Lumped Method Research Articles

Enhanced Solubility and Miscibility of CO2-Oil Mixture in the Presence of Propane under Reservoir Conditions to Improve Recovery Efficiency

The existence of propane (C3H8) in a CO2-oil mixture has great potential for increasing CO2 solubility and decreasing minimum miscibility pressure (MMP). In this study, the enhanced solubility, reduced viscosity, and lowered MMP of CO2-saturated crude oil in the presence of various amounts of C3H8 have been systematically examined at the reservoir conditions. Experimentally, a piston-equipped pressure/volume/temperature (PVT) cell is first validated by accurately reproducing the bubble-point pressures of the pure component of C3H8 at temperatures of 30, 40, and 50 °C with both continuous and stepwise depressurization methods. The validated cell is well utilized to measure the saturation pressures of the CO2-C3H8-oil systems by identifying the turning point on a P-V diagram at a given temperature. Accordingly, the gas solubilities of a CO2, C3H8, and CO2-C3H8 mixture in crude oil at pressures up to 1600 psi and a temperature range of 25–50 °C are measured. In addition, the viscosity of gas-saturated crude oil in a single liquid phase is measured using an in-line viscometer, where the pressure is maintained to be higher than its saturation pressure. Theoretically, a modified Peng–Robinson equation of state (PR EOS) is utilized as the primary thermodynamic model in this work. The crude oil is characterized as both a single and multiple pseudo-component(s). An exponential distribution function, together with a logarithm-type lumping method, is applied to characterize the crude oil. Two linear binary interaction parameters (BIP) correlations have been developed for CO2-oil binaries and C3H8-oil binaries to accurately reproduce the measured saturation pressures. Moreover, the MMPs of the CO2-oil mixture in the presence and absence of C3H8 have been determined with the assistance of the tie-line method. It has been found that the developed mathematical model can accurately calculate the saturation pressures of C3H8 and/or CO2-oil systems with an absolute average relative deviation (AARD) of 2.39% for 12 feed experiments. Compared to CO2, it is demonstrated that C3H8 is more soluble in the crude oil at the given pressure and temperature. The viscosity of gas-saturated crude oil can decrease from 9.50 cP to 1.89 cP and the averaged MMP from 1490 psi to 1160 psi at 50 °C with the addition of an average 16.02 mol% C3H8 in the CO2-oil mixture.

Suboptimal Analysis of the Differential System of the Conceptual Trailer Air Brake Valve

Motivation: To increase the efficiency of the brake valve by adding a corrective member. Background: The speed of response and smooth transition between modes of operation in the braking system are the primary research questions. Objective and research question: Will the optimal selection of the input parameters of the differentiating part of a conceptual brake valve ensure the speed of operation and enable a smooth transition from the accelerating mode to the tracking mode? Methods: The mathematical model of the differentiating part of the brake valve uses the lumped method, and the solution was obtained by numerical means. Results: Within the assumed range of variation of spring stiffness and control piston bore throughput, the distribution maps of action times and piston lift were determined, and the optimal configuration of the analyzed input parameters was obtained by a genetic algorithm. Future research: future activities will focus on the development of a system of smooth variation of the throughput of the connecting chamber of the differential part of the valve. Conclusions: The determined maps of functional parameter distributions are the basis for the selection of components of the braking system; optimization indicates the directions of modification of the valve in order to obtain an acceptable performance system.

Advancing bioethanol production with a new kinetic model based on structure-oriented lumping for cellulose conversion

Bioethanol, as a significant renewable energy source, plays a crucial role in alleviating the energy crisis and reducing greenhouse gas emissions. This research constructed a kinetic model for the hydrolysis of cellulose into bioethanol using the Structure-Oriented Lumping (SOL) method. Three vector units were defined to represent the structure of cellulose and its products, and five reaction rules were used to generate an 18-step reaction network. Reaction rate constants for these reactions were determined for various catalysts using genetic algorithms, and catalyst performance was analyzed based on these rate constants. Results demonstrated a high degree of agreement between experimental data and model predictions over time for the yield of cellulose and its products across four model applications using 16 different catalysts, effectively predicting yield variations with the maximum mean absolute error (MAE) not exceeding 6.3 % and the minimum being as low as 0.8 %. The predictive accuracy of the model provides a robust basis for analyzing catalyst performance through four distinct model applications: 1. In the catalyst hydrolysis of cellulose to ethanol by 5Ru-25 W/HZSM-5, the model identified the hydrogenolysis of EG (k13) as the rate-determining step (RDS). 2. The model explored the impact of Cu-WOx/SiO2 catalysts loaded with various metals (X = None, Pd, Au, Ru), demonstrating how different metal loadings influence the RDSs for the production of EG and ethanol from cellulose. Notably, catalysts loaded with Ru significantly enhanced the RDS (km) for EG, thereby increasing its yield. 3. The model highlighted subtle influences on the RDS for cellulose hydrolysis to EG under catalysts prepared using different methods and carriers. However, fundamentally, these changes did not alter the rate-limiting step (k7), but merely affected the magnitude of the RDS rate. 4. For multiple diols, the model revealed that different catalysts have distinct rate-determining steps, yet the yields of these products consistently correlate with their respective RDS rates. In addition, distinct from traditional thermodynamic analyses that explain catalyst reactivity and efficiency, this study delved into the nuanced association between catalysts and key reaction steps from a kinetic perspective, offering a new dimension of understanding of the catalytic process.

Simulation-Driven Universal Surrogates of Coupled Mechanical Systems: Real-Time Simulation of a Forestry Crane

Abstract Preparing simulation-driven surrogates for a coupled mechanical system can be challenging because the associated mechanical and actuator dynamics demand high-fidelity numerical solutions. Proposed here is a universal hydraulic surrogate (UHS), which can provide solutions to high-fidelity mechanical systems with a universal actuator in a surrogate-assisted monolithic approach. The UHS acts as an alternative to the standard lumped fluid theory by eliminating the hydraulic pressures differential equations. A surrogate-assisted universal actuator uses an approximated model to define hydraulic force in high-fidelity mechanical systems. The approximated force model was developed through training against the dynamics of a one-dimensional (1D) hydraulic cylinder and spring-damper. A covariance matrix adaption evolutionary strategy (CMA-ES) was used as an optimization algorithm to minimize differences between the standard dynamics and UHS approaches at the position and velocity levels. The robustness of resulting UHS was validated to predict the behaviors of the simple four-bar mechanism and the forestry crane. The focus was on numerical accuracy and computational efficiency. The maximum percent normalized root mean square error (PN-RMSE) between the states of the approximated force model and lumped fluid theory were approximately 2.04% and 6.95%, respectively. The proposed method was approximately 52 times faster than the standard lumped fluid theory method. By providing accurate predictions outside the training data, the simulation-driven UHS promises better computational performance leading to real-time simulation solutions for the coupled mechanical systems. The UHS can be applied in simulation, optimization, control, state and parameter estimation, and Artificial Intelligence (AI) implementations for coupled mechanical systems.

Mass lumping of stable generalized finite element methods for parabolic interface problems

Stable generalized finite element method (SGFEM) for interface problem is based on simple mesh independent of interface curves and possesses merits of optimal convergence rates, conditioning of same order as that of finite element method (FEM), robustness, and freedom from any penalty parameters or stability schemes. This paper investigates mass lumping of SGFEM for parabolic interface problems. The mass lumping is important for computational reduction and maximum principle preserving. The difficulty in the mass lumping of conventional generalized FEM (GFEM) and SGFEM consists in their incorporation of extra enriched functions. The existing mass lumping methods of GFEM cannot work properly due to features of SGFEM that enriched shape functions vanish on mesh nodes, and the nodes are enriched partially rather than totally. In this study, we propose two mass lumping schemes for the SGFEM. The first one is to only lump the FEM part, and enriched parts are kept fixed. This scheme enables us to execute a rigorous optimal convergence analysis. It is noted that a theoretical analysis on the mass lumping of GFEM has not been available yet in the GFEM field. The second scheme is to further compress the enriched part and intersection part of mass matrix separately. The lumped mass matrix is almost diagonal, and there is only a line of nonzero entries in the intersection part of mass matrix. Numerical experiments indicate that two schemes both produce the optimal convergence rates; their errors are almost the same as those of SGFEM without using the mass lumping.

Application of a property prediction model based on the structure oriented lumping method in the fluid catalytic cracking process

Based on the Structure Oriented Lumping (SOL) method and the Artificial Neural Network (ANN) algorithm, a SOL-ANN property prediction model was constructed to predict the properties of molecules and products in the fluid catalytic cracking (FCC) process. The properties of each structural vector in the molecular composition matrices of gasoline and diesel were calculated. The influences of reaction temperature on the properties of gasoline and diesel were investigated from the perspective of molecular composition. When the reaction temperature increased from 490 °C to 510 °C, the content of aromatics and olefins in gasoline and the content of aromatics in diesel increased, resulting in the research octane number (RON) of gasoline increasing by 2.96 units and the cetane number (CN) of diesel decreasing by 1.37 units. Using the molecular composition information of products to calculate the properties of molecules and products could guide the product quality evaluation and process optimization.

Modelling of piston pneumatic engine operation using the lumped method

In recent years, a significant increase in interest in alternative vehicle power sources has become apparent. Beyond the primary trend, electric drives, there can also be distinguished much less frequently considered pneumatic drives. One could partly attribute the low popularity of pneumatic drives to the relatively low energy density of compressed air, which negatively affects the achieved performance. The study presented focuses on developing a computational model of a piston pneumatic engine, which enables the analysis of the impact of parameters such as engine compression ratio, compressed air supply pressure, inlet valve opening time, and inlet valve opening moment in relation to TDC, on its energy and economic indicators. The object of research is an internal combustion engine from a moped converted to operate with compressed air. The modelling approach has two parts: mechanical and pneumatic. The second part uses the lumped method because of the ability to model complex elements with idealized finite elements corresponding to concentrated volumes and resistances. The engine performance analysis includes the parametric influence of the compression ratio, supply pressure, inlet valve opening angle in relation to crankshaft rotation, and total inlet valve opening time on the torque, power, and mass flow rate of air supplied to the engine. The Brake Specific Air Consumption parameter values, equivalent to the specific fuel consumption of internal combustion engines, were also determined. For the calculated parameters, one estimates the external characteristics of the engine using, among other things, the Leiderman-Khlystov method. Obtained results improved the achieved torque value by 35.4% and engine power by 15.3%, with a negligible increase in mass flow rate concerning the initial values reached by the pneumatic engine. The developed model enables the optimization of operating parameters of the compressed air supply system according to selected criteria. Improvement of the pneumatic engine performance parameters is essential to increase the popularity of pneumatic drives.

Investigating the characteristics of biomass wastes via particle feeder in downdraft gasifier

Particle feeding plays a crucial role in the gasifier due to its effects on the efficiency and performance metrics of the thermochemical process. Investigating particle size distribution's impact on downdraft gasification reactor performance, this study delves into the significance of feedstock characteristics (moisture, volatile matter, fixed carbon, and ash contents) during the particle feeding stage. Various biomass wastes (date palm waste, olive pomace and sewage sludge) at diverse compositions and sizes are subjected to empirical determination of mass flow rates (MFR), power ratings, and storage times for each feedstock. The preheating process in the gasifier is considered, employing both an approximation and analytical solution. In addition, the influence of the equivalence ratio (ER) on the syngas yield is analyzed. The collected data reveals that for average particle size of 200 μm, the highest MFR (in g/min) are 0.518 ± 0.033, 7.691 ± 0.415, and 16.111 ± 1.050, for palm wood biomass, olive pomace and sewage sludge, respectively. Smaller particles (80 μm) led to extended storage times. Moreover, the lumped capacitance approximation method consistently underestimates preheating time, with a percentage error of 6.26%–17.08%. Response surface methodology (RSM) optimization analysis provides optimal gasification conditions for palm wood biomass, olive pomace, and sewage sludge with maximum cold gas efficiencies (CGEs) of 58.01%, 63.29%, and 52.27%. The peak conversion was attained at gasification temperatures of 1089.83 °C, 1151.93 °C, and 1102.91 °C for palm wood biomass, olive pomace, and sewage sludge, respectively. In addition, gasification equilibrium model determined optimal gasification temperatures as 1150 °C for palm biomass, 1200 °C for olive pomace, and 1150 °C for sewage sludge with respective syngas efficiencies of 59.62%, 64.13%, and 53.66%. Consequently, the examination of the dosing procedure, preheating dynamics, particle dimensions, ER, storage time, and their combined impacts offer practical insights to effectively control downdraft gasifiers in handling a variety of feedstocks.

Molecular-level kinetic modelling for the pyrolysis of high-density polyethylene in a two-stage process

A two-stage process has been developed for the pyrolysis of high-density polyethylene to obtain light olefins, where probable mechanisms for each stage pyrolysis were proposed in our previous study. This work aims to establish molecular-level kinetic models for the first-stage pyrolysis at a lower temperature and for the second-stage pyrolysis at a higher temperature, respectively, to predict the overall reaction performances in accordance to the role of detailed mechanisms. A structure-oriented lumping (SOL) method based molecular-level kinetic model can effectively describe the first-stage pyrolysis, while a detailed molecular-level kinetic model is developed for the second-stage pyrolysis to track the evolutions of all alkanes, olefins, and diolefins, with special focus on the formation of light olefins. The established separate models can achieve the automatic generation of complex reaction networks and present good agreement with experimental data obtained from the first- and second-stage. In addition, the first-stage model indicates that the random scission plays an important role in the pyrolysis process at lower temperatures, while the chain-end scission mechanism dominates the second-stage reaction to produce light olefins at higher temperatures. As a whole, the molecular-level modelling scheme behaves excellently at a wide range of temperature, which provides guidance for upgrading the pyrolysis process.

Research on hydrogen risk prediction in probability safety analysis for severe accidents of nuclear power plants

The risk of hydrogen combustion after the Fukushima nuclear accident has always been a topic of concern for the nuclear power industry. In the hydrogen risk assessment of probability safety analysis (PSA) in nuclear power plants, the traditional methods by using lumped parameter program method is fast but may have large uncertainties, while the newly developed CFD analysis method is more accurate but has not yet been widely applied to the hydrogen risk analysis of PSA due to a variety of factors. The lumped parameter analysis program MAAP is used firstly to obtain the hydrogen parameters under the severe accident of small LOCA in this paper, based on China's third-generation large-scale pressurized water reactor (PWR) nuclear power plant HPR1000, and then the probability of deflagaration to detonation (DDT) for hydrogen risk is analyzed with uncertainty. Secondly, the CFD software GASFLOW program is used to analyze the same accident sequence to obtain more accurate hydrogen distribution and other parameters, and at the same time to obtain the DDT probability value of hydrogen risk. The hydrogen distribution obtained by CFD calculation can be used to guide the uncertainty value of the lumped parameter program to produce more accurate DDT value of hydrogen risk. The analysis results show that there is a certain uncertainty in hydrogen risk assessment when using lumped parameter program method, which can be corrected by combining the gas distribution analysis results given by CFD software, to obtain a more accurate and reliable probability value, so as to provide a more accurate reference for PSA analysis and to improve the overall safety of the nuclear power plant.

Frequency convergence characteristics of lumped mass Galerkin meshfree methods

Frequency convergence characteristics of lumped mass Galerkin meshfree methods

Mass and Force Lumping: An Essential Enhancement to the Intrinsic Beam Finite Element Discretization

This paper introduces the novel application of the mass and force lumping technique to enhance the finite element discretization of the fully intrinsic beam formulation. In our aeroelastic system model, 2-D unsteady aerodynamics were incorporated alongside simple calculations for thrust and gravity. Through the central difference discretization method, the discretized system was thoroughly examined, shedding light on the advantages of the mass and force lumping approach. With the use of a first-order lumping method, we successfully reconstructed the inertia matrices, external forces, and moments. The resulting equations are more systematically structured, facilitating the extraction of a regular state-space linear system using the direct index reduction method post-linearization. Numerical results further confirm that the proposed techniques can effectively capture the nonlinear dynamics of aeroelastic systems, enabling equation reconstruction and leading to significant benefits in system order reduction and flight dynamical analysis.

Model reduction for ‐induced vesicle fusion dynamics

AbstractIn this work, we adapt an established model for the ‐induced fusion dynamics of synaptic vesicles and employ a lumping method to reduce its complexity. In the reduced system, sequential ‐binding steps are merged to a single releasable state, while keeping the important dependence of the reaction rates on the local concentration. We examine the feasibility of this model reduction for a representative stimulus train over the physiologically relevant site‐channel distances. Our findings show that the approximation error is generally small and exhibits an interesting nonlinear and non‐monotonic behavior where it vanishes for very low distances and is insignificant at intermediary distances. Furthermore, we give expressions for the reduced model's reaction rates and suggest that our approach may be used to directly compute effective fusion rates for assessing the validity of a fusion model, thereby circumventing expensive simulations.

Robust H∞ Performance Analysis of Uncertain Large-Scale Networked Systems

This paper considers the robust H∞ performance problem of continuous-time uncertain large-scale networked systems (LSNSs). The systems consist of numerous arbitrarily connected subsystems, each of which has different dynamics. Currently it is computationally difficult to manage systems with the existing lumped analysis method; therefore, exploiting the structural properties of the systems, sufficient conditions are derived for robust H∞ performance. Based on these results, an analysis condition that depends only on the parameters of each single subsystem is further obtained. Some numerical simulations are proposed to verify the validity and superiority of the developed conditions.

Comparison of lumping methods to adaptive characterization in representing phase equilibria of hydrocarbon mixtures using PC-SAFT EOS

This work compared three classical lumping and Lage's re-characterization methods in representing the C7+ fraction of hydrocarbon mixtures with fewer pseudo-components. Two gas condensates, whose compositions are available in the literature, were used in the analysis. As all re-characterization methods are independent of the thermodynamic model, we chose the PC-SAFT equation of state to model the mixtures. Using all methods, we compared phase diagrams and liquid dropouts in flashes calculated using the original mixtures' composition and the re-characterized mixtures. Lage's method showed the best representation of the thermodynamic properties of the original mixtures for any number of pseudo-components. Using three pseudo-components, its accuracy for all relevant thermodynamic properties of the mixture is better, frequently by order of magnitude, than for all the other methods using four pseudo-components. For the tested cases, Lage's method needed only half of the pseudo-components of the other methods to represent the C7+ fraction with similar accuracy.

RESEARCH IN THE FIELD OF PVT-CALCULATIONS FOR ACCURATE FLUID DESCRIPTION

Lumping methods for oil components require a more detailed approach to refine the description of fluids in an oil production area. These methods allow you to gradually increase the dynamics of the behavior of hydrocarbon deposits and increase their reserves. To date, the lumping method is relevant as an attractive way to spend on reservoir compositional modeling. The authors of the article describe PVT-calculations that have been developed for many years of illness, in the treatment of diseases of the cardiovascular system. They explain the approaches of different lumping methods. This article discusses different types of lumping methods such as classical, statistical, and machine learning based lumping.

Self-Optimizing Control Strategy for Distributed Parameter Systems

Real-time optimization (RTO) has been a popular approach for addressing optimal operation by repetitively optimizing online. However, this approach is impractical for distributed parameter systems (DPSs) due to its expensive computational cost. Self-optimizing control (SOC) has emerged as a promising alternative strategy, which achieves acceptable optimality by controlling the designed controlled variables (CVs) at constant set points without reoptimizing. Motivated by this, the existing lumped parameter SOC method is for the first time expanded to a typical class of DPSs based on a high-fidelity discrete-space model. Starting from an infinite-order system itself, the SOC problem is constructed as the minimal loss functional regarding the CVs through the operator operation and variational method. To obtain an operational analytical solution of CVs, the optimization problem is reformulated based on the discrete-space system derived by the finite difference. Considering the variety of sensor and actuator placements, the CVs are analytically designed with the minimal static loss through the stacking matrix approach. Finally, a case study of a plug-flow reactor is presented to demonstrate the feasibility of the proposed approach to achieve optimal operation for DPSs.

Predicting the Physicochemical Properties of Molecules in Petroleum Based on Structural Increments

The structure-oriented lumping (SOL) method has been widely applied to molecular-level modeling and optimization in the refining industry. Calculating the physicochemical properties of products obtained by the SOL models can effectively guide the evaluation of product quality and optimization of the process. In this study, the SOL method was improved by extending the structural increments from 22 to 38 to describe the molecules in petroleum more accurately. According to the basic law that the properties and structures of molecules are inseparable, the structural increments with similar physical meanings were combined into a functional group to reduce the dimension to 11 characteristic parameters to describe the molecular structure, and a property prediction method that can be combined with the molecular-level refining models based on the optimized SOL method was constructed. In addition, the accuracy of the selection and definition of the 11 functional groups was verified by analyzing and discussing the effects of functional groups on the properties, which, in turn, ensured the accuracy of the property prediction models. Compared with other property prediction methods, this method can be combined with the SOL method to provide reliable predictions of the boiling point, critical temperature, critical volume, critical pressure, density, cetane number, motor octane number, and research octane number of molecules.

A coupling model of fluid catalytic cracking and diesel hydrotreating processes to study the effects of reaction temperature on the composition of diesel

The coupling optimization between different plants was the most difficult and key problem in refineries. To accurately describe the effective transfer of material flow information between Fluid Catalytic Cracking (FCC) and Diesel Hydrotreating (DH) processes and realize the coupling simulation for these processing units in refineries, a coupling model of FCC and DH processes using a fractionation tower simulation system was established to calculate the hydrocarbon compositions of diesel based on the Structure Oriented Lumping (SOL) method. The fractionation tower simulation system developed by MATLAB software was used to divide the molecular composition matrix of FCC product into the molecular composition matrices of dry gas, liquefied petroleum gas, gasoline, diesel, and oil slurry. The molecular composition matrix of diesel contained 73, 69, 183, 121 and 743 structural vectors representing paraffins, olefins, naphthenes, aromatics and non-hydrocarbon molecules, respectively. The fractionation ratios of the hydrocarbon group compositions with carbon numbers between 5 and 12 in the molecular composition matrix of gasoline and diesel were calculated. The effective transmission of material flow in the FCC and DH processes was accurately expressed by the transmission of the molecular composition matrix of diesel obtained by the fractionation tower simulation system. The effects of FCC and DH reaction conditions on the hydrocarbon compositions of diesel were calculated at the molecular level by the FCC-DH process coupling model. Through the FCC-DH process coupling model using a fractionation tower simulation system, the transformation laws of hydrocarbon and non-hydrocarbon molecules in different devices could be revealed to provide guidance for reducing the content of polycyclic aromatic hydrocarbons and sulfur in diesel, optimizing operating conditions and controlling product quality indicators.

Numerical Study of Two-Stage Temperature Control Strategy for High-Temperature Stability of Satellite-Borne Fiber Optic Gyroscope

Abstract Fiber optic gyroscopes (FOGs) are widely used in attitude control systems of spacecraft such as satellites and Mars rovers for their superior spatial adaptability. However, changes in ambient temperature can cause errors in the FOG and reduce its output accuracy. In this paper, a fuzzy two-stage temperature control strategy applied to a satellite-borne three-axis integrated fiber optic gyroscope (TAIFOG) is proposed. And the control rules of the fuzzy two-stage temperature controller are described in detail. A thermodynamic model that can quickly and accurately respond to the dynamic thermal characteristics of the satellite-borne TAIFOG is also constructed based on the lumped method. The effectiveness of the proposed fuzzy two-stage temperature control strategy in improving the temperature stability of the satellite-borne TAIFOG in orbit is verified through numerical studies. Numerical results show that this fuzzy two-stage active temperature control strategy can fundamentally improve the thermal state of the satellite-borne TAIFOG and ensure that its sensitive element fiber optic coils maintain high-temperature stability while the TAIFOG is in orbit. In addition, the startup time of TAIFOG is reduced to 308 s compared to the case without active temperature control, which is a reduction of 96.27%. This active temperature control strategy is well suited for engineering applications to improve FOG output accuracy.