Folyóiratban és konferencia kiadványban megjelent cikkek
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1998). The hyperbolic tangent distribution family. Powder Technology, 97, 100-108
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1998). The hyperbolic tangent distribution and its applications I. Mathematical foundations. Hung. J. Ind. Chem., 26, 89-96
Blickle T., Nirnsee-Bányai B., Ulbert Zs. (1998). The hyperbolic tangent distribution function and its applications III. Fluidizing granulation. Hung. J. Ind. Chem., 26 (4), 297-302
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1995). Characterization of mixing in suspension by a function between mean residence time and particle size distribution in mechanically stirred precipitation system. In Proc. of the Eleventh International Conference on Crystal Growth, DACG, Hague, Netherlands
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1996). Characterization of mixing of suspension in a mechanically stirred precipitation system. Journal of Crystal Growth, 166, 1064-1067
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1996). The hyperbolic tangent distribution and its applications II. The influence of some of the precipitation parameters on the particle size distribution of products. Hung. J. Ind. Chem., 24, 259-262
Konferencia előadások
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1995). A kristályosítók populációs modelljeiről. Műszaki Kémiai Napok’95, Veszprém, április 4-6.
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1995). A tangenshiperbolikus eloszlásfüggvény alkalmazási lehetőségeinek vizsgálata precipitációs kristályosításnál. Műszaki Kémiai Napok’95, Veszprém, április 4-6.
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1995). Characterization of mixing in suspension by a function between mean residence time and particle size distribution in mechanically stirred precipitation system. The Eleventh International Conference on Crystal Growth, Hague, Netherlands, 18-23 June
Farkas B., Blickle T., Ulbert Zs., Hasznosné Nezdei M. (1996). Módszer kidolgozása szuszpenziók kevertségének jellemzésére precipitációs kristályosításnál. Műszaki Kémiai Napok ‘96, Veszprém, április 23-25.
Theses
The new scientific results presented in dissertation are summarized in the following theses.
Thesis 1. Model development of continuous MSMPR and MSCPR crystallizers.
1. Population balance models have been developed for dynamic analysis of continuous MSMPR (mixed suspension, mixed product removal), MSCPR (mixed suspension, classified product removal) isothermal and cooling crystallizers. The mathematical models consist of the population balance of crystals, mass balance for solute and solvent, and, in the case of cooling crystallizers, the energy balance for the slurry. The balances include the selection function, which describes the classified product removal.
2. A detailed mathematical model has been developed for dynamic simulation of continuous MSMPR (mixed suspension, mixed product removal) vacuum crystallizers. In the model, the dynamics of both the crystal slurry and that of the vapour phase are taken into account. The model consists of the population balance of crystals, the volume balance of the slurry, the mass balance for solute and solvent and the energy balance for the slurry. As for the vapour phase, the mass balance of solvent and the energy balance have been set up. The mathematical models of the slurry level controller and of the pressure controller of the vapour phase have completed the balance equations.
Thesis 2. Model development of continuous mixed suspension non-perfectly micromixed isothermal crystallizer.
A new mathematical model has been applied for dynamic study of crystallization processes under non-perfect micromixing conditions in mixed suspension isothermal crystallizers. The model consists of two population balance equations: the population balance for crystals and the population balance for fluid elements, which describes the variation and concentration distribution of the fluid elements. The micromixing occurs through the mass exchange between the fluid elements, described by the coalescence-redispersion model, which is included in the population balance of fluid elements. In respect to the concentration distribution of the fluid elements, an average nucleation and growth rate were introduced.
Thesis 3. Numerical solution of mathematical models.
1. In the case of continuous MSMPR isothermal, cooling and vacuum crystallizers and continuous mixed suspension non-perfectly micromixed crystallizer, the ordinary differential equations system for the moments of size distribution have been derived by the moment transformation of the population balance equations. Algorithms have been developed for the solution of population balance equations of continuous MSMPR, MSCPR isothermal and cooling crystallizers by using finite element orthogonal collocation as a method of weighted residuals.
2. In connection with the finite element orthogonal collocation solution, an adaptive algorithm has been developed for adjusting calculation domain and the suitable
distribution of finite elements. In the algorithm the length of calculation domain is defined by the maximum crystal size, and the distribution of the finite elements is done according to the first order derivatives of the population density function describing the crystal size distribution.
Thesis 4. Dynamic simulation of continuous MSMPR and MSCPR isothermal crystallizers.
1. It has been shown by simulating the continuous MSMPR isothermal crystallizer that increase of parameters of the nucleation rate expression destabilises the crystallizer and sustained oscillations are obtained in the yield of crystallizer and average crystal size. The increase of crystal growth rate stabilises the crystallizer and advantageously increases the dominant size interval of crystals. It has been shown that simultaneous application of the adaptive finite element distribution method and of the finite element orthogonal collocation provides an efficient solution method for the population balance equation of crystals and, consequently, for determination of dynamic changes of crystal size distribution. The dynamic behaviour of the crystal size distribution greatly depends on the parameters of nucleation rate expression.
2. In the dynamic simulation of continuous MSCPR crystallizer it has been shown that the accelerated removing of fines stabilises the unstable crystallizer, while the accelerated removing of crystals of large size increases the amplitude of oscillations generated in an unstable crystallizer. It was shown that the yield of crystallizer and, as a consequence, the amplitude of oscillations of the yield of crystallizer as well as the average crystal size decrease, while the frequency of oscillations increases by the increase of accelerated removal at any size interval. It was showed that the dominant size interval of the crystal size distribution decreases by the increase of accelerated removal.
Thesis 5. Dynamic simulation of continuous MSMPR cooling and vacuum crystallizers.
1. In the analysis of dynamic behaviour of continuous MSMPR cooling crystallizer it has been shown that perturbation of the feed variables greatly influences the temperature and the level of supersaturation in the crystallizer. The increase of feed solute concentration increases the yield of crystallizer and the average crystal size.
The increase of feed temperature and feed flow rate decreases the yield of crystallizer and the average crystal size. The dynamics of the crystal size distribution, determined by the adaptive finite element orthogonal collocation solution, shows that perturbation of feed variables does not change advantageously the steady state exponential size distribution.
2. The dynamic simulation of continuous MSMPR cooling crystallizer under the conditions of size dependent growth rate of crystals showed that the size dependent crystal growth appears as an accelerated removal and advantageously decreases the values of size distribution. At the start-up of crystallizers the dominant size interval of crystals increases, while the steady state value of average crystal size decreases by the effect of size dependent growth rate. The presence of size dependent crystal growth does not change the yield of crystallizers.
3. The dynamic analysis of continuous MSMPR vacuum crystallizer showed that changes in the feed temperature and vapour phase pressure have advantageous influence on the thermodynamic behaviour and supersaturation level of crystallizer as well as the boiling rate of solvent. The yield of crystallizers and the average crystal size decrease by increasing the feed temperature and vapour phase pressure.
Thesis 6. Dynamic simulation of continuous mixed suspension non-perfectly micromixed isothermal crystallizers.
In the dynamic simulation of crystallization processes under non-perfect micromixing conditions, it has been shown that dynamic behaviour of crystallizers under partial segregation of the fluid phase differs significantly from that of MSMPR crystallizers. The steady state values of the average crystal size and average fluid element concentration decrease, while the steady state value of the yield of crystallizers increases by the increase of segregation level. It has been shown that the steady state value of average crystal size in the case of perfectly micromixed fluid phase increases, while in the case of partial segregation decreases by the increase of average residence time. The steady state value of the average fluid element concentration decreases by increase of average residence time at any level of micromixing.
Irodalom
Abegg C.F., Stevens J.D., Larson M.A. (1968). Crystal size distributions in continuous crystallizers when growth rate is size dependent. AIChE J., 14, 118-122
Akoglu K., Tavare N.S., Garside J. (1984). Dynamic simulation of a non-isothermal MSMPR crystallizer. Chem. Eng. Commun., 29, 353-367
Anshus B.E., Ruckenstein E. (1973). On the stability of a well stirred isothermal crystallizer. Chem. Eng. Sci., 28, 501-513
Babuska I., Chandra J., Flaherty J.E. (1983). Adaptive computational method for partial differential equations, Philadelphia: Society for Industrial and Applied Mathematics Becker Jr.G.W., Larson M.A. (1969). Mixing effects in continuous crystallization.
Chem. Eng. Prog. Symp. Ser., 65 (95), 14-23
Beckman J.R., Randolph A.D. (1977). Crystal size distribution dynamics in a classified crystallizer: Part II. Simulated control of crystal size distribution. AIChE J., 23 (4), 510-520
Berglund K.A., Larson M.A. (1984). Modeling of growth rate dispersion of citric acid monohydrate in continuous crystallizers. AIChE J., 30 (2), 280-287
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1995). A kristályosítók populációs modelljeiről. Műszaki Kémiai Napok’95, Veszprém, április 4-6.
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1998a). The hyperbolic tangent distribution family. Powder Technology, 97, 100-108
Blickle T., Lakatos B.G., Mihálykó Cs., Ulbert Zs. (1998b). The hyperbolic tangent distribution and its applications I. Mathematical foundations. Hung. J. Ind. Chem., 26, 89-96
Blickle T., Nirnsee-Bányai B., Ulbert Zs. (1998c). The hyperbolic tangent distribution function and its applications III. Fluidizing granulation. Hung. J. Ind. Chem., 26 (4), 297-302
Blickle T., Lakatos B.G., Mihálykó Cs. (2002). Véges mikrokevertségű oldatban történő kristálynövekedés sztochasztikus modellje. Műszaki Kémiai Napok’02 Konferencia Kiadvány, Veszprém, 317-322
Bohlin M., Rasmuson A.C. (1992). Application of controlled cooling and seeding in batch crystallization. Can. J. Chem. Eng., 70, 120-126
Bourne J.R., Hungerbuehler K., Zabelka M. (1976). Industrial Crystallization (edited by Mullin J.W.). New York: Plenum Press
Bourne J.R., Rohani S. (1983). Mixing and fast chemical reaction VII: Deforming reaction zone model for the CSTR. Chem. Eng. Sci., 38, 911-916
Bransom S.H. (1960). Factors in the design of continuous crystallizers. Brit. Chem.
Eng., 5, 838-844
Canning T.F., Randolph A.D. (1967). Some aspects of crystallization theory: Systems that violate McCabe’s Delta L law. AIChE J., 13 (1), 5-10
Cayey N.W., Estrin J. (1967). Secondary nucleation in agitated, magnesium sulfate solutions. Ind. Eng. Chem. Fundam., 6, 13-20
Chang C.-T., Epstein M.A.F. (1982). Identification batch crystallization: Control strategies using characteristic curves. AIChE Symp. Ser., 78 (215), 68-75
Chang R.-Y., Wang M.-L. (1984). Shifted Legendre function approximation of differential equations; Application to crystallization processes. Comput. Chem.
Eng., 8 (2), 117-125
Clontz N.A., McCabe W.L. (1971). Contact nucleation of magnesium sulfate heptahydrate. Chem. Eng. Prog. Symp. Ser., 67 (100), 6-17
Curl R.L. (1963). Dispersed phase mixing: I. Theory and effects in simple reactors.
AIChE J., 9 (2), 175-181
Danckwerts P.V. (1953). Continuous flow system: Distribution of residence times.
Chem. Eng. Sci., 2, 1-18
Danckwerts P.V. (1958). The effect of incomplete mixing on homogeneous reactions.
Chem. Eng. Sci., 8, 93-102
David R., Villermaux J. (1975). Micromixing effects on complex reactions in a CSTR.
Chem. Eng. Sci., 20, 1309-1313
David R., Villermaux J., Marchal P., Klein J.P. (1991). Crystallization and precipitation engineering - IV. Kinetic model for adipic acid crystallization. Chem. Eng. Sci., 46, 1129-1136
Dirksen J.A., Ring T.A. (1991). Fundamentals of crystallization: Kinetic effects of particle size distributions and morphology. Chem. Eng. Sci., 46 (10), 2389-2427 Eaton J.W., Rawlings J.B. (1990). Feedback control of chemical processes using on-line
optimization techniques. Comput. Chem. Eng., 14 (4/5), 469-479
Eek R.A., Dijkstra S., Van Rosmalen G.M. (1995). Dynamic modeling of suspension crystallizers using experimental data. AIChE J., 41 (3), 571-584
Epstein M.A.F., Sowul L. (1980). Phase space analysis of limit cycle development in CMSMPR crystallizers using three-dimensional computer graphics. AIChE Symp.
Ser., 76 (193), 6-17
Evangelista J.J., Katz S., Shinar R. (1969). Scale-up criteria for strirred tank reactors.
AIChE J., 15 (6), 843-853
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1995). A tangenshiperbolikus eloszlásfüggvény alkalmazási lehetőségeinek vizsgálata precipitációs kristályosításnál. Műszaki Kémiai Napok’95, Veszprém, április 4-6.
Farkas B., Blickle T., Ulbert Zs., Hasznos-Nezdei M. (1996). The hyperbolic tangent distribution and its applications II. The influence of some of the precipitation parameters on the particle size distribution of products. Hung. J. Ind. Chem., 24, 259-262
Gardini L., Servida A., Morbidelli M., Carra S. (1985). Use of orthogonal collocation on finite elements with moving boundaries for fixed bed catalytic reactor simulation. Comput. Chem. Eng., 9 (1), 1-17
Garside J. (1985). Industrial crystallization from solution. Chem. Eng. Sci., 40 (1), 3-26 Garside J., Tavare N.S. (1985). Mixing, reaction and precipitation: Limits of
micromixing in an MSMPR crystallizer. Chem. Eng. Sci., 40 (8), 1485-1493
Gelbard F., Seinfeld J.W. (1978). Numerical solution of the dynamic equation for particle systems. J. Comput. Phys., 28, 357-375
Girolami M.W., Rousseau R.W. (1985). Size-dependent crystal growth – A manifestation of growth rate dispersion in the potassium alum-water system. AIChE J., 31 (11), 1821-1828
Gupta G., Timm D.C. (1971). Predictive-corrective control for continuous crystallization. Chem. Eng. Prog. Symp. Ser., 67 (100), 121-128
Hounslow M.J., Ryall R.L., Marshall V.R. (1988). A discretized population balance for nucleation, growth and aggregation. AIChE J., 34, 1821-1832
Hounslow M.J. (1990). A discretized population balance for continuous systems at steady state. AIChE J., 36 (1), 106-116
Hulburt H.M., Katz S. (1964). Some problems in particle technology. A statistical mechanical formulation. Chem. Eng. Sci., 19, 555-574
Hulburt H.M., Stefango D.C. (1969). Design models for continuous crystallizers with double drawoff. Chem. Eng. Prog. Symp. Ser., 65 (95), 50-58
Ishii T., Randolph A.D. (1980). Stability of the high yield MSMPR crystallizer with size-dependent growth rate. AIChE J., 26 (3), 507-510
Janse A.H., de Jong E.J. (1976). The occurence of growth dispersion and its consequences. in Industrial Crystallization ’75 (edited by Mullin J.W.). Amsterdam:
North-Holland, 145-154
Jerauld G.R., Vasatis Y., Doherty M.F. (1983). Simple conditions for the appearance of sustained oscillations in continuous crystallizers. Chem. Eng. Sci., 38 (10), 1675-1681
Jones A.G. (1974). Optimal operation of a batch cooling crystallizer. Chem. Eng. Sci., 29, 1075-1087
Jones A.G., Mullin J.W. (1974). Programmed cooling crystallization of potassium sulphate solutions. Chem. Eng. Sci., 29, 105-118
Kaczmarski K., Mazzotti M., Storti G., Morbidelli M. (1997). Modeling fixed-bed adsorption columns through orthogonal collocations on moving finite elements.
Comput. Chem. Eng., 21 (6), 641-660
Kraljevich Z.I., Randolph A.D. (1978). A design oriented model of fines dissolving.
AIChE J., 24, 598-606
Kumar S., Ramkrishna D. (1997). On the solution of population balance equations by discretization - III. Nucleation, growth and aggregation of particles. Chem. Eng.
Sci., 52 (24), 4659-4679
Lakatos B.G., Blickle T. (1995). Nonlinear dynamics of isothermal CMSMPR crystallizers: A simulation study. Comput. Chem. Eng., 19, S501-S506
Lakatos B.G., Sapundzhiev T.J. (1995). Sustained oscillations in isothermal CMSMPR crystallizers: Effect of size-dependent crystal growth rate. ACH - Models in Chemistry, 132 (3), 379-394
Lakatos B.G. (1996). Uniqueness and Multiplicity in isothermal CMSMPR crystallizers.
AIChE J., 42(1), 285-289
Lang Y.-D., Cervantes A.M., Biegler L.T. (1999). Dynamic optimization of a batch cooling crystallization process. Ind. Eng. Chem. Res., 38, 1469-1477
Larson M.A., Garside J. (1973). Crystallizer design techniques using the population balance. The Chemical Engineer (London), 274, 318-328
Larson M.A., White E.T., Ramanarayanan K.A., Berglund K.A. (1982). Growth rate dispersion in MSMPR crystallizers. Paper presented at AIChE annual meeting, Los Angeles, California
Lei S.-J., Shinnar R., Katz S. (1971). The stability and dynamics of a continuous crystallizer with fines trap. AIChE J., 17, 1459-1470
Levenspiel O. (1999). Chemical Reaction Engineering, New York: John Wiley & Sons Luyben W.L. (1973). Process Modelling, Simulation and Control for Chemical
Engineers. New York: McGraw-Hill
Manjaly J. (1977). Mphil Thesis, University of London
Marchal P., David R., Klein J.P., Villermaux J. (1988). Crystallization and precipitation engineering - I. An efficient method for solving population balances in crystallization with agglomeration. Chem. Eng. Sci., 43, 59-67
Matthews H.B., Rawlings J.B. (1998). Batch crystallization of photochemical:
Modeling, control, and filtration. AIChE J., 44 (5), 1119-1127
Midlarz J., Jones A.G. (1989). On numerical computation of size-dependent crystal growth rates. Comput. Chem. Eng., 13 (8), 959-965
Miers H.A., Isaac F. (1906). J. Chem. Soc., 89, 413
Mucskai L. (1971). Kristályosítás, Budapest: Műszaki Könyvkiadó
Muhr H., David R., Villermaux J. (1996). Crystallization and precipitation engineering - VI. Solving population balance in the case of the precipitation of silver bromide crystals with high primary nucleation rates by using the first order upwind differentation. Chem. Eng. Sci., 51 (2), 309-319
Mullin J.W., Nyvlt J. (1971). Programmed cooling of batch crystallizers. Chem. Eng.
Sci., 26, 369-377
Nicmanis M., Hounslow M.J. (1998). Finite-element methods for steady-state population balance equations. AIChE J., 44 (10), 1279-1297
Nielsen A.E. (1964). Kinetics of precipitation. New York: Macmillan
Ostwald W. (1897). Studien über die bildung und umwandlung fester körper. Zeitschrift für Physilische Chemie, 22, 289-330
Ottino J.M. (1980). Lamellar mixing models for structured chemical reactions and their relationship to statistical models: Macromixing and micromixing and the problem of averages. Chem. Eng. Sci., 35, 1377-1391
Petzold L.R. (1983). A description of DASSL: a differential-algebraic system solver. in Scientific Computing (edited by Stepleman R.S.). Amsterdam: Nort-Holland, 65-68 Pohorecki R., Baldyga J. (1983). The use of a new model of micromixing for
determination of crystal size in precipitation. Chem. Eng. Sci., 38, 79-83 Prasher C.L. (1987). Crushing and Grinding Process Handbook. New York: Wiley Ramkrishna D. (1985). The status of population balances. Chem. Eng. Sci., 3 (1), 49-95 Ramkrishna D. (2000). Population balances. San-Diego: Academic Press
Randolph A.D., Larson M.A. (1962). Transient and steady state distributions in continuous mixed suspension crystallizers. AIChE J., 8, 639-645
Randolph A.D. (1964). A population balance for countable entities Can. J. Chem. Eng., 42, 280-281
Randolph A.D., Larson M.A. (1965). Analog simulation of dynamic behavior in a mixed crystal suspension. Chem. Eng. Prog. Symp. Ser., 61 (55), 147-154
Randolph A.D. (1969). Effect of crystal breakage on crystal size distribution in a mixed suspension crystallizer. Ind. Eng. Chem. Fundam., 8, 58-63
Randolph A.D., Beer G.L., Keener J.P. (1973). Stability of the class II classified product crystallizer with fines removal. AIChE J., 19 (6), 1140-1149
Randolph A.D., White E.T. (1977). Modeling size dispersion in the prediction of crystal-size distribution. Chem. Eng. Sci., 32, 1067-1076
Randolph A.D., Beckman J.R., Kraljevic Z.I. (1977). Crystal size distribution dynamics in a classified crystallizer: Part I. Experimental and theoretical study of cycling in a potassium chloride crystallizer. AIChE J., 23 (4), 500-510
Randolph A.D., Larson M.A. (1988). Theory of particulate processes, Second Edition.
New York: Academic Press
Rawlings J.B., Witkowski W.R., Eaton J.W. (1992). Modelling and control of crystallizers. Powder Technology, 69, 3-9
Rawling J.B., Miller S.M., Witkowski W.R. (1993). Model identification and control of solution crystallization processes: A review. Ind. Eng. Chem. Res., 32, 1275-1296 Rice A.W., Toor H.L., Manning F.S. (1964). Scale of mixing in a stirred vessel. AIChE
J., 10, 125-129
Rohani S. (1986). Dynamic study and control of crystal size distribution (CSD) in a KCl crystallizer. Can. J. Chem. Eng., 64, 112-116
Rohani S., Bourne J.R. (1990). Self-tuning control of crystal size distribution in a cooling batch crystallizer. Chem. Eng. Sci., 45 (12), 3457-3466
Rohani S., Tavare N.S., Garside J. (1990). Control of crystal size distribution in a batch cooling crystallizer. Can. J. Chem. Eng., 68, 260-267
Sastry K.V.S., Gaschignard P. (1981). Discretization procedure for the coalescence equation of particulate processes. I&EC Fundamentals, 20, 355-361
Shiau L.D., Berglund K.A. (1990). Growth rate dispersion in batch crystallization.
AIChE J., 36, 1669-1672
Sherwin M.B., Shinnar R., Katz S. (1967). Dynamic behavior of the well-mixed isothermal crystallizer. AIChE J., 13 (6), 1141-1154
Sherwin M.B., Shinnar R., Katz S. (1969). Dynamic behavior of isothermal well-stirred crystallizer with classified outlet. Chem. Eng. Prog. Symp. Ser., 65 (95), 75-90 Singh P.N., Ramkrishna D. (1977). Solution of population balance equations by MWR.
Comput. Chem. Eng., 1, 23-31
Sisak Cs., Blickle T., Ulbert Zs., Szajáni B. (1997). Effects of formation conditions on size distribution of thermogel beads for cell immobilisation. In Proc. of the International Symposium Immobilised Cells: Basics and Applications Progress of Biotechnology, Amsterdam: Elsevier
Takiyama H., Matsuoka M. (2002). Design of seed crystal specifications for start-up operation of a continuous MSMPR crystallizer. Powder Technology, 121, 99-105 Tavare N.S., Chivate M.R. (1977). Analysis of batch evaporative crystallizers. Chem.
Eng. J., 14, 175-180
Tavare N.S., Garside J., Chivate M.R. (1980). Analysis of batch crystallizers. Ind. Eng.
Chem. Proc. Des. Dev., 19, 653-665
Tavare N.S. (1985). Growth rate dispersion. Can. J. Chem. Eng., 63, 436-442 Tavare N.S. (1986). Mixing in continuous crystallizers. AIChE J., 132, 705-732 Tavare N.S. (1987). Batch crystallizers: A review. Chem. Eng. Commun., 61, 259-318 Tavare N.S. (1989). Micromixing limits in an MSMPR crystallizer. Chem. Eng.
Technol., 12, 1-12
Tavare N.S. (1994). Mixing, reaction and precipitation: An interplay in continuous crystallizers. Chem. Eng. Sci., 49 (24B), 5193-5201
Tavare N.S. (1995a). Industrial Crystallization. Process Simulation, Analysis and Design (edited by Luss D.). New York: Plenum Press
Tavare N.S. (1995b). Mixing, reaction and precipitation: Interaction by exchange with mean micromixing models, AIChE J., 41 (12), 2537-2548
Timm D.C, Larson M.A. (1968). Effect of nucleation kinetics on the dynamic behavior of a continuous crystallizer. AIChE J., 14 (3), 452-457
Ulbert Zs., Blickle T., Mihálykó Cs., Lakatos B.G. (1995a). Identification of the mathematical model of batch grinding. Hung. J. Ind. Chem., 23 (3), 161-165
Ulbert Zs., Blickle T., Mihálykó Cs., Lakatos B.G. (1995b). Identification of the Mathematical Model of Batch Grinding. Second International Workshop on Modeling, Identification and Control in Chemical Engineering, Schwerte, Germany, June 7-9
Ulbert Zs,. Blickle T., Mihálykó Cs., Lakatos B.G. (1998). A szakaszos őrlés matematikai modelljének identifikálása. Magyar Kémikusok Lapja, 53 (8-9), 390-396
Villadsen J., Michelsen M.L. (1978). Solution of Differential Equation Models by Polynomial Approximation. NJ, Englewood Cliffs: Prentice-Hall
Villadsen J.V., Stewart W.E. (1967). Solution of boundary-value problems by orthogonal collocation. Chem. Eng. Sci., 22, 1483-1501
Volmer M., Weber A., (1926). Z. Phys. Chem., 119, 277-301
Weinstein H.J., Alder R.J. (1967). Micromixing effects in continuous chemical reactors.
Chem. Eng. Sci., 24, 1513-1517
White E.T., Wright P.G. (1971). Magnitude of size dispersion effects in crystallization.
Chem. Eng. Prog. Symp. Ser., 67 (100), 81-87
Witkowski W.R., Rawlings J.B. (1987). Modelling and control of crystallizers.
Proceedings of the 1987 American Control Conference, Minneapolis, MN, 1400-1405
Wulkow M., Gerstlauer A., Nieken U. (2001). Modeling and simulation of crystallization processes using parsival. Chem. Eng. Sci., 56, 2575-2588
Zumstein R.C., Rosseau R.W. (1987a). Growth rate dispersion in batch crystallization
Zumstein R.C., Rosseau R.W. (1987a). Growth rate dispersion in batch crystallization