Калориметрия теплового потока и ДСК — важные инструменты исследования и создания математических моделей технологических объектов Текст научной статьи по специальности «Химические технологии»

В результате серии вычислительных экспериментов построена кавитационная характеристика насоса (рис.6) которая имеет хорошее качественное согласование с теоретическими данными [3].

Заключение

Разработана математическая модель течения жидкости в центробежном насосе с учетом возникновения кавитации. Расчеты, проведенные в программном комплексе ANSYSCFX ,выявили наличие зон пониженного давления и зон кавитации. При уменьшении давления, подаваемого на вход центробежного насоса, зоны кавитации становятся больше. Кавитационная характеристика, построенная в результате вычислительных экспериментов, имеет хорошее согласование с теоретическими сведениями.

Литература

1. Лепешкин А.В., Михайлин А.А., Шейпак А.А. Гидравлика и гидропневмопривод. В 2-х частях. Ч. 2: Гидравлические машины и гидропневмопривод: Учебник /Под ред. А.А. Шейпака. 4-е изд., доп. и перераб. - М.: МГИУ, 2007. - 352 с.

2. Ansys CFX solver Theory guide, Release 14.5.

3. S. Christopher and S. Kumaraswamy Experimental Study of Cavitation Hysteresis on Radial Flow Pump // Institution of Engineers (India) Journal-MC, Vol.92, pp.34-39

Шариков Ю.В. \ Шариков Ф.Ю. 2, Титов О.В.3

'Профессор, доктор технических наук; 2Ведущий научный сотрудник, кандидат химических наук; 3ассистент, кандидат технических наук, Национальный минерально-сырьевой университет «горный» (горный университет) КАЛОРИМЕТРИЯ ТЕПЛОВОГО ПОТОКА И ДСК - ВАЖНЫЕ ИНСТРУМЕНТЫ ИССЛЕДОВАНИЯ И СОЗДАНИЯ МАТЕМАТИЧЕСКИХ МОДЕЛЕЙ ТЕХНОЛОГИЧЕСКИХ ОБЪЕКТОВ

Аннотация.

В статье рассматривается опыт применения Дифференциальной Сканирующей Калориметрии (ДСК) и калориметрии теплового потока (Кальве) для изучения кинетики сложных многостадийных промышленных процессов, имеющих большое практическое значение. Была исследована информативность калориметрических данных и процедура их обработки совместно с аналитическими данными для решения обратных задач химической кинетики.

Ключевые слова: Калориметрия, кинетика, математическое моделирование

Sharikov I.V. \ Sharikov F.I.2, Titov O.V.3

'Professor, Dr. of Science (Chem. Engng.); ^Leading research scientist, PhD (Chemistry); 3asistant, PhD (Chem. Engng.)

National mineral resources university (mining university)

DSC AND HEAT FLUX CALORIMETRY - IMPORTANT AND POWERFUL TOOLS FOR TECHNOLOGICAL PROCESSES STUDY AND MATHEMATICAL MODELING

Abstract.

The article examines the possibilities and experience of applying Thermogravimetry - Differential Scanning Calorimetry (TG/DSC) and heat flux (Calvet) calorimetry techniques to kinetic study of complicated multi-stage industrial reactions of considerable practical importance. Self-descriptiveness of calorimetric data and the procedures of their treatment together with analytical information for solving inverse kinetic tasks have been studied.

Keywords: Calorimetry, kinetics, mathematical modeling.

Introduction

DSC and Calvet calorimetry are widely used in numerous studies on the structure and properties of various chemical compounds. Their application to the development of chemical processes mathematical models related to further simulating a definite industrial reactor are not quite common yet, although heat flux calorimetry is an important and powerful tool to provide necessary information on the reaction rate for the majority of chemical reactions that take place in the system under investigation and provide a heat effect.

Heat flux calorimeter allows you to detect and record heat flow that occurs in the cell or vessel with the sample due to chemical reactions and phase transformations. These changes in the heat content can be described by the following system of equations:

dQ r p (1)

gen=X wj ■ Hj+X q, ■ Q,; j=1,..R; *=и.P

dt

j=1

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dci

dt

Wij

R N

XX Wj

j=l i=l

Nr Np

-kj П ci+k - j ■ П ci

i=1

=Nr+1

(2)

(3)

Where Qgen - total amount of absorbed (or evolved) heat in a chemical process, kJ.

Wlj conversion rate in the reaction of i-th component of the reaction mixture for j-th chemical reaction.

кj = exp(ln(k 0,j) - (Ej /RT))

kmol /(m • min)

- rate constant for the direct reaction;

k-j = exp(ln(k 0,-j) - (E- j/RT))

- rate constant for the inverse reaction;

H j - heat effect of j-th chemical reaction, kJ / kmol; q ,0

- rate and heat effect value of the i-th phase transition;

P - number of phase transformations in the system; t - current process time, min.

R series of parallel chemical reactions and P series of parallel phase transformations usually take place in a multiphase reaction system.

dQ /dt

We can measure either total heat release rate gen/ , using DSC or Calvet calorimetry technique, or total heat release rate together

with the change in mass of the sample m (t) as a function of time using TG/DSC technique - as observed responses. Thus we have only generalized responses for the course of the entire process in the case. However, these curves have a large number of points, including the extreme points and inflection points as well. These features make the heat production curve highly informative, and it is possible to select characteristic points in order to perform product analysis in these points and finally to describe a quite complicated and detailed physicochemical mechanism of the process, taking into account the possible intermediate steps.

In order to understand how precisely we can determine kinetic parameters of the model, we solved the problem of modeling an ideal established process to determine its kinetic parameters that we knew beforehand. To do this we have simulated an array of experimental data that reflected the behaviour of an ideal process with heat generation in a calorimetric cell. We solved numerically the system of kinetic equations describing the process with two consecutive exothermic reactions of the 1-st order:

ki k 2

A ^ B ^ C

H1 H 2

(4)

A mathematical model that describes kinetic behaviour of a process with the selected scheme of chemical reactions in a batch ideal reactor with a given temperature profile is as follows:

dcA

dt

exp(ln k 01

E.) c

R . T ^A

dcB

dt

dcF

dt

exp(ln k 01- Rt ) • ca - exp(ln k 02- -Rt ) • cb ; exp(ln k 02- Rt } • cb ;

(5)

f = H 1exp(ln k01 - R) ■ ca

T = T(t)

H2exp(ln k02

E 2 ) .

R . T cb

Through solving this system of differential equations we generated some kinetic data to be used as quasi-experimental data for verifying the procedure of searching a solution for the problem of parametric identification for fully observed objects. Solution of these model equations was performed with the following values of kinetic parameters of the model (4) (see Table 1).

Table 1. Kinetic parameters used for generating quasi-experimental data to be used for modeling the search procedure for these kinetic

constants.

lnK01 = 25 [1/min] E1 = 100 kJ/mol H1 = 30 kJ/mol

lnK02 = 8 [1/min] E2 = 40 kJ/mol H2 = 10 kJ/mol

The following concentration values were used as initial conditions for the solution of the equations (5) to generate quasi-experimental

data.

Table 2. Initial conditions for concentrations used for generating quasi-experimental data to be used for modeling the search procedure

Ca(0) 10 kmol/m3

Ca(0) 0 kmol/m3

Ca(0) 0 kmol/m3

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Temperature mode was chosen as linear heating from 400 to 500K with в = 1K/min (100 min). Solution of the direct kinetic task was carried out in software environment ReactOp Cascade, ver. 3.20 [1, 2]. Figure 1 shows the solution results for system of equations (5) with the values of kinetic parameters and initial conditions given in Tables 1 and 2.

Fig. 1. Results of numerical solutions of equations (5) with the kinetic parameters and initial conditions given in Tables 2, 3.

A) Integral responses for the components; B) Differential responses for the components These results of simulation were used as experimental data to investigate the possibility to find the exact kinetic parameters from real experimental data that are usually obtained in the result of a calorimetric run. The procedure that is used now is to determine the kinetic parameters from experimental data in the result of minimizing the sum of squared deviations between experimental (real) and calculated data. This value is a complex function of the kinetic parameters set, hence their determination is to find a minimum of the many variables function [1, 2]:

K S

R =

KS

11 (:

(calc)

x*,* ■

(exp

■x k ,x

) = R(uP)

(6)

Using these calculated curves as experimental data, we were solving the inverse kinetic task. The values given in Table 3 were used as initial estimations to begin the search.

Table 3. Initial values for searching the kinetic parameters.__________________________________________________________

Kinetic parameter Reaction 1 Reaction 2

lnK0j , [1/min] 18 3

Eaj , kJ/mol 80 15

Hj , kJ/mol 20 12

Rq 752058

To define the mismatch function R “step-by-step’ we were taking each time various response combinations: first - all concentrations together with heat production rate; then we expelled concentration responses from the mismatch function R, and finally we expelled the heat production rate response and only the concentrations were left. Each time the searching procedure was begun from the same point for initial conditions (see Table 2). It was found that the most informative experimental responses were either heat production rate, or the integral heat production response. Figure 2 shows the mismatch at the starting point when we were using the heat production rate response, and Figure 3 shows the final mismatch between (quasi)experimental and calculated curves. The kinetic parameters found in the result match the original values given in Table 1 with a high precision. The whole procedure confirmed reliably the high self-descriptiveness of heat production curves (both - differential and integral). The possibility to use the results of kinetic runs with measuring heat production rate in a heat flux calorimeter has been demonstrated. The kinetic model developed in this way can be further used for determining the optimum operation conditions of an industrial reactor.

Fig. 2. The mismatch between experimental (points) and

calculated data (solid curve) at the starting point, with the kinetic parameters given in Table 3. The value of mismatch function R = 683.73 (initial value, before searching procedure).

nonlinear programming techniques. The minimum point was reached in 19 iterations. The value of the mismatch function R = 8.76-10"23 - in the final point, after search.

Experimental results and discussion

The following processes were selected for the experimental study, kinetic analysis and further mathematical modeling: 1) production of alumina via calcination of the nepheline charge, 2) production of the cement clinker and

Calcination processes of cement charge and alumina production by the sintering nepheline charge are industrially important and contain many common reactions. Both these processes are run with overall weight loss and a noticeable heat absorbtion, and it is of interest to apply a TG/DSC technique in order to get the experimental data on real industrial kiln charges, compare the data for similar reactions within kinetic analysis and fulfill the whole procedure of modeling and optimization for these important industrial processes.

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The sequence of chemical transformations that takes place at heating the nepheline and lime charge for alumina production and raw mixture charge for cement clinker production is shown in Table 4 [4].

Table 4. Chemical reactions at sintering the nepheline and lime charge for alumina production and raw mixture charge for cement _______________________________________________________clinker production.______________________________________________________

Nepheline-lime charge for alumina production Raw mixture charge for cement clinker production

H2O1 ^H2° Qi CaCO3^CaO+CO2~Q2 Na2CO3^Na2O+CO2-Q3 AhO3 H2O—AI2O3+H2O-Q5 Al2O3 •.3H2O^AhO3+3H2O-Q6 Na2O+ AhO3^2NaAlO2+Q7 Na2O+Fe2O34>2NaFeO2+Q8 2CaO+2SiO2 —2CaOSi O2+Q9 CH4+2O2—CO^+2H2O+Q10 H2O1 —H2O — Q1 CaCO3 ^CaO+COg-Q MgCO 3 ^MgO+CO2-Q3 AhO3-2(SiO2) 2H2O+2CaO—2(2CaO■ SiO2)+MgO+Q5 2CaOMgO-2SiO2+2CaO—2(2CaO-SiO2)+MgO+Q6 CaOMgO-SiO2+CaO—2CaO-SiO2+MgO+Q7 2CaOAl2O3-SiO2+CaO—3CaOAl2O3+SiO2+Q8 2CaO+SiO2—2CaOSiO2+Q9 2CaO-SiO2+CaO— 3CaO-SiO2+Qw 3CaO+ A^O3—3CaO AI2O3+Q11 4CaO+ Al^^3+Fe^^3—4<Ca^ Al^^3-Fe2O3+Qj2

Kinetic runs were performed using the instrument STA-429 NETZSCH-Geratebau GmbH. TG/DSC responses were measured. Heating law in these runs was introduced in a table form and it was the same as the real time-temperature profile along the axis of an industrial furnace for producing cement clinker and nepheline sintering batch, respectively. Initial experimental data were processed to necessary units and their kinetic analysis was performed due to the models given in Table 4 in accordance with the procedure described above. Comparison of experimental and simulated kinetic curves after the procedure completion with the found values of kinetic parameters is given in Figures 4-7.

Fig. 4. Comparison of experimental (points) and calculated (solid line) curves of the sample mass loss at heating a dry blend of nepheline

charge

Fig. 5. Comparison of experimental (points) and calculated (solid line) curves of the sample heat absorption rate at heating a dry blend of nepheline charge.

Fig. 6. Comparison of experimental (points) and calculated (solid line) curves of the sample mass loss at heating a dry feed mixture for the production of cement clinker.

Fig. 7. Comparison of experimental (points) and calculated (solid line) curves of the sample heat absorption rate at heating a dry feed mixture for the ___________production of cement clinker.___________

The values of kinetic parameters found for the corresponding models of both these processes are given in Table 5. It can be noticed that the kinetic parameter values for the same reactions occurring in both processes are found to be rather close. It indicates of the validity of the quasi-homogeneous model assumption that has been applied for modeling these industrial processes. The contribution of diffusion resistance seems to be almost the same as well.

Table 5. Heat effect values, activation energy values and logarithms of rate constant pre-exponential factors found in the result of

kinetic analysis.

Mineral Cement charge Alumina-containing charge

CaCOj

ln(Ko), \1/min] 13.37 13.33

Ea, kJ/mol 102.17 102.77

ln(Keo), \1/min\ 15.01 15.69

Ee, kJ/mol 60.0 60.0

ЛИ, kJ/kmol 165914.78 165734.65

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MgCO3

ln(Ko), [1/min] 2.61 2.0

Ea, kJ/mol 89.63 92.42

ln(Keo), [1/min] 93.18 93.18

Ee, kJ/mol 187.06 187.12

AH, kJ/kmol 68819.37 68642.72

Al2O3<2SiO2«2H2O

lnKo, [1/min] 4.9 4.89

Ea, kJ/mol 48.35 48.46

AH, kJ/kmol -237744 -237698

NaAlO2^6SiO2r2H2O

lnKo, [1/min] 9.86 9.86

Ea, kJ/mol 20.84 20.84

AH, kJ/kmol -66948 -66936

Al2O3<3H2O

lnKo, [1/min] 10.47 10.48

Ea, kJ/mol 11.22 11.36

AH, kJ/kmol 52891.0 52859.0

NaAlO2^6SiO2r2H2O

lnKo, [1/min] 2.19 2.15

Ea, kJ/mol 48.84 48.82

AH, kJ/kmol 102920.0 103004.0

Fe(OH)3

lnKo, [1/min] 4.73 4.72

Ea, kJ/mol 36.16 36.16

AH, kJ/kmol 10292.0 10268.0

Conclusion

Mathematical models of sintering charges for alumina production and cement clinker production developed with applying STA and XRD techniques made it possible to describe the complicated chemical transformations with weight loss and heat absorbtion in rotary tubular kilns. They have been successfully used for optimization of these industrial processes with the use of nonlinear programming mathematical methods.

References

1. Шариков Ю.В., Белоглазов И.Н. Моделирование систем. /Часть 1. Синтез моделей технологических объектов на базе уравнений гидродинамики и химической кинетики. Санкт-Петербургский государственный горный университет, Санкт-Петербург, 2011, 108с.

2. Шариков Ю.В., Белоглазов И.Н. Моделирование систем./ Часть 2. Методы численной реализации математических моделей. Санкт-Петербургский государственный горный университет, Санкт-Петербург, 2011, 118с.

3. Лайнер А.И. Еремин Ю.А. Певзнер И.З. Производство глинозема//М., Металлургия, 1978 г., 344с.

4. Теория цемента/Под ред. А.А.Пащенко.-Киев; Будевшник, 1991.

Шариков Ф.Ю.1, Шариков Ю.В.2

'Ведущий научный сотрудник, кандидат химических наук; 2Профессор, доктор технических наук; Национальный минеральносырьевой университет «горный» (горный университет)

ИССЛЕДОВАНИЕ КИНЕТИКИ ПРОЦЕССА МОДИФИКАЦИИ ХЛОРСОДЕРЖАЩЕЙ ЭПОКСИДНОЙ СМОЛЫ С ИСПОЛЬЗОВАНИЕМ КАЛОРИМЕТРИИ ТЕПЛОВОГО ПОТОКА.

Аннотация

Приведены результаты исследования процесса каталитического модифицирования хлорсодержащих эпоксидных смол типа «Оксилин» бутандиолом-1,4 с применением калориметрии теплового потока. Проведено исследование кинетики процесса при различных температурах и начальных соотношениях реагентов. Разработана математическая модель процесса и определены ее параметры при решении обратной задачи. Модель использована для определения оптимальных условий проведения процесса.

Ключевые слова: эпоксидные смолы, модификация, кинетика, калориметрия, математическое моделирование.

F.I Sharikov1, I.V. Sharikov2

^Leading research scientist, PhD (Chemistry); 2Professor, Doctor of Science (Chem.Engng.); National Mineral Resources University

"Mining university”.

KINETIC STUDY OF MODIFICATION OF CHLORINE CONTAINING EPOXXY RESINS WITH USING HEAT FLUX

CALORIMETRY

Abstract

The results of a kinetic calorimetric study for the catalytic modification of chlorine-containing epoxy resins "Oksilin" with butanediol-1,4 are presented. Experimental data were obtained at various temperatures and initial reagent concentrations. The process kinetic model has been developed and its parameters have been obtained through solving an inverse task. The model was used for further analysis of the process and searching its optimal running conditions.

Keywords: epoxy resins, modification, kinetics, calorrimetry, mathematical modeling

Important industrial process that has been studied and simulated with using heat flux calorimetry by proposed way is modification of epoxy resins with a bifunctional alcohol - butanediol-1,4. In order to develop a kinetic model of the process of epoxy oligomers modification we performed a kinetic study of the reaction with applying Calvet calorimeter C80 of SETARAM Instrumentation. Two commercially important makes of epoxy oligomers - "ED-20" and "OKSILIN-6" - were selected for the study. The homogeneous catalyst used was NaOH solution of a known concentration or butanediol-1,4 alcoxide solution in the same butanediol-1,4.

Special cylindrical high-pressure ampoules made of stainless steel were used for the kinetic experiments. Ampoules had special stirrers inside to additionally mix the viscous “liquid-liquid” reaction mixture via reversing the calorimetric block. O-ring gaskets were made of teflon, and the ampoules were made of the same stainless steel that is proposed to be used for an industrial reactor unit.

Kinetic experiments on modifying epoxy resins "ED-20" and "OKSILIN-6" were run in a wide range of experimental conditions (molar ratio of the reagents "epoxy group - alcohol": 1:20 + 1:1; catalyst concentration: 0.1^0.4 mas.%; temperature mode: linear heating in the range 35^195°C at heating rates 0.5 and 0,2°C/min and isothermal modes at 110,120,130 and 150°C. Kinetic curves of heat production rate for the given experimental conditions were obtained, overall heat effect value of the complex reaction was measured and the reaction

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