MOLECULAR DIFFUSION

Molecular diffusion

• Mass transfer process can take place in a gas or vapour or in a liquid, and it can result from the random velocities of the molecules (molecular diffusion) or from the circulating or eddy currents present in a turbulent fluid (eddy diffusion).
• Molecular diffusion occurs due to movement of individual molecule through a substance by virtue of their thermal energy
• The phenomenon of molecular diffusion ultimately leads to completely uniform concentration of substances throughout solution which may initially have been nonuniform.
• For example:-

1. If a drop of blue copper sulphate solution is placed in a beaker of water, the copper sulphate eventually permeate the entire liquid. the blue color in times everywhere uniform, and no subsequent changes occurs.
2. In a two phase system not at equilibrium, such as layer of ammonia and air as a gas solution in contact with a layer of liquid water, spontaneous alteration through molecular diffusion also occurs, ultimately bringing the entire system to a state of equilibrium, after that diffusion stops.

• Hence in molecular diffusion ,if solution is not uniform everywhere in concentration of its constituents, the solution is spontaneously brought to uniformity by diffusion.
• It means that molecular diffusion is the mechanism of mass transfer in stagnant fluids or in fluids which are moving in laminar flow and the mass transfer takes place from a place of high concentration to low concentration.
• The rate at which a solute moves at any point in any direction must therefore depend upon concentration gradient at that point and in that direction.
• rate = molar flux [mol/ (area)(time)]
• The area is measured in the direction normal to the diffusion

HOW PROCESS CONTROL

Consider the tank heater system shown in Figure 

Assumption

Fi, Ti = flow rate (ft3/min) and temperature(°F) of entering liquid into the tank

F = flow rate of steam which heated liquid (lb/mm).

F, T = the flow rate and temperature of the stream leaving the tank. 

The tank is considered to be well stirred, which implies that the temperature of the effluent is equal to the temperature of the liquid in the tank. 

Objectives

• To keep the effluent temperature T at a desired value Ts
• To keep the volume of the liquid in the tank at a desired value Vs 

To maintain the temperature of effluent ‘T’ at desired temperature ‘Ts’

• The operation of the heater is disturbed by external factors such as changes in the feed flow rate and temperature (Fiand Ti).
• If nothing changed, then after attaining T = Ts and V = Vs, we could leave the system alone without any supervision and control.
• Consequently, some form of control action is needed to alleviate the impact of the changing disturbances and keep T and V at the desired values.
• In Figure we see such a control action to keep T = Ts when Ti or Fi, changes.
• A thermocouple measures the temperature T of the liquid in the tank.
• Then T is compared with the desired value Ts, yielding a deviation ε = Ts - T.
• The value of the deviation ε is sent to a control mechanism which decides what must be done in order for the temperature T to return back to the desired value T. 
• If ε > 0, which implies that T < Ts, the controller opens the steam valve so that more heat can be supplied.
• On the contrary, the controller closes the steam valve when ε < 0 or T> Ts.
• It is clear that when T = Ts (i.e., ε = 0), the controller does nothing.
• This control system, which measures the variable of direct importance (T in this case) after a disturbance had its effect on it, is called the feedback control system. 
• The desired value Ts is called the set point and is supplied externally by the person in charge of production.

To maintain the temperature of effluent ‘T’ at desired temperature ‘Ts’

• Returning to the tank heater example, we realize that we can use a different control arrangement to maintain T= Ts when Ti, changes.
• Measure the temperature of the inlet stream T, and open or close the steam valve to provide more or less steam.
• Such a control configuration is called feedforward control.
• The feedforward control does not wait until the effect of the disturbances has been felt by the system, but acts appropriately before the external disturbance affects the system, anticipating what its effect will be. 

To maintain the height of liquid ‘h’ in the tank at 

desired level ‘hs’

• In Figure we see a control action to keep h = hs when Ti or Fi, changes. So that tank will not overflow or go dry
• A level measuring device measures the height h of the liquid in the tank.
• Then h is compared with the desired value hs, yielding a deviation ε = h - hs.
• The value of the deviation ε is sent to a control mechanism which decides what must be done in order for the height h to return back to the desired value hs.
• It may open or close the valve that affects the effluent flow rate F
• It is also feedback control systems act post facto (after the fact), that is, after the effect of the disturbances has been felt by the process.
• If ε > 0, which implies that h < hs, the controller opens the steam valve so that more heat can be supplied.
• On the contrary, the controller closes the steam valve when ε < 0 or T>Ts.
• It is clear that when T = Ts (i.e., ε = 0), the controller does nothing.
• This control system, which measures the variable of direct importance (T in this case) after a disturbance had its effect on it, is called the feedback control system. 
• The desired value Ts is called the set point and is supplied externally by the person in charge of production.

DEFINITION OF RATE OF REACTION

Definition of rate of reaction

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.

Following is single phase reaction

Rate of reaction of component A

-rA = rate of disappearance of A, minus sign means disappearance
The rates of reaction of all components in above reaction are related by

The rate of change in a number of moles of any component i due to reaction is dNi/dt, then the rate of reaction in its various forms is defined as follows.
Based on unit volume of reacting fluid,


Based on unit mass of solid in fluid-solid systems


Based on unit interfacial surface in two-fluid systems or based on unit surface of solid in gas-solid systems


Based on unit volume of solid in gas-solid systems


Based on unit volume of reactor, if different from the rate based on unit volume of fluid




In homogeneous systems the volume of fluid in the reactor is often identical to the volume of reactor. In such a case V and Vr are identical.
so that

CLASSIFICATION OF VARIABLES IN CHEMICAL PROCESS CONTROL

Classification of variables in chemical process control

In controlling a process there exist two types of classes of variables.

Input Variable

This variable shows the effect of the surroundings on the process. It normally refers to those factors that influence the process.

• An example of this would be the flow rate of the steam through a heat exchanger that would change the amount of energy put into the process. There are effects of the surrounding that are controllable and some that are not.

There are two types of inputs.

Manipulated(or adjustable) inputs :

These are the variable in the surroundings can be control by an operator or the control system in place.

• The values of manipulated inputs can be adjusted freely by the human operator or a control mechanism.

Disturbances:

These are the input variable that can not be controlled by an operator or control system.

• There exist both measurable and immeasurable disturbances.
• The values disturbances are not the result of adjustment by an operator or a control system.

Output variable-

Output variable also known as the control variable.

These are the variables that are process outputs that effect the surroundings.

Measured output variables:-

The values of measured output variables are known by directly measuring them

Unmeasured output variables:-

The values of unmeasured output variables are not or cannot be measured directly

Example CSTR with cooling jacket

• Consider a continuous stirred tank reactor (CSTR) in which an irreversible exothermic reaction A ---> B takes place. The heat of reaction is removed by a coolant medium that flows through a jacket around the reactor

where

• Input variables: CAi ,Ti, Fi, Tci, Fc
• Output variables: Fc, Tc0, CA, T, F

Case 1:- If the inlet stream in the CSTR system comes from an upstream unit have no control.

• Disturbances: CAi, Fi, Ti

Case 2:- If the coolant flow rate is controlled by a control valve, then

• Manipulated variable: Fc
• Disturbance: Tci 

Case 3:- If the flow rate of the effluent stream is controlled by a valve

• Manipulated variable: F

PROCESS CONTROL

Process control

Process control is a mixture between the statistics and engineering discipline that deals with the mechanism, architectures, and algorithms for controlling a process.

• Structure of chemical process plant is very complex
• Any chemical plant consists of various process units which are inter connected with one another in a systematic manner
• The main objective of any plant is to convert certain raw materials into the desired product using available sources of energy
• Other objectives- safety, product specification, environmental regulations, operation constraints, economics
• These all these parameters are controlled by an arrangement of various equipment like measuring devices, valves, controller

Examples of controlled processes are:
1. Controlling the temperature of a water stream by controlling the amount of steam added to the shell of a heat exchanger.

2. Operating a jacketed reactor isothermally by controlling the mixture of cold water and steam that flows through the jacket of a jacketed reactor.

3. Controlling the height of fluid in a tank to ensure that it does not overflow.

THERMODYNAMIC SYSTEM

Thermodynamic system

Thermodynamics is the science relating heat and work transfers and the related changes in the properties of the working substance. The working substance is isolated from its surroundings in order to determine its properties.

 

SYSTEM

Thermodynamic system is defined as a quantity of matter or a region in space upon which attention is concerned in the analysis of a problem.

• A system may be either an open one, or a closed one, referring to whether mass transfer or does not take place the boundary.

SURROUNDING

Everything external to system is call surrounding or the environment.

BOUNDARY

A physical or imaginary surface, enveloping the system and separating it from the surroundings.

• The boundary may be either fixed or moving.

UNIVERSE

A system and surrounding together comprise a universe.

RATE OF REACTIONS

Rate of reactions

The rate of reaction tells us how fast a number of moles of one chemical species are being consumed to form another chemical species.

• The term chemical species refers to any chemical component or element with a given identity.
• The identity of a chemical species is determined by the kind, number, and configuration of that species atoms.

Chemical reaction has taken place when a detectable number of molecules of one or more species have lost their identity and assumed a new form by a change in the kind or number of atoms in the compound and/or by a change in structure or configuration of these atoms.

• In this classical approach to chemical change, it is assumed that the total mass is neither created nor destroyed when a chemical reaction occurs.
• The mass referred to is the total collective mass of all the different species in the system.
• However when considering the individual species involved in a particular reaction, we do speak of the rate of disappearance of mass of a particular species.
• The rate of disappearance of a species say species A is the number of A molecules that lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reaction.
• In order for a particular species to "appear" in the system some prescribed fraction of another species must lose its chemical identity.
• There are three basic ways a species may lose its chemical identity:

1. Decomposition:- ln decomposition the molecule loses its identity by being broken down into smaller molecules. atoms. or atom fragments. 
2. Combination:- A molecule may lose its species identity is through combination with another molecule or atom.
3. Isomerization:- Here, although the molecule neither adds other molecules to itself nor breaks into smaller molecules. it still loses its identity through a change in configuration.