Process Calculation Examples

Example 1

The side product of a chemical company is a mixture with 82 weight % of species A, and the remaining is species B. In this mixture, species A is the valuable component. If this mixture is sold with this composition, its price is 1.12 USD per kg. However, if the percentage of species A can be increased to 96%, the price in the market will be 1.58 USD per kg. It is proposed that a stream of species C will be used to strip the species B as shown below. In this process, 2 kg of C should be used for each kg of B entering the process.

As a chemical engineer, you are requested to show whether this investment is profitable or not. The cost of species C is 0.48 USD per kg and the production cost (including energy, labour, depreciation of equipment and all others) is 0.5 USD per kg of B stripped (i.e. kg of B in stream 3). Follow these steps to solve this problem:

a) Determine the degree of freedom,

b) Determine all the flowrates and compositions,

c) Calculate the production cost of stream 4 per kg and compare it with the market price of mixture with 96% species A

Solution

 

 

Example 2

CO combines with Cl₂ to form COCl₂ gas. The feed to a reactor operating at steady state is a mixture of only CO and Cl₂. After the reaction the product contains 12 mol COCl₂, 3 mol Cl₂ and 8 mol CO.

a) What is the percent excess,

b) What is the conversion of the limiting reactant,

c) What is the amount of feed in kg.

Solution

Introduction into Reaction Engineering

Usually, a Chemical Engineer is hired to:

·       maintain and operate a process

·       fix some perceived problem

·       increase capacity or selectivity at minimum cost

Some of the major challenges in the design of chemical reactors include:

·       Searching for alternate processes to replace old ones

·       Finding ways to make a product from different feedstocks

·       Reducing or eliminating a troublesome by product

The reaction rate is the rate at which a species loses its chemical identity per unit volume. The rate of a reaction can be expressed as the rate of disappearance of a reactant or as the rate of appearance of a product. Consider species A:

Catalysts are an important aspect of reaction engineering. They alter the speed of a reaction by lowering the activation energy of a reaction. The activation energy of a reaction is the amount of energy needed to produce a forward or reverse reaction. In the following figure we can see the activation energy of a non catalytic reaction (red line), while the green line represents the same reactions activation energy when a catalyst is used.

Examples 

What are reversible reactions?

Force and Pressure

Force

Force is defined using Newton’s second law of motion which states that the net force F_net acting on a body of mass m, is proportional to the time rate of change of its momentum. If the mass is constant, the net force is proportional to the product of the mass of the body and its acceleration. Thus,

where a = dv/dt is the acceleration of the body and K is a proportionality constant to be determined by the units used. In SI system, K = 1 and force has the units of newton, N, or kg.m/s².

Pressure

The pressure, P, of a fluid on a surface is defined as the normal force exerted by the fluid per unit area of the surface, i.e.,

Pressure has the units of Pa (N/m²) in SI units. Absolute pressure refers to the absolute value of the force per unit area exerted on the containing wall by a fluid. Gauge pressure is the difference between the absolute pressure and the local atmospheric pressure. Vacuum represents the amount by which the atmospheric pressure exceeds the absolute pressure. This can be shown schematically:

From these definitions we can see that:

·      Absolute pressure cannot be negative.

· Vacuum cannot be greater than the local atmospheric pressure.

A system is said to be in mechanical equilibrium with its surroundings when there is no pressure difference between them, i.e.,

P_sys = P_surr            Condition of mechanical equilibrium

Isobaric Process: This is a process that takes place at constant pressure. It is important to note that if the initial and final states are at the same pressure, this does not necessarily imply an isobaric process.

Example 1

Which of the following processes would you consider to be isobaric for analysis purposes?

a) A valve is opened in a tank of compressed air. (Non-isobaric process)

b) Heat is added to boiling water on the stove. (Isobaric Process)

c) Air is compressed in a compressor. (Non-isobaric process)

d) A tank of compressed air leaks air through a tiny pinhole leak. (Non-isobaric but if short time periods are involved, it may be considered isobaric)

e) The air in the cylinder with a frictionless piston held by a constant weight on it as heated. (Isobaric Process)