CRE Lecture Notes

CHE511 Chemical Reaction Engineering Dr. J.B. Taboada – Lecture notes

A PRIORI Concentration – In chemistry, concentration is the amount of a component in a given volume of solution. Expressions of Concentration: Molarity (in units of mol/L, molar, or M) or molar concentration denotes the number of moles of a given substance per liter of solution. A capital letter M is used to abbreviate units of mol/L. Molality (mol/kg, molal, or m) denotes the number of moles of solute per kilogram of solvent (not solution). For instance: adding 1.0 mole of solute to 2.0 kilograms of solvent constitutes a solution with a molality of 0.50 mol/kg. Such a solution may be described as "0.50 molal". The term molal solution is used as a shorthand for a "one molal solution", i.e. a solution which contains one mole of the solute per 1000 grams of the solvent. The normality of a solution is the number of gram equivalent weight of a solute per liter of its solution. A normal is one gram equivalent of a solute per liter of solution. The definition of a gram equivalent varies depending on the type of chemical reaction that is discussed — it can refer to acids, bases, redox species, and ions that will precipitate. Equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is the mass of a given substance which will: (1) supply or react with one mole of hydrogen ions (H+) in an acid–base reaction; or (2) supply or react with one mole of electrons in a redox reaction. ex. HCl has 1 eq while KMnO4 has 5 eq. The mole fraction Χ, (also called molar fraction) denotes the number of moles of solute as a proportion of the total number of moles in a solution. For instance: 1 mole of solute dissolved in 9 moles of solvent has a mole fraction of 1/10 or 0.1. Mole fractions are dimensionless quantities. (The mole percentage or molar percentage, denoted "mol %" and equal to 100% times the mole fraction, is sometimes quoted instead of the mole fraction.) Mass percentage denotes the mass of a substance in a mixture as a percentage of the mass of the entire mixture. (Mass fraction xm can be used instead of mass percentage by dividing mass percentage to 100.) Mass-volume percentage, (sometimes referred to as weight-volume percentage or percent weight per volume and often abbreviated as % m/v or % w/v) describes the mass of the solute in g per 100 mL of the resulting solution. Mass-volume percentage is often used for solutions made from a solid solute dissolved in a liquid. For example, a 40% w/v sugar solution contains 40 g of sugar per 100 mL of resulting solution. Volume-volume percentage (sometimes referred to as percent volume per volume and abbreviated as % v/v) describes the volume of the solute in mL per 100 mL of the resulting solution. This is most useful when a liquid - liquid solution is being prepared, although it is used for mixtures of gases as well. For example, a 40% v/v ethanol solution contains 40 mL ethanol per 100 mL total volume. The percentages are only additive in the case of mixtures of ideal gases. The formal (F) is yet another measure of concentration similar to molarity. Formal concentrations are sometimes used when solving chemical equilibrium problems. It is calculated based on the formula weights of chemicals per liter of solution. The difference between formal and molar concentrations is that the formal concentration indicates moles 1


of the original chemical formula in solution, without regard for the species that actually exist in solution. Molar concentration, on the other hand, is the concentration of species in solution. The parts-per notation is used in some areas of science and engineering because it does not require conversion from weights or volumes to more chemically relevant units such as normality or molarity. It describes the amount of one substance in another, and is thus related to the mass fraction. It is the ratio of the amount of the substance of interest to the amount of that substance plus the amount of the substance it is in. Parts per hundred (denoted by '%' [the per cent symbol], and very rarely 'pph') - denotes the amount of a given substance in a total amount of 100 regardless of the units of measure as long as they are the same. e.g. 1 gram per 100 gram. 1 part in 102. Parts per thousand (denoted by '‰' [the per mille symbol], and occasionally 'ppt', but this usage can be confusing because it more often denotes parts per trillion) denotes the amount of a given substance in a total amount of 1000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per gram, or 1 gram per kilogram. 1 part in 103. Parts per million ('ppm') denotes the amount of a given substance in a total amount of 1,000,000 regardless of the units of measure used as long as they are the same. e.g. 1 milligram per kilogram. 1 part in 106. Parts per billion ('ppb') denotes the amount of a given substance in a total amount of 1,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per tonne. 1 part in 109. Parts per trillion ('ppt') denotes the amount of a given substance in a total amount of 1,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per kilotonne. 1 part in 1012. Parts per quadrillion ('ppq') denotes the amount of a given substance in a total amount of 1,000,000,000,000,000 regardless of the units of measure as long as they are the same. e.g. 1 milligram per megatonne. 1 part in 1015.

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INTRODUCTION General Schematic diagram of a Chemical Plant:

Chemical Engineer RECYCLE

M

P

P

MECHANICAL TREATMENT

M

MECHANICAL TREATMENT PHYSICAL TREATMENT

PHYSICAL TREATMENT CHEMICAL REACTION

The design of chemical reactors is probably the one area of interest in engineering that is unique to chemical engineering, and it is probably this function more than anything else, which justifies the existence of chemical engineering as a distinct branch of engineering.1 Design of Chemical Reactors requires knowledge of: • • • • •

Thermodynamics – the amount of heat liberated/absorbed ∆Hr: positive/endothermic; negative/exothermic. Chemical Kinetics – what are the expected changes; how fast or slow is the chemical reaction. Fluid Mechanics – what are the dynamics of fluid (liquid/gas) flow. How ideal is the mixing process. Heat and Mass Transfer – Thermodynamics/Continuity equation (batch/semi-batch/continuous process); and Economics – profit geared higher value products.

Classification of Reactions: • • •

•

Homogeneous – A reaction is homogeneous if it takes places in one phase only. Heterogeneous – A reaction is heterogeneous if it requires the presence of at least two phases to proceed (ex. Solid/liquid or Solid/gas catalysis). Catalytic – A reaction that requires the presence of Catalysts (homogeneous/heterogeneous). Ex. Homogeneous: Transesterification of Oil (acid or base catalyzed reactions); Heterogeneous: Fisher-tropsch process (using Fe based catalysts for the conversion of CO2 and H2 to hydrocarbons. Non Catalytic – No catalysts involved.

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Chemical Reaction Engineering An Introduction to the Design of Chemical Reactors, Octave Levenspiel, John Wiley & Sons, Inc. 1962

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Table 1. Classification of Chemical Reactions. Noncatalytic

Catalytic

Homogeneous

Heterogeneous

Assignment: Fill up table 1 with examples. Rate of Reaction Based on unit volume of reacting fluid,

ri =

dN i moles i formed = Vdt (unit volume fluid )(time )

Based on unit volume of reactor,

ri ' =

dN i moles i formed = V r dt (unit volume reactor )(time )

Based on unit interfacial surface,

ri " =

dN i moles i formed = S dt (unit surface)(time )

Based on unit mass of solid,

ri " ' =

dN i moles i formed = W dt (unit mass of solid )(time )

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Example: Chemical A is being converted into chemical R in a vessel packed with non-porous, spherical catalyst beads. The specific surface area of the catalyst is 60 ft2/ft3 of packed bed, its bulk density is 180 lb/ft3 of packed bed, and the porosity of the bed ∈ = 0.40. The stoichiometric equation is A → 2R

and the rate of disappearance of A based on unit mass of catalyst is proportional to the concentration of A present in the gas. Thus in English units, using hours, we find from experiment dN A − rA"' = − = 0 .1 C A W dt The negative sign shows that the rate of change of A is negative, or that A disappears. (a) Write out the given rate equation showing the units of the various terms; (b) Find rA’, the rate based on unit volume of reactor; (c) Find rA, the rate based on unit volume of fluid; and (d) Find rA”, the rate based on the unit surface of catalyst. Answers: (a) –rA”’= 0.1 (ft3 voids/lb solid (hr)) CA (moles A/ft3 voids) (b) –rA’ = 18 (ft3 voids/ft3 reactor (hr)) CA (moles A/ft3 voids) (c) –rA = 45 (1/hr) CA (moles A/ft3 voids) (d) –rA” = 0.3 (ft3 voids/ft2 surface (hr)) CA (moles A/ft3 voids) Important parameters to consider when translating reaction rates (applicable when dealing with heterogeneously catalyzed reactions): 1. Concentration is the amount in moles per volume fluid. In packed bed reactors, concentration is CA (moles A/ft3 voids); Figure 1.

Figure 1 shows a flow through a packed bed reactor. The beads represent solid catalyst particles, and the voids or empty spaces between particles represent the paths where the fluid/reactant flows. 2. Bulk density of catalyst, W/Vr, is the mass of the catalyst per reactor volume (lb solid)/ft3 reactor); 3. Porosity, V/Vr, is the amount of voids (empty space) in the reactor per reactor volume (ft3 voids/ft3 reactor); 4. Specific surface area of catalyst is the catalyst surface per reactor volume, S/Vr, ft2 surface/ft3 reactor.

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BASIC CONCEPTS

Definition of Rate of Reaction, (-rA)

The study of Chemical Reactor Engineering is based on modeling and evaluating the performance of a certain reactor. As a basic step, we start our study by performing mole balances on each chemical species in the system. This chemical specie could be any chemical compound or element with a distinct identity. The identity of chemical species is determined by the kind, number, and configuration of that species’ atoms [Fogler, 4th Ed., 2004]. Two given chemical species could still be different, even though they have the same number of atoms of each element, if they exhibit different configurations. As a result these almost identical species demonstrate different chemical as well as physical, and optical properties from each other. When there is an apparent change in the number of molecules of one or more species, by losing its identity and assuming a new one, a chemical reaction has taken place. However, from the Universal Law, matter is neither created nor destroyed. Therefore, we can account for the certain changes during a chemical reaction by performing a mole balances over the reaction system. The rate at which a given chemical reaction proceeds can be expressed as the rate of disappearance of reactants or the rate of formation of products. For instance, if we have a certain chemical specie A reacting to form B, the numerical value of the rate of reaction, -rA, can be defined as the number of moles of A reacting (or disappearing) per unit time

per unit volume (mol/dm3-s). Although the definition states that the rate is a measure of the change of moles of reacting specie per unit time, it does not mean that the rate is a differential function of the species concentration. We will show later on that this case is only true for a constant-volume batch reactor. The misconception in the definition

stems from the fact that most experiments carried out to obtain data on the chemical reaction rate were laboratory bench-scale experiments. In fact, the chemical reaction rate is an intensive quantity and depends on temperature and concentration. Therefore, the reaction rate equation in general is essentially an algebraic equation and a function of concentration, i.e. -rA = [k (T)][ f (CA, CB, …)]

(eqn. 0.1)

Where k is reaction rate constant, which is a function of temperature, T, and CA, CB, … are the corresponding concentrations of the reactants. 6


For first order elementary reactions the reaction rate reduces to the equation:

-rA = k·CA

(eqn. 0.2)

In general, the reaction rate equation for elementary reactions can be written as :

-rA = k·CA n

(eqn. 0.3)

where n is the reaction order. Moreover, the reaction rate constant as mentioned earlier is a function of temperature, and is actually not a constant per se. This dependence on temperature by the specific reaction rate, k, follows the correlation given by the Arrhenius equation: k (T) = A·e –E/RT

where

(eqn. 0.4)

A = pre-exponential factor or frequency factor E = activation energy, J/mol or cal/mol R = gas constant = 8.314 J/mol-K = 1.987 cal/mol-K T = absolute temperature, K

The units of the specific reaction rate constant depend on the reaction order. Example, for first order reaction, to have (-rA) with units moles/volume-time, the rate constant, k, must have the units of time-1. Equation 0.4 implies that the specific reaction rate constant is dependent on temperature or the reaction and on the Energy of Activation. By definition the energy of activation is the minimum energy required that must be possessed by the reactants in order for the reaction to proceed. Figure 0.1 illustrates this:

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Enthalpy [J/mol]

E Reactants

-∆Hr Products

∆HREACTION = ∆HPRODUCTS - ∆H REACTANTS ∆H = negative (-) by exothermic reaction = positive (+) by endothermic reaction Figure 0.1

As the kinetic rate constant, k, is an exponential function of the Energy of Activation and of the reaction temperature, these parameters dictate on how fast or slow the reaction proceeds. The higher the activation energy, the slower the reaction becomes, however, raising the reaction temperature can compensate this. Other Units for the Rate In heterogeneous reaction systems, reactions that involve in more than one phase, the rate of reaction is usually expressed not in terms of reaction volume, but in terms of either catalyst mass or catalyst surface area. For example, in a gas-solid catalytic reaction, the definition of the reaction rate is –rA’, moles of A reacted per unit time per unit mass of catalyst (mole/s-g cat.), or –rA”, moles of A reacted per unit time per unit surface area of catalyst (mole/s-m2 cat.). These rate definitions are further elaborated in unit 2.

The General Mole Balance Equation

In order to perform the mole balance on any system, we need to identify first the system boundaries. Take for instance a given system volume in figure 0.1, where the rate of inflow of a certain chemical specie A is represented by FA0 , moles per unit time. Here, A undergoes a chemical reaction and the unconverted A flows out of the system, represented by FA, moles per unit time.

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System Volume Conversion

FA0

FA

Figure 0.2 Balance on system volume

A general mole balance on species A at any instant in time, t, is given by the equation: Rate of Accumulation of A within the system (moles/time)

Accumulation dN A dt

=

Rate of flow of A into the system (moles/time)

-

Rate of flow of A out of the system (moles/time)

-

Rate of consumption of A in the system (moles/time)

+

Rate of generation of A in the system (moles/time)

=

In

-

Out

-

Converstion

=

FA0

-

FA

-

Converstion

(eqn. 0.5)

where NA represents the number of moles of species A in the system at time t. Assuming that the system variables (e.g. temperature, catalytic activity, concentration) are spatially uniform throughout the system volume, the rate of conversion can be written as the product of the reaction rate and the reaction volume. Conversion = (-rA) ·V

(eqn. 0.6)

Where V is the reaction volume, giving the units of the conversion term as moles / time.

Combining equations 1.5 and 1.6, we have:

dN A = FA0 − FA − (− rA ⋅ V ) dt

(eqn. 0.7)

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Batch Reactors

Consider the chemical reaction of reactant A forming product B in a batch reactor. A batch reactor has neither inflow nor outflow of reactants or products, while the reaction is being carried out. Thus equation 1.7 reduces to simply: dN A = rA ⋅ V dt

(eqn. 0.8)

Since NA is just a product of the reaction volume V and of the concentration of the reactant, here CA. Thus for constant-volume batch reaction, equation 1.8 resolves to: dC A = rA dt

(eqn. 0.9)

Here we can say that the rate of reaction is a differential function of the reactant concentration. That is why, as mentioned earlier, this definition is only true particularly for constant-volume batch reaction.

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CRE Lecture Notes

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