Fines Dissolution Research Articles

Analysis of an integro‐differential model for bulk continuous crystallization with account of impurity feeding, dissolution/growth of nuclei and removal of product crystals

In this study, the theory of continuous crystallization from a supersaturated solution is developed, taking the concentration‐dependent fines dissolution, product removal, and feed supply rates into account. These rates make it possible to control the operation mode of the crystallizer and obtain the required supersaturation of the solution, the desired crystal‐size distribution in the supersaturated liquid, and the necessary crystal removal rate of the product. The steady‐ and unsteady‐state solutions of model equations are found analytically. It is shown that the non‐stationary crystal‐size distributions approach the stationary distribution with increasing time. The theory developed is the basis for investigating the linear and nonlinear stability of the crystallizer with allowance for the concentration‐dependent fines dissolution, product removal and feed supply rates.

On the Theory of Unsteady-State Operation of Bulk Continuous Crystallization

Motivated by an important application in the chemical and pharmaceutical industries, we consider the non-stationary growth of a polydisperse ensemble of crystals in a continuous crystallizer. The mathematical model includes the effects of crystal nucleation and growth, fines dissolution, mass influx and withdrawal of product crystals. The steady- and unsteady-state solutions of kinetic and balance equations are analytically derived. The steady-state solution is found in an explicit form and describes the stationary operation mode maintained by the aforementioned effects. An approximate unsteady-state solution is found in a parametric form and describes a time-dependent crystallization scenario, which tends toward the steady-state mode when time increases. It is shown that the particle-size distribution contains kinks at the points of fines dissolution and product crystal withdrawal. Additionally, our calculations demonstrate that the unsteady-state crystal-size distribution has a bell-shaped profile that blurs with time due to the crystal growth and removal mechanisms. The analytical solutions found are the basis for investigating the dynamic stability of a continuous crystallizer.

PERFORMANCE OF UREA/NaOH AS A GREEN SOLVENT IN DISSOLVING RECYCLED CELLULOSIC FIBER FINES RESIDUES

Using lignocellulosic materials for producing more value-added bioproducts is an attractive mission. Fiber fines, which represent an important part of the wastes generated by paper recycling mills, have been considered in the current research. Dissolving these lignocellulosic residues in environmentally friendly and inexpensive solvents can be a great achievement. For this purpose, the performance of urea/sodium hydroxide in dissolving printing and writing pulp (RPW) fines was investigated. Although using sodium hydroxide alone had a positive effect on the dissolution of recycled printing and writing pulp (RPWP) fines, the addition of urea increased the dissolution of fines from 23% to 56%. Different levels of urea consumption had no significant effect on the dissolving process. The performance of the urea/sodium hydroxide system in dissolving fines suspensions with different concentration (1, 3 and 5%) showed that reducing the concentration leads to an increase in fines dissolution (56, 36 and 7%, respectively). The results of FTIR confirmed the presence of cellulose without any hemicelluloses and lignin in the dissolving part. The results of X-ray diffraction analysis of soluble cellulose showed that the type-I cellulose structure probably changed to type-II cellulose. No reduction in the DP of dissolved cellulose and the integrated structure of the final cellulosic film confirmed by the FE-SEM images affirmed the successful dissolution of the RPWP fines in this system.

A Selective Dissolution Process Featuring a Classification Device for the Removal of Fines in Crystallization

The presence of fine crystals is a common condition that may hinder the downstream processing of a powder obtained through a crystallization process. This study investigates through simulations a process featuring a hydrocyclone for their removal. Hydrocyclones, solid–liquid separation devices widely applied in several fields of chemical engineering, enable the classification of suspended solids based on their size. The classification step allows for a selective dissolution of the fine crystals, thus leading to a more efficient process when compared to a simpler temperature cycle, where partial dissolution of larger crystals is deliberately though reluctantly accepted. A pathway for the selection of a suitable hydrocyclone design is outlined, and a novel graphical tool useful to describe the performance of the device for the fines separation task is presented. The selection of the operating variables and their operating window is discussed, and their effect on the overall process is elucidated. The design space and the performance of the selective fines removal process is investigated by coupling for the first time the detailed modeling of fines dissolution by heating and crystallization by cooling, both based on population balance equations, and the hydrocyclone behavior, for which an established model due to Braun is used. Simulation runs are presented for different scenarios and allow assessing the process performance in terms of reductions of fines, processing time, and energy demand, thus providing a valuable insight into its applicability.

A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

A continuous multi-stage mixed-suspension mixed-product-removal crystallization system with fines dissolution

This work demonstrates how crystal particle size is affected by the addition of fines dissolution in a mixed suspension mixed product removal (MSMPR) cascade system. The cooling crystallization of paracetamol in water was used as a case study. Two MSMPR cascade configurations were evaluated: (i) nucleation-growth (NG), and (ii) nucleation-dissolution-growth (NDG). Simulation results demonstrate that adding a dissolution step in the MSMPR cascade configuration increases the average product crystal size. Larger crystals and a narrower distribution were obtained due to the removal of fine crystals through the continuous process. However, a small decrease in the achievable yield was observed. Experimental results also showed a similar effect on the final mean size and CSD. The results demonstrate that a dissolution stage can be optimized to increase the final crystal size and CSD by varying the dissolution temperature to optimize the CSD with minimum effect on the achievable yield.

Improving crystal size distribution by internal seeding combined cooling/antisolvent crystallization with a cooling/heating cycle

This work investigates the effect of internal seeding and an initial cooling/heating cycle on the final crystal size distribution (CSD) during a combined cooling/antisolvent crystallization of l-asparagine monohydrate from it’s aqueous solution using isopropyl-alcohol as antisolvent. Internal seeds were generated by one-pot addition of various amounts of antisolvent to the crystallizer. It was then followed by a cooling/heating cycle to dissolve the fines produced and thus obtain a suitable initial seed. A combined cooling/antisolvent crystallization was then followed by employing a linear cooling profile with simultaneous addition of antisolvent with a constant mass flow rate to promote the growth of the internally generated seeds. The amount of initial antisolvent influences the characteristics of the internal seeds generated and the effect of initial amount of antisolvent on the final CSD is investigated. It was found that the introduction of a single cooling/heating cycle significantly improves the reproducibility of final CSD as well as the mean size. Overall, the study indicates that the application of internal seeding with a single cooling/heating cycle for fines dissolution is an effective technique to tailor crystal size distribution.

Optimal control of univariate and multivariate population balance systems involving external fines removal

We propose an algorithm for optimal control of univariate and multivariate population balance systems governed by a class of first-order linear partial differential equation of hyperbolic type involving size dependent particle growth and filtering. In particular, we investigate the impact of filtering on the optimal control outcomes. To this end, we apply a recently developed polynomial method of moments and a standard steepest descent gradient-based optimization scheme to batch crystallization benchmark problems involving external fines removal. Numerical evaluations for various case-studies aiming at minimizing the mass of grown nuclei in the context of crystal shape manipulation demonstrate the effectiveness of fines dissolution. We also validate the accuracy of the proposed method of moments by utilizing a known numerical moving grid discretization method as a reference. Our results are of interest for the control of a wide range of population balance systems in various applications such as pharmaceutics, chemical engineering, particle shape engineering.

The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution

This article is concerned with the numerical investigation of one-dimensional population balance models for batch crystallization process with fines dissolution. In batch crystallization, dissolution of smaller unwanted nuclei below some critical size is of vital importance as it improves the quality of product. The crystal growth rates for both size-independent and size-dependent cases are considered. A delay in recycle pipe is also included in the model. The space–time conservation element and solution element method, originally derived for non-reacting flows, is used to solve the model. This scheme has already been applied to a range of PDEs, mainly in the area of fluid mechanics. The numerical results are compared with those obtained from the Koren scheme, showing that the proposed scheme is more efficient.

Crystallization of Glycine by Drowning-Out Combined with Fines Dissolution and Cooling Process with in Situ Control using Focused Beam Reflectance Measurement and Attenuated Total Reflection–Fourier Transform Infrared Spectroscopy

The DFC process (a combined process of drowning-out, fines dissolution, and cooling crystallization) was applied for the crystallization of glycine. The DFC process encourages seed crystals to grow further by the dissolution of fines generated by drowning-out. Therefore, glycine crystals obtained through the DFC process have relatively large size and uniform size distribution with high product yield compared with those obtained by conventional crystallization methods. In the present work, an operating strategy of the DFC process with in situ control was proposed. First, antisolvent is injected until generation of fine particles is assumed to be completed. Second, fines dissolution by heating is conducted until fine particles are mostly dissolved. Here, generation and dissolution of fine particles are monitored by focused beam reflectance measurement and attenuated total reflectance–Fourier transform infrared. The main advantage of the in situ controlled approach demonstrated in the present work is no requirement for any predetermined data and a reduction of the operating time compared with the previously proposed DFC process, in which operating profile is predetermined by the mass balance equations.

Crystallization of RDX by Drowning-Out Combined with Fines Dissolution and Cooling Process

A new process of drowning-out combined with fines dissolution and cooling crystallization (the DFC process) was proposed to recover 1,3,5-trinitro-1,3,5-triazinane (RDX) from RDX/γ-butyrolactone solution with relatively large crystal size and high yield. In this process, fine crystals induced by drowning-out are dissolved into the solution by heating so that the dissolved solute can contribute to grow seed crystals by cooling. The DFC process is repeated to reach the desired yield. Estimation of the amount of antisolvent for drowning-out is made by a simple mass balance model in which the mass of fine particles produced by drowning-out equals to that dissolved. Considering dissolution of seeds at the fines dissolution stage, an empirical parameter α which is smaller than 1 was employed for the estimation of the optimum amount of antisolvent added. α = 1 indicates that effect of dissolution of seeds is negligible. In the present work, initial seeds were prepared by rapid injection of 15 g of water into a s...

Seeding strategies and residence time characteristics of continuous preferential crystallization

This contribution investigates the effects of different seeding strategies and residence time characteristics on the dynamics of a Mixed Suspension Mixed Product Removal (MSMPR) crystallizer equipped with a fines dissolution unit. For the first time continuous preferential enantioselective crystallization is investigated. The fines dissolution is included as recycle streams around the MSMPR crystallizer. Moreover, primary heterogeneous and secondary nucleation mechanisms along with size-dependent growth rates are taken into account. A semi-discrete high resolution finite volume scheme (FVS) is employed for discretizing the derivatives with respect to the length coordinate. The resulting ordinary differential equations (ODEs) are solved by a Runge–Kutta method of order four. Several numerical case studies are carried out. The results support process design and optimization.

Efficient solution of a batch crystallization model with fines dissolution

In this paper, an efficient and accurate numerical method is proposed for solving a batch crystallization model with fines dissolution. The dissolution of small crystals (fines dissolution) is useful for improving the quality of a product. This effectively shifts the crystal size distribution (CSD) towards larger crystal sizes and often makes the distribution narrower. The growth rate can be size-dependent and a time-delay in the dissolution unit is also incorporated in the model. The proposed method has two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for moments and solute mass is numerically solved in the time domain of interest. These discrete values are used to get growth and nucleation rates in the same time domain. In the second part, the discrete growth and nucleation rates along with the initial CSD are used to construct the final CSD. The analytical expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). A Gaussian quadrature method, based on orthogonal polynomials, is used for approximating integrals in the ODE-system of moments and solute mass. The efficiency and accuracy of the proposed numerical method is validated by a numerical test problem.

Numerical solution of a multi-dimensional batch crystallization model with fines dissolution

In this article a mathematical model for two-dimensional batch crystallization process with fines dissolution is presented. The fines dissolution is useful for improving the quality of a product and facilitates the downstream process like filtration. The crystals growth rates can be size-dependent and a time-delay in the recycle pipe is incorporated in the model. The high resolution finite volume schemes, originally derived for general systems in divergence form, are used to solve the resulting model. The schemes have already been used for the simulation of complex problems in gas dynamics and were found to be computationally efficient, accurate, and robust. The numerical test problems of this manuscript verify the capability of the proposed schemes for solving batch crystallization models.

Effect of fines dissolution on the performance of preferential crystallization for the production of pure enantiomers

Effect of fines dissolution on the performance of preferential crystallization for the production of pure enantiomers

Numerical approximations of a population balance model for coupled batch preferential crystallizers

This article is concerned with the numerical approximations of population balance equations for modeling coupled batch preferential crystallization processes. The current setup consists of two batch crystallizers interconnected with two fines dissolution pipes. The crystallization of both enantiomers is assumed to take place in separate crystallizers after seeding with their corresponding crystals. The withdrawn fines are assumed to be dissolved in the dissolution unit after heating. crystallizer, the crystallizer temperature before entering to the opposite crystallizer. Two types of numerical methods are proposed for the simulation of this process. The first method uses high resolution finite volume schemes, while the second method is the so-called method of characteristics. On the one hand, the finite volume schemes which were derived for general system in divergence form, are computationally efficient, give desired accuracy on coarse grids, and are robust. On the other hand, the method of characteristics is in general a powerful tool for solving growth processes, has capability to overcome numerical diffusion and dispersion, gives highly resolved solutions, as well as being computationally efficient. A numerical test problem with both isothermal and non-isothermal conditions is considered here. The numerical results show clear advantages of the proposed schemes.

Numerical solutions of population balance models in preferential crystallization

This article focuses on the implementation of numerical schemes to solve model equations describing preferential crystallization for enantiomers. Two types of numerical methods are proposed for this purpose. The first method uses high resolution finite volume schemes, while the second method is the so-called method of characteristics (MOC). On the one hand, the finite volume schemes which were derived for general system in divergence form are computationally efficient, give desired accuracy on coarse grids, and are robust. On the other hand, the MOC offers a technique which is in general a powerful tool for solving growth processes, has capability to overcome numerical diffusion and dispersion, gives highly resolved solutions, as well as being computationally efficient. Several numerical test examples for a preferential crystallization model with and without fines dissolution under isothermal and non-isothermal conditions are considered. The comparison of the numerical schemes demonstrates clear advantages of the finite volume schemes and the MOC for the current model.

Application of population balances in the chemical industry — current status and future needs

This contribution deals with the application of population balances in the chemical industry for the modelling of dispersed phase systems. Two examples involving industrial production processes are presented. The first example concerns the investigation of sustained oscillations occurring in a production scale crystallizer equipped with an external fines dissolution loop. For this example it will be shown, that population balance-based models can be used to analyse and overcome such oscillations. The second example describes questions occurring in the design and the operation of a solids production process. To investigate these questions, population balance-based models in connection with flow sheet simulation techniques can be used.In the second part of this contribution future needs for a more routine application of population balances are identified from an industrial point of view.

Nonlinear Oscillations in Ammonium Sulfate Crystallization: A Comparison of Different Model Predictions

In this paper, the focus is on nonlinear oscillations of ammonium sulfate crystallization. This system has been studied intensively in the past and can be viewed as a standard test system for crystallization processes. The focus is on crystallizers with fines dissolution and classified product removal. Using methods from numerical bifurcation analysis, we investigate how stability in such a system depends on the various operational parameters, like cut sizes and recycle rates of fines dissolution and product classification. Theoretical predictions of three different population models are compared with each other: (i) a model with simple kinetics and ideal fines classification, (ii) a model with complex kinetics involving breakage due to attrition and ideal fines classification, and (iii) a model with simple kinetics and nonideal fines classification. It is found that predictions of the instability regions with models i and ii are rather close. In contrast, the nonideal fines classification can change the stability rather drastically.

Modeling, simulation and stabilizing H∞-control of an oscillating continuous crystallizer with fines dissolution

In this contribution, a detailed model for a continuous crystallizer with fines dissolution is derived. The main focus of this article is the identification of physical reasons responsible for oscillations occurring in these crystallization plants. In contrast to many other crystallization models used in literature for the investigation of such limit cycles, detailed kinetic expressions for crystal growth and attrition, as well as for the separation of fines in the annular zone, are incorporated. By dynamic simulations of the model and by comparison with measured data, an undesired dissolution of larger crystals can be identified as a possible reason for the appearance of sustained oscillations. Finally, a stabilizing feedback controller is designed using H ∞-theory. It is demonstrated in simulations that this controller enables stable operation of the crystallizer even at a high fines dissolution rate.