Mid Sweden University

This article focuses on a multiscale modelling approach to describe the delignification of softwood during the kraft pulping process. A framework for modelling the lignocellulosic feedstock on a fibre scale which considered the fundamental chemical components of wood as a distributed variable is re-assessed and extended to include chip-level phenomena such as diffusion limitations and initial component distributions within a softwood chip mixture. A new description of the wood chip is presented using a finite volume discretisation along one spatial dimension by simultaneously considering the anisotropic structural differences of the wood. Additionally, based on literature data, a distinction between the softwood chips' early- and latewood regions with their differences in densities and chemical composition is suggested. The presented model framework uses published sub-models for kinetics, diffusion etc. The validation and estimation of the remaining parameters are conducted from experimental data that quantifies the kappa number distribution of individual softwood fibres after kraft pulping. The investigation hypothesises a Gaussian distribution for the initial chemical component distribution within wood chips from a well-defined region. In contrast, a Log-normal distribution is used to describe the initial chemical distribution within a softwood chip mixture. The established sub-models for the kraft pulping process's kinetics and mass transfer phenomena could not predict the experimental data satisfactorily. However, modifying the sub-models by including a change in lignin reactivity and a temperature dependency of the lignin reactivity decline during the delignification progress could predict the essence of the observed experimental kappa number distribution. 

The hydrolysis kinetics of 7-methyl-1,5,7triazabicyclo[4.4.0]dec-5-enium acetate [mTBDH][OAc] was investigated in a comprehensive study by the utilization of the well-known Schlenk technique to achieve a better understanding of its stability for dry-jet wet spinning applications (e.g., Ioncell) and due to the course of operation for recovery methods like fractional distillation. Decomposition behavior as a function of temperature, time, acid-base stoichiometry, and water content was extensively analyzed and characterized by nuclear magnetic resonance spectroscopy (NMR), capillary electrophoresis (CE), and thermogravimetric analysis (TGA). Furthermore, kinetic models were formulated for the prediction of the stability and the results were compared with the closely related amidine-based analogues 1,5diazabicyclo[4.3.0]non-5-enium acetate [DBNH][OAc] and 1,8-diazabicyclo[5.4.0]undec-7-enium acetate [DBUH][OAc].

In the present work, the influence of solution viscosity on growth kinetics and purification efficiency in layer melt crystallization was investigated. Melt crystallization experiments were conducted for three different types of aqueous sucrose solution as they are ideal solutions and a relatively wide viscosity range can be investigated with a moderate change of freezing points. The aqueous 10 wt%, 23 wt%, and 30 wt% sucrose solutions have a dynamic viscosity value of 2.01 mPas, 4.74 mPas, and 7.21 mPas at their respective freezing points of −0.63 °C, −1.78 °C, and −2.64 °C. The solution temperature distribution was predicted by computational fluid dynamics (CFD) simulations run in COMSOL Multiphysics 5.6 software. Experimental results showed that a higher solution viscosity caused a higher crystal layer impurity and lower crystal yields in static layer melt crystallization. The cooling process of different solutions predicted by a CFD heat transfer study showed that the supersaturation region is wider for less concentrated solutions as cooling proceeds more rapidly. Hence, the temperature gradients obtained follow the boundary layer theory, i.e., the thinner the boundary layer, the faster the heat transfer. 

This study reports liquid–liquid equilibrium (LLE) and liquid–liquid–liquid equilibrium (LLLE) data for binary (phenol + n-dodecane, or n-hexadecane) and ternary (water + phenol + n-dodecane, or n-hexadecane) systems measured under atmospheric pressure. The compositions of coexisting phases were determined with analytical and cloud point methods at temperatures 298 K – 353 K. The Non–Random Two–Liquid (NRTL) excess Gibbs energy model was employed to correlate the measured systems. The binary interaction parameters were regressed using analytical LLE and cloud point data. In addition, the parameters were also calculated using the binary LLE data combined with the isothermal vapor–liquid data from the literature applying the NRTL–RK (Redlich–Kwong) property method. The average absolute deviations in liquid mole fraction obtained with the NRTL model (using six adjusted parameters) for the LLE and VLE experimental data were 0.006 and 0.014 respectively. The phase equilibria of binary phenol + hydrocarbon (n-dodecane or n-hexadecane) systems were modeled at the temperature range of 313 K – 573 K. 

A population balance framework based on high order moment conserving method of classes is extended to capture surfactant dynamics and its effect on drop size distributions. The proposed method is flexible for incorporating various closure models for drop breakage and coalescence, mass transfer, and physical equilibria between dispersed and continuous phase as well as for adsorption to the interface. The method is first schematically explained and derived in a generic form, and then appropriate closure models are discussed. The model is accurate and fast and can be implemented in process models, parameter optimization algorithms, and computational fluid dynamics software due to its high accuracy with limited number of additional variables. 

Renewable raw materials such as lignocellulose are inherently complex and demanding in chemical processing compared to petroleum-based feedstocks. This article addresses the challenge of developing a general model framework for modelling lignocellulosic feedstock on a fibre scale, considering its inherent heterogeneous nature in terms of the fundamental chemical component distribution in addition to its anisotropic structural properties. The presented model is tested and validated for the well-established kraft pulping process. Simulations and parameter estimation are carried out to investigate the kappa number distribution of softwood fibres during kraft pulping by using experimental data from the literature showing non-uniform delignification. A moving grid discretisation method for the distributed concentration variables is used to predict the reaction of the wood solids. The results suggest that an inherent fundamental chemical component distribution can be hypothesised as one source of the non-uniform delignification. The model indicates that a Gaussian distribution can be assumed for the initial lignin concentration within softwood. In addition, an investigation of the lignin kinetics suggests that the reactivity of lignin during kraft pulping decreases as the delignification progresses. 

In the present study, the effects of different structures of the involved compounds (such as cation, anion, and hydrocarbon) in the ternary systems on the distribution coefficient of the thiophene between ionic liquid and hydrocarbon-rich phases have been studied using Quantitative Structure-Property Relationship (QSPR). By a comprehensive literature survey, the experimental data of the distribution of thiophene for 84 different ternary systems with 763 data points have been collected. The data set includes 14, 10, and 10 different cation, anion, and hydrocarbon structures, respectively. A general QSPR model has been developed to evaluate the simultaneous effect of the hydrocarbon structure, the cation structure, and the anion structure on the thiophene distribution between the hydrocarbon and ionic liquid-rich phases. The selected molecular descriptor in this model was simple descriptor of the number of carbon atom (nC) for the cation structure, the number of nitrogen atom (nN) for the anion structure, and “Pol” for the hydrocarbon structure. The outcome of the internal validation, the external validation, and the statistical evaluation of the final QSPR models (R2 = 0.91, %AARD = 17.28) confirmed the acceptable prediction capability. The Liquid-Liquid Equilibrium (LLE) data has also been generated using the QSPR approach for a vast number of non-studied ternary systems for the first time. The LLE data of four different ternary systems ([C2MIM][EtSO4] (1) - Thiophene (2) - Cyclohexane, Methyl cyclohexane, n-Nonane, n-Decane (3)) was measured experimentally. The comparison of the measured experimental data and the predicted data using the developed QSPR model confirmed the validity of the QSPR developed model, again. 

A continuous flow apparatus was applied to measure the phase equilibrium at 523 K and 573 K. The performance of the apparatus was analysed with the determination of vapor pressures of water at the temperatures (T = 453 K and 473 K). The measured water vapor pressures deviated from the literature values less than 1 %. Vapor pressures of n-dodecane, n-hexadecane and phenol were measured at the temperatures (T = 523–623 K) and, the bubble point pressures of n-dodecane + phenol and n-hexadecane + phenol were measured at the temperatures (T = 523 K and 573 K). The measured vapor pressures of the pure components were compared with the literature values. Relative vapor pressure deviated from the literature value less than 2 % for all the measured vapor pressures. The measured vapor pressures value in this work agreed well with the literature, which indicates that the measurement apparatus and the method can produce good-quality data. The measured bubble point pressures for the n-dodecane + phenol and n-hexadecane + phenol systems were modeled with Peng-Robinson and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state and Non-random Two-liquid (NRTL) activity coefficient model. The measured systems were at first modeled with Peng-Robinson and Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equations of state without binary interaction parameters. Additionally, the parameters were regressed to optimize the performance of the models. The NRTL activity coefficient model described the behaviour of the measured and the literature data better than the equations of state. Furthermore, the Peng-Robinson equation of state resulted in better predictions than PC-SAFT equation of state even without binary interaction parameters regression. Both equations of state modeled the phase equilibrium behaviour of the system well. The n-dodecane + phenol system showed azeotropic behaviour. 

The prediction of the particle-size distribution (PSD) of the particulate systems in chemical engineering is very important in a variety of different contexts, such as parameter identification, troubleshooting, process control, design, product quality, production economics etc. The time evolution of the PSD can be evaluated by means of the population balance equation (PBE), which is a complex integro-differential equation, whose solution in practical cases always requires sophisticated numerical methods that may be computationally tedious. In this work, we propose a novel technique that tackles this issue by using an analytical time-stepping procedure (ATS) to resolve the PSD time dependency. The ATS is an explicit time integrator, taking advantage of the linear or almost linear time dependency of the discretized population balance equation. Thus, linear approximation of the source term is a precondition for the ATS simulations. The presented technique is compared with a standard variable step time integrator (MATLAB ODE15s stiff solver), for practical examples e.g. emulsion, aging cellulose process, cooling crystallization, reactive dissolution, and liquid-liquid extraction. The results show that this advancing in time procedure is accurate for all tested practical examples, allowing reproducing the same results given by standard time integrators in a fraction of the computational time. 

Mercury has been applied as a sealing and pressure transmission fluid in many experimental phase equilibrium studies employing the synthetic visual method as well as a moving piston in analytical isobaric and/or isothermal methods. However, mercury is highly toxic and therefore its use is restricted by authorities such as those of the European Union. A new apparatus employing nontoxic GaInSn liquid metal alloy as a sealing, moving piston, and pressure transmission fluid for phase equilibrium measurements with a nonvisual variable volume method is presented. The vapor pressures of toluene, hexylbenzene, and 2-ethylnaphtalene are provided within the applied temperature range of 400-620 K. New values for the parameters of the DIPPR 101 and Wagner equations, and PC-SAFT equation of state were regressed. The results demonstrate that GaInSn can be used in phase equilibrium cells as a very convenient substitute for mercury, especially at high temperatures.