Maximum Absolute Relative Deviation Research Articles

Solubility measurement of methane in triethylene glycol aqueous solutions (90,95,98 wt.% triethylene glycol) from 298 to 323 K and 0.17 to 2.5 MPa

Limited phase equilibria data exists for the methane + water + triethylene glycol system. In this work, new phase equilibrium data were measured for this system for a temperature range of 298 to 323 K and a pressure range of 0.17 to 2.5 MPa. These data add to the information that is required in the design of TEG contactor units since they normally operate over a temperature and pressure range of 283 to 329 K, and 2 to 10 MPa respectively. The data were measured using a static synthetic apparatus. The measured data were modelled in Apen Plus V12.1 using the Cubic Plus Association equation of state. The model correlation yielded a satisfactory description of the measured data since the maximum absolute average relative deviation in pressure was 4.30 %.

Experimental investigation of liquid thermal diffusivity for fatty acid methyl/ethyl esters by dynamic light scattering method

Fatty acid methyl/ethyl esters have a potential application as fuel or fuel additives in internal combustion diesel engine. The present work focused on the determination of the liquid thermal diffusivity of six fatty acid methyl esters (FAMEs) and four fatty acid ethyl esters (FAEEs) over a wide temperature range from (303.15 to 473.15) K by dynamic light scattering (DLS) method. Results demonstrated that the liquid thermal diffusivity of FAMEs and FAEEs decreased as the increasing temperature but increased as the increasing carbon chain. Furthermore, the polynomial correlation of the liquid thermal diffusivity against the temperature was proposed. The maximum relative deviation (MRD) and absolute average relative deviation (AARD) between experimental data and the corresponding calculated values from the correlation were 2.00% and 1.00%, respectively. The obtained experimental data and proposed correlation in this study provide necessary data support for future industry applications of FAMEs and FAEEs as fuels or fuel additives in internal combustion engines.

P-T-x Measurement and Modeling of Methane + Propane + Methanol or 2,2′-[Ethane-1,2-diylbis(oxy)] Di(ethan-1-ol) and Methane + Propane + Methanol + 2,2′-[Ethane-1,2-diylbis(oxy)] Di(ethan-1-ol) Systems

Limited phase equilibria data exist for multicomponent systems encountered in the natural gas processing industry. To address this gap, bubble point measurements were performed for methane + propane + methanol; methane + propane + (2,2′-[ethane-1,2-diylbis(oxy)] di(ethan-1-ol) or triethylene glycol); methane + propane + methanol + triethylene glycol systems in the temperature range of 283.16 to 323.16 K and a pressure range of 0.78 to 13.79 MPa. A visual synthetic high-pressure cell comprising a sapphire tube of 33 cm3 working volume was used. The new experimental P-T-x data were modeled using the Cubic Plus Association (CPA) model and the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) model. Model correlations with the CPA model yielded better results than those with the PC-SAFT model, with a maximum absolute average relative deviation in pressure of 6.97% and 7.33%, respectively. The CPA model predictions based on binary parameters alone do not adequately describe phase behavior of multicomponent systems.

Modeling Liquid Thermal Conductivity of Low-GWP Refrigerants Using Neural Networks

The thermal conductivity of refrigerants is needed to optimize and design the main components of HVAC&R systems. Consequently, it is crucial to have reliable models that are able to accurately calculate the temperature and pressure dependence of the thermal conductivity of refrigerants. For the first time, this study presents a neural network specifically developed to calculate the liquid thermal conductivity of various low-GWP-based refrigerants. In detail, a feed-forward network algorithm with 5 input parameters (i.e., the reduced temperature, the critical pressure, the acentric factor, the molecular weight, and the reduced pressure) and 1 hidden layer was applied to a large dataset of 3404 experimental points for 7 halogenated alkene refrigerants. The results provided by the neural network algorithm were very satisfactory, achieving an absolute average relative deviation of 0.389% with a maximum absolute relative deviation of 6.074% over the entire dataset. In addition, the neural network ensured lower deviations between the experimental and calculated data than that produced using different literature models, proving its accuracy for the liquid thermal conductivity of the studied refrigerants.

A discretization method for the characterization of a plate heat exchanger working as evaporator during transient conditions

In this work, a method for the characterization of a plate heat exchanger working as evaporator is presented. It is based on a one-dimensional discretization of the exchanger, which solves the heat transfer balance equations by means of an iterative methodology based on a heat transfer area converging method. The inputs of the method are the flow rates of the fluids, the inlet enthalpy of the refrigerant, the superheating, and the inlet temperature and pressure of the secondary fluid. Once the inlet pressure of the refrigerant is assumed, pressure drop is calculated in each cell and then enthalpy. The consideration of the proper heat transfer coefficient (HTC) correlations allows the calculation of the heat transfer area, which is after compared to the actual one. The method has been validated by means of a database of 366 experimental data obtained for eight plate heat exchangers working as evaporators by using six different refrigerants, namely R134a, R1234yf, R513A, R744, R290, and R507A. As the method requires suitable correlations for the calculation of the HTC and pressure drop, several correlations for the HTC and Δp found in the literature are studied and the results obtained by using them are presented in terms of the maximum absolute relative deviation (MARD). The results corresponding to the correlation which yields the best results are graphically represented. Finally, the method is used to predict the evaporator performance operating in transient conditions. The results obtained show an excellent agreement with the experimental results collected during the transient operation of a transcritical CO2 water heater coupled to a storage tank.

Measurement and correlation of isobaric molar heat capacities of deep eutectic solvents consisting of choline chloride and triethylene glycol

Deep eutectic solvents are environmentally friendly substitutes to room temperature ionic liquids in broad engineering applications like biofuel purification, polymer synthesis, gas capture, and organic extraction. In this work, the isobaric molar heat capacities of deep eutectic solvents consisting of choline chloride and triethylene glycol (in molar ratio of 1: 3, 1: 4, and 1: 5) are investigated by flow method in the temperature from 334.91 K to 364.98 K and pressure from 0.19 MPa to 25.21 MPa. The relative expended uncertainty of measurement system is calculated to be 1.4 % within 95 % degree of confidence. Experimental results show that the isobaric molar heat capacity increases linearly with higher temperature and lower pressure. With choline chloride added in triethylene glycol, the heat capacity decreases linearly with the decreasing of triethylene glycol molar fraction. Finally, the correlation of these binary mixtures is established based on the experimental data with the maximum absolute relative deviation and average absolute relative deviation of 1.01 % and 0.31 %, respectively.

Measurement of the Isobaric Heat Capacity for Methyl Hexanoate and Ethyl Hexanoate at Temperatures from 313 to 433 K and Pressures of up to 10 MPa

In this article, a calorimeter was established on the basis of steady-flow calorimetry. The present calorimeter was utilized to measure the isobaric heat capacity (cp) of target fluids. First, water was measured to verify the reliability of the experimental system. Then the measurements of cp for methyl hexanoate and ethyl hexanoate were carried out at temperatures from 313 K to 433 K and pressures of up to 10 MPa. To implement easier industrial application, a correlation was proposed on the basis of the experimental data to calculate the cp values of methyl hexanoate and ethyl hexanoate, with maximum absolute relative deviations of 0.77% and 0.65%, respectively. The newly reported data will be helpful for use with methyl hexanoate and ethyl hexanoate.

GEANT4 Simulation for Radioactive Particle Tracking (RPT) Technique.

In the past two decades, the radioactive particle tracking (RPT) measurement technique has been proven to visualize flow fields of most multiphase flow systems of industrial interest. The accuracy of RPT, and hence the data obtained, depend largely on the calibration process, which stands here as a basis for two subsequent processes: tracking and reconstruction. However, limitations in the RPT calibration process can be found in different experimental constrains and in assumptions made in the classical Monte Carlo approach used to simulate number of counts received by the detectors. Therefore, in this work, we applied a GEANT4-based Monte Carlo code to simulate the RPT calibration process for an investigated multiphase flow system (i.e., gas–liquid bubble column). The GEANT4 code was performed to simulate the number of counts received by 28 scintillation detectors for 931 known tracer positions while capturing all the types of photon interaction and overcoming solids’ angle limitations in classical approaches. The results of the simulation were validated against experimental data obtained using an automated RPT calibration device. The results showed a good agreement between the simulated and experimental counts, where the maximum absolute average relative deviation detected was about 5%. The GEANT4 model typically predicted the number of counts received by all the detectors; however, it over-estimated the counts when the number of primary events applied in the model was not the optimal.

Measurement of the critical temperature and critical pressure of isopropanol and isobutanol blended with gasoline components

Isopropanol and isobutanol are potentially partial substitutes for gasoline. The critical properties of isoalcohol-gasoline blends are of great importance to optimize their combustion and emission performance in engines. In this paper, the critical temperature (Tc) and critical pressure (pc) of eight miscible systems (isopropanol/isobutanol + n-hexane, isopropanol/isobutanol + n-heptane, isopropanol/isobutanol + n-octane, isopropanol/isobutanol + n-heptane + isooctane) were measured by the flow method in the range of 497.69–569.21 K and 2.495–4.766 MPa. Experimental results show that the addition of isopropanol and isobutanol can significantly reduce the Tc of C6-C8 alkanes by 0–60.85 K and increase the pc by 0–2.271 MPa. A model for calculating the Tc and pc of these mixtures is presented based on the Redlich–Kister equations. The maximum average absolute relative deviations of the Tc and pc are 0.08% and 0.46%, respectively.

Lower flammability limits of ethanol, acetone and ethyl acetate vapor mixtures in air

This work is aimed at investigating the lower flammability limits (LFLs) of ethanol, acetone, and ethyl acetate vapor mixtures in air with various mole fractions. The LFLs were measured by a self-made experimental apparatus. Besides, a theoretical calculation model of LFL based on adiabatic constant pressure was established. The heat release, adiabatic flame temperature and the sensitivity of mass burning rate on LFL are analyzed. The results indicated that as the mole fraction of a single substance in a binary mixture or a ternary mixture increases, the LFL changes monotonically. The calculated LFLs are in good agreement with the experiment. The maximum absolute deviation and relative deviation are 0.2% and 6.47% respectively. The trends of heat release and adiabatic flame temperature (AFT) are consistent, meanwhile, the trends of LFL are opposite to them. Besides, the trend of the total peak of heat release rate at LFL is consistent with the heat release. H + O2 < = > O + OH mainly reduces the heat release rate, and CH3 + O < = > CH2O + H mainly increases the heat release rate. The sensitivity coefficients of the maximum main chain branching reaction H + O2 < = > O + OH and the main termination reaction H + O2 (+M) < = > HO2 (+M) of the mass burning rate at the LFL are almost the same.

Isothermal vapor–liquid equilibrium of ternary system (difluoromethane + propane + trifluoroiodomethane) at temperatures ranging from 263.15 K to 303.15 K

In this paper, a static analytical apparatus has been developed to measure the vapor–liquid phase equilibrium property. The saturated vapor pressures of R32, R290, and R13I1 at temperatures from 253.15 to 303.15 K were measured. Satisfactory agreement with published calculation and experimental data are found and the reliability of the experimental setup is verified. The vapor–liquid phase equilibrium data for R32 + R290 + R13I1 ternary system were measured at 263.15, 283.15, and 303.15 K. The standard uncertainties were estimated to be 13 mK for temperature, 1300 Pa for pressure and 0.008 for mole fraction. The data were regressed by the PR-vdW model and the PR-NRTL-MHV2 model. The PR-NRTL-MHV2 model gives a better description of the experimental values with maximum average absolute relative deviations of 0.9% for pressure and maximum absolute deviation of 0.016 for vapor mole fraction. No azeotropic behaviour can be observed for the ternary system.

Isothermal vapour-liquid equilibrium of (difluoromethane + trifluoroiodomethane) at temperatures ranging from 253.150 K to 293.150 K

In this paper, the isothermal vapour-liquid equilibrium (VLE) data for pure difluoromethane (R32) and trifluoroiodomethane (R13I1) and their binary mixtures have been measured based on a vapour – phase single recirculation method. The data were collected for five temperatures from 253.150 K to 293.150 K. The experimental VLE data were regressed by PR-MHV2-NRTL model and PR-vdW model. The deviation curves of pressures and vapour compositions for the binary system between experimental and calculated values were given. The results indicated that the maximum mean absolute relative deviation of pressure (MARDp) for PR-MHV2-NRTL is 0.54%, which shows a better fit than PR-vdW with a maximum MARDp of 2.73%. The maximum mean absolute deviation of vapour phase mole fraction (MADy) for PR-MHV2-NRTL and PR-vdW are 0.013 and 0.010, respectively. The azeotropic behaviours were found at T = (253.150, 263.150, 273.150) K, while the zeotropic behaviours were found at 283.150 K and 293.150 K.

Study on a Dynamic Numerical Model of an Underground Air Tunnel System for Cooling Applications—Experimental Validation and Multidimensional Parametrical Analysis

The underground air tunnel system shows promising potentials for reducing energy consumption of buildings and for improving indoor thermal comfort, whereas the existing dynamic models using the computational fluid dynamic (CFD) method show computational complexity and are user-unfriendly for parametrical analysis. In this study, a dynamic numerical model was developed with the on-site experimental calibration. Compared to the traditional CFD method with high computational complexity, the mathematical model on the MATLAB/SIMULINK platform is time-saving in terms of the real-time thermal performance prediction. The experimental validation results indicated that the maximum absolute relative deviation was 3.18% between the model-driven results and the data from the on-site experiments. Parametrical analysis results indicated that, with the increase of the tube length, the outlet temperature decreases with an increase of the cooling capacity whereas the increasing/decreasing magnitude slows down. In addition, the system performance is independent on the tube materials. Furthermore, the outlet air temperature and cooling capacity are dependent on the tube diameter and air velocity, i.e., a larger tube diameter and a higher air velocity are more suitable to improve the system’s cooling capacity, and a smaller tube diameter and a lower air velocity will produce a more stable and lower outlet temperature. Further studies need to be conducted for the trade-off solutions between air velocity and tube diameter for the bi-criteria performance enhancement between outlet temperature and cooling capacity. This study proposed an experimentally validated mathematical model to accurately predict the thermal performance of the underground air tunnel system with high computational efficiency, which can provide technical guidance to multi-combined solutions through geometrical designs and operating parameters for the optimal design and robust operation.

Measurement of critical temperature and critical pressure of tert-butanol and alkane mixtures

Tert-butanol is a good additive for improving gasoline performance, but as two of the most important thermodynamic properties, the critical temperature (Tc) and critical pressure (pc) of tert-butanol and alkane systems have not been studied. In this work, the experimental data of the Tc and pc of five binary systems (tert-butanol + cyclohexane, tert-butanol + n-hexane, tert-butanol + n-heptane, tert-butanol + n-octane, and tert-butanol + n-nonane) and a ternary system (tert-butanol + n-heptane + n-octane) were obtained using a flow method. The Tc and pc of the binary systems were fitted using the Redlich–Kister equations with maximum average absolute relative deviations (AARDs) of 0.19% and 0.36% for Tc and pc, respectively. The Tc and pc for tert-butanol + n-heptane + n-octane were correlated by Singh and Sharma's equations and Cibulka's equations with AARDs less than 0.09% and 0.32%, respectively. The experimental data of Tc and pc were also used to verify and improve the accuracy of our previous prediction model.

Modeling recovery of natural gas from hydrate reservoirs with carbon dioxide sequestration: Validation with I\u0121nik Sikumi field data

Fundamental understanding of guest gas replacement in hydrate reservoirs is crucial for the enhanced recovery of natural gas and carbon dioxide (CO2) sequestration. To gain physical insight into this exchange process, this work aims at developing and validating a clathrate hydrate model for gas replacement. Most of the practical concerns associated with naturally occurring gas hydrates, including hydrate formation and dissociation in interstitial pore space between distributed sand particles in the presence of salt ions and in irregular nanometer-sized pores of those particles, irregularity in size of particles and shape of their pores, interphase dynamics during hydrate formation and decay, and effect of surface tension, are addressed. An online parameter identification technique is devised for automatic tuning of model parameters in the field. This model is employed to predict the laboratory-scale data for methane hydrate formation and decomposition. Subsequently, the model is validated with the field data of the Prudhoe Bay Unit on the Alaska North Slope during 2011 and 2012. In this Iġnik Sikumi field experiment, mixed CO2 (i.e., CO2 + N2) is used as a replacement agent for natural gas recovery. It is observed that the proposed formulation secures a promising performance with a maximum absolute average relative deviation (AARD) of about 2.83% for CH4, which is even lower, 0.84% for CO2 and 1.67% for N2.

Utilization of the Copula-Based Composite Likelihood Approach to Improve Design Precipitation Estimates Accuracy

Coupling of the bivariate copula function and likelihood function was utilized for parameter estimation in precipitation frequency analysis. In this method, data of various lengths in a homogeneous region were incorporated into a multivariate framework. Therefore, the information contained in one series can be employed to improve the accuracies of the design values of other series. Annual precipitation data collected from 36 stations in the Guanzhong region, China, were used as a case study. To obtain more reliable estimates, the stationarity and serial independence of each series were tested first. Then, the entire study region was divided into four homogeneous sub-regions, and frequency analyses were carried out in each sub-region. Two measures, the standard error of fit (SEF) and the maximum absolute relative deviation (MARD), were used to compare the goodness-of-fit of the copula-based composite likelihood approach with the univariate method. Results showed that the SEF and MARD values of the design precipitation values obtained from the copula-based composite likelihood approach were lower than those from the univariate method, and the decrease became more significant for stations with a shorter series in the bivariate composite case. Therefore, this study indicates the advantage of the use of a copula-based composite likelihood approach for improving the accuracy of design precipitation values.

Improved enthalpy prediction of hydrocarbon fractions with a modified alpha function for the Peng-Robinson equation of state

In this paper, a pragmatic technique has been developed and validated to predict ideal gas heat capacities and enthalpies for normal alkanes/alkenes as well as hydrocarbon fractions over a wide range of temperatures and pressures. More specifically, an existing correlation has been modified to more accurately determine the ideal gas heat capacities for normal alkanes/alkenes, especially for heavy hydrocarbons. Then, a reliable and convenient enthalpy algorithm for hydrocarbon fractions has been proposed by incorporating a recently modified alpha function into the Peng-Robison equation of state (PR-EOS) together with the newly modified ideal gas heat capacity correlation. As for the new database of ideal gas heat capacities with 340 data points of normal alkanes, the newly modified correlation leads to more accurate predictions, yielding an absolute average relative deviation (AARD) of 1.24% and a maximum absolute relative deviation (MARD) of 6.21% compared with 6.96% and 10.69% from the Kesler and Lee correlation, respectively. To further validate the newly developed correlation, another database of 279 data points of normal alkenes that is excluded for correlation development shows an AARD of 2.04% and a MARD of 2.58% in comparison of 8.44% and 10.57% from the Kesler and Lee correlation, respectively. Also, an algorithm has been proposed to predict the enthalpy with AARDs of 1.25% and 2.78% and MARDs of 2.06% and 3.51% for two representative hydrocarbon fractions (i.e., the light naphtha and Alaska naphtha), respectively.

Liquid viscosities for methyl hexanoate, methyl heptanoate, methyl caprylate, and methyl nonanoate at high pressures

The experimental measurements for liquid viscosities of four fatty acid methyl esters, including methyl hexanoate, methyl heptanoate, methyl caprylate, and methyl nonanoate, were carried out with a falling-cylinder viscometer. For the present measurement, the temperature ranges were from 292 K to 362 K and the pressure was reached to 30 MPa. The combined expanded relative uncertainty of the viscosity measurements was within 0.03 with 0.95 confidence level. The viscosity data for each studied esters were correlated by Andrade-Tait equation, and the average absolute relative deviation between the experimental data and calculated values is 0.31%, 0.44%, 0.38%, and 0.25% for methyl hexanoate, methyl heptanoate, methyl caprylate, and methyl nonanoate, respectively. The maximum absolute relative deviation is 1.09%, 1.28%, 1.28%, and 0.75%.

Temperature and pressure dependence of densities and viscosities for binary mixtures of methyl decanoate plus n-heptane

New experimental densities and viscosities data for binary mixtures of methyl decanoate plus n-heptane were reported at temperatures of (298.15, 308.15 and 318.15) K and pressures of (0.1–15) MPa. The expanded uncertainty for density measurement is estimated to be 2 kg m−3 and the relative expanded uncertainty for viscosity measurement is estimated to be 0.03. A fitting equation was proposed to correlate the density of the binary mixture and Grunberg-Nissan equation was used to predict the viscosity of the binary mixture, respectively. The maximum absolute relative deviations between the experimental results and calculation values for densities and viscosities were 0.11% and 5.94%, respectively.

Measurement on the thermal conductivity of five saturated fatty acid ethyl esters components of biodiesel

The utilization of biodiesel, which is considered as a renewable, biodegradable and clean-burning transportation fuel consisting of fatty acid alkyl esters, is a promising way to replace fossil fuels. Thermal conductivity is a very important thermophysical property of the biodiesel. In this work, the liquid thermal conductivity of five saturated fatty acid ethyl esters (ethyl myristate, ethyl laurate, ethyl caprate, ethyl caprylate and ethyl heptanoate) were measured with the temperature ranging within (290.64–393.88) K, (274.73–400.08) K, (270.00–400.44) K, (254.76–400.37) K, (250.38–393.46) K, respectively. The total relative standard uncertainty of the experimental results was estimated to be less than 2% and repeatability was better than ±0.5%. The experimental results of each substance were fitted as a function of temperature. The average absolute relative deviation and maximum absolute relative deviation between the experimental data and calculated results were 0.19% and 0.36% for ethyl myristate, 0.15% and 0.54% for ethyl laurate, 0.17% and 0.38% for ethyl caprate, 0.23% and 0.66% for ethyl caprylate, 0.19% and 0.52% for ethyl heptanoate, respectively.