Differential Energy Balance Research Articles

Artificial Neural Networks-based models for an internally cooled liquid desiccant dehumidifier

Abstract Air-conditioning systems condense air water vapor to achieve dehumidification. This process entails excessive cooling followed by reheating, resulting in high energy usage. As a more energy-efficient alternative, liquid desiccant-based dehumidification eliminates the need for excess cooling by dehumidifying through an absorption process. Advanced internally cooled liquid-desiccant dehumidifiers enhance overall air conditioning efficiency by incorporating internal cooling mechanisms. These devices are three-stream heat and mass exchangers, involving air, liquid desiccant, and cooling water. Simulating them involves discretization and solving comprehensive partial differential mass and energy balance equations to capture the interconnected heat and mass transfer phenomena. The models require detailed dehumidifier information, are computationally expensive, and pose challenges in convergence. These requirements make them unsuitable for integration into Building Energy Simulation software or inclusion within a comprehensive air-conditioning system model. This study aims to generate models with less computational demands during simulation using artificial neural networks. A comprehensive finite difference model was used to generate training data for developing the neural network. Various network configurations were explored to assess their impact on prediction precision. The trained network, integrated into an independent code, underwent evaluation for prediction accuracy using a distinct dataset from the training stage, proving accurate to simulate the internally cooled dehumidifier, reaching R-values up to 0.96 for the 5 predicted outlet variables. This is the initial step towards incorporating neural network models into specialized Building Energy Simulation software, as the foundation for conducting system-level, transient, and long-term simulations.

New optimum configuration for the FGM rotating disc in gas turbines using combined thermal-mechanical analysis: An analytical approach

The gas turbine is one of the most suitable equipment for various applications. Usually, a gas turbine comprises a set of discs to maintain turbine blades. The rotating disc in gas turbines is one of the critical components affected by various thermal and mechanical loads. The current article considers a new rotating disc with variable thickness (power-law profile). The functionally graded material has been used as the disc material, and the disc’s properties vary with temperature and location. Therefore, the mechanical and thermal behaviours of the disc are a function of temperature and location. The differential energy balance equation has been derived for analysing the new disc. In the performed analysis, the conduction and convection heat transfer coefficients vary with temperature and location; thus, the derived final heat transfer equation has high nonlinearity. One of the efficient expansion methods, the so-called Differential Transformation Method (DTM), is used for the governed equation’s analytical solution, and the numerical solution is used for validation. Then, the stress analysis is performed using analytical expressions according to the temperature profile. The impacts of geometrical and thermophysical characteristics on the temperature and stress distribution are evaluated using the analytical solution in the new disc. The comparison of displacement and stresses in the new FGM disc and old discs shows that the thermo-mechanical performance of the new proposed disc is improved significantly.

SPyCE: A structured and tailored series of Python courses for (bio)chemical engineers

In times of educational disruption, significant advances in adopting digitalization strategies have been accelerated. In this transformation climate, engineers should be adequately educated to face the challenges and acquire the new skills imposed by Industry 4.0. Among these, one of the most highly requested tools is Python. To tackle these aspects, this work establishes a pedagogical framework to teach Python to chemical engineers. This is achieved through a hands-on series of Python courses (sPyCE), covering topics as chemical reaction engineering and machine learning. Part of the series has been embedded in the curriculum of a Bachelor’s-level course at the Technical University of Denmark (DTU). Overall, students found the course to be useful; using Python, they solved systems of differential equations, mass and energy balances, set stoichiometric tables, regressions, simulations and more. Motivated by the large applicability and relevance of the covered topics, sPyCE is made publicly available on GitHub.

Mapping of operating windows for methane and ethane pyrolysis in the pulsed compression reactor by experiments and modelling

By modelling and experiments optimal operating conditions for methane (between 1000 and 3000 K, 300 bar) and ethane pyrolysis (between 800 and 3200 K, 400 bar) in the pulsed compression reactor (PCR) were evaluated. The PCR is a free piston reactor that can compress a gas from atmospheric pressure up to 600 bar in a single pulse. A differential internal energy balance was used for solving the temperature and pressure during the compression. The GERG-2008 equation of state was used to account for non-idealities. To predict the reaction products, both chemical equilibrium (EQ) and kinetic models available from literature were evaluated. The kinetic models (GRI-mech, Holmen et al., 1995 etc.) did not predict part of the experiments well. The EQ model predicts trends well. Therefore, the EQ model was used to map the operating domains. The aim is to reach a maximum concentration of products (olefins and aromatics) in the product gas and a conversion of 20% or more. For methane pyrolysis at 1600 K and 320 bar with nitrogen as diluent and an initial gas temperature of 588 K, the model analysis led to an experimentally observed factor 5.2 increase in ethylene in the outlet (1.4%mol) compared to a previous optimum point (Slotboom et al., 2021). With ethane pyrolysis 9% of ethylene was obtained at a conversion of 66% with an ethylene selectivity of 61% around 1480 K and 400 bar. Further analysis with the EQ model showed that for the thermal coupling of methane with an initial gas temperature of 773 K, conversion is possible without diluting with nitrogen. For ethane decomposition nitrogen is always needed as a diluent up to 773 K.

Limits of Performance of Polyurethane Blowing Agents

A MATLAB program was developed to simulate urethane-forming reactions by solving over a dozen differential equations, energy balance, mass balance, and constitutive equations simultaneously. The simulation program was developed for half a decade to simulate the basic kinetics of polyurethane reactions and more complex phenomena that cannot be obtained in laboratories. In the current investigation, the simulation is applied to determine the limits of the performance of polyurethane foam formation. n-pentane, cyclohexane, and methyl formate were used as physical blowing agents, and water was used as a chemical blowing agent. The simulation code increases the accuracy of the results and makes the foam performance process less time- and money-consuming. Specifically, the MATLAB code was developed to study the impact of physical and chemical blowing agents at different loadings on the performance of rigid polyurethane foams. Experimental data were used to validate the simulation results, including temperature profiles, height profiles, and the tack-free time of urethane foam reactions. The simulation results provide a window for the proper type and the optimum amount range of different physical and chemical blowing agents.

Comprehensive analysis of design software application in solar distillation units

The use of solar stills in rural regions are becoming increasingly popular as it is an economical solution for drinking water from saline water sources. Many researchers have worked for the improvement of conventional solar still to enhance productivity. Costly and time-consuming processes of operation in solar stills encourage many scholars to analyze mathematical simulation. This paper presents comprehensive reviews of the application of different design software to solar still systems. Design software is essential for developing and analyzing the mathematical models and predicting the most suitable performance parameters for the enhanced production rate of distilled water for still systems. Numerical modeling of solar still systems is necessary to analyze and investigate air movement, temperature variation for knowing water temperature, and air temperature through software like CFD, MATLAB, FORTRAN, TRYNSYS AutoCAD. The simulation technique's application using CFD is made with TRNSYS, FLUENT, ANSYS, FORTRAN and MATLAB which are useful tools to develop such mathematical models for the prediction of flow parameters. Engineering Equation Solver (EES) package and COMSOL Multiphysics solve the differential energy balance equation. All newly developed software employed for the utility of still solar systems is discussed. This article provides a comprehensive overview of the various software tools used in solar still to help researchers, scientists, and academicians.

An Analytical Study of Internal Heating and Chemical Reaction Effects on MHD Flow of Nanofluid with Convective Conditions

This research investigates the influence of the combined effect of the chemically reactive and thermal radiation on electrically conductive stagnation point flow of nanofluid flow in the presence of a stationary magnetic field. Furthermore, the effect of Newtonian heating, thermal dissipation, and activation energy are considered. The boundary layer theory developed the constitutive partial differential momentum, energy, and diffusion balance equations. The fundamental flow model is changed to a system of coupled ordinary differential equations (ODEs) via proper transformations. These nonlinear-coupled equations are addressed analytically by implementing an efficient analytical method, in which a Mathematica 11.0 programming code is developed for numerical simulation. For optimizing system accuracy, stability and convergence analyses are carried out. The consequences of dimensionless parameters on flow fields are investigated to gain insight into the physical parameters. The result of these physical constraints on momentum and thermal boundary layers, along with concentration profiles, are discussed and demonstrated via plotted graphs. The computational outcomes of skin friction coefficient, mass, and heat transfer rate under the influence of appropriate parameters are demonstrated graphically.

Kinetic modeling of industrial steam cracker

A comprehensive mathematical model is a very useful tool for the selection of feedstock, optimized cracker product mix, downstream production planning, and optimized plant performance. As a part of achieving this prime objective, a mathematical model has been developed for the simulation of the radiation section of a steam cracker unit. The model involves solving differential component, energy, and momentum balance equations numerically to generate temperature, concentration, and pressure profiles along the length of the reactor tube. The model has been developed in FORTRAN using the lSODE solver. The model considers 19 free radicals and 35 molecules connected over 433 reactions. The model was used to simulate the performance of propane and ethane cracking. The model predicted propane conversion is 95.55 against the plant data of 95% at a coil outlet temperature of 845 ​°C and the corresponding predicted ethylene and propylene yield is 34.49 and 11.53% respectively. The model has been validated for ethane cracking performance. The model predicted ethylene yield is in good agreement with that of plant values for ethane cracking. The model provides a basis for the optimization of process parameters for the given geometry. The model is useful to answer what-if questions and to investigate operational strategies.

Continuous integrated filtration, washing and drying of aspirin: digital design of a novel intensified unit

Abstract Within the recent modernization of pharmaceutical manufacturing, an important milestone consists in developing enabling technologies for end-to-end continuous production of drug products. Continuous filtration, washing and drying of active pharmaceutical ingredients from mother liquors in upstream manufacturing are critical steps for achieving end-to-end continuous production. In this work, we develop a mathematical model for a novel intensified carousel system capable of continuously filtering, washing and drying a slurry stream into a dry crystals cake. The mathematical model consists of detailed dynamic differential mass, energy and momentum balances, capable of tracking the solvents and impurities content in the cake (critical quality attributes) across the entire carousel. We successfully demonstrate the model features by identifying the probabilistic design space in a simulation study for the isolation of aspirin crystals in the carousel, accounting for model uncertainty through Monte Carlo simulations.

Modeling of Infrared Radiation Drying Traction Engine Insulation by Energy Balance Equation

The article describes the proposed way of applying the energy balance equation to simulate the drying of traction engines using infrared radiation through the gradual implementation of simulation, refining model parameters at each stage. This allows one to select the optimal parameters of the design and operation modes of hardware systems of the accelerated drying of thermal insulation efficiently and with a high degree of accuracy. One of the simplest approaches to mathematical models from the point of view of machine computing calculations is to compose a differential energy balance equation. However, this approach reduces the accuracy of the results due to the assumptions that are used in the process of creating mathematical models. To solve this problem, a new approach based on multi-structural dynamic mathematical models is proposed. The developed model allows one to determine the temperature of the conductor and polymer insulation heating, taking into account the specified properties. The application of the Matlab Simulink software module facilitates this process by increasing only the number of blocks.

Development and computational fluid dynamics (CFD) simulation of cryostat thermal shielding for a portable high purity germanium (HPGe) gamma spectrometer

The effect of vacuum degradation in cryostat of a gamma spectrometer on the steady-state temperature of thermal shield and its efficiency are analyzed in this study. Considering the thermal load due to radiation, the thermal conductivity of residual gases and shield supports, the steady-state temperature of the shield is determined based on the differential energy balance equation for a simplified thermal model of the cryostat. A more complex model corresponding to the design of a real cryostat is simulated using computational fluid dynamics. The obtained temperature distribution is presented. The simulated results are compared with experimental data measured on an operating cryostat with a cryocooler in the temperature stabilization mode. The same measurements were carried out for a cryostat with and without a thermal shield, as well as with multilayer insulation. The obtained results confirm that the thermal shield provides decreasing heat transfer even for a vacuum degradation in a cryostat.

Model establishment and performance evaluation of a modified regenerative system for a 660 MW supercritical unit running at the IPT-setting mode

Abstract: Improving denitrification efficiency of supercritical unit for peak load regulation by changing feed water temperature has become a focus of thermal power engineering under wide load. However, the effect mechanism of feed water temperature on the performance of supercritical unit is indistinct absolutely at the intermediate point temperature (IPT)-setting mode, which obstructs the performance optimization and the excavation of energy saving of supercritical unit with a change of feed water temperature aims at improving denitrification efficiency of supercritical unit. For the purpose, a closed cycle theory in which thermal power unit operating parameters interact and form a closed influence mechanism was defined and proposed, with such a core ideology, the performance analysis and assessment models under IPT-setting mode is constructed on the differential theory, energy balance and thermodynamics method, and the accuracy of established model is verified. These developed models are applied to assess the operational performance and to identify energy saving potential of supercritical unit for peak load regulation. Subsequently, a typical 660 MW ultra-supercritical coal fired power plant is selected as a reference case. Not only a quantitative analysis of effect of increasing feed water temperature adding HP heaters on supercritical unit performance is performed, but the effect of reducing feed water temperature stopping HP heaters on supercritical unit performance is implemented as well at the IPT-setting mode. Finally, the influence mechanism of feed water temperature on boiler thermal efficiency, steam turbine thermal consumption rate, standard coal consumption rate, power generation, denitrification efficiency, NOx production, steam temperature and other operating parameters of supercritical unit is absolutely revealed on IPT-setting mode. The investigation results show that the sensitivity of feed water temperature to supercritical unit performance varies greatly in different range of feed water temperature, especially when the feed water temperature is heated to the near the pseudo critical temperature, a dramatic change would take place in operation parameters of supercritical unit. Such a viewpoint is presented rigorously that increasing feed water temperature does not always achieve energy saving for supercritical units, also contrary to the existing viewpoint.

Modeling and simulation of cooling water systems subjected to fouling

This paper presents the modeling and simulation of cooling water systems, encompassing the cooling tower, the pump, the set of interconnected pipe sections, and the coolers. The model is composed of mass, energy, and mechanical energy balances, also contemplating the influence of the fouling rate in the heat exchangers. The simulation can determine the flow rates and temperatures along the network for each time instant during the investigated time period. The fouling rate evaluation considers its dependence with local temperature and velocity. Consequently, the heat exchanger equations are not represented by analytical solutions, but by differential energy and mechanical energy balances which allow the determination of the fouling rate at each point along the heat exchanger surface (i.e. the fouling thermal resistance and the corresponding deposit thickness are calculated at each point along the thermal surface of each cooler). The utilization of the proposed approach is demonstrated through three examples of cooling water systems. The first example contains one cooler and illustrates that the system behavior is the result of the hydraulic and thermal interactions among its elements (cooling tower, pump, pipe sections, and coolers), which indicates that analysis focusing on isolated elements may compromise the accuracy of the simulation results. The second example explores the inclusion of control loops in the proposed model. The third example is composed of three coolers and analyzes the interactions of multiple exchangers aligned in parallel, which shows that the behavior of each cooler in the network depends on the operation of the other exchangers in the system.

Fast and reliable flux map on cylindrical receivers

The thermal design of external solar receivers is a complex problem, in which the main input is the flux caused by the entire heliostat field on the cylindrical receiver surface. In this work, a fast and reliable model of flux distribution on the cylindrical receiver is proposed. This new cylinder flux map is based on the HFLCAL model for the analytic flux density sent by a heliostat on its image plane and the projection, in the direction of the central reflected ray, of any point in the plane image onto the cylindrical surface. The heliostat flux density includes shading and blocking, cosine of the incidence angle, atmospheric attenuation and effective reflectivity. A differential energy balance supports the coherence of the new model, i.e. the power contained in a differential of area in the image plane has to be equal to the power contained in the projected differential of area onto the cylinder. As an application of this new flux distribution on cylindrical receivers, we present the receiver sizing for a Noor III-like 150 MWe plant, with 7400 heliostats, in which the minimum LCOE gives the receiver diameter and a preliminary receiver height. With the help of the new flux map, this height is analysed to verify the maximum allowable flux. A multi-aiming strategy suggested by Vant-Hull (2002) and put into practice by Sanchez-Gonzalez and Santana (2015) is used to spread the hot spots along the receiver height. The PC CPU time to produce a coherent flux map on the cylinder is around six seconds.

Effect of Flowing Seawater on Supercritical CO2 - Superheated Water Mixture Flow in an Offshore Oil Well Considering the distribution of heat generated by the work of friction

The modeling of thermal fluid (mostly reported for saturated steam) flow in wells involving steady-state heat transfer inside wellbores and transient heat transfer in sea water or formation is reviewed and inherited. It is a good addition of modeling of supercritical/superheated fluid to the existing body of literature. The flow of supercritical CO2 coupled with superheated water (SHW) in offshore wells is described by means of the differential mass, energy and momentum balance equations along the vertical wellbores. The effect of supercritical CO2 on pressure and temperature of the multi-component thermal fluid is expressed in terms of the real gas model (the S-R-K model). The differential equations are solved with finite difference method on space involving the constant injection parameters at wellhead. It is found out that: (a). while seawater has a significant influence on temperature drop in wellbores, its effect on pressure profiles is weak. (b). both temperature and superheat degree decrease with increasing of the content of supercritical CO2. Besides, study of the effect of injection rate and pressure is conducted.

Water vapour transport in a soil column in the presence of an osmotic gradient

In arid and semi-arid regions because of water access and soil salinity problems extending of agriculture to a new area has been faced with restriction. Knowledge of the transport process of moisture and energy in subsurface soil is vital to understanding the environmental and economic impact of agricultural practices in these areas. This study was conducted to: (a) assess the relative importance of water vapour movement under moisture, temperature and osmotic gradients on moisture and energy budget in the presence of salts, (b) evaluate the temperature differential method to estimate evaporation in 30minute interval. The experiment was conducted in a sandy soil column that was buried in the field and irrigated with a pore volume of 50g/L NaCl solution. Three reference air-dried sandy soil cylinders were buried beside the column. Water content, temperature and electrical conductivity of soil water in depths of 1, 5 and 10cm of the column as well as surface temperature of soil column and air-dried soil cylinders; and temperature of 5cm depth in air-dried cylinders were monitored. The result showed that nearly 96% of vapour transfer was due to temperature gradient. Although the osmotic effect on vapour movement was less than 3%, nevertheless still was more than moisture gradient effect in current work. The contribution of the water vapour flux to the total moisture flux was 5%. The heat transported by vapour flux was significant and accounted for 45% of total heat flux in 1–5cm depth and up to 30% at 5–10cm depth. The observed difference between estimated cumulative evaporations using the differential method and energy balance equation was less than 5%.

Modeling and simulation of paraffin solubility in circular pipes in laminar regime flow

Abstract The paraffinic wax deposition of the crude oil reduces pipe’s flow area, causing, consequently, larger costs for the oil industry. The solubilization of paraffin using solvents is a viable solution, especially in pipes within treatment plants and oil processing, where use other methods has been restricted, such as the “pig”. This paper proposes a method to calculate the paraffin wax solubility in solvent, based on solid–liquid thermodynamic approach for this was proposed a discredited mathematical model for heat and mass transfer. The simplified model is able to successfully reproduce many of the known trends of the paraffin solubility. These models were implemented in programming software, where it was possible to obtain results, as variations in the length of pipe, type of solvent and inlet temperature. The models produced adequate solutions, maintaining continuity of differential energy and mass balance equations, with a viable physical interpretation.

Creating Reduced Kinetics Models That Satisfy the Entropy Inequality

In simulating chemically reacting flows, the differential entropy inequality (the local form of the second law of thermodynamics) must be satisfied in addition to the differential mass, momentum, and energy balances. Previously, we have shown that entropy violations occur when using a global/reduced mechanism. Herein we show that entropy violations also occur when using a detailed/skeletal/reduced mechanism. Using a recent theorem of “Slattery et al. (2011, “Role of Differential Entropy Inequality in Chemically Reacting Flows,” Chem. Eng. Sci., 66(21), pp. 5236–5243),” we illustrate how to modify a reduced chemical kinetics model to automatically satisfy the differential entropy inequality. The numerical solution of a methane laminar flame was improved when using reduced chemical kinetics modified in this way. In addition, an ad hoc temperature limiter is no longer necessary.

Analytical solution for combined heat and mass transfer in laminar falling film absorption with uniform film velocity – Isothermal and adiabatic wall

In the present study the Laplace transform is applied to the partial differential equations obtained from the differential energy and absorbate balances for the combined heat and mass transfer problem in laminar falling films with uniform film velocity.By means of the inverse Laplace transform an analytical solution is provided for the isothermal as well as for the adiabatic wall boundary condition. Temperature and mass fraction profiles across the film as well as the evolution of the absorbed mass flux as a function of the flow length are presented for the adiabatic wall condition as well as for the isothermal wall with different wall temperatures. Furthermore, the influence of the Lewis number on the absorbed mass flux is discussed.In addition, the present method allows to apply other wall boundary conditions than the isothermal or the adiabatic wall boundary, which will be addressed in a subsequent study.

Modeling US adult obesity trends: a system dynamics model for estimating energy imbalance gap.

We present a system dynamics model that quantifies the energy imbalance gap responsible for the US adult obesity epidemic among gender and racial subpopulations. We divided the adult population into gender-race/ethnicity subpopulations and body mass index (BMI) classes. We defined transition rates between classes as a function of metabolic dynamics of individuals within each class. We estimated energy intake in each BMI class within the past 4 decades as a multiplication of the equilibrium energy intake of individuals in that class. Through calibration, we estimated the energy gap multiplier for each gender-race-BMI group by matching simulated BMI distributions for each subpopulation against national data with maximum likelihood estimation. No subpopulation showed a negative or zero energy gap, suggesting that the obesity epidemic continues to worsen, albeit at a slower rate. In the past decade the epidemic has slowed for non-Hispanic Whites, is starting to slow for non-Hispanic Blacks, but continues to accelerate among Mexican Americans. The differential energy balance gap across subpopulations and over time suggests that interventions should be tailored to subpopulations' needs.