Kinetics Archives - Engineeringness

Non Isothermal and Non Ideal Flow Reactors | A Breakdown Of Reactor Design

Hassan Ahmed — Thu, 16 May 2024 01:52:04 +0000

Non Isothermal Reactors

Firstly, we will be taking a look into energy balances on reactors to give us a better understanding of the equations and assumptions used in the Non-Isothermal and Non-Ideal Flow reactors. The First 2 terms that need to be understood are, Isothermal and Adiabatic.

What Does Isothermal Mean?

Isothermal which refers to a system at a constant temperature,

What Does Adiabatic Mean?

Adiabatic involves no heat entering or leaving the system.

What Is An Open System?

Open systems refers to mass being able to enter and leave the system. Moreover, Temperature can also be lost to or gained from the surrounding.

What Is An Energy Balance?

An Energy balance is simply the difference in the energy input and output. An energy balance equation can be used on open systems and can be relatively easy to do or challenging when more components and different phases are present.

Energy Balance Diagram For An Open System

The energy balance equation for an open system is:

The enthalpy of reaction at a certain temperature (T) is worked out using the enthalpy of products and reactants:

Non-Ideal Flow Reactors

In reality reactors can never be ideal and it cannot be assumed. The flow will always deviate and for flow reactors, non-ideal flow patterns can cause issues.

CSTR (Continuous stirred-tank reactor):

There will be stagnant or dead regions where no mixing of fluids and no flow. This causes the fluid to sit in place and reduce the volume of the CSTR for reactions.

In the event where the fluids flow from the inlet to the outlet, this is called short-circuiting and the fluid won’t mix or spend enough time in the reactor.

PFR (Plug Flow Reactor):

The ideal plug flow isn’t possible in reality as fluids will mix along the length of the PFR.

Fluids closer to the walls will travel at a slower rate than fluid closer to the centre of the reactor and this will cause mixing along the axis of PFR.

Turbulent mixing and molecular diffusion will lead to mixing along the length of the PFR.

What Is Residence Time Distribution and How To Calculate Residence Time Distribution

Residence time distribution (RTD) is the probability distribution of the time that a solid or fluid spends inside the reactor and is the main method that can be measured to understand the types of flow encountered in non-ideal flow reactors. TRD is denoted with the symbol, E and will tell us the amount of time (age) the material spends in the exit stream of the reactor.

t – age. It is time spent in reactor, you will find that age young and older as used to denote time, as long as you remember that age is time spent in reactor. The terms younger and older are the same. They are seen as as less time spent in the reactor (younger) and More time spent in the reactor (older).

the RTD is normalised to unity (integrated between zero and infinity):

How To Measure The Residence Time Distribution

The RTD is measured using the pulse experiment, which involves injecting a pulse dye or tracer dye into the fluid before entering the reactor, then measuring the dye concentration over a period of time and the results when graphed will be normalised. The concentration is proportional to the RTD and gives an area under the graph of unity (1).

You will need to divide the measured concentration curve, C_pulse by the area under the curve. The area under the graph can be found by integration or by the expression M/ (mass of tracer/volumetric flow rate) assuming that C_pulse is mass per unit volume.

Example Residence Time Distribution

Step experiment and F curve:

Here we have a steady yellow tracer flow at t = 0. The tracer concentration at the outlet will increase as time increases, C_step will equal the inlet concentration. This concentration divided by the final concentration is called the F curve. The final concentration of the tracer is mass flow rate divided by volumetric flow rate.

We can now say that at any time greater than t = 0, that the yellow tracer in the exit stream is younger than age t, and the fraction of yellow tracer at the outlet is equal to the fraction of the exit stream younger than time t, which is written as:

Graphs to show concentration vs time

State Of Mixing and RTD:

To find out the conversion of the reactants the state of mixing as well as the RTD need to be known. There are two terms we describe the state of mixing:

The State of Mixing | Macrofluid and Microfluid:

Macrofluid: Globules of fluids act as their own batch reactors and will spend different amounts of time in the reactor and have a different conversions than other globules. Also, o mixing between globules of fluid that aren’t the same age, such as very viscous fluids or solids.
Microfluid: Individual globules can move anywhere in the reactor such as an ideal CSTR, examples of these include gases and not very viscous liquids.

For batch reactors, to work out the concentration of a species let’s call it A for an element of age t and average using the RTD the equation would be:

Hassan Ahmed

Hassan graduated with a Master’s degree in Chemical Engineering from the University of Chester (UK). He currently works as a design engineering consultant for one of the largest engineering firms in the world along with being an associate member of the Institute of Chemical Engineers (IChemE).

The post Non Isothermal and Non Ideal Flow Reactors | A Breakdown Of Reactor Design appeared first on Engineeringness.

An In Depth Guide To Basic Reaction Kinetics

Dr. Adam Zaidi — Thu, 30 Jul 2020 21:47:12 +0000

Basic Reaction Kinetics

The reaction rate, r_i (also referred to as the rate of reaction) is a measure of how fast a reaction is and is defined using several ways:

$r_{i} = \frac{1}{V} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{V o l u m e o f f l u i d \times t i m e}$

${r_{i}}^{‘} = \frac{1}{M} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{M a s s o f s o l i d \times t i m e}$

${r_{i}}^{‘ ‘} = \frac{1}{S} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{S u r f a c e a r e a \times t i m e}$

${r_{i}}^{‘ ‘ ‘} = \frac{1}{V_{s}} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{V o l u m e o f s o l i d \times t i m e}$

${r_{i}}^{‘ ‘ ‘ ‘} = \frac{1}{V_{r}} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{V o l u m e o f r e a c t o r \times t i m e}$

One of the benefits of the reaction rate is that if the reactor is scaled up the rate of reaction will be the same, which simplifies the process of reactor scale up, so no long equations are needed every time the reactor volume changes. Thus, the reaction rate is an intensive quantity as its magnitude is independent of the size of the system (i.e. changing reactor size).

For reagents, reaction rates are negative and for products the reaction rates are positive, this is because reagents are used up in reactions, and products are formed. An example of this would be the reaction:

$a A + b B \to cC$

to write this out in terms of reaction rates, the species (A, B, or C) and the stoichiometric coefficient (a, b and c) are required, and the concept stated above: the reagents being negative and the products being positive.

$- \frac{r_{A}}{a} = - \frac{r_{B}}{b} = \frac{r_{C}}{c}$

(1.0)

Example: To prove that the reactions rates are equal

A reactor with fluid volume 1 m³ has a reaction with the reaction time being 10 seconds, and we are told that 5 moles of B are formed, prove that the rates are equal.

Hint: use the reaction rate definitions, looking closely at parameters you have been given and equation 1.0.

$- \frac{r_{A}}{2} = \frac{r_{B}}{1}$

(1.1)

With the parameters of volume of fluid and time the reaction rate used is:

$r_{i} = \frac{1}{V} \frac{∆ N_{i}}{∆ t} = \frac{M o l e s o f s p e c i e s ‘ i ‘ f o r m e d}{V o l u m e o f f l u i d \times t i m e}$

Using the stoichiometry, we know that for every 1 mole of species B formed 2 moles of species A are required, thus as 5 moles of B are formed then 10 moles of A are required as the stoichiometry is 2:1.

$r_{A} = \frac{- 10 m o l o f A}{1 m^{3} \times 10 s} = - 1 m o l o f A r e q u i r e d / m^{3} s$

$r_{B} = \frac{5 m o l o f B}{1 m^{3} \times 10 s} = + 0.5 m o l o f B r e q u i r e d / m^{3} s$

Then insert reaction rates into equation 1.1:

$- \frac{r_{A}}{2} = \frac{r_{B}}{1}$

$- \frac{- 1}{2} = \frac{0.5}{1}$

$\frac{0.5 m o l}{m^{3} s} = \frac{0.5 m o l}{m^{3} s}$

Rate Equations

For any chemical reaction equation, a rate equation can be used which links the forward reaction rate with the concentration or pressure of the reactants. These are more complicated functions of reagents and (sometimes) product concentrations for a non-elementary reaction.

Reactions can be classified under these terms:

Homogeneous: consists of only one phase
Heterogeneous: more than one phase needed for the reaction
Catalytic or noncatalytic
Exothermic or endothermic
Elementary or nonelementary
Single reaction or multiple reactions (and within latter: series or parallel, and combinations)

Writing out a rate equation:

Taking an example reaction:

$A + B \to C$

The rate equation would simply be:

$- r_{A} = K_{A} C_{A}^{a} C_{B}^{b}$

And using equation 1.0 we know that the rate equation concerning species B would be the same as that of species A. K is the rate constant which is proportionally constant that indicates the relationship between the molar concentration of reactants and the rate of a chemical reaction (Helmenstine, 2018), and the rate constant concerning each species is:

$\frac{K_{A}}{a} = \frac{K_{B}}{b}$

Given a rate equation:

$- r_{A} = K_{A} C_{A}^{a} C_{B}^{b}$

The reagents a and b are not always the stoichiometric coefficients, we say that the reaction n order concerning A and b^th order concerning B and the overall order is n = a + b.

The molecularity of an elementary reaction is the number of molecules involved in the reaction. The order can be fractional values and molecularity is always a whole number.

Equilibrium Constant

For an equilibrium reaction, the rate of the forward reaction is the same as the rate of the backward reaction and the concentration doesn’t change.

$- r_{A, f o r w a r d s} = r_{A, b a c k w a r d s}$

(1.2)

For the reaction:

$aA + bB ⇌ cC + dD$

The equilibrium constant K_C (also written as K_eq or K) can be defined as:

$K_{C} = \frac{{[C]}_{e q}^{c} {[D]}_{e q}^{d}}{{[A]}_{e q}^{a} {[B]}_{e q}^{b}}$

(1.3)

The position of the equilibrium is determined by the entropy change, the enthalpy change, and the conditions the reaction is under such as temperature and pressure.

Assuming the reaction is elementary (stoichiometric coefficients are usually 1 for all species) the forward and backward reaction can be stated:

$r_{A, f o r w a r d s} = - k_{1} {[A]}^{a} {[B]}^{b}$

$r_{A, b a c k w a r d s} = k_{- 1} {[C]}^{c} {[D]}^{d}$

k₁ represents the rate constant for the backward reaction and k_-1 represents the rate constant for the forward’s reaction

Thus, we can know to prove equilibrium constant K_Cequation 1.3, by first using equation 1.2:

$- k_{1} {[A]}_{e q}^{a} {[B]}_{e q}^{b} = k_{- 1} {[C]}_{e q}^{c} {[D]}_{e q}^{d}$

when rearranged will give:

$K_{C} = \frac{{[C]}_{e q}^{c} {[D]}_{e q}^{d}}{{[A]}_{e q}^{a} {[B]}_{e q}^{b}}$

References

Helmenstine, A. M. (2018, September 27). What Is the Rate Constant in Chemistry? Retrieved from ThoughtCo: https://www.thoughtco.com/reaction-rate-constant-definition-and-equation-4175922

Dr. Adam Zaidi

Dr. Adam Zaidi, PhD, is a researcher at The University of Manchester (UK). His doctoral research focuses on reducing carbon dioxide emissions in hydrogen production processes. Adam’s expertise includes process scale-up and material development.’

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