Mass Transfer Equations Research Articles

Effects of Congestion in Human Lung Investigated Using Dual-Scale Porous Medium Models.

Chronic obstructive pulmonary disease (COPD) is a primary chronic respiratory disease associated with pulmonary congestion that restricts airflow and thereby affects the exchange of gases between the alveoli and the blood capillaries in the lungs. Dual scale-global and local-porous medium models have been developed and reported in this work, to study the effects of air-side congestion on the blood-oxygen content in the alveolar region of the human lung. The human lung is model as a global, equivalent, heterogeneous porous medium comprising three zones with distinct permeabilities related to their progressively complex branching structure. Airflow for each breathing cycle is determined by solving mass and momentum transfer equations across the three porous medium zones. The congestion is introduced by appropriate modification of the porous medium properties of the zones considered. The congestion-affected air velocity reaching Zone 3 is given as input to a separate "local model" employed at several locations of the alveoli of Zone 3. The local model determines the oxygen content in the blood flow in the capillaries of the alveoli by solving suitable mass, momentum and species transport equations. The transient simulation results performed for a long duration of multiple breathing cycles, demonstrate that a normal, healthy human lung is functional for up to 40% volume congestion or when 50% of the lung is congested to about 23.5%. Increasing congestion beyond this value, quickly-within a few hours-depletes the oxygen exchange in the blood flow of the alveolar region (of Zone 3), leading to hypoxemia. The effects of congestion progression on oxygen exchange dynamics determined through the dual-scale porous medium modelling approach provide researchers and medical professionals with in silico predictive estimates to generate treatment strategies for chronic respiratory diseases.

Quick Computing CFD Model to Predict Chemical Pollution in Room

Purpose. The problem of accidental contamination of workspaces attracts special attention, since in the event of such extreme situations, intense chemical contamination of the air in work areas occurs. This poses a threat of toxic exposure to workers. When assessing the consequences of such situations, it is necessary to take into account the time factor, in particular, to quickly determine the creation of concentrations of chemically hazardous substances. In this regard, an urgent task is to develop effective mathematical models for rapid assessment of the consequences of extreme situations in the working areas of chemically hazardous facilities. The paper considers a CFD model for analyzing the process of chemical air pollution in a workspace during an accidental release of a chemically hazardous substance. The solution of the problem is based on the numerical integration of the fundamental equations of continuum mechanics. Methodology. To calculate the air velocity field in the working room during the operation of supply and exhaust ventilation, a mathematical model of the motion of an inviscid fluid was used. The equation of convective diffusion motion was used to calculate the concentration of a chemically hazardous substance in the workspace. The integration of the modeling equations was carried out using finite difference schemes. Findings. A dynamic model has been created to calculate the spread of a chemically hazardous substance in a workspace. On the basis of the built CFD model, a computer program was created to conduct a computational experiment. Originality. A CFD model has been created to predict the level of air pollution in a workspace in the event of toxic gas emissions. The model is based on the fundamental equations of aerodynamic mechanics and mass transfer. The model makes it possible to determine the effect of the ventilation mode, the intensity of emission of a chemically hazardous substance, the location of equipment in the workspace, and the dynamics of the formation of concentration fields. Practical value. The developed CFD model can be used to quickly analyze the consequences of accidental emissions of a chemically hazardous substance in a workplace and assess the risk of toxic exposure of workers.

Modeling the Influence of Raleigh Numbers on Thermal and Fluidic Behaviors in a Trapezoid-shaped Cell

We model the influence of Raleigh numbers in a trapezoidal cavity. One wall among the sloping walls is exposed to a heat flux density Q=100 W/ m<sup>2 </sup>and the other inclined wall is kept adiabatic. The temperature of the two horizontal walls is assumed to be constant such that T<sub>sup</sub>=305K is greater than T<sub>inf</sub>=300K. The equations of heat and mass transfer which direct our template are described by the Navier-Stockes equation. These equations are discretized using the finite difference method and solved by the Thomas and Gauss-Seidel algorithms. Thus, we analyze the effects of the Raleigh numbers (<i>Ra</i>) on temperature profiles T = 303.15 K and speeds v = 0 m/s. For a variation of <i>Ra</i>=10<sup>3</sup>-10<sup>5</sup>, we note that the convective exchanges of the confined air and the different walls become preponderant with the increase in the Rayleigh number. Also, we contact that the speed of the confined air remains high along the horizontal walls for a <i>Ra</i> high number, but low near the inclined walls. These results show the effects of natural convection in this trapezoidal cavity.

Modeling of the Nanofiltration Process Based on Convective Diffusion Theory

The article formulates the state of the problem of improving the theoretical calculation of the nanofiltration kinetic characteristics in the time cycle of separation of industrial solutions containing copper(II), iron(III), trisodium phosphate and OP-10 (a wetting agent used in electroplating, a product of treating a mixture of mono- and dialkylphenols with ethylene oxide) using the equations of convective diffusion, hydrodynamics and mass transfer. To calculate the kinetic characteristics of the nanofiltration process, the mathematical model was improved by numerically solving the equations of convective diffusion, the Navier–Stokes equation and the flow continuity equation in a polar coordinate system with initial and boundary conditions. The theoretical results obtained in the process of an analytical solution of the system of equations allow calculating changes in concentrations in the permeate and retentate tracts and the permeate volume during nanofiltration separation. The acceptability of the developed nanofiltration method for separating solutions is assessed by comparing the calculated data according to the mathematical model with the experimental data obtained on the nanofiltration unit during separation of solutions containing copper(II), iron(III), trisodium phosphate and OP-10.

Comparative numerical study of the energy performance of two different configurations of a hybrid photovoltaic/thermal air collector

Solar energy is a renewable alternative to fossil fuels. When solar energy is converted into electricity by photovoltaic (PV) solar modules, the heat generated increases the temperature of the PV solar cells and, as a result, reduces their electrical efficiency. Several techniques are used to cool PV solar cells in order to reduce their operating temperature. One technique is the use of hybrid photovoltaic/thermal (PVT) solar collectors, which simultaneously produce electricity and useful heat. In the airflow channel, the heat and mass transfer equations and those derived from the energy balance on the solid layers of the collector were discretized using the finite difference method with an implicit alternating directions (ADI) scheme. All the algebraic equations obtained after discretization were solved using the Thomas algorithm. The aim is to make a numerical comparison of the energy performance of the Verre-PV-Tedlar and Verre-PV-Verre flat-plate air PVT hybrid solar collectors in the climatic conditions of Lomé, Togo. Under the same operating conditions, the average electrical efficiencies of the Verre-PV-Verre and Verre-PV-Tedlar flat-plate air PVT hybrid collectors are 15.34% and 13.85% respectively. There is a 1.49% improvement in electrical efficiency for a Verre-PV-Verre air-source PVT hybrid collector compared with a Verre-PV-Tedlar PVT hybrid collector. The Verre-PV-Verre flat plate PVT air hybrid collector has an average daily electrical energy gain of 0.564 kWh and a thermal energy gain of 0.839 kWh, while the Verre-PV-Tedlar flat plate PVT air hybrid collector has an average daily electrical energy gain of 0.548 kWh and a thermal energy gain of 1.403 kWh.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Theoretical investigations on the purification of petroleum using desulfurization process: Analysis and optimization of process

This paper introduces a comprehensive approach for predicting chemical concentrations (C) of sulfur compound in a two-dimensional space (x, y) by numerical solution of mass transfer equation and integration of machine learning. Data of training/validation are obtained from mass transfer modeling on adsorption separation utilizing porous adsorbent for petroleum desulfurization. Mass transfer modeling data were utilized for machine learning models which included three different regression models, namely Support Vector Machine (SVM), Decision Tree Regression (DT), and Multilayer Perceptron (MLP). The hyper-parameters of these base models were optimized using the Grey Wolf Optimization (GWO) algorithm. The ensemble models, denoted as ADA-DT, ADA-MLP, and ADA-SVM were assessed based on key performance metrics, including R2, MAE, RMSE, and MAPE. Results demonstrated the efficacy of the ensemble models in capturing complex relationships within the dataset. ADA-DT obtained an exceptional R2 score of 0.99031, highlighting its outstanding predictive accuracy. Similarly, ADA-MLP and ADA-SVM showed great accuracy, achieving R2 of 0.88272 and 0.96842, respectively. In this study, we uncover valuable insights into the application of ensemble methods and hybridized optimization methods for accurate and robust regression modeling in chemical concentration prediction scenarios applicable for petroleum engineering.

Improved Fracture Permeability Evaluation Model for Granite Reservoirs in Marine Environments: A Case Study from the South China Sea

Permeability is a crucial parameter in the exploration and development of oil and gas reservoirs, particularly in unconventional ones, where fractures significantly influence storage capacity and fluid flow. This study investigates the fracture permeability of granite reservoirs in the South China Sea, introducing an enhanced evaluation model for planar fracture permeability based on Darcy’s law and Poiseuille’s law. The model incorporates factors such as fracture heterogeneity, tortuosity, angle, and aperture to improve permeability assessments. Building on a single-fracture model, this research integrates mass transfer equations and trigonometric functions to assess intersecting fractures’ permeability. Numerical simulations explore how tortuosity, angle, and aperture affect individual fracture permeability and the influence of relative positioning in intersecting fractures. The model makes key assumptions, including minimal consideration of horizontal stress and the assumption of unidirectional laminar flow in cross-fractures. Granite outcrop samples were systematically collected, followed by full-diameter core drilling. A range of planar models with varying fracture apertures were designed, and permeability measurements were conducted using the AU-TOSCAN-II multifunctional core scanner with a steady-state gas injection method. The results showed consistency between the improved model and experimental findings regarding the effects of fracture aperture and angle on permeability, confirming the model’s accuracy in reflecting the fractures’ influence on reservoir flow capacity. For intersecting fractures, a comparative analysis of core X-ray computed tomography (X-CT) scanning results and experimental outcomes highlighted discrepancies between actual permeability measurements and theoretical simulations based on tortuosity and aperture variations. Limitations exist, particularly for cross-fractures, where quantifying complexity is challenging, leading to potential discrepancies between simulation and experimental results. Further comparisons between core experiments and logging responses are necessary for model refinement. In response to the challenges associated with evaluating absolute permeability in fractured reservoirs, this study presents a novel theoretical assessment model that considers both single and intersecting fractures. The model’s validity is demonstrated through actual core experiments, confirming the effectiveness of the single-fracture model while highlighting the need for further refinement of the dual-fracture model. The findings provide scientific support for the exploration and development of granite reservoirs in the South China Sea and establish a foundation for permeability predictions in other complex fractured reservoir systems, thereby advancing the field of fracture permeability assessment.

Process intensification in the direct contact membrane distillation (DCMD) desalination by patterning membrane surface: A CFD study

In this research, the impact of pattern geometry on the intensification of the performance of surface patterned membranes for saline water desalination by direct contact membrane distillation (DCMD) is investigated by computational fluid dynamics (CFD) simulation. The Comsol Multiphysics software was applied to solve the governing transport equations for heat, momentum, and mass transfer. The result of the model was validated by the published experimental data, and the maximum deviation was <10 %. The target was to maximize the permeate flux by altering surface pattern geometry and dimensions. Based on the previous studies, a prism pattern was chosen in this work, and the influences of pattern type (3 types), pattern dimension (25–150 µm valley depth), and the distance between the valleys (0–400 µm) were studied on the temperature polarization coefficient (TPC) and DCMD permeate flux. The results showed that the pattern with a valley depth of 25 µm and a distance between the valleys of 300 µm had the best performance in DCMD operation. In this situation and feed temperature of 80 °C, a TPC of 0.78 and a water flux of 49.3 kg m-12.h were attained. The characteristics of flow close to the patterned membrane surface were also investigated, and it was observed that there are weak shear stresses in the lower zone of the valleys, while stronger shear stresses are created in the upper regions that are responsible for improving the TPC and water flux in the patterned membranes.

Numerical investigation of turbulent mass transfer processes in turbulent fluidized bed by computational mass transfer

Turbulent fluidized bed possesses a distinct advantage over bubbling fluidized bed in high solids contact efficiency and thus exerts great potential in applications to many industrial processes. Simulation for fluidization of fluid catalytic cracking (FCC) particles and the catalytic reaction of ozone decomposition in turbulent fluidized bed is conducted using the Eulerian–Eulerian approach, where the recently developed two-equation turbulent (TET) model is introduced to describe the turbulent mass diffusion. The energy minimization multi-scale (EMMS) drag model and the kinetic theory of granular flow (KTGF) are adopted to describe gas–particles interaction and particle–particle interaction respectively. The TET model features the rigorous closure for the turbulent mass transfer equations and thus enables more reliable simulation. With this model, distributions of ozone concentration and gas–particles two-phase velocity as well as volume fraction are obtained and compared against experimental data. The average absolute relative deviation for the simulated ozone concentration is 9.67% which confirms the validity of the proposed model. Moreover, it is found that the transition velocity from bubbling fluidization to turbulent fluidization for FCC particles is about 0.5 m·s–1 which is consistent with experimental observation.

Exact analytical solution of the equations for a quasiequilibrium two-phase domain: permeability and interdendritic spacing

This study is concerned with the theoretical description of a quasi-stationary process of directional crystallization of binary melts and solutions in the presence of a quasi-equilibrium two-phase region. The quasi-equilibrium process is ensured by the fact that the system supercooling is almost completely compensated by heat released during the phase transformation. Quasi-stationarity of the process determining constancy of the crystallization rate is ensured by given temperature gradients in the solid and liquid phases. The system of heat and mass transfer equations and boundary conditions to them under these assumptions is dependent on a single spatial variable in the reference frame moving with the crystallization rate relative to a laboratory coordinate system. Exact analytical solutions to the formulated problem in parametric form are obtained. The parameter of the solution is the solid phase fraction in a two-phase region. The distributions of temperature and impurity concentration in the solid, liquid and two-phase regions of the crystallizing system, the rate of solidification, and the spatial coordinate in the two-phase region depending on the solid phase fraction in it are found. An algebraic equation for the solid phase fraction at the interface between the solid material and the two-phase region is derived. Exact analytical solutions show that the impurity concentration in the two-phase layer increases as the solid phase fraction increases. Moreover, the solid phase fraction at the interface solid phase — two phase region and its thickness increase as the temperature gradient in the solid phase and the solidification rate increase. The developed theory allows us to determine analytically the permeability of the two-phase region and a characteristic interdendritic spacing in it. Analytical solutions show that the relative permeability in the two-phase region increases from a certain value at the interface with the solid phase to unity at the interface with the liquid phase. The selection theory of stable dendritic growth allows us to determine analytically a characteristic interdendritic distance in the two-phase layer that decreases as the temperature gradient in the solid phase increases. An increase of impurity in the molten phase gives a decrease in the interdendritic spacing within a two-phase region.

DEVELOPMENT OF THE THEORY OF GAS FUEL COMBUSTION TAKING INTO ACCOUNT MODERN KINETIC MECHANISMS OF COMBUSTION

An actuality of modernizing advancement the modern adopted combustion theory is due to a significant change in the composition of fuels at the market of developed countries by rejection of basic mineral (organic) fuels (fossil fuels), which have been used in the world for 250 years. The transformation of traditional fuels’ orientation towards an application of carbon-free fuels, primarily to hydrogen and its mixtures with natural gas. Each way of mentioned activity is connected with to ensure an environmental decarbonisation. Criteria for evaluating the CO2 emissions by fuels’ choice and selection have been proposed while numerical calculations of the specific CO2 content in the combustion products of the hydrocarbon-hydrogen mixture jʹ and j have been evaluated. It is possible to reduce these values when adding the shared H2 in the fuels (m3 CO2/ MJ; kg CO2/ MJ). Considering the combustion process in combustion systems (combustion chambers, boilers, furnaces) at constant pressure (p =const, dp =0 — isobaric process), the enthalpy of the reactants’ flow of the mixture (total (chemical) enthalpy I) can serve as a measure of the specific energy of the reacting mixture. An approach is proposed, according to which the main equations of heat and mass transfer in the torch (premixed flame) are composed basing upon the principle of conservation the total (chemical) enthalpy representing energy as basic function. The basic approach to the development of a modern combustion theory is focused on the concept of T. von Karman, according to which the combustion process is considered as “aerothermochemistry”, i.e. the description of physical and chemical processes is based on the combination of heat and mass transfer equations with chemical kinetics’ equations. At the current period, the problem of chemical kinetics (burning process) is considered through the combustion mechanisms of basic fuels, which consist of a large number of equations for molecules and particles involved in process at various stages of the combustion — from the preheating of the reaction mixture and through the stage of ignition (or self-ignition) — to the final temperature of flue gases. The laminar combustion velocity SL is a determinative characteristic of the combustible properties of gas fuels and, accordingly, of the safety restrictions by the fuel choice. Quantitative values of SL for the separate basic fuels, including the hydrogen, both the organic (fossil fuels) and alternative ones could be differed by an order of magnitude and more. The problem of estimable forecasting the SL value provides an option of the composition of the fuel-oxidant mixture in the industry, power and municipal energetics. The SL value’s prediction makes an especially important action at the current stage of modelling completion with an account of the global warming and by preventing an excess of CO2 emissions, including involvement of hydrogen-containing gases by substitution the carbon-friendly fuels, firstly the fossil fuels. The contemporary theory of combustion has been developed by extensive use the adequate kinetic mechanism GRI-Mech 3.0, the universality of which has been confirmed by our calculations of SL values for a wide range of the gas fuels — from methane CH4 to hydrogen H2 and their mixtures. An advanced modern theory of combustion using the adequate and approved GRI-Mech 3.0 combustion kinetic mechanism has been developed. The universality of this mechanism is confirmed by our calculations of SL values for a wide range of gaseous fuels — from methane CH4 to hydrogen H2 and their mixtures (mixed gases MG). For further analysis and development, the model of combustion in the reacting flow by Y.B. Zeldovich and D.A. Frank-Kamenetsky was used, considering the transfer processes of total enthalpy I as the energy characteristic of the combustible mixture. The kinetic component (on the example of natural gas) is taken into account using the combustion mechanism for GRI-Mech 3.0. The latter summarizes the combustion process of through 325 constituent reactions for 53 components. The adequacy of the combustion model proposed in the paper is confirmed by numerical examples of the coincidence of numerical SL values: ours — calculated; literary — experimental. The validity of experimental values of SL is provided by the use of different methods of measuring the SL. Calculations of the specific total enthalpy I of the reacting mixture along the length x º l (thickness of the front for a homogeneous flame in a one-dimensional formulation) have been performed as a result of researches confirmed the initial position: I(x) = const with deviations for CH4 +7 % / –2 %; for H2 +9,2 % / –2,8 % in relation to the heat of combustion. Bibl. 52, Fig. 9, Tab. 3.

Simulation of plaque formation in a realistic geometry of a human aorta: effects of endothelial layer properties, heart rate, and hypertension.

Nowadays, cardiovascular diseases are the most common cause of death worldwide. Besides, atherosclerosis is a cardiovascular disease that occurs with persistent narrowing of arteries, especially medium and large-sized arteries. Atherosclerosis begins with a local elevation in the permeability of the arterial wall as a result of endothelial inflammation. Subsequently, excess LDL permeates into the arterial wall. Then, through several chemical responses and reactions, foam cells are produced. These foam cells serve as a crucial indicator for assessing the development of atherosclerosis within the arteries. In this study, the effect of endothelial layer modeling, heart rate (HR) and hypertension on the foam cell accumulation is numerically investigated in a patient-specific geometry of the human thoracic aorta. Navier-Stokes, Darcy, and mass transfer equations are used to obtain the velocity and concentration field within the domain. Regarding the dependence of endothelial cell properties on time-averaged wall shear stress, it is observed that foam cells are mainly concentrated in the outer curvature of the aortic arch, downstream of the left subclavian artery. However, considering oscillatory-shear-rate as the determinant of endothelial cell properties leads to the accumulation of foam cells in the inner curvature of the descending aorta. Regarding the HR, with the increase of HR, the volume average concentration of the foam cell decreases. However, there is no substantial difference between the cases of different HRs. Moreover, foam cell concentration significantly increases in the hypertension case. This result implies that a slight increase in the blood pressure may induce irreparable problems in the circulatory system.

Predicting the Consequences of an Emergency at a Railway Station

Purpose. The paper considers the problem of determining the size of the damage zones in the event of an emergency at a railway station due to a tanker fire. The task of forecasting is to determine the zones of thermal pollution, as well as chemical and mechanical pollution. The main objective of the study is to create numerical models for calculating the zones of mechanical and thermal pollution in the event of a fire at a railway station. Methodology. To analyze the size and intensity of zones of thermal, chemical, and mechanical environmental pollution in the event of an extreme situation at a railway station, we used the equations of heat and mass transfer and Newton's second law for modeling mechanical environmental pollution. To solve the equations, numerical methods such as Euler's method and finite difference schemes were used. On the basis of the developed numerical models, a computer code was created to conduct a computational experiment. Findings. Modern computer models for assessing the zones of chemical, thermal, and mechanical pollution in the event of an extreme situation have been developed. The results of computer modeling are presented. Originality. A set of numerical models for computer simulation of heat and mass transfer processes and dynamics of point motion has been created, which allows conducting a computational experiment to determine the contamination zones during a fire at a railway station. Practical value. A computer code was developed on the basis of the created mathematical models. This code is a tool for solving important problems in the field of environmental safety and civil protection. The computer code makes it possible to quickly determine the intensity and size of environmental pollution zones in the event of an extreme situation.

Computational experiment in creating a virtual design system for drum dryerswith a heat pump

One of the effective areas of research of real technological processes is the creation of virtual processes and its components. In the work, virtual computer models have been created that establish a connection between the mathematical model of the drying process and the simulated design of a two–section drum dryer equipped with an absorption water–ammonia heat pump. To simulate the drying process, a mathematical model based on differential equations of heat and mass transfer A.V. Lykov, algorithmic and software of the drying process were used and a single virtual system was created that allows simulating the drying process of cereals, oilseeds and legumes in a drum dryer in real time over a wide range of regime parameters. To conduct a computational experiment in one of the CAD systems, a three–dimensional visualization of a drum dryer was performed and a graphical shell of the LabVIEW environment was used with a set of all the tools necessary for data collection, analysis and presentation of the results obtained. 3D execution of the drum dryer in CAD (computer–aided design system) made it possible to simulate the real conditions of its operation, compare alternative options and select the best design solutions.

New dimensionless equation for mass transfer at acetone evaporation under forced convection

Equations of evaporation rate were collected from literature for different liquids. These relationships directly result in the evaporation rate or the Sherwood number. Experiments were made for vaporization of acetone from a heated vessel, at different air velocities and temperatures of air and liquid surface. The effect of the different setting parameters, and the different directions of the heat flow on the evaporation rate were studied. As expected, when the air velocity and the temperature of the liquid were higher, the evaporation was faster, but when the temperature of the air was higher, the evaporation rate was lower. Based on the measurement results, a new dimensionless equation was created to determine the evaporation rate of acetone. The new equation and the correlations from the literature were compared with the results determined from the measurement data. Two of the ten correlations did not prove to be applicable to the measurement results, three correlations showed serious deviations, while five correlations gave fairly good results. Among these five correlations, the new dimensionless equation proved to be the most accurate for determining the evaporation rate of acetone in the examined range.

Model development using hybrid method for prediction of drug release from biomaterial matrix

A comprehensive multi-scale computational strategy was developed in this study based on mass transfer and machine learning for simulation of drug concentration distribution in a biomaterial matrix. The controlled release was modeled and validated via the hybrid model. Mass transfer equations along with kinetics models were solved numerically and the results were then used for machine learning models. We investigated the performance of three regression models, namely Decision Tree (DT), Random Forest (RF), and Extra Tree (ET) in predicting medicine concentration (C) based on r and z data. Hyper-parameter optimization is conducted using Glowworm Swarm Optimization (GSO). Results revealed high predictive accuracy across all models, with ET demonstrating superior performance, achieving a coefficient of determination value (R2) of 0.99854, an RMSE of 1.1446E-05, and a maximum error of 6.49087E-05. DT and RF also exhibit notable performance, with coefficients of determination equal to 0.99571 and 0.99655, respectively. These results highlight the effectiveness of ensemble tree-based methods in accurately predicting chemical concentrations, with Extra Tree (ET) Regression emerging as the most promising model for this specific dataset.

Modeling and optimization for the continuous catalytic reforming process based on the hybrid surrogate optimization model

To address the modeling and optimization challenges of the complex reaction system in the continuous catalytic reforming process, a new integrated simulation and optimization framework is presented. First, a detailed mechanism model is established based on a reaction network involving 32 components and 50 reactions, coupled with mass transfer, heat transfer, pressure drop, and catalyst deactivation equations. Then, to solve the differential-algebraic equations in the mechanism model, a multi-objective hybrid optimization method with the adaptive infill strategy is introduced. GAMS and MATLAB are integrated to perform a joint iterative solution. Finally, two cases are conducted with the proposed algorithm. Results show that the mechanism model calculation deviations are below 4 % of reactor temperature, pressure, and composition distribution, and the Pareto front of various production plans is obtained. The accurate simulation and rapid trade-off optimization among the key goals can be achieved to provide scientific decision support for enterprise production.

Enhancing transport processes in stratified fluids: Exploring rotational and stretching effects coupled with magnetic fields, heat, mass transfer and thermal/solutal slip

This research paper presents an in-depth investigation into the complex interactions governing stratified fluid flow in the presence of rotational and stretching phenomena, magnetic field influences, heat and mass transfer effects, and the incorporation of thermal and solutal-slips at fluid interfaces. Stratified fluid systems are commonly encountered in various natural and industrial processes, ranging from geophysical flows to chemical engineering applications, making a thorough understanding of these phenomena paramount.The study commences by formulating a comprehensive set of governing equations that account for the unique interplay of these multifaceted physical phenomena. Integrating thermal and solutal slip conditions at fluid interfaces introduces innovative prospects for precisely controlling and manipulating mass and heat transfer in these systems. This research paper extensively explores layered fluid dynamics, encompassing phenomena such as rotation and stretching, influences from magnetic fields, effects of heat and mass transfer, and the examination of thermal and solutal slip conditions. The insights obtained from this study not only enhance our comprehension of multi-physics fluid dynamics but also offer practical implications for streamlining processes across diverse fields. The principal findings and implications of this research can be summarized as follows: Various factors that affect fluid flow exhibit evident and discernible patterns. The mathematical model includes the Navier-Stokes equations with rotational and stretching terms, the Maxwell equations describing magnetic field effects, and the transport equations for heat and mass transfer. Additionally, thermal and solutal slip conditions at the fluid interfaces are incorporated to capture boundary layer dynamics.Numerical simulations are conducted to explore the intricate dynamics arising from this amalgamation of physical effects. The results reveal complex flow patterns, including stratification, boundary layer development, and vortical structures, offering insights into the behavior of fluids under the joint influence of rotational and stretching phenomena, magnetic fields, and thermal and solutal gradients. Furthermore, the impact of key parameters, such as rotation rate, stretching rate, magnetic field strength, and concentration gradients, is systematically analyzed to elucidate their effects on flow characteristics, heat and mass transfer rates, and concentration profiles within the stratified fluid layers. The Soret effect, or thermophoresis, causes nanoparticles to migrate away from hot regions due to fluid molecule flow and high energy levels. Elevating ξNt results in decreased heat and mass transfer. The Prandtl number shows minimal influence on heat and mass transfer when increased. The disk separation, and fluid viscosity, significantly affect the rotational spectrum. As the rotational parameter increases, heat and mass transfer decrease.

Computational modeling of petroleum purification for removal of sulfur compounds: Process analysis for reduction of environmental impacts and material costs

In the course of this investigation, three machine learning models (Gaussian Process Regression, Decision Tree Regression, and Kernel Ridge Regression) were examined for determining the correlation between the input variables (x and y) which are spatial coordinates of model’s geometry, and the content of species in adsorption for sulfur capture. For the process modeling, mass transfer was analyzed, and the concentration distribution of sulfur compound was obtained via numerical solution of mass transfer equations, and then used for machine learning models. The machine learning models were trained using a dataset of 19,000 observations, and their performance was assessed through metrics including R2 score, MAE, and RMSE. Analysis of the results reveals that Decision Tree Regression surpassed the other two models in performance, with an R2 score of 0.9989, MAE of 6.64405E-01, and RMSE of 1.1277E+00. Gaussian Process Regression had an R2 score of 0.97106, MAE of 3.65541E+00, and RMSE of 5.6821E+00, while Kernel Ridge Regression had an R2 score of 0.86347, MAE of 8.26121E+00, and RMSE of 1.1330E+01. The Clonal Selection Algorithm was used for hyper-parameter optimization for all models. These findings demonstrate the potential of machine learning techniques for accurately and reliably predicting the concentration of chemical species and highlight the importance of considering the choice of model and hyper-parameter optimization for optimal performance.