative humidity levels. We show that, for the first time, the entire range of an SCG curve can be captured by a single physics-based model. The predicted SCG curves reveal that the development of repulsive disjoining pressure behind the crack tip can be responsible for the reduced apparent fracture toughness in a sorptive environment. The shape of the SCG curve, and its changes with respect to the environment, is found to critically depend on the assumed transport models.

A Microfluidic Model of AQP4 Polarization Dynamics and Fluid Transport in the Healthy and Inflamed Human Brain: The First Step Towards Glymphatics‐on‐a‐Chip (Adv. Biology 12/2022)

A Microfluidic Model of AQP4 Polarization Dynamics and Fluid Transport in the Healthy and Inflamed Human Brain: The First Step Towards Glymphatics‐on‐a‐Chip (Adv. Biology 12/2022)

Computational pulmonary edema: A microvascular model of alveolar capillary and interstitial flow.

We present a microvascular model of fluid transport in the alveolar septa related to pulmonary edema. It consists of a two-dimensional capillary sheet coursing by several alveoli. The alveolar epithelial membrane runs parallel to the capillary endothelial membrane with an interstitial layer in between, making one long septal tract. A coupled system of equations is derived using lubrication theory for the capillary blood, Darcy flow for the porous media of the interstitium, a passive alveolus, and the Starling equation at both membranes. Case examples include normal physiology, cardiogenic pulmonary edema, noncardiogenic edema Acute Respiratory Distress Syndrome (ARDS) and hypoalbuminemia, and the effects of positive end expiratory pressure. COVID-19 has dramatically increased ARDS in the world population, raising the urgency for such a model to create an analytical framework. Under normal conditions, the fluid exits the alveolus, crosses the interstitium, and enters the capillary. For edema, this crossflow is reversed with the fluid leaving the capillary and entering the alveolus. Because both the interstitial and capillary pressures decrease downstream, the reversal can occur within a single septal tract, with edema upstream and clearance downstream. Overall, the interstitial pressures are found to be significantly more positive than values used in the traditional physiological literature that creates steep gradients near the upstream and downstream end outlets, driving significant flows toward the distant lymphatics. This new physiological flow may provide a possible explanation to the puzzle, noted since 1896, of how pulmonary lymphatics can function so far from the alveoli: the interstitium can be self-clearing.

Causative Role of Anoxic Environment in Bacterial Regulation of Human Intestinal Function.

Life on Earth depends on oxygen; human tissues require oxygen signaling, whereas many microorganisms, including bacteria, thrive in anoxic environments. Despite these differences, human tissues and bacteria coexist in close proximity to each other such as in the intestine. How oxygen governs intestinal-bacterial interactions remains poorly understood. To address to this gap, we created a dual-oxygen environment in a microfluidic device to study the role of oxygen in regulating the regulation of intestinal enzymes and proteins by gut bacteria. Two-layer microfluidic devices were designed using a fluid transport model and fabricated using soft lithography. An oxygen-sensitive material was integrated to determine the oxygen levels. The intestinal cells were cultured in the upper chamber of the device. The cells were differentiated, upon which bacterial strains, a facultative anaerobe, Escherichia coli Nissle 1917, and an obligate anaerobe, Bifidobacterium Adolescentis, were cultured with the intestinal cells. The microfluidic device successfully established a dual-oxygen environment. Of particular importance in our findings was that both strains significantly upregulated mucin proteins and modulated several intestinal transporters and transcription factors but only under the anoxic-oxic oxygen gradient, thus providing evidence of the role of oxygen on bacterial-epithelial signaling. Our work that integrates cell and molecular biology with bioengineering presents a novel strategy to engineer an accessible experimental system to provide tailored oxygenated environments. The work could provide new avenues to study intestine-microbiome signaling and intestinal tissue engineering, as well as a novel perspective on the indirect effects of gut bacteria on tissues including tumors. The online version contains supplementary material available at 10.1007/s12195-022-00735-x.

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review.

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality.