Free-radical solution polymerization of styrene in a tubular reactor--effects of recycling.
The styrene sty·rene
A colorless oily liquid from which polystyrenes, plastics, and synthetic rubber are produced. Also called vinylbenzene. free-radical solution polymerization Solution polymerization is a method of industrial polymerization. In this procedure, a monomer is dissolved in a non-reactive solvent that contains a catalyst. The heat released by the reaction is absorbed by the solvent, and so the reaction rate is reduced. reaction in a tubular loop reactor is studied here both experimentally and through simulation. An attempt is made to compare the performances of tubular loop reactors when the recycle ratio is varied, based on steady-state and dynamic responses and on the quality of the polymer produced at different conditions. It is shown here that steady-state responses of loop reactors and traditional tubular reactors are very similar as far as the quality of the polymer obtained is concerned. Therefore, the recycle ratio cannot be used as a fundamental operation parameter for grade transitions at plant site. However, it is also shown that the recycling of polymer material is very important to accelerate the attainment of the final steady-state in tubular reactor configurations, because recirculation Noun 1. recirculation - circulation again
circulation - the spread or transmission of something (as news or money) to a wider group or area of material homogenizes the distorted radial profiles of the axial flow velocities.
Solution and bulk polymerization polymerization
Any process in which monomers combine chemically to produce a polymer. The monomer molecules—which in the polymer usually number from at least 100 to many thousands—may or may not all be the same. reactions have originally been performed in stirred-batch reactors. As demand for polymeric polymeric /poly·mer·ic/ (pol?i-mer´ik) exhibiting the characteristics of a polymer.
1. Having the properties of a polymer.
2. materials increased, continuous new polymerization technologies based on stirred tank reactors were then developed. The switch from batch to continuous mode of operation and, in particular, for performing polymerization reactions in stirred tank reactors, seems to have been a quite natural technology improvement. However, because of the large viscosity changes observed during polymerization reactions and of the poor heat transfer capabilities of the stirred tanks, operation of these vessels became a challenging task for process design engineers.
These characteristics encouraged the use of tubular reactors in polymerization processes because of the simple geometry, high heat transfer capabilities and relatively low operational costs of the tubular configuration. Since the late 1960s, academic and industrial researchers have investigated the feasibility and operability Operability is the ability to keep a system in a functioning and operating condition. In a computing systems environment with multiple systems this includes the ability of products, systems and business processes to work together to accomplish a common task such as finding and of tubular polymerization reactors (e.g. 1-5]. Although some studies have combined experimental work with mathematical modeling, most of the investigations have been theoretically oriented. These studies have shown that the interaction of fluid mechanics fluid mechanics, branch of mechanics dealing with the properties and behavior of fluids, i.e., liquids and gases. Because of their ability to flow, liquids and gases have many properties in common not shared by solids. and kinetic modeling may be a very important issue for the proper design of tubular reactors because of the strong dependence of the viscosity of the polymer solution upon the reactor temperature, the solution composition and the average molecular weight (2, 6, 7). In addition, plugging of the reactor tubes and broadening of the molecular weight distribution of the polymer produced are other issues of concern, caused mainly by the distor ted velocity profiles within the reactor vessel.
The operational difficulties found in tubular reactors may be minimized if a recycling stream is introduced. Lynn and Huff (8) seem to be the first to propose the use of a polymer recycling stream to overcome some difficulties associated with the tubular operation. The use of loop reactors, as tubular reactors with recycling are usually referred to, has been suggested to improve the performance of tubular reactors (9). The use of static mixers in the reactor was studied by Meyer and Renken (10), who concluded that the design of the static mixers may change considerable the micromixing efficiency. Particularly, they also verified that different degrees of internal mixing may be reached in loop reactors when the recycle ratio is varied.
Despite the potential applicability of loop reactors for carrying out both bulk and solution free-radical polymerization reactions, very few studies are available in the literature concerning the reactor steadystate and dynamic behavior and about the properties of the polymer produced. Tien et al. (9) presented the first experimental investigation of bulk loop polymerization reactors. They studied the thermal bulk polymerization of styrene in a static-mixed loop reactor connected in series to a standard tubular reactor. They used the loop reactor for pre-polymerizing styrene at conversions up to 60% and found that the loop reactor behaved as an ideal continuous stirred tank reactor for recycle ratios as low as 10. They pointed out that using the loop reactor for pre-polymerization seems to be economically attractive due to its low energy consumption, when compared to other conventional systems based on batch or continuous stirred tanks.
Fleury et al. (11) studied the operability of a loop reactor pilot-plant, which performed the solution polymerization of methyl methacrylate methyl methacrylate
n an acrylic resin, CH2 = C(CH3)COOCH3, derived from methyl acrylic acid. Monomer is the single molecule and polymer is the polymerization product. . Owing to owing to
Because of; on account of: I couldn't attend, owing to illness.
owing to prep → debido a, por causa de the strong gel-effect associated to this particular polymerization system, thermal instabilities and ignition-extinction phenomena were found to occur for recycle ratios up to 10. Belkhiria et al. (12) and Melo et al. 13) performed residence time distribution (RTD RTD returned to duty (US DoD)
RTD Ready to Drink
RTD Richmond Times-Dispatch
RTD Regional Transportation District
RTD Research, Technological Development
RTD Research and Technology Development
RTD Real-Time Data ) experiments and verified that at high recycle ratios loop reactors possess the same RTD of continuous stirred tank reactors. Besides, Belkhiria et al. also found that during copolymerization copolymerization (kōpäl´imrizā´sh reactions, depending on the monomer added in excess, the stable and safe operating conditions of the reactor might change.
Regarding the patent literature, in 1980 Montedison Spa (14) patented a chemical reactor Chemical reactor
A vessel in which chemical reactions take place. A combination of vessels is known as a chemical reactor network. Chemical reactors have diverse sizes, shapes, and modes and conditions of operation based on the nature of the reaction system "in the form of a closed loop" that "has a section comprising a bundle of tubes leading back to a circulation pump." This patent claims that this reactor "is particularly suitable for polymerizing vinyl monomers." Later on, BASF BASF Bar Association of San Francisco (since 1872; San Francisco, California)
BASF Badische Anilin und Soda Fabrik (German chemical products company)
BASF Builders Association of South Florida (15) patented a chemical "process for bulk polymerisation or solution polymerisation of vinyl monomers in an essentially back-mixing reaction apparatus designed as a forced-circulation reactor" with the forced-circulation reactor "designed as a shell-and-tube reactor." More recently, BASF (16) patented a "process for the continuous preparation of polymers from reaction components" by "bulk or solution polymerization, where the reaction components are passed through the tubes of a recycle reactor, the recycle reactor has at least one tube bundle reactor with straight tubes."
The literature review presented above reinforces the fact that the solution polymerization in tubular reactors and tubular reactors with recycle remains a topic of relevant academic and industrial investigation. One open matter in the literature regards the control of the product quality of the polymer materials produced in tubular reactors and tubular reactor with recycle. Although efforts have been made to characterize the polymer produced under different operating conditions in loop reactors (e.g. 10, 12), no systematic work has been carried out in order to compare the performance of loop and tubular reactors, as far as product quality is concerned.
In the present communication, an attempt is made to compare the steady-states and dynamic responses of tubular and loop reactors and to compare the quality of the polymer produced in both reactor configurations. Simulation and experimental results are presented to support the analysis. A lab scale reaction apparatus was set up for carrying out the solution polymerization of styrene. The polymerization of styrene is studied here because of its relevant participation in the worldwide production of commodity thermoplastics. Today, poly (styrene) is among the most heavily used materials. Applications range from foam cups, containers and protective packing, to automotive and appliance parts, wall tiles, furniture, luggage and many more (17). Besides, the kinetics kinetics: see dynamics.
Kinetics (classical mechanics)
That part of classical mechanics which deals with the relation between the motions of material bodies and the forces acting upon them. of the free-radical polymerization of styrene is very well documented in the literature and data banks of kinetic parameters for this specific polymerization system are abundant (18).
This paper is organized in two main parts. initially, results concerning the steady-state behavior of both loop and tubular reactors are presented. The main objective is to investigate the performance of these reactors in terms of monomer conversion and polymer properties related to the molecular weight distribution (MWD MWD Metropolitan Water District of Southern California
MWD Measurement While Drilling (oil drilling)
MWD Morgan Stanley Dean Witter (stock symbol)
MWD Molecular Weight Distribution
MWD Military Working Dog ). Afterwards, an experimental investigation concerning the dynamics of these reactors is presented. Step perturbations of the recycle ratio are introduced in order to investigate the role of material recirculation on the tubular reactor dynamics. It is shown that the quality of the final polymer material is relatively insensitive to modifications of the recycle ratio, implying that the recycle ratio cannot be used as the main manipulated variable for grade transitions. However, it is also shown that dynamic responses are much faster when the recycle ratio is high, owing to the homogenization homogenization (həmŏj'ənəzā`shən), process in which a mixture is made uniform throughout. Generally this procedure involves reducing the size of the particles of one component of the mixture and dispersing them evenly of the distorted velocity profiles within the reaction tubes.
Figure 1 shows a diagram of the polymerization process and the general equipment used in this work. The setup had been originally used for tubular operation only (5), but was flexible enough to accommodate an additional recycle stream. The reactor is a 8.35 mm OD 316 SS tube, 1.0 mm wall thickness, coiled with a mean-coil diameter of 30.0 cm. The reactor has a total length of 12 m and is kept inside an insulation jacket. The reaction mixture was stored in a 4 liter Pyrex [R] glass tank. Nitrogen was used for the dual purpose of sparging The term sparging may mean:
A computer program was used to control the pump operation and to monitor flow rates. The heating system consisted of an electrical resistance, whose voltage was controlled with the data acquisition system Labview [R] (National Instruments Co.). A continuous blower was used to circulate air through the enclosure in order to avoid temperature variations across the jacket cross-sections. Temperature in the reactor was monitored by means of two thermocouples (placed at the top and bottom of the reactor, respectively) and was controlled by Labview[R].
Depending on the position of the valves Vi and V2, the reactor could be run with or without recirculation of the outlet mixture. For the case of operating the reactor with partial recirculation of the outlet mixture, a second Masterflex[R] variable speed peristaltic pump A peristaltic pump is a type of positive displacement pump used for pumping a variety of fluids. The fluid is contained within a flexible tube fitted inside a circular pump casing (though linear peristaltic pumps have been made). (model 7550-60, Barnant Co.) was used. Monomer conversion was monitored with an in-line digital density meter (model mPDS 2000, Anton Paar Co.). Offline analyses of gel-permeation chromatography were performed to determine the molecular weight distributions of the polymer produced.
Operation Without Recirculation
Prior to the reactor start-up, the feed tank is loaded with a specified amount of a solution containing known composition of styrene, toluene toluene (tōl`yēn') or methylbenzene (mĕth'əlbĕn`zēn), C7H8 , and benzoyl peroxide benzoyl peroxide
A flammable white granular solid used as a bleaching agent for flour, fats, waxes, and oils, and in pharmaceuticals.
n 1. , resulting in a pre-defined concentration of the initiator. After the homogenization of the feed tank mixture, nitrogen is sparged. Pump B1 is then started at maximum flow rate, in order to fill the reactor with the desired solution. After cleaning and filling the reactor, which can be noticed by monitoring the outlet mixture density, pump B1 is initiated. For all experiments presented in this work, a feed flow rate of 2 mL/min was used. The heating system is started and the data acquisition package Lavbiew[R] is used to set the reactor Jacket temperature at the desired value. From this point on, the setup operates steadily and the monomer conversion is monitored by measuring the mixture density at the outlet of the tube.
Operation With Recirculation
For the case of recirculating the reactor outlet mixture, two distinct procedures are used for recirculation started at the very beginning of the reaction and for recirculation started during the course of the reaction. In the first case, valves V1 and V2 are positioned in order to permit recycle. As soon as the reactor and the recirculation lines are filled with the monomer-solvent-initiator mixture, pumps B2 and B1 are started. Henceforth, the experimental procedure used is similar to the one used without recirculation. The second case (recirculation started during the course of the reaction) is similar to the first one. After positioning valves V1 and V2 so that recycle is possible, some time is required to fill up the recirculation line with the reaction mixture. Afterwards, the experimental procedure is similar to the one used without recirculation. After each experiment, toluene is allowed to flow through the reactor for a period of time corresponding to at least two reactor average residence times in o rder to remove the polymer solution from the reactor. Toluene is also left inside the reactor in order to minimize the presence of oxygen in subsequent experiments and to keep the reactor walls free of polymer.
Styrene (polymerization grade with minimum purity of 99.9%) has been provided by Nitriflex S.A. and was used without further purification. Toluene (analytical grade with minimum purity of 99.9%) was purchased from Quimex[R] and benzoyl peroxide (95% of purity) was purchased from Reagen[R]. Nitrogen (minimum purity 99.9% mol/mol) was acquired from AGA SA. The experiments were performed using various monomer/solvent feed molar molar /mo·lar/ (mo´lar)
1. pertaining to a mole of a substance.
2. a measure of the concentration of a solute, expressed as the number of moles of solute per liter of solution. Symbol M, , or mol/L. ratios and the initiator was dissolved in toluene and styrene to make a solution with desired molar concentration Noun 1. molar concentration - concentration measured by the number of moles of solute per liter of solution
concentration - the strength of a solution; number of molecules of a substance in a given volume .
The experimental monomer conversion has been determined indirectly from an in-line digital density meter placed at the reactor outlet. Given a monomer/solvent feed ratio, the monomer conversion is related to the solution density according to according to
1. As stated or indicated by; on the authority of: according to historians.
2. In keeping with: according to instructions.
3. the following expression
d(x) = a + bx, (1)
where x is the monomer conversion.
Equation 1 is valid for a specific reference or calibration temperature and for a specified solvent content. However, during an experimental run, the temperature of the solution entering the density meter may differ from the reference temperature and, therefore, the density measurement must be corrected before Eq 1 is used. Stevens (19) reported that for polymer solutions the density dependence on the temperature may be given by the following expression
1/d(T) = [alpha] + [beta]T. (2)
At a given reference or calibration temperature one may also write that:
1/d([T.sub.r]) = [alpha] + [beta][T.sub.r]. (3)
[beta](T - [T.sub.r]) = 1/d(T) - 1/d([T.sub.r]). (4)
In Equations 2-4, parameter [beta] is a correction temperature factor. Because different monomer/solvent feed ratios were used in the experimental runs performed in this work, parameter [beta] was estimated for each one of the ratios. Table 1 presents the summary of the density-conversion expressions obtained and the respective values of the parameter [beta]. At a monomer/solvent feed ratio of [phi] = 70/30, the polymer solution becomes too viscous even for operation at low conversions, rendering the operation unfeasible. Therefore, this feed ratio was added to Table 2 only for the sake of completeness. In Fig. 2, calculated densities using Eq 1 are compared to their experimental counterparts. As it may be observed, the relations given in Table 1 provide an accurate and reliable measure of the monomer conversion.
Gel permeation chromatography Gel permeation chromatography (GPC) is a separation technique based on hydrodynamic volume (size in solution). Molecules are separated from one another based on differences in molecular size. This technique is often used for polymer molecular weight determination. was used to determine the number- and weight-average molecular weight weight-average molecular weight: see molecular weight. of the poly(styrene) samples. Four columns of Ultra-Styragel (Waters 600E GPC (1) A PC that uses the Linux-based gOS operating system. See gOS.
(2) (GPC Group) Originally the Graphics Performance Characterization committee of the NCGA, the GPC Group is now part of Standard Performance Evaluation Corporation (SPEC) and oversees the following ) were used in a series of decreasing pore size ([10.sup.5], [10.sup.4], [10.sup.3], and 500A). HPLC/Spectra grade THE (Tedia[R]) was applied with a flow rate of 1 mL/min at 40[degrees]C.
As mentioned previously, the free-radical polymerization of styrene has already been extensively investigated in the literature (18). Therefore, rate constants and other kinetic parameters were used in this paper as provided by other works (see Table 2). The kinetic mechanism considered here involves the following basic steps (21).
Chemical initiation: I [[right arrow].sup.[k.sub.d]] 2R *,
R * + M [[right arrow].sup.[k.sub.i]] [P.sub.1] *.
Thermal initiation: 3M [[right arrow].sup.[k.sub.it]] 2[P.sub.1] *.
Propagation: [P.sub.i] * + M [[right arrow].sup.[k.sub.p]] [P.sub.i+1] *.
Chain transfer to solvent: [P.sub.i] * + S [[right arrow].sup.[k.sub.trs]] [[LAMBDA The Greek letter "L," which is used as a symbol for "wavelength." A lambda is a particular frequency of light, and the term is widely used in optical networking. Sending "multiple lambdas" down a fiber is the same as sending "multiple frequencies" or "multiple colors. ].sub.i] + S *,
S * + M [[right arrow].sup.[k.sub.trs]] [P.sub.1] *.
Chain transfer to monomer: [P.sub.i] * M [[right arrow].sup.[k.sub.trm]] [[LAMBDA].sub.i] + M *,
M * + M [[right arrow].sup.[k.sub.trm]] [P.sub.1] *.
Termination by combination: [P.sub.i] * + [P.sub.j] * [[right arrow].sup.[k.sub.trc]] [[LAMBDA].sub.i+j].
Quasi-steady state assumption and long-chain approximation (22) were used to obtain the expressions for the total concentration of free-radicals and rates of monomer consumption. The so-called gel-effect was described according to the expression proposed by Hut and Hamielec (21) for the bulk polymerization of styrene
[k.sub.tc] = [k.sub.tc0] exp exp
2. exponential (- 2([A.sub.1][w.sub.p] + [A.sub.2] [w.sup.2.sub.p] + [A.sub.3] [w.sup.3.sub.p])). (5)
where [k.sub.tc0] is the termination constant at low conversions and [w.sub.p] is the polymer weight fraction. In the original presentation of Eq 5, [w.sub.p] represented the overall monomer conversion. Monomer conversion was replaced by polymer weight fraction in order to account for the presence of a solvent, used experimentally in the present work. Parameters [A.sub.1], [A.sub.2], and [A.sub.3] are linear functions of the reactor temperature, given by
[A.sub.1] = 2.57 - 5.05 X [10.sup.-3]T, (5a)
[A.sub.2] = 9.56 - 1.76 X [10.sup.-2]T, (5b)
[A.sub.3] = -3.03 + 7.85 X [10.sup.-3]T, (5c)
where T is given In Kelvin kelvin, abbr. K, official name in the International System of Units (SI) for the degree of temperature as measured on the Kelvin temperature scale.
A unit of measurement of temperature. .
Finally, in order to calculate the main averages of the molecular weight distribution (MWD) of the dead polymer chains, the well-known method of moments was used (23).
Reactor Mathematical Modeling
In the present paper, the reactor behavior is described in accordance with the mathematical model developed by Vega et al (5). Vega et al. showed that the simplifying assumptions of parabolic par·a·bol·ic also par·a·bol·i·cal
1. Of or similar to a parable.
2. Of or having the form of a parabola or paraboloid. velocity profile, constant physical properties and isothermal i·so·ther·mal
Of, relating to, or indicating equal or constant temperatures.
having the same temperature. operation conditions were sufficient to describe reasonably well the experimental dynamic behavior of a tubular reactor carrying out the solution polymerization of styrene, in spite of the significant flow distortions expected at the analyzed operation conditions, as computed with the help of a very detailed reactor model. The assumption of a parabolic velocity profile may be poor when larger tube diameters are considered. However, implementing a more sophisticated velocity profile is straightforward, as presented by Chen and Nauman (6). For the tubular reactor, the purely convective, transient mass-balance equation (24) is given by
[partial][C.sub.i](z, t)/[partial]t + [v.sub.z](r) * [partial][C.sub.i](z, t)/[partial]z = [R.sub.i](z, t), (6)
where [C.sub.i](z, t) is the molar concentration of species the reactor (i may represent either monomer, initiator or any of the first three moments of the MWD), [R.sub.i](z, t) is the rate of molar consumption of species i due to the chemical reaction, [v.sub.z](r) is the parabolic axial velocity profile in the reactor, t is the time and z is the reactor length. By considering that the tubular reactor has a total length L, the boundary conditions of Eq 6 are given as follows
[C.sub.i](0, t) = [C.sub.iF], (7)
when the reactor operation is performed without recycling, and
[C.sub.i](O, t) = Rec/1 + Rec [C.sub.i] (L, t) 1/1 + Rec [C.sub.iF], (8)
when partial recycling of material is imposed in the reactor operation. It should be pointed out that the feed molar concentration ([C.sub.i](L, t)) of species i due to recycling is taken as an average at the reactor outlet, and is given by
[C.sub.i](L, t) = 1/[Q.sub.F] [[Integral].sup.R.sub.0] 2[pi]r [1 - [(r/R).sup.2]][v.sub.max] [C.sub.i](r, L, t)dr. (9)
In Equation 8, operation parameter Rec stands for the reactor recycle ratio, defined as the ratio of the flow rate of recycled polymer mixture and the feed flow rate. In both cases, we have
[C.sub.i](z, 0) = [C.sub.i0]. (10)
In order to solve Eq 6, the radial direction was discretized using an orthogonal collocation method In mathematics, a collocation method is a method for the numerical solution of ordinary differential equation and partial differential equations and integral equations. The idea to choose a finite-dimensional space of candidate solutions (usually, polynomials up to a certain , whereas the axial coordinate was discretized in finite elements. Average profiles were calculated by numerical quadrature quadrature, in astronomy, arrangement of two celestial bodies at right angles to each other as viewed from a reference point. If the reference point is the earth and the sun is one of the bodies, a planet is in quadrature when its elongation is 90°. . Radial collocation collocation - co-location points were chosen to be the roots of the orthogonal polynomial polynomial, mathematical expression which is a finite sum, each term being a constant times a product of one or more variables raised to powers. With only one variable the general form of a polynomial is a0xn+a generated by the following weight function (5)
[PHI](r) = ([R.sup.2] - [r.sup.2]). (11)
The resulting set of ordinary differential equations was solved by means of a standard, fourth-order Runge-Kutta integration method.
Steady-state as well as dynamic responses are presented here at the reactor outlet. Initially, it is aimed to validate the reactor model described in the previous section. Experiments were performed at the operation conditions listed in Table 3. Figures 3-5 illustrate the ability of the reactor model to describe the experimental results. In Fig. 3, experimental and calculated monomer steady-state conversions are presented for reactor operation with and without recycling of material (i.e., loop and tubular operation, respectively). One may notice that at low conversions the reactor model is able to fit very well the experimental data, for both loop and tubular operation. However, at high monomer conversions, the model predictions systematically differ from those observed experimentally.
According to Fig. 3 and Table 3, higher monomer conversions are attained at higher temperatures, as expected (cf. experiments B, D, G, and I). At higher conversions, the so-called gel-effect becomes more pronounced and the solution viscosity increases dramatically. Higher monomer conversions are predicted by the model systematically, possibly because of the overestimation o·ver·es·ti·mate
tr.v. o·ver·es·ti·mat·ed, o·ver·es·ti·mat·ing, o·ver·es·ti·mates
1. To estimate too highly.
2. To esteem too greatly. of the gel-effect given by Eq 5. This may be explained by the fact that this equation was fitted using free-radical bulk styrene polymerization data (20) and did not take into account, explicitly, the presence of the solvent. Therefore, the experimental reaction conditions may be milder than those predicted by the model. The behavior is not observed at low conversions because here the gel-effect is less important. Besides, as will be shown later, it may take too long for actual steady-state condition In telecommunication, the term steady-state condition has the following meanings:
A comparison among tubular and loop operation is shown in Figs. 6-8. For all the variables analyzed, it is shown that the performance of the loop and tubular reactors are similar for both experimental and simulated data. it is important to notice that the final polymer molecular weight distributions are very alike for both tubular and loop reactor operation. These results seemed a bit surprising at first sight. Therefore, the reactor mathematical model was used to simulate a multitude of different reaction conditions in order to investigate in detail the results obtained.
Similarity between loop and tubular operation was found when different axial velocity profiles were used for simulation, indicating that this variable is not fundamental for explanation of the results obtained. Typical simulation results are presented in Fig. 9 for the weight-average molecular weight, when results obtained with the parabolic velocity profile are compared with the results obtained for a flat plug-flow condition. Note that for both loop and tubular reactor operation, results are virtually identical. This behavior may be explained by the fact the at the reactor exit, the average values of the properties do not differ significantly, because of the averaging of the results provided by the distinct streamlines.
Another parameter investigated was the propagation constant For an electromagnetic field mode varying sinusoidally with time at a given frequency, the propagation constant is the logarithmic rate of change, with respect to distance in a given direction, of the complex amplitude of any field component. , aiming to simulate the kinetics of free-radical vinyl polymerization systems possessing higher propagation rates. Figure 10 shows that a two-fold increase in the propagation constant does play a significant role on the dynamic evolution of the weight-average molecular weight. Once more, no appreciable difference is found on the steady-state values reached by both loop and tubular reactors.
The influence of the reactor average residence time upon the process behavior was also investigated. Figure 11 illustrates that this parameter plays a negligible role on the polymer quality obtained when results obtained for the MWD for both loop and tubular reaction operations are compared.
Appreciable differences could only be observed with operation at high temperatures. Figure 12 shows that very different polymer properties may be obtained at higher temperatures with the loop and tubular reactors. This behavior may be attributed to the strong gel-effect observed at such conditions. This effect becomes less important during the operation with recycle because in this case the polymer solution is more homogeneously distributed along the reactor. The gel-effect seems to be, then, the most important parameter affecting the properties of the polystyrene produced in loop and tubular free-radical polymerization reactors. Figure 13 provides additional evidence of this behavior. Steady-state polydispersity indices are plotted against the solvent volumetric volumetric /vol·u·met·ric/ (vol?u-met´rik) pertaining to or accompanied by measurement in volumes.
Of or relating to measurement by volume. feed fraction at moderate temperatures. One may notice that when the solvent volumetric feed fraction becomes 0.50, discrepancies between loop and tubular reactor polydispersity indices begin to be observed. In the limit of bulk polymerization, loop and tubular reactors produce quite different polystyrenes. However, differences may be regarded to be large only when the solvent feed fraction is below 0.20. This would necessarily lead to use of extruder reactors and it may be wondered whether the addition of a recycle stream would make such sense in this case.
A perhaps unfortunate consequence of the results presented above is that, for free-radical solution polymerization reactions, improvement of the internal mixing in the reactor through manipulation of the recycle ratio generally does not result in opportunities for polymer grades transitions. In spite of that, recycling of the outlet polymer solution may be very useful as far as the process dynamics is concerned, as discussed in the next section.
Figure 14 shows the typical reactor approach to steady-state after start-up. Operation is performed with recycling of material since the start-up, with a recycle ratio of Rec = 35. In order to verify the degree of mixing during the reaction, a unit step in the recycle ratio (Rec = 50) was applied after steady-state had been reached. It is shown that the unit step in the recycle ratio does not change the reactor steady-state, indicating that at Rec = 35, the reactor is operating with perfect mixing Perfect mixing is a term heavily used in relation to the definition of models that predict the behavior of chemical reactors. Perfect mixing assumes that there are no spacial gradients in a given physical envelope, such as:
Regarding the temperature dynamics, Fig, 14 shows that the reactor temperature may experience large fluctuations around its set-point if the jacket temperature is not controlled properly, due to the large heat capacity of the recycled material. If the reactor temperature is properly controlled, Fig. 15 shows that recycling of material does not play a significant role on the reactor dynamics, allowing the proper decoupling Decoupling
The occurrence of returns on asset classes diverging from their normal pattern of correlation.
Take for example stock and corporate bond returns, which normally rise and fall together. of the temperature and conversion trajectories. However, if the reactor temperature is not controlled, Fig. 16 shows that higher monomer conversion may be attained after ceasing of polymer recycling. This is a strong evidence of the importance of the gel-effect upon the process performance.
It is well established and accepted in the literature that during polymerization reactions in tubular reactors, a sluggish-moving stream of polymer solution flows close to the reactor inner walls, presenting higher monomer conversion when compared to the central core, fast-flowing polymer solution (c.f. 4, 6-8, 25-28). Thus, imposing material recycling during the tubular reactor operation enhances product homogeneity by flattening of the axial velocity profiles, Simultaneously increasing the reaction rates due to the gel-effect and leading to higher monomer conversions.
Distorted axial velocity profiles in tubular polymerization reactors have been a matter of long discussions in the past, as pointed out in the references cited above. This behavior, however, has been described based mostly on theoretical rheokinetics, fluid-dynamic considerations. To the best of our knowledge, the first study to present some experimental evidence of distorted axial velocity profiles in tubular polymerization reactors was that of Chen and Nauman (6). They determined the reactor residence time "washout washout
to disperse or empty by flooding with water or other solvent.
medullary solute washout
a syndrome in which the relative hyperosmolarity of the renal medulla is reduced due to an excessive loss of sodium and chloride from " function theoretically by means of flow models and experimentally by inert tracer techniques. The measured washout function confirmed the presence of velocity profile elongation elongation, in astronomy, the angular distance between two points in the sky as measured from a third point. The elongation of a planet is usually measured as the angular distance from the sun to the planet as measured from the earth. during the solution polymerization of styrene. Vega et al. (5) also observed indirectly the existence of distorted axial velocities profiles in the tubular reactor solution polymerization of styrene. They observed this behavior after injecting a small amount of an inhibition agent at the reactor inlet, after steady-stat e had been attained during the solution polymerization of styrene. They concluded that the reactor dynamic response would only be explainable by assuming the existence of very distorted axial velocity profiles, very similar to the one depicted In the previous paragraph.
In order to perform a more detailed examination of this behavior and, in particular, confirm the existence of distorted velocity profiles, a tubular reactor experiment with long time duration was performed. According to Fig. 17, experimentally one could easily decide to stop the run after about four hours of reactor operation and conclude that steady-state would have been reached. However, what Fig. 17 shows is that monomer conversion continues to increase at a very slow pace at the reactor exit, because the sluggish-flowing polymer solution close to the reactor inner walls slowly reaches the outlet sampling point. Therefore, if a small amount of inhibition agent were injected at the reactor inlet, a two-step drop in the monomer conversion would be observed, as reported by Vega et al. ( 5).
Another long-time experiment was performed for the dual purpose of replicating the tubular reactor behavior described in the previous paragraph, and applying a disturbance to the process by imposing material recycling at a given time during the reaction. Figure 18 shows the typical behavior already presented in Fig. 17 for experimental times below 15 h. A conversion drift of more than 10% was observed between reaction times 4 h and 15 h, and seemingly the reactor had not reached the steady-state solution yet. At time 15 h, recycling of material was started and held for about four hours of operation. Temperature and conversion were kept at lower values on purpose, in order to minimize transient gel-effect perturbations. After material recycling was ceased, it was observed that the reactor presented much faster dynamics and that it took less time to reach the same steady-state achieved before the process disturbance. It must be emphasized that a conversion drift of about 20% was observed between reaction times 4 h and 23 h. Particularly, the oscillatory oscillatory
characterized by oscillation.
see pendular nystagmus. behavior observed after the second perturbation perturbation (pŭr'tərbā`shən), in astronomy and physics, small force or other influence that modifies the otherwise simple motion of some object. The term is also used for the effect produced by the perturbation, e.g. indicates that the real steady-state conversion is around 70%, and not 50%, as observed at time 4 h. These results indicate that recycling of material during tubular reactor operation not only speeds-up the approach to steady-state but also allows higher monomer conversion to be achieved. Therefore, it may be said that although the recycle ratio cannot be used as the main manipulated variable during grade transitions, the recycle ratio stream may be of fundamental importance for reduction of grade change transients and optimization of process operation at plant site.
An investigation has been done in order to compare the performance of tubular and loop reactors when carrying out the free-radical solution polymerization of styrene. An important conclusion concerns the fact that loop reactors behave essentially as tubular reactors at steady-state conditions, as far as the quality of the polymer obtained is concerned. Therefore, the recycle ratio cannot be used as a fundamental parameter for grade transitions. However, it was found that the recycling of material may be very important during grade transitions for it accelerates the attainment of the steady-state In tubular reactors, because recirculation of material homogenizes the distorted radial profiles of the axial flow velocities. It should be pointed out that the results presented here are not specific for the polystyrene free-radical solution polymerization. Instead, they probably remain valid for other vinyl monomer free-radical solution polymerization reactions being performed in both tubular reactors and tubular re actors with recycle, as qualitative results are not sensitive to modification of model parameters.
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Table 1 Density-Temperature Dependence Correlation for Various Monomer/ Solvent Feed Volumetric Ratios [phi] d (kg/[m.sup.3]) [T.sub.r] [beta] ([m.sup.3]/ ([degrees]C) [degrees]C/kg) 40/60 d = 877.33 + 58 . x 26 1.270 x [10.sup.-9] 50/50 d = 882.77 + 75 . x 30 1.190 x [10.sup.-9] 60/40 d = 884.98 + 95 . x 30 1.153 x [10.sup.-9] 70/30 d = 889.15 + 109 . x 31 1.140 x [10.sup.-9] Table 2 Kinetic Parameters for the free-Radical Polymerization of Styrene. Step Symbol Unit Thermal initiation [k.sub.it] [m.sup.6]/kg[mol.sup.2]/s Initiation with initiator [k.sub.d] 1/s Propagation [k.sub.p] [m.sup.3]/kgmol/s Chain transfer to solvent [k.sub.trs] [m.sup.3]/kgmol/s Chain transfer to monomer [k.sub.trm] [m.sup.3]/kgmol/s Termination by combination [k.sub.trc] [m.sup.3]/kgmol/s Step Equation Thermal initiation 1.99 * [10.sup.6] exp(-14,842/T) Initiation with initiator 1.712 * [10.sup.15] exp(15,924/T) Propagation 1.051 * [10.sup.7] exp(-3,577/T) Chain transfer to solvent 7 * [10.sup.-5] [k.sub.p] Chain transfer to monomer 1.2 * [10.sup.-5] [k.sub.p] Termination by combination 1.255 * [10.sup.9] exp(-844/T) Step Reference Thermal initiation Cutter and Drexler (1982) Initiation with initiator Cutter and Drexler (1982) Propagation Hui and Hamielec (1972) Chain transfer to solvent Brandrup and Immergut (1989) Chain transfer to monomer Brandrup and Immergut (1989) Termination by combination Hui and Hamielec (1972) Table 3 Operation Conditions of the Steady-State Experiments. Experiment Tag Symbol Prameter [phi] T ([degrees]C) A Plus sign 40/60 60 B Open lozenge 40/60 90 C Filled lozenge 50/50 60 D Open square 50/50 90 E Filled square 50/50 60 F Filled circle 60/40 60 G Open triangle 60/40 90 H Filled triangle 60/40 60 I Open star 40/60 90 Experiment Tag [C.sub.IF] (Kgmol/[m.sup.3]) A 0.05 B 0.05 C 0.05 D 0.05 E 0.10 F 0.05 G 0.05 H 0.05 * I 0.05 Fresh initiator.
The authors would like to thank CNPQ-Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, FAPERJ-Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro, and CAPES-Coordenacao de Aperfeicocamento de Pessoal de Nwel Superior, for supporting this research and providing scholarships. The authors also thank Nitriflex Resinas S.A. for providing styrene monomer.
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RELATED ARTICLE: NOMENCLATURE
C = Molar concentration (kgmol/[m.sup.3]).
d Solution density (kg/[m.sup.3]).
L = Reactor length (m).
MWD = Molecular weight distribution.
NAMW NAMW National Air Mail Week
NAMW Number Average Molecular Weight = Number average molecular weight.
PD = Polydispersity index In organic chemistry, the polydispersity index (PDI), is a measure of the distribution of molecular mass in a given polymer sample. The PDI calculated is the weight average molecular weight divided by the number average molecular weight. .
Q = Flow rate ([m.sup.3]/s).
R = Reaction rate [kgmol/[m.sup.3]/s) or inner reactor radius (m).
Rec = Recycle ration.
T = Temperature ([degrees]C).
t = Time (h).
v = Flow velocity In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of the fluid. Definition
The flow velocity of a fluid is a vector field
WAMW WAMW Weight-Average Molecular Weight = Weight average molecular weight The weight average molecular weight is a way of describing the molecular weight of a polymer. Polymer molecules, even if of the same type, come in different sizes (chain lengths, for linear polymers), so we have to take an average of some kind. .
x = Monomer conversion.
z = Axial coordinate (m).
Greek Letters Greek letters,
n.pl symbols based on the Greek alphabet that are used to represent phenomena and objects in science.
[alpha] = Parameter in the density-temperature dependence correlation ([m.sup.3]/kg).
[beta] = Parameter in the density-temperature dependence correlation ([m.sup.3]/kg/[degrees]C).
[phi] = Monomer/solvent feed volumetric ratio.
[PHI] = Weight function in the orthogonal collocation method.
O = Related to the initial condition.
t = Chemical species (either monomer (M), initiator (I), or any of the first three moments of the MWD).
F = Related to feed conditions.
max = Related to the maximum flow velocity in the axial direction.
r = Related to the reference temperature.
z = Related to the axial velocity.
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