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Explain how a stirred tank reaction works.

Short Answer

Expert verified
Answer: The key factors affecting the reaction rate in a stirred tank reactor include the concentration of reactants, temperature, reaction kinetics, and mass transfer limitations.

Step by step solution

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1. Introduction to Stirred Tank Reactor

Stirred tank reactors (STRs) are widely used in chemical engineering processes for various applications such as mixing, reactions, and heat and mass transfer. They are typically vessels that are filled with a mixture of reactants and equipped with a stirring or mixing device to ensure optimal mixing and improved contact between the reactants.
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2. Components of a Stirred Tank Reactor

The main components of a stirred tank reactor include the reactor vessel, the stirring or mixing device (usually an impeller mounted on a central shaft), the feed and exit nozzles, and temperature control equipment (such as heating or cooling coils or a jacket around the reactor).
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3. Mixing and Homogeneity inside the Reactor

The stirring device inside the reactor creates a turbulent flow regime that promotes the thorough mixing of the reactants. This ensures a homogenous mixture, which is important for achieving good conversion rates, better heat and mass transfer, and overall process efficiency.
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4. Residence Time Distribution

In a stirred tank reactor, the flow patterns are characterized by the residence time distribution (RTD), which is a measure of the time different fluid particles spend in the reactor. An ideal stirred tank reactor exhibits a perfect mixing condition, meaning that all fluid particles spend the same amount of time inside the reactor. This is described by the exponential decay RTD function: E(t) = \frac{1}{\tau} e^{-\frac{t}{\tau}}, where E(t) is the RTD function, t is time, and τ is the mean residence time.
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5. Reaction Kinetics and Mass Transfer

The rate of the reactions inside the stirred tank reactor depends on various factors such as the concentration of reactants, temperature, reaction kinetics, and mass transfer limitations. In a perfectly mixed reactor, the concentration of the reactants and the products are assumed to be uniform throughout the reactor, and the overall reaction rate can be described by a rate expression depending on the order of the reaction and the concentration of reactants.
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6. Design and Performance Evaluation

The design of a stirred tank reactor is based on its intended use, process requirements, and constraints. Important factors to consider include reactor size, stirrer type and speed, operating temperature and pressure, and other equipment needed for heat and mass transfer or separation processes. The performance of a stirred tank reactor is evaluated by its conversion efficiency, reaction rate, energy consumption, and product quality. In summary, a stirred tank reaction involves the use of vessels equipped with a stirring device to mix the reactants. The reactor is designed to ensure optimal mixing, residence time distribution, reaction kinetics, and mass transfer. These factors collectively influence the reactor's performance and overall efficiency.

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Most popular questions from this chapter

The reaction of certain chemical compounds can be modeled using a differential equation of the form \(y^{\prime}(t)=-k y^{n}(t),\) where \(y(t)\) is the concentration of the compound for \(t \geq 0, k>0\) is a constant that determines the speed of the reaction, and \(n\) is a positive integer called the order of the reaction. Assume that the initial concentration of the compound is \(y(0)=y_{0}>0\). a. Consider a first-order reaction \((n=1)\) and show that the solution of the initial value problem is \(y(t)=y_{0} e^{-k t}\). b. Consider a second-order reaction \((n=2)\) and show that the solution of the initial value problem is \(y(t)=\frac{y_{0}}{y_{0} k t+1}\). c. Let \(y_{0}=1\) and \(k=0.1 .\) Graph the first-order and secondorder solutions found in parts (a) and (b). Compare the two reactions.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If the growth rate function for a population model is positive, then the population is increasing. b. The solution of a stirred tank initial value problem always approaches a constant as \(t \rightarrow \infty\) c. In the predator-prey models discussed in this section, if the initial predator population is zero and the initial prey population is positive, then the prey population increases without bound.

The Gompertz growth equation is often used to model the growth of tumors. Let \(M(t)\) be the mass of a tumor at time \(t \geq 0 .\) The relevant initial value problem is $$ \frac{d M}{d t}=-r M \ln \left(\frac{M}{K}\right), M(0)=M_{0} $$ a. Graph the growth rate function \(R(M)=-r M \ln \left(\frac{M}{K}\right)\) (which equals \(M^{\prime}(t)\) ) assuming \(r=1\) and \(K=4 .\) For what values of \(M\) is the growth rate positive? For what value of \(M\) is the growth rate a maximum? b. Solve the initial value problem and graph the solution for \(r=1, K=4,\) and \(M_{0}=1 .\) Describe the growth pattern of the tumor. Is the growth unbounded? If not, what is the limiting size of the tumor? c. In the general solution, what is the meaning of \(K ?\) where \(r\) and \(K\) are positive constants and \(0 < M_{0} < K\)

Make a sketch of the population function (as a function of time) that results from the following growth rate functions. Assume the population at time \(t=0\) begins at some positive value.

The following models were discussed in Section 1 and reappear in later sections of this chapter. In each case carry out the indicated analysis using direction fields. A model that describes the free fall of an object in a gravitational field subject to air resistance uses the equation \(v^{\prime}(t)=g-b v,\) where \(v(t)\) is the velocity of the object, for \(t \geq 0, g=9.8 \mathrm{m} / \mathrm{s}^{2}\) is the acceleration due to gravity, and \(b>0\) is a constant that involves the mass of the object and the air resistance. Let \(b=0.1 \mathrm{s}^{-1}\). a. Draw the direction field for \(0 \leq t \leq 60,0 \leq y \leq 150\). b. For what initial values \(v(0)=A\) are solutions increasing? Decreasing? c. What is the equilibrium solution?

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