Semibatch Polymerization

As reactant monomer converts into polymer chains, the density of the reacting mixture often changes notably. This example looks at how this effect impacts the total production of polymer in a process. The liquid phase polymerization takes place in a semibatch reactor, where two operating conditions are compared. In the first scenario, the feed of monomer to the reactor is turned off once the maximum volume capacity is reached. In a second scenario, the feed of monomer is allowed to continuously compensate for the volume change due to chemical reaction.

The model illustrates the use of the Semibatch reactor type, which is predefined in the Reaction Engineering interface in the Chemical Reaction Engineering Module. It also shows how to set timed events, in this case for controlling the reactant feed to the reactor. This example reproduces results found in Ref. 1.

Model Definition

A liquid phase polymerization can be modeled as a first order irreversible reaction:

In the above equations, M denotes the monomer, P the polymer, r is the reaction rate (SI unit: mol/(m3·s)), k is the rate constant (SI unit: 1/s), and cM is the concentration of the monomer. This process takes place in the presence of water.

The polymerization takes place in a semibatch reactor with a volume capacity of 20 m3. Initially the reactor is charged with 10 m3 of water. Pure monomer enters the reactor with a volumetric flow rate of vf = 1 m3/min.

Figure 1 shows a schematic representation of the semibatch reactor.

Figure 1: The Semibatch reactor is a predefined reactor type in the Reaction Engineering interface.

The following mass balance describes the semibatch reactor:

(1)

In Equation 1, ci is species molar concentration (SI unit: mol/m3), cf,i is the species concentration (SI unit: mol/m3) of the associated feed stream vf,i (SI unit: m3/s), and Ri denotes the species rate expression (SI unit: mol/(m3·s)). Vr labels the reactor volume (SI unit: m3) and is a function of time. For ideal mixtures:

where vp is the volumetric production rate due to chemical reaction:

(2)

In Equation 2, νij is the stoichiometric coefficient of species i in reaction j, Mi denotes the species molecular weight (SI unit: kg/mol), ρi is the species density (SI unit: kg/m3), and rj is the reaction rate (SI unit: mol/(m3·s)) of reaction j.

In the present example, the density of the monomer is 800 kg/m3, 1100 kg/m3 for the polymer, and 1000 kg/m3 for water. Hence, as polymer is being formed, the volume of the reacting mixture decreases (vp is negative). The model investigates two operating conditions:

•

Operating condition 1 — The monomer feed (1 m3/min) is shut off once the reactor volume reaches 20 m3, which occurs after 11.2 minutes. The reaction is then allowed to go to completion.

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Operating condition 2 — The monomer feed is adjusted to keep the reactor filled while the reaction goes to completion. This is accomplished by setting the volumetric feed equal to −vp, for t > 11.2 minutes.

Results

Figure 2 illustrates the volumetric flow rate of the feed stream, vf.

Figure 2: The volumetric flow rate of the feed stream (m3/s) as function of time (minutes) for operating condition 1 (solid line) and 2 (dash-dotted line).

Figure 3 shows the reactor volume as function of the runtime, illustrating the two operating conditions listed above.