나일론 6 반응기의 모델링 및 그의 중합특성

안  영 철

경남대학교 공과대학 정밀화학공학부

Modeling of Nylon 6 Reactors and Their Polymerization Characteristics

Young-Cheol Ahn

Division of Fine Chemistry and Chemical Engineering, Kyungnam University

Introduction

As a polymer of considerable commercial significance, nylon-6 is produced by water initiated polymerization of □-caprolactam. Reimschuessel et al. [1, 2] initially suggested the following three major reversible reactions for the mechanism of nylon-6 polymerization : (a) ring opening reaction, in which the ring of the monomer, □-caprolactam, is opened by water molecules to form aminocaproic acid; (b) polycondensation reaction in which the amine and carboxylic end-groups react to form large polymer chains via amide linkages, while water forms as a condensation product; (c) polyaddition reaction in which monomer adds on to the growing polymer chains. Later, Tirrell et al. [3] incorporated the reaction with monofunctional acids (modifiers) in their kinetic scheme. Arai and co-workers [4] have coupled the ring-opening and polyaddition reactions of cyclic dimer into the Reimschuessel et al.'s [1, 2] basic reactions.

Models of three-stage nylon-6 reactors with intermediate mass transfer have been numerically studied by Gupta et al. [5] The study considered only the diffusional mass transfer of water through the reaction mass. Recently, Ahn [6] studied the effect of diffusional water removal and heat transfer in a nylon-6 reactor and showed that the interfacial area and temperature are the major factors affecting the degree of polymerization and polydispersity. Ahn [7] also modelled the top portion of a commercial atmospheric nylon-6 reactor, VK-column, by continuous flow stirred tank reactor. He suggested a positive way of saving energy without affecting the reaction characteristics, which is to keep the reaction temperature and the water concentration constant by reducing both the feed water content and the jacket temperature.

In this study, systems of a continuous flow stirred tank reactor and a tubular reactor connected in series with partial zone of diffusional water removal incorporated in tubular reactor are introduced. In these systems, the effects of feed acetic acid content and diffusional water removal on the zeroth, first and second moments and the polydispersity of the polymer have been investigated numerically.

Process Modeling

In an atmospheric reactor system, more than an exact amount of water is premixed with reactants and then the mixture is fed to the reactor where according to Raoult's law only the equilibrated amount of water participates in the reaction and the excess water is vented out as vapor. Because of the mixing effects caused by boiling of excess water, the top portion of the atmospheric reactor is modelled by a continuous flow stirred tank reactor. The reaction that matters for the control of degree of polymerization in polycondensation reaction is where water is formed as a condensate. This water greatly affects the chemical reaction equilibrium so that we cannot obtain a polymer of high molecular weight that is desirable for industrial application. Therefore, this condensation water must be removed from the reaction mass. One approach to this goal is design of such reactors that effectively remove the condensation water by contacting reaction mass with inert dry gas, as suggested by several authors [5, 6]. Inert gas bubbles are injected into an intermediate position of the tubular reactor and removed at the outlet position. These bubbles are modeled as hollow sphere. Three types of tubular reactors are schematically shown in Fig. 1 and named as R-1, R-2 and R-3.

The basic reactions briefly mentioned in the Introduction are coupled together to form a complete reaction system. The rate constants for the five reactions are corresponding to the reactions between functional groups. The polymerization reaction is well described by an autocatalytic reaction, and the forward reaction rate constant [eqn: k_i] ([eqn: i =]1, 2, 3, 4, 5) is expressed in terms of the acid end-group concentration (in mol/kg mixture) as

[eqn: k_i = k_i^0 + k_i^c~ left( sum_n=1^inf [ S_n ] + sum_m=1^inf [ A_m ] right) == k_i^0 + k_i^c ( □_0 + □_0^prime )]	(1)

where [eqn: [S_n ]] is the concentration of polymer of chain length [eqn: n] with amine end-group, [[eqn: A_m]] is the concentration of polymer of chain length [eqn: m] with acetyl end-group, [eqn: □-_0] is the zeroth moment of polymers with amine end-group, and [eqn: mu_0^prime] is the zeroth moment of polymers with acetyl end-group. The [eqn: nu]-th moments of polymers are generally expressed by

[eqn: □_□ = sum_n=1^inf n^□ [ S_n ]]	(2)

[eqn: □_□^prime = sum_m=1^inf m^□ [ A_m ]]	(3)

where the values of [eqn: nu] are 0, 1, 2 and 3 for the two different kinds of polymers.

For the part of the CSTR, the analysis has been performed by establishing the material and energy balance equations and solving them by Newton-Raphson method [7]. The reaction rates in the model are expressed in terms of concentrations, and the material and energy balances have been set up for the CSTR. These equations constitute twelve simultaneous equations for the unknown solution vector

[eqn: under x = [ F, F_v , C_1 , W , S_1 , S , S_c , C_2 , A_1 , T, c_p , rho ]^T]	(4)

The balance equations for the first and second moments can also be established for the CSTR and solved by Newton-Raphson Method [7]. For the tubular reactor, the mass and energy balance equations are given the same as those in the literature [6]. From the solutions of the zeroth, first and second moments, the number- and weight-average chain lengths are computed, and the polydispersity index is given by the ratio of the weight-average chain length to the number-average chain length.

Results and Discussion

For the analysis, the size of the reactor has been selected in reference to a commercial VK-column reactor that is frequently used for nylon-6 polymerization. The reactor is assumed to have a capacity of processing 12 tons per day (=500 kg/hr) based on □-caprolactam. The top portion of it, which is modeled as a CSTR, has a volume of 0.6 m3. The heat exchanger located here is assumed to have an area of 46 m2. The overall heat transfer coefficient of 57256.105 cal/hr·m2·K is assigned as before [7]. Based on the □-caprolactam consumption, the amount of water to be added is set at 4.0 vol% and the amount of acetic acid is varied between 0 and 0.5 vol%. The feed and jacket temperatures are set at 85 ℃ and at 260 ℃, respectively. The remaining portion of the reactor is modeled as a tubular reactor, in a region of which the reaction mass contacts with inert dry gas bubbles. The typical dimension of the inert dry gas bubbles has been selected such that the inner radius is 0.005 m and the outer radius is 0.030 m.

Ring opening reaction of □-caprolactam forms amine and carboxylic end-groups at the ends of the chain. The active site that is chemically attacked by monomer is the amine end-group. Therefore, in order to protect a polymer chain from growing monofunctional acid is used to substitute a unactive end-group for the amine end-group and thus the degree of polymerization is controlled. In this research, acetic acid has been chosen as the monofunctional acidic catalyst and its effect on the polymerization of nylon-6 has been investigated. As for the CSTR, the computational results show that for the given process condition the reactor temperature stands still at around 237 ℃ and the water concentration does not deviate much from 0.18 mole/kg. The conversion increases from 0.46 to 15.39 % as the feed acetic acid content is increased from 0 to 0.5 vol%. The number and weight average chain lengths are also affected by the feed acetic acid content. For the same increment of the feed acetic acid content, the number average chain length increases from 7.39 to 12.89 and the weight average chain length increases from 13.24 to 61.62. As a result, in CSTR, the polydispersity index increases from 1.79 to 4.78 for the increment of the feed acetic acid content from 0 to 0.5 vol%. Thus, in the CSTR, the conversion and the oligomer characteristics are greatly affected by the acetic acid content.

The reactants from the CSTR continues to flow into the tubular reactor systems where the reactions proceed further to complete. The temperature profiles of the reactor system is shown in Fig. 2. The acetic acid promotes the initiation of polymerization and the temperature profiles are shifted toward upstream since the acetic acid has carboxylic end-group that catalyzes the reaction in an autocatalytic manner. The removal of water by diffusion has an effect of temperature increase since it breaks the equilibrium and promotes the polycondensation reaction which is exothermic. In Fig. 3, we can see that the addition of acetic acid promotes consumption of water at an earlier stage of polymerization, but it eventually increases the water concentration. This is also due to the dual characteristics of the acetic acid. That is, at an earlier stage the acid promotes the ring-opening reaction which consumes water while at a later stage the termination reaction prevails and produces water as a by-product. Thus, the conversion is increased by addition of acetic acid at an earlier stage. However, the diffusional removal of water does not greatly affect the monomer conversion.

In Fig. 4 we can see that the number average chain length becomes smaller as the feed acetic acid content is increased. On the other hand, the number average chain length increases with diffusional water removal so that we can modify the polymer end-groups by combination of feed acetic acid content and diffusional water removal without affecting the number average molecular weight.

In the CSTR, the polydispersity index is greatly affected by the feed concentration of the acetic acid. However, as the reaction mixture continues to flow through the tubular reactor, the polydispersity indices approach to values of ∼2 that is recognized as the equilibrium polydispersity index for nylon-6. The polydispersity index is not affected by the diffusional water removal.

References

1. H. K. Reimschuessel and K. Nagasubramanian, Chem. Eng. Sci., 27, 1119 (1972).

2. H. K. Reimschuessel, J. Polym. Sci. Macromol. Rev., 12, 65 (1977).

3. M. V. Tirrell, G. H. Pearson, R. A. Weiss, and R. L. Laurence, Polym. Eng. Sci., 15, 386 (1975).

4. Y. Arai, K. Tai, H. Teranishi, and T. Tagawa, Polymer, 22, 273 (1981).

5. S. Gupta, A. Kumar, and K. K. Agrawal, J. Appl. Polym. Sci., 27, 3089 (1982).

6. Y.-C. Ahn, Polym. Eng. Sci., 37(2), 484 (1997).

7. Y.-C. Ahn, Hwahak Konghak(J. Korean Inst. Chem. Eng.), 35(6), 856 (1997).