A new approach for isothermal calorimetric technique

Using flexible heat flux sensors mounted on the lateral and bottom of outside reactor wall, a new approach is developed for isothermal calorimetric technique to overcome the disadvantages of heat flow calorimetric methods. Although the proposed system needs a calibration procedure before or after the reaction completion to evaluate the lateral heat transfer area, the measurement is versatile and totally independent of the reaction media, jacket fluid, and the variations of heat transfer coefficient. Knowledge of the variations of the heat transfer coefficient is essential for the effective control and scale up of a reactor and can be inferred by the new method during the reaction. The stirrer power and the heat loss can be determined easily as well. No pre-calibration is needed for the sensors and no heating element is applied inside the reactor for temperature control. Experiments are carried out to validate the performance of the new proposed technique. With the help of a heater, the heat generated in the reactor is measured at various levels of power input. The predicted heater power inputs are in good agreement with the corresponding heat inputs. The relative detection limit in the range of 0.8–1 W L⁻¹ is expected for this technique. Using the hydrolysis of acetic anhydride, the heat of reaction at 25°C is determined, which is within the range reported in the literatures. The capability of the system to deal with the variations in the overall heat transfer coefficient is also demonstrated using a simulated reaction.     

Heat capacity of cheese

The heat capacity of several samples of hard cheese, semi-hard cheese and soft cheese was determined by conventional differential scanning calorimetry (DSC) and by temperature modulated DSC. Additionally, the gross composition of the cheeses was analysed, and equations from the literature were used to calculate the heat capacity therefrom. Both analytical methods were suitable to determine the heat capacity of the cheese samples whereas only one out of three equations proposed for the calculation of the heat capacity of foods from composition data led to results which were comparable with analytical data. As the equation coefficients for particular constituents are responsible for the deviations in the calculated heat capacities the differences between calculated and measured values increase with a decreasing moisture content of the cheeses.     

Comparison of linear and non-linear equations for univariate calibration

Univariate data accumulated for the purpose of calibration of chromatographic and spectroscopic methods often exhibit slight but definite curvature. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = a + bx(m), (m not equal to 1) is compared with the commonly used linear equation, y = a + bx, as well as the quadratic equation, y = a + bx + cx2. All equations were applied to high quality HPLC calibration data using unweighted least squares. Parameter estimates and their standard errors were calculated for each equation. Standard errors and 95% prediction intervals in analyte concentrations were estimated with the aid of the fitted equations and their respective covariance matrices. Results indicate that the non-linear and quadratic equations each provide a better fit than the linear equation to the data considered here, as judged by the Akaikes information criterion (AIC), the adjusted coefficient of multiple determination, the magnitude and scatter of residuals, standard errors in estimated analyte concentrations and lack of fit analysis of variance (ANOVA). While the difference between the equations y = a + bx + cx2 and y = a + bx(m) as judged by the same criteria is more marginal, this work suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low noise calibration data which exhibit slight curvature.     

Numerical solution of nonlinear and non-isothermal general rate model of reactive liquid chromatography

Abstract

A nonlinear general rate model (GRM) of liquid chromatography is formulated to analyze the influence of temperature variations on the dynamics of multi-component mixtures in a thermally insulated liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection–diffusion reaction partial differential equations (PDEs) coupled with nonlinear algebraic equations for reactions and isotherms. The model equations are solved numerically by applying a semi-discrete high-resolution finite volume scheme (HR-FVS). Several numerical case studies are conducted for two different types of reactions to demonstrate the influence of heat transfer on the retention time, separation, and reaction. It was found that the enthalpies of adsorption and reaction significantly influence the reactor performance. The ratio of density time heat capacity of solid and liquid phases significantly influences the magnitude and velocity of concentration and thermal waves. The results obtained could be very helpful for further developments in non-isothermal reactive chromatography and provide a deeper insight into the sensitivity of chromatographic reactor operating under non-isothermal conditions.     

The use of advanced calorimetric techniques in polymer synthesis and characterization

Progress in the understanding of polymer synthesis, including the crucial step of initiation and undesired side reactions, and in characterization of polymers, especially their thermal behaviour, are directly related to advances in calorimetric technologies.

In polymer synthesis, since polymerization reactions are highly exothermic, reaction calorimetry (RC) is an appropriate technique for on-line process monitoring. Measurements are non-invasive, rapid, and straightforward. Viscosity increase and fouling at the reactor wall are typical features of many polymerizations. The global heat transfer coefficient, UA, also changes drastically when viscosity increases and affects the accuracy of calorimetric measurements. Our approach was focused on oscillating temperature calorimetry (TOC). Reactions were performed with two different reaction calorimeters, i.e. an isoperibolic calorimeter and a Calvet-type high sensitivity differential calorimeter, respectively. Special attention was paid to the interpretation of the measured signals to obtain reliable calorimetric data. The evolution of heat transfer coefficient was followed by performing two Joule effect calibration experiments, before and after the reaction, and the two values interpolated to obtain the desired profile of UA. A differentiation method based on the convolution of the measured heat flow by the generated one was used for determining the time constants and deconvoluting the measured heat flow.

With respect to polymer characterization, pressure-controlled scanning calorimetry, also called scanning transitiometry, is now a well established technique. The transitiometer was coupled to an ultracryostat to work at low temperature. The assembly was used to follow the pressure effect on phase change phenomena such as fusion/crystallization and glass transition temperature T_g of low molecular weight substances or high molecular weight polymers.     

Phenomenological study on heat and mass coupling mechanism of waxy crude oil pipeline transport process

Based on the phase equilibrium model of the paraffin wax precipitation in the process of oil pipeline transportation, theory and method of non-equilibrium thermodynamics were applied to obtain the linear phenomenological equations for the cross-interaction of heat and mass transfer during pipeline transport, which were derived from the irreversible entropy production rate equation. Then, the analysis of the irreversible heat flow and the mass flow were carried out, and the mathematical expressions of the phenomenological coefficient of liquid phase, the phenomenological coefficient of solid phase flow, and the heat flow phenomenological coefficient were obtained. Taking a waxy crude oil transportation pipeline in Daqing Oilfield as an example, based on the analysis of liquid–solid phase equilibrium, the irreversible linear phenomenological mechanism of heat and mass coupling in waxy crude oil pipeline transportation was analyzed in detail from three levels: phenomenological coefficients which reflect characteristic of the effect of force on flow in heat and mass transfer; thermodynamic forces which trigger heat and mass transfer; transmitted heat and mass flow density, providing a theoretical basis for the further study of the wax deposition in the process of pipeline transportation.     

Dynamic calibration and dissolved gas analysis using membrane inlet mass spectrometry for the quantification of cell respiration

A membrane inlet mass spectrometer connected to a miniaturized reactor was applied for dynamic dissolved gas analysis. Cell samples were taken from 7 mL shake flask cultures of Corynebacterium glutamicum ATCC 13032, and transferred to the 12 mL miniaturized reactor. There, oxygen uptake and carbon dioxide and its mass isotopomer production rates were determined using a new experimental procedure and applying nonlinear model equations. A novel dynamic method for the calibration of the membrane inlet mass spectrometer using first-order dynamics was developed. To derive total dissolved concentration of all carbon dioxide species (C(T)) from dissolved carbon dioxide concentration ([CO(2)](aq)), the ratio of C(T) to [CO(2)](aq) was determined by nonlinear parameter estimation, whereas the mass transfer coefficient of CO(2) was determined by the Wilke-Chang correlation. Subsequently, the suitability of the model equations for respiration measurements was examined using residual analysis and the Jarque-Bera hypothesis test. The resulting residuals were found to be random with normal distribution, which proved the adequacy of the application of the model for cell respiration analysis. Hence, dynamic changes in respiration activities could be accurately analyzed using membrane inlet mass spectrometry with the novel calibration method.     

Specific detection of acetyl-coenzyme A by reversed-phase ion-pair high-performance liquid chromatography with an immobilized enzyme reactor

A selective chromatographic detection system for the determination of acetyl-coenzyme A (CoA) is reported. The short-chain acyl-CoA thioesters were separated by reversed-phase ion-pair high-performance liquid chromatography (HPLC), and then acetyl-CoA was selectively detected on-line with an immobilized enzyme reactor (IMER) as a post-column reactor. Thio-CoA liberated enzymatically from acetyl-CoA was determined spectrophotometrically after reaction with Ellman's reagent in the reagent stream. The IMER with phosphotransacetylase had a substrate specificity sufficient to determine acetyl-CoA and was active and stable in the mobile phase containing methanol and the ion-pair reagent. The calibration graph was linear between 0.2 and 10 nmol, with a detection limit of 0.05 nmol. This HPLC system with detection by IMER allows the selective identification and determination of acetyl-CoA in a mixture of acetoacetyl-CoA and 3-hydroxy-3-methylglutaryl-CoA, which are difficult to separate with ion-pair HPLC.     

Polymer crystallization dynamics,as reflected by differential scanning calorimetry. Part 1: On the calibration of the apparatus

In this paper a method for the calibration of the heat transfer coefficient between pan and furnace is given. This (second) calibration is necessary in addition to the usual calibration of the temperature scale. Indeed, with increasing cooling rates as required for kinetic measurements, the finite heat flow resistance between pan and furnace becomes evident anyway. We also propose to enlarge this resistance deliberately, in order to separate the time scales of the control system and of the exponential return of the heat flow curve to the base line, as occurring after completion of the phase transition. Only in this way can the heat transfer coefficient be determined with some accuracy. Another advantage of a lowered heat transfer coefficient will be treated in a third paper. It enables an approximate treatment of polymer crystallization kinetics.     

Mathematical Simulation and Design of Three-Phase Bubble Column Reactor for Direct Synthesis of Dimethyl Ether from Syngas

A three-phase reactor mathematical model was set up to simulate and design a three-phase bubble column reactor for direct synthesis of dimethyl ether (DME) from syngas, considering both the influence of part inert carrier backmixing on transfer and the influence of catalyst grain sedimentation on reaction. On the basis of this model, the influences of the size and reaction conditions of a 100000 t/a DME reactor on capacity were investigated. The optimized size of the 10000 t/a DME synthesis reactor was proposed as follows: diameter 3.2 m, height 20 m, built-in 400 tube heat exchanger (φ38×2 mm), and inert heat carrier paraffin oil 68 t and catalyst 34.46 t. Reaction temperature and pressure were important factors influencing the reaction conversion for different size reactors. Under the condition of uniform catalyst concentration distribution, higher pressure and temperature were proposed to achieve a higher production capacity of DME. The best ratio of fresh syngas for DME synthesis was 2.04.     

Heat loss corrections for heat capacity flow calorimeters

A single equation describes all linear thermal models for the heat losses in heat capacity flow calorimeters. This equation is used to correct for heat losses by extrapolating the apparent heat capacity to the zero value of a modified reciprocal flow rate. The method, which does not require an auxiliary pump, has been successfully tested for aqueous sodium chloride solutions to 300.8°C, with the derived apparent molar heat capacities being in agreement with literature values. Aqueous solutions of 2-methylpropan-2-ol (t-butanol) gave anomalous results requiring further investigation. Two other correction methods are both consistent with the new method but apply less generally and require care in the evaluation of the correction factors.     

Quenching of Flame Propagation with Heat Loss

The steady propagation of a planar laminar premixed flame, with a one-step exothermic reaction and linear heat loss, is studied. The corresponding travelling wave equations are solved numerically. The dependence of the flame velocity on the heat loss parameter is determined and compared with known results obtained by asymptotic expansion and other approximations. Due to the introduction of an ignition temperature the problem can be reduced to a bounded interval (of length L) and the graph of flame speed versus heat loss parameter can be parametrised by L. The numerical method is tested in the case of a step function nonlinearity when the exact solution of the differential equations can also be calculated.     

Experimental Evaluation of Procedures for Heat Capacity Measurement by Differential Scanning Calorimetry

Experimental evaluation of the procedures adopted for heat capacity measurements employing differential scanning calorimetry (DSC) has been carried out by taking nickel and sapphire as test samples. Among the various methodologies reported in literature, the absolute dual step method was chosen for this purpose due to its simplicity and minimum number of measurements required. By proper temperature and heat flux calibration employing indium as reference, it was possible to obtain the calibration factor independent of temperature. This was ascertained by analysing other pure metals namely Sn, Zn, Cd, and Pb and determining their melting temperatures and heats of melting. Various operator- and sample-dependent parameters such as heating rate, sample mass, the structure of the sample, reproducibility and repeatability in the measurements were investigated. Heat capacities of both nickel and sapphire have been determined using the above method. Further, the heat capacity of nickel has also been determined using the widely employed three-step method taking sapphire as the heat flux calibration standard. Both methods yielded the comparable heat capacity values for nickel. Based on the parameters investigated and their influence, it could be concluded that reasonably precise and accurate heat capacity measurements are possible with DSC. One advantage of this method is the elimination of a separate calibration run using a reference material of known heat capacity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temperature oscillation calorimetry by means of a Kalman-like observer: the joint estimation of Qr and UA in a stirred tank polymerization reactor

The present work is concerned with the joint estimation of the rate of heat produced by the emulsion terpolymerization of styrene, butyl acrylate and methyl methacrylate (Q_r), and the overall heat transfer coefficient (UA) from temperature measurements and reactor heat balance. By making specific assumptions on the dynamics of the parameters UA and Q_r, we designed a Kalman-like observer to carry out the estimation of these two time-varying parameters, without the need for neither additional measurements nor on-line samples. Temperature oscillations are induced in the cooling jacket in order to ensure the observability of the system. One further aspect of our approach is that it only requires the reactor energy balance to perform the estimation.     

Comparing Methods for Calculating the Heat Flow Rate of Reactions in Different Bench-Scale Calorimeters

Summary: A transfer function of the RC1e™ (Mettler-Toledo) calorimeter was obtained by calibration with a heating cartridge. With this function it was possible to determine the heat flow rate and total heat of different polymerization reactions. The calorimeter operates in isothermal as well as in isoperibolic mode. Additionally, 1-vinyl-2-pyrrolidone and acrylic acid were polymerized in a three-neck flask. In this common laboratory device the heat flow rate was obtained by using a transfer function calculated by calibration with a heating cartridge. Thus, the heat of polymerization can be obtained without using a calorimeter and without solving the heat balance equation.     

Heat capacities and entropies of linear,aliphatic polyesters

New measurements of the heat capacity in the melt of poly(trimethylene succinate) (PTMS), poly(trimethylene adipate) (PTMA), and poly(hexamethylene sebacate) (PHMS) from 310 to 400 K are presented. Based on these data and literature data on eight other molten polylactones and poly(ethylene sebacate) (PES), an addition scheme is developed for linear, aliphatic polyesters that leads to the equation: which represents the ATHAS-recommended melt heat capacities for all linear polyesters. Combining previously discussed solid heat capacities, derived from an approximate frequency spectrum, with the new liquid heat capacities, the various thermodynamic functions (enthalpy, entropy, and Gibbs function) could be derived using the ATHAS computation scheme. The average value of residual entropy at zero kelvin of 5.3 ± 1.8 J/(K mol) per mobile bead for glassy linear polysters was found to be somewhat higher than for many other polymers in the data bank, but closer to that observed for linear, aliphatic polyamides. The phase transitions of PTMS, PTMA, and PHMS are also analyzed using the quantitative baselines available from the heat capacity study.     

含氮合成气在三相淤浆床-固定床中直接合成二甲醚

在三相淤浆床－固定床反应装置中,研究含氮合成气直接合成二甲醚。使用双功能混合催化剂,粒度为0.15 mm～0.18 mm。在220 ℃～260 ℃、3.0 MPa～7.0 MPa、空速1 000 mL·g-1·h-1时考察了温度、压力及两种反应器中催化剂的装填比例对CO转化率及二甲醚选择性的影响。结果表明,一氧化碳转化率随反应压力的增加而提高,随着温度升高二甲醚的选择性变化不大,CO转化率的升高较明显,因此在催化剂活性适宜的温度范围内,该反应装置可以采用较高的反应温度。当260 ℃、7.0 MPa、三相床与固定床中催化剂比例为1∶1时,CO的转化率可达84.5％,二甲醚的选择性为78.7％。淤浆床－固定床反应装置具有操作稳定性好、CO转化率高的优点。催化剂在该装置中反应370 h活性没有明显下降。     

Heat Capacity Measurements Using Temperature-modulated Heat Flux DSC with Close Control of the Heater Temperature

The determination of heat capacity data with sawtooth-type, temperature-modulated differential scanning calorimetry is analyzed using the Mettler-Toledo 820 ADSC™temperature-modulated differential scanning calorimeter (TMDSC). Heat capacities were calculated via the amplitudes of the first and higher harmonics of the Fourier series of the heat flow and heating rates. At modulation periods lower than about 150 s, the heat capacity deviates increasingly to smaller values and requires a calibration as function of frequency. An earlier derived correction function which was applied to the sample temperature-controlled power compensation calorimeter enables an empirical correction down to modulation periods of about 20 s. The correction function is determined by analysis of the higher harmonics of the Fourier transform from a single measurement of sufficient long modulation period. The correction function reveals that the time constant of the instrument is about 5 s rad⁻¹ when a standard aluminum pan is used. The influence of pan type and sample mass on the time constant is determined, the correction for the asymmetry of the system is described, and the effect of smoothing of the modulated heat flow rate data is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Using the Transfer Function of an Isoperibolic Reaction Calorimeter for Thermo-kinetic Analysis

It is an aim of the present work to determine the chemical heat flow rate of a reaction without explicitly solving the heat balance equations. Therefore, it is necessary to calculate the heat flow rate directly from the temperature course of an experimentally determined reaction. For this transformation the transfer function of the calorimeter is needed 1 . An isoperibol reaction calorimeter was used for the experiments. With different calibrations and gained transfer functions, it is shown that the chemical heat flow rate can be determined from the temperature course of a reaction. The evaluation is fast and easy to use, which improves automation and prevents possible input errors.