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ISSN 2522-1841 (Online) ISSN 0005-2531 (Print)
UDC 66.095.2/661.71
DEVELOPMENT OF A NON-STATIONARY MATHEMATICAL MODEL FOR THE PROCESS OF POLYMERIZATION OF PROPYLENE
A.M.Aliyev, A.R.Safarov, I.V.Balayev, I.I.Osmanova, A.M.Guseynova, F.G.Bayramov
M.Nagiyev Institute of Catalysis and Inorganic Chemistry, NAS of Azerbaijan
agil_s@mail.ru
Received 20.06.2020 Accepted 07.08.2020
The mathematical model has been developed for the process polymerization propylene proceeding under unsteady conditions due to the toxic effect of methylacetylene on it, leading to decrease of the productivity and quality of polypropylene. Non-stationary function to maintain the productivity at the optimum level obtained during the process in stationary conditions has been proposed. Using this mathematical model allow ones control the process, stabilize it at any time of the polymerization operation. The control scheme of algorithm of this process has been created.
Keywords: polymerization ofpropylene, non-stationary function, non-stationary model, initiator.
doi.org/10.32737/0005-2531-2020-4-6-11
Introduction
Polypropylene (PP) is the second most common polymer after polyethylene in the world. Demand for it is growing steadily. It increases by 4-6% annually. Polypropylene of all grades is physiologically harmless, therefore it is widely used in medicine, in housing construction, as well as for various household products and consumer goods. On an industrial scale, PP are prepared by propylene polymerization using Ziegler-Natta catalysts. A feature of organome-tallic catalysts of the Ziegler-Natta type is the ability to impart a certain stereoregular structure (isotactic) to PP molecules, which determines the enhanced physicochemical properties of the polymer. Isotactic polypropylene is technically the most important and promising, since it has high rigidity and hardness. The necessary conditions for polymerization are the presence of a pressure of at least 10 atm and a temperature of up to 800C. The reaction time is 4-6 h in reactors with a volume of 50-120 m3. The conversion is 98%. Polymerization is carried out in a solvent medium, usually a liquid hydrocarbon (gasoline, n-heptane, white spirit). The volume ratio of propylene:solvent is 1.5:1 [1, 2].
The technological process for the production of polypropylene consists of the operations of preparing catalyst complex, polymerizing liquefied propylene, washing the polymer suspension, squeezing out the polymer by centrifu-gation, drying, granulating, filling and packag-
ing. Due to the not always achievable purity of propylene entering the polymerizer, the station-arity of the process is violated, that negatively affects on productivity of the resulting product, reducing it. This can be avoided by introducing in stationary kinetic model selected of function control mathematical model of the process that affords chance of directing the process to necessary side and preserving required productivity of polypropylene.
The mechanism and mathematical description of the process
Scientists of the University of Massachusetts studied the kinetics of suspension polymerization in a semi-batch reactor on the rac-Et(Ind)2ZrCl2/MAO metallocene catalyst complex [3]. The main goal of their work was to determine the effect of monomer concentration and temperature on the course of polymerization, to develop a kinetic model, and to estimate kinetic constants. The work was carried out at three temperatures (50, 65 and 750C) and four partial pressures of the monomer (1.5, 2.5, 3.2, 3.8 atm). As a result, the profile of the polymerization reaction rate was determined, which is characterized by the period between the activation of the process until its maximum rate is reached and the subsequent gradual chain termination (deactivation).
The kinetic mechanism of the process is represented by the following scheme:
Initiation C* + M- kin ->Ri
Chain growth R + M- kr ->Ri+i
Chain transfer to monomer R + M- kir ->Dj + R
Deactivation (Chain break) Ri kd ■>Di + Cd
Secondary inclusion R + M- ks ->Pi+i
Chain growth after a break p + M ksp - R+i
Chain transfer after a break P + M kstr ^D + R
(1)
However, it was found that the rates of secondary inclusion, chain growth after a break and chain transfer after secondary inclusion hardly affects the reaction rate. Therefore, the simplified equation of speed, including initiation, chain development, chain transfer to the monomer and deactivation has the following form: kr C M , Mr —k it i
r t )= (e—^ — e—k
kd — k,„M
where C - active catalyst center; C* - inactive
catalyst center; D, - chain break with i-th monomer; kin, kr - chain initiation and growth rate constants, 1mol-1 s-1; kd - chain break rate constant, 1/s; M - monomer; P, - chain with i-th monomer; Ri - active chain with i-th monomer; t - contact time, s.
Arrhenius dependent on temperature at calculating of kinetic rate constants was assumed:
E
k (T )= A, exp
RT
(3)
where the activation energy E, of the polymerization process and the preexponential factor Ai were adjustable parameters for each rate constant k
The constants of the kinetic model are shown in Table 1.
The thermal effect of propylene polymerization makes up about 58.7 kJ/mol or 1385 kJ/kg (2.4 times less than at ethylene polymerization).
Table 1. Kinetic constants
This makes possible to remove the heat of polymerization through the jacket of the apparatus, cooled by water, without resorting to special methods of heat removal (boiling solvent, gas circulation etc.) [3]. In this regard, the heat balance of the process can be described by the equation:
qM = Cp (T - T0) G w, (4)
where q - the thermal effect of reaction, cal/kg; M - monomer amount, kg/h; Cp - heat capacity of water, cal kg-1 K-1; T - reactor temperature, K; T0 - cooling water temperature, K; Gw - water amount, kg/h.
With increasing temperature, the reaction rate and, consequently, the yield of polypropylene are increasing. From this point of view, it would be advisable to maintain the temperature as high as possible. In this case, the heat of reaction would be improved due to the temperature difference between the coolant and the reaction mass. However, with an increase of temperature above 800C (353 K), the yield of atac-tic polypropylene increases significantly and the yield of isoatactic decreases.
Therefore, at the temperature of the reactor T, determined from equation (4),
T =
qM + CpTG
CpGw
(5)
a restriction should be imposed: T<353 K.
Parameters £m, 1mol-1 s-1 k, l mol-1 s-1 K, 1/s
ln4 10.24 24.05 13.42
E (kDj/mol) 43.05 52.32 62.03
T°C - - -
50 3.07-10-3 97.5 6.3610-5
65 6.2740-3 231 1.77 10-4
75 9.7440-3 395 3.3410-4
Both working pressures, and the temperature, also significantly affect the rate of polymer-rization of propylene. The reaction rate is a linear function of the partial pressure of propylene, that is, how many times the pressure increases, so many times the polymerization will increase. However, increasing the pressure leads to a sharp increasing the solubility of propylene in the hydrocarbon solvent. High solubility leads to a great increase in the cost of propylene evaporation, solvent vapor condensation and propylene compression during the evaporation stage. In addition, the conduct of the polymerization process at high pressures requires increasing the pressure in the pipelines of liquids (propylene, solvent, catalyst complex) while entering to the reactor, which complicates operation [5]. Taking into account the number of these features the polymerization process of propylene at conduct in a solvent medium pressure in the reactor remains constant, equal to 10 atm (dP/dx=0).
Equations (2), (5) constitute the mathematical model of the process proceeding under stationary conditions, provided that pure propyl-ene is introduced into the polymerization reactor. However, during the pyrolysis of propane, in addition to propylene, by-products are also formed, containing the small amount of methylacetylene, which is difficult to separate from the reaction mixture and pollutes the raw feed to the polymerization. Despite the fact that it undergoes the selectively hydrogenation at the Ethylene-Polyethylene plant in an isothermal tubular reactor and is partially converted into propylene, however, even the remaining insignificant part of methylacetylene (1-3 ppm), interacting with the initiator, leads to the formation of undesirable for the polymerization process products, as a result of what the amount of disintegrating initiator (active catalyst complex) per unit time increases, which leads to a decrease in the molecular weight of the polymer, i.e. its quality.
To suspend the decomposition of the initiator, by as proposed the function that takes into account the toxic effect of methylacetylene on it. Poisoning occurs on the account of adsorbing
methylacetylene contained in the feed stream and which is a poison for the initiator. We assume that the speed of its movement from the flow to the centers of the initiator is proportional to the number of unpoisoned centers and the concentration of the poison in the gas phase. It, in turn, is equal to the speed of movement of the total number of active centers (Ct) from the surface:
dC dC
pc
dt dt
k (C - C„) Cp,
(6)
where Ccl - initially present the total number of centers (active); C - concentration of poisoned (inactive) centers; (cC - Cpc) - number of non-poisoned centers; C - concentration of poison (methylacetylene) in the gas phase; c -total number of active centers.
Dividing (1) on C'c and denoting by Y part of the poisoned centers from their total
C
number Y = —, we obtain from (1):
/-it 1 v y
Cc
d Y
— = k (1 - Y )• Cp, (7)
integrating which, we have:
(1 - Y) = e-ktCp (8)
Part of the centers suitable for adsorption - (1-Y), is the activity of the initiator. Denoting 1-Y=0 and considering that the concentration of poisons Cp is proportional to the amount of raw materials supplied for polymerization (Cp~FC3 H6), we obtain the following expression for the initiator deactivation function:
_ ^-M1-«)FC3H6
0 = e
(9)
where k - the rate constant of the decomposition of the initiator depending on reaction time
E Ein
equal to k = Ae RT; T - process temperature, K; A - preexponential factor; a - mole fraction of methylacetylene in raw material; Fc H ^ - amount
of propylene entering the polymerizer, kmol/h; t - reaction time, h; Ein - activation energy of the
initiator decomposition reaction, kJ/mol; R - gas constant, kDj /(molK).
By least square method [6] hase been found: ko=0.55 10-6, £=21.35 kDj/mol.
To maintain the rate of polymerization and obtain polypropylene of the same quantity and quality as under stationary conditions (without taking into account the undesirable effect of methylacetylene), we introduce in the equation of the process rate going under stationary conditions (2) the nonstationarity function 0, which will correct the change in the activity of the catalyst depending on the reaction time:
r(t) = ^ ^M (e-k,„Mt _ e_k
() K _ kmM (
t )e. (10)
Equations (5), (10), with regard for expression (9), will form a complete mathematical model of the propylene polymerization process under unsteady conditions, the use of which will allow maintain the productivity of polypropylene on the required optimum level.
Figure presents the flowchart of algorithm of the control of this process for the pro-pylene polymerization process proceeding under nonstationary conditions, with a description of the actions performed in the blocks.
Blocks 1,2. Input of initial data for the calculation according to the non-stationary model, including gc H^ and gm. Block 3. Calculation of the current value gpp. Block 4. Comparison gpp with its optimal value g found
when optimizing the CTC under stationary conditions. If the stated condition g^ ~ g°pt is fulfilled, the input values of propylene and initiator are fixed and transmitted to the mode stabilization unit 13. If this condition is violated, we will alternately change the values of the parameters g and g in order to obtain the specified polypropylene productivity. Block 5. With a positive value of (g™nrt _ g°pt), we will de-
crease the propylene feed, with a negative value - we will increase it (blocks 6,7). Block 8. The stated condition -(g™1"' ~ g°pt) is checked. If it is
fulfilled, then the signal about the required amount of propylene is sent to the input block 2 of the initial data and the calculation starts at the new value of g and the initial value g .
If not, then we proceed to correct this situation by varying the second parameter - the amount of the supplied initiator. Block 9. Find the difference between gnonstand gopt. If it is positive,
then we decrease the initiator feed (block 10), if it is negative, we increase it (block 11). Block 12. Check the condition ~(gp°nst ~ g°pt). If it is executed, then the values of the input parameters gc H and gin are fixed. By alternately changing
the input values of propylene and initiator, the polypropylene yield will reach optimum. The selection Ag^ and Agm is carried out in such
way that the value of the function 0 is within the limits close to unity. If the condition is not met, then the selection of new initial data is in progress and the calculation of the new version begins (block 14).
Conclusion
On the basis of the developed mathematical model of the propylene polymerization process under non-stationary conditions, it is possible to more accurately determine the polymer yield already taking into account the poisonous effect of methylacetylene on the catalyst. In the case of a change in the productivity of polypropylene gpp compared with its amount obtained under stationary conditions by changing the value of 0 it will be possible to regulate the process, keeping the polypropylene yield at the desired, optimal level. The new 0 value is obtained by alternately changing the amounts of propylene g and initiator g fed to the poly-merizer.
The flowchart of algorithm of the propylene polymerization process control.
References
1. Ivaniukov D.V., Fridman M.L. Polipropilen. M.: Himiia, 1974. 268 s.
2. White Dzh., Choid D. Polietilen, polipropilen i drugie poliolefiny. Izd-vo: Professiia, 2006. 262 s.
3. Ramon A.Gonzalez-Ruiz, Bernabe Quevedo-San-chez, Roberrt L.Laurence, Michael A.Henson, E. Bryan Coughlin. Kinetic Modeling of Slurry Propylene Polymerization using rac-Et(Ind)2ZrCl2/MAO
American Institute of Chemical Engineers Journal (AIChE Journal). 2006. V. 52. No 5. P. 1824-1835.
4. Usacheva T.S. Obshchaia himicheskaia techno-logiia polimerov. Ch. 2. Osnovy tekhnologii sinte-za polimerizatcionnykh polimerov: GOU VPO Ivan. gos. him.-tekhnol. un-t. Ivanovo. 2006. 60 s.
5. Korshak V.V. Tekhnologiia plasticheskikh mass. M.: Himiia, 1985, 560 s.
6. Balayev V.A., Mammadov N.S. idaraetma obyektla-rinin riyazi modelferinin alinmasi. Baki, 2010, 411 s.
PROPiLENiN POLiMERLO^MO PROSESiNiN QEYRi-STASiONAR RiYAZi MODELiNiN YARADILMASI
A.M.Oliyev, A.R.Saf3rov, i.V.Balayev, i.i.Osmanova, A.M.Hüseynova, E.F.Oliyev
Qeyri-stasionar §araitda gedan propilenin polimerla§ma prosesinin riyazi modeli yaradilib. Bu qeyri-stasionarligin asas sabablarindan biri propanin piroliz zamani maqsadli mahsuldan - propilendan alava metilasetilenin yaranmasini qeyd etmak olar. Metilasetilenin polimerla§ma prosesinda zahar tasirli i§tiraki, alinan polipropilenin mahsuldarligini va keyfiyyatini a§agi salir. Mahsuldarligi optimal saviyyada saxlanilmasi maqsadila metilasetilenin zaharverici tasirini nazara alan qeyri-stasionar funksional asililiq taklif olunub. Asililigi prosesin riyazi modelina daxil etmakla polimerla§ma qurgusunuda gedan prosesin istanilan zaman stabilla§dirmasina imkan veracak. Baxilan prosesin idaraetma algoritminin blok sxemi tartib edilib.
Agar sözlzr: propilenin polimerh§m3si, qeyri-stasionar funksiya, qeyri-stasionar model, inisiator.
РАЗРАБОТКА НЕСТАЦИОНАРНОЙ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ПРОЦЕССА ПОЛИМЕРИЗАЦИИ ПРОПИЛЕНА
А.М.Алиев, А.Р.Сафаров, И.В.Балаев, И.И.Османова, А.М.Гусейнова, Э.Ф.Алиев
Разработана математическая модель процесса полимеризации пропилена, протекающего в нестационарных условиях из-за отравляющего воздействия на него метилацетилена, приводящего к снижению производительности и качества полипропилена. Для сохранения производительности на оптимальном уровне, полученном при проведении процесса в стационарных условиях, предложена функция нестационарности, использование которой в математической модели позволит управлять процессом, стабилизируя его в любой момент времени работы полимеризатора. Разработана блок-схема алгоритма управления процессом полимеризации пропилена.
Ключевые слова: полимеризация пропилена, функция нестационарности, нестационарная модель, инициатор.
