Thermodynamics: Entropy and its measurement

Entropy is a property of the system used to find the direction of a process.  It is calculated as [dQ(rev)/T] for a change of state. If we have a reversible process the change in total entropy (system + surrounding) is zero and if the process is irreversible, the change in total entropy is positive. Entropy is a state function, then why does it care about the process whether it is reversible or irreversible?

Change in entropy of system will remain same whether the process is reversible or irreversible. It depends only on the states of the system. But the states of surrounding will depend on the path taken to carry out changes in the state of a system. Therefore the states of surrounding will be different for different paths taken to carry out changes in system. Hence the entropy of surrounding will change with the path. That's why the total entropy change will depend on the path taken. For a reversible process minimum amount of heat is required to get a specified amount of work. Therefore the entropy change will be minimum i.e. zero. and if the process is irreversible the amount of heat will increase resulting in positive entropy change. So it is said that Entropy of the universe never decreases.

Save energy for better tomorrow

Energy is a major concern today. The petroleum resources are depleting and the renewable sources except hydro power have their limitations. The major source of energy will be nuclear in the future, but one way we all can produce energy i.e. by saving it today.  

To save energy, we switch off the equipments like fan, bulb, TV etc, but how can we say that energy has been saved? If we take an example of AC diesel generator, if we are not taking any power from it, are we saving energy in terms of fuels? The generator will consume fuel, similar will be case with thermal plant. They are producing electricity, we use it or not, it will consume fuel. Then how do we save it?

As we switch off the lights, fans, or other equipment on a large scale, the load on plant reduces, which will make it consume less fuel. One fan or bulb may not contribute a lot, but it will be added for every equipment which is put off and collectively it will make a difference. The plant will consume fuel according to the base load, whether we use it or not, but as the load increases, the fuel consumption will increase. So save electricity save fuel save future. 

Mechanical Operation: Screen Efficiency/Effectiveness

Screens are used to separate particles based on their sizes. Separation is important for various processes in chemical industries. The efficiency of a screen is defined as the sharp separation of particles. An ideal screen means all desired particles (specified particle size) are recovered 100% from the feed and no undesired particles come with the desired one. 

the efficiency of screen depends on

1. When the screens are used for many times, the screen gets damaged. The wires displace from their original position which leads to changes in mesh opening.

2. The time of operation and capacity (i.e. feed rate) also affect the effectiveness of screen. 

3. Moisture content also effect the effectiveness of screen.

4. orientation of particle

The efficiency of screen is defined as : recovery × rejection

Recovery: the fraction of desired particle recovered from feed:P(yP)/F(yF) 

Rejection: the fraction of undesired particle rejected:R(1-yR)/F(1-yF)

F, P, R are the feed rate, product (desired size) and reject flow rate.

yF, yP, yR are the fraction of desired product in feed, product and reject.

ideally yP should be 1 and yR should be 0 and the recovery and rejection both should be 1

Now the question rises how to find yF, yP, yR?

suppose we have a mixture of 3 different sizes material say 4, 5 and 6 cm & 5 cm is the desired size particle, now, how can we calculate the mass fraction of 5 cm size particle?

In industrial screens there will be some overlapping of particle sizes, i.e. there will be presence of oversize material and undersized  particle in streams. for that we will use new screens on a sample of 3 streams which has an efficiency of 1 (new screen, less capacity, standard moisture content and proper orientation). this fraction calculated will be used to find the efficiency of the industrial screen.  

Thermodynamics: Solution Property based Problems

1. A binary mixture containing species 1 and 2 forms an azeotrope at 105.4°C and 1.013 bar. The liquid phase mole fraction of component 1 of this azeotrope is 0.62. At this temperature, the pure component vapour pressure for species 1 and 2 are 0.878 bar and 0.665 bar respectively. Assume that the vapour phase is an ideal gas mixture. Find the activity coefficients in a solution containing 40% of species1.      

2.      At 25°C and atmospheric pressure the volume change of mixing of binary liquid mixtures of species 1 and 2 is given by the equation:

∆V=  x1x2(45x1 +25x2 )

Where ∆V is in cm³/mol, at these conditions V₁=110 and V₂= 90 cm³/mol. Determine the partial molar volumes  in a mixture containing 40 mol% of species 1 at given conditions.                       

3. The partial pressure (approximate) of alcohol in alcohol water system behaviour can be represented in the figure below. The figure is divided in three sections. Select the suitable equation from Raoutlt's Law, Modified Raoult's Law and Henry Law for partial pressure applicable in these regions.

4. Fugacity coefficient of species (i ) in solution and activity coefficient of species (i) in solution

Mechanical Operation: Sphericity

Sphericity is a shape factor used to find the resemblance shape of irregular particles with a spherical particles. A spherical particle is symmetrical and has no orientation issue. there are correlations which can be used for a spherical particles like pressure drop in fluidised bed. In order to use the correlation for irregular shape particle, sphericity is used. 

Sphericity is defined as surface-volume ratio for a sphere of diameter Dp divided by the surface-volume ratio for the particle whose nominal size is Dp. The nominal diameter of the particle is generally found from screen analysis and the diameter of sphere is calculated by equating the volume of particle equal to sphere. The maximum value of sphericity is 1, because a sphere has minimum surface area for a given volume among all shape.  

Thermodynamics: Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic property of great importance defined by the expression:
G = H - TS. Enthalpy (H) is the maximum energy that a system can have at a particular state and the energy (TS) is the energy that has to be rejected to surrounding according to the 2nd law of thermodynamics. Therefore G represents the maximum usable energy that we can extract from the system at constant temperature and pressure.

For an open system the differential form of Gibbs free energy having its variables pressure and temperature are easily measured and controllable. Most chemical reactions occur at constant temperature and pressure. The partial molar Gibbs free energy has a special name i.e. chemical potential.

The other properties can also be expressed in terms of Gibbs free energy. Therefore, it is also termed as generating function.

Thermodynamics: Maxwell Equations Significance and understanding

Enthalpy and Internal energy for an ideal gas is a function of temperature only, but for real gases these also depends on one other parameter i.e. volume or pressure. In order to find change in internal energy and enthalpy for a real gas we need to get the expression in terms of measuring parameters like pressure, temperature and volume. Entropy is one important parameter in determining the change in internal energy and enthalpy for real gases. So it is necessary to first find change in entropy with pressure, temperature and volume keeping one other parameter constant. Maxwell equations tell the change in entropy w.r.t. pressure and volume.


 

These equations look somewhat difficult but there is an easier way to understand these equations:

every relation hold the change in entropy with volume at constant T & P and change in entropy with pressure at constant T & V. 

if we see the dimensional consistency, the terms W=-PdV and Q_Rev = TdS have the units of energy. So, these appear in opposite positions in the equations on left and right sides to make the equations dimensionally consistent. so like dS/dV=dP/dT

Now we have to see the constraint, like temperature. Temperature is in denominator on the right, so if we want it on left, then the constraint on the right will be V, (i.e. denominator on the left). 

Now the sign convention, when the volume increases of the system, the entropy increases, so the change in entropy with volume is positive, and when the pressure increases, the entropy decreases so the change in entropy with pressure is negative, and there will be a negative sign with the equations of change in entropy with pressure.

Program to design distillation column by FUG (Short cut) Method

Program to design distillation column by FUG (Short cut) Method
there are two methods to analyze a distillation column. one is graphical ( McCabe–Thiele method & Ponchon-Savarit ) and other is analytical (FUG: Fenske-Underwood-Gilliland). In FUG method minimum trays are calculated by Fenske equation, minimum reflux by undrewood equation and theoretical stages by Gilliland equation.

Take composition of pentane, hexane, heptane, octane as an input from the user:
    xipent=input('enter the composition of pentane');
    xihex=input('enter the composition of hexane');
    xihept=input('enter the composition of heptane');
    xioct=input('enter the composition of octane');
    pt=input('enter the total pressure');

Program to calculate bubble point and dew point at the Feed composition
To calculate bubble point and dew point we require the values of saturation pressure and distributive coefficient K for each component at different temperatures. So we  have prepared a separate function called psat() for the claculation of pressure in which the value of assumed temperature is passed as an argument. This has also served to reduce the program length because it is required to calculate pressure in every iteration untill the condition of ∑Ki*xi=1.0 is satisfied. The definition of the function is:
            function[prpent,prhex,prhept,proct]=psat(t)
            penta=13.7667;pentb=2451.88;pentc=-41.136;
            hexa=13.8193;hexb=2696.04;hexc=-48.833;
            hepta=13.8622;heptb=2910.26;heptc=-56.718;
          octa=13.9346;octb=3123.13;octc=-63.515;
            prpent=exp(penta-((pentb/(t+pentc))));
            prhex=exp(hexa-((hexb/(t+hexc))));
            prhept=exp(hepta-((heptb/(t+heptc))));
            proct=exp(octa-((octb/(t+octc))));
         end

Now the main body of the programme for calculation of bubble point where the function psat() has been called is:
disp('now firstly bubble point and dew point claculations will be done')
    for t=323:0.1:423
            [p,q,r,s]=psat(t);
            kipent1=p/pt;
            kihex1=q/pt;
            kihept1=r/pt;
            kioct1=s/pt;
            sumkixi=(kipent1*xipent)+(kihex1*xihex)+(kihept1*xihept)+(kioct1*xioct);
            if(sumkixi>0.99&sumkixi<1)
                disp('the bubble point of the mixture is')
                disp(t)
                break
            end
    end
    disp('the value of equilibrium constant of light key at bubble point is:')
    disp(kihex1)
    disp('the value of equilibrium constant of heavy key at bubble point is:')
    disp(kihept1)
    for temp=343:0.1:573
        [a,b,c,d]=psat(temp);
            kipent=a/pt;
            kihex=b/pt;
            kihept=c/pt;
            kioct=d/pt;
            sumy=(xipent/kipent)+(xihex/kihex)+(xihept/kihept)+(xioct/kioct);
        if(sumy>0.99&sumy<1)
            disp('the dew point of the mixture is')
            disp(temp)
            break
        end
    end

program to calculate minimum number of trays by Fenske equation
alpha=kihex1/kihept1;
disp('the value of relative volatility is')
disp(alpha)
disp('the composition of light key that is of hexane in distillate is:')
mlkd=(0.98*xihex);
disp(mlkd)
disp('the composition of heavy key that is of heptane in distillate is:')
mhkd=(0.01*xihept);
disp(mhkd)
disp('the composition of light key that is of hexane in bottom is:')
mlkb=(xihex-mlkd);
disp(mlkb)
disp('the composition of heavy key that is of heptane in bottom is:')
mhkb=(xihept-mhkd);
disp(mhkb)
disp('now the minimum number of stages by Fenske equation is calculated')
disp('the fenske equation is:')
disp('Nmin=ln[(xdi/xbi)/(xdj/xbj)]/((ln alphaij)-1)')
disp('where, Nmin= minimum number of trays')
disp('alpha= relative volatility')
nmin=(log(((mlkd/mhkd)/(mlkb/mhkb)))/log(alpha))-1;
disp('the minimum number of trays required are')
disp(nmin)
disp('minimum number of stages including reboiler are')
nminn=nmin+1;

program to calculate minimum reflux ratio is:
disp('now the calculation of minimum reflux by undrewood method is done:')
disp('Rdm+1= summation[(alphai*xdi)/(alphai-phi)]')
disp('where phi= root of the equation whose value lie between the relative volativity of heavy key and light key')
disp('Rdm=minimum reflux ratio')
disp('alphai=relative volativity of respective components')
disp('xdi=compositions in distillate of respective components')
alpha1=kipent1/kihept1;
alpha2=kihex1/kihept1;
alpha3=kihept1/kihept1;
alpha4=kioct1/kihept1;
for phi=alpha3:0.1:alpha2
  sumf=((alpha1*xipent)/(alpha1-phi))+((alpha2*xihex)/(alpha2-    phi))+((alpha3*xihept)/(alpha3-phi))+((alpha4*xioct)/(alpha4-phi));
if(sumf>-0.9999&sumf<1)
 disp('the value of phi is')
       disp(phi)
       break;
   end;
end;
disp('we need 98% recovery of hexane and 1% heptane in distillate')
 disp('the moles of all the four components in distillate are calculated below by simple material balnce calculations:')
mpent=xipent*100;
mhex=mlkd*100;
    mhept=mhkd*100;
moct=0;
disp('the moles of pentane in distillate is:');
disp(mpent)
disp('the moles of hexane in distillate is:');
disp(mhex)
disp('the moles of heptane in distillate is:');
disp(mhept)
disp('the moles of octane in distillate is:');
disp(moct)
summoles=mpent+mhex+mhept+moct;
disp('the total moles in distillate are')
disp(summoles)
sumrd=(((alpha1*(mpent/summoles))/(alpha1-phi))+((alpha2*(mhex/summoles))/(alpha2-phi))+((alpha3*(mhept/summoles))/(alpha3-phi))+((alpha4*(mpent/summoles))/(alpha4-phi)))-1;
    disp('minimum reflux ratio is')
disp(sumrd)

5. program to calculate theoretical stages by Gilliland method is:

disp('now the calculations will be done on the basis of Gilliland corelations for claculating actual number of stages')
disp('actual reflux ration is taken as 1.5 times the minimum reflux ratio')
rd=1.5*sumrd;
x=(rd-sumrd)/(rd+1);
y=1-exp(((1+(54.4*x))/(11+(117.2*x)))*((x-1)/(x.^0.5)));
n=(y+nminn)/(1-y);
disp('required number of stages are')
disp(n)

Coded by: Ravisha Goswami and group
(B.Tech 2010-2014, Chemical Engg., BTKIT Dwarahat)

Chemical Reaction Engineering: Non Ideal Reactor

In general we study about ideal reactors like batch reactor, continuous stirred tank reactor (CSTR), plug flow reactor (PFR). Batch reactor is a unsteady state uniform reactor, PFR is a steady state non uniform reactor and CSTR is a steady state and uniform reactor. but in actual conditions the reactors deviate from their ideality. There are some reason like channeling, dead zone, bypass, back mixing etc. Due to these factors the behavior of an ideal reactor changes. The real flow pattern is found from the RTD (residence time distribution) curve. RTD shows the concentration of a tracer in output which was injected into the reactor. from the shape of RTD curve we can analyse the behavior of the reactor.

There are different models which can be used to find the non ideal behavior of the reactor like compartment model, dispersion model and Tanks in Series model. Dispersion model and Tanks in Series model shows the deviation from plug flow reactor. For an ideal plug flow behavior, the dispersion number (D/ul) will be 0 and the number of tanks in series will be infinite (∞). In PFR every cross section shows a CSTR so a PFR represent an infinite number of CSTRs connected in series.       

Programming based Projects in Chemical Engineering

Now a days computer programming is playing an important role in chemical engineering. before going for a pilot plant we study the system through simulation software like HYSYS. So learning computer programming is an important curriculum in engineering. there are a lots of projects that can be done with the help of programming in B. Tech and M. Tech. One is design of Distillation column by Shortcut method and Rigorous calculations. The further modification in the project can be done by considering the non-ideality of the solution i.e. calculating the activity coefficients.

There are many equations which can be used to find the activity coefficients, of which Margules and van Laar equations are used when the nature of the species is similar. Wilson equation, Non-random two-liquid (NRTL) equation, are based on the local composition concept instead of overall mixture composition, Universal quasi-chemical (UNIQUAC) equation and Universal functional activity coefficient (UNIFAC) method based on extension of quasi-chemical theory of liquid mixtures to solutions containing molecules of different sizes.

Thermodynamics: Residual Properties or Departure functions

Thermodynamic properties like enthalpy and entropy for any substance ideal or real, we can use Maxwell's equations, Thermodynamic Diagrams, property table like saturated steam and superheated steam  or activity coefficient. in addition to these, we can get the approximate values by using Residual Properties which are defined as the difference between the value of thermodynamics property at specified conditions and the thermodynamic property for ideal substance at same specified condition.

Chemical Reaction Engineering: Thiele modulus and its significance

Thiele modulus shows the effect of diffusion in the reaction kinetics. The Thiele modulus is given by mL = L(k/D)^0.5 The ratio of rate constant to diffusivity. The large vale of Thiele modulus represents small value of diffusivity i.e. diffusion resistance affects the overall rate of reaction. If mL<0.4, the diffusion resistance can be ignored. By calculating Thiele modulus, we can see the effect of diffusion resistance. If diffusion resistance is significant for a particular catalyst, we can decrease the resistance either by increasing the diffusivity i.e. increasing the temperature and decreasing the pressure, or by reducing the length of diffusion i.e. size the catalyst particles. Shorter the particles, lesser will be the length for diffusion and lesser will be the resistance.

Internal Energy and Enthalpy

A system have two kinds of stored energies, internal energy (U) and enthalpy (H). The internal energy is the energy required to establish the system and enthalpy is the energy required to establish the system and make a space for it (U + PV). A flowing stream has the energy equivalent to enthalpy, while a system in non flow condition has energy equivalent to internal energy.

Thermodynamics: Vapor Liquid Equilibrium

When we say the vapors are in equilibrium with the liquid, what property of the two phases will be equal? Whether it is temperature, pressure, concentration or something else that will be same? 
Equilibrium stands for no net driving force, so what is the driving force for vapor liquid system?
It is chemical potential or fugacity that is same in two phases.

Suppose we have a liquid mixture of ethyl alcohol (NBP 78.5°C) and water (NBP 100°C). At any temperature, there will be some amount of alcohol & water vapors in contact with the liquid phase. Ethyl alcohol is more volatile as compared to water, so ethyl alcohol has more concentration in the vapor phase and but how it will be calculated?

The amount of alcohol & water in vapor phase can be calculated by their vapor pressure at that temperature. The vapor pressure of alcohol is always greater than that of water. For example at 80°C the vapor pressure of alcohol is 1 atm while that of water is less, which will be 1 atm at 100°C. Therefore, at equilibrium: for ideal system i.e. ideal gas phase and ideal liquid phase (Raoult’s law):
P_Ty_A = Pv_Ax_A;  

Pv_{A is the vapor pressure of component A at specified temperature. yA is the mole fraction of component A in vapor phase and} xA _{is the mole fraction of component A} in liquid.

If partial pressure of component A (P_Ty_A) is less in vapor phase than corresponding to liquid phase (Pv_Ax_A), evaporation continues (increases y) till both are equal. and if partial pressure is greater than _{in vapor phase than corresponding to liquid phase,} condensation will start and continues (decreases y) till both are equal. 

So condensation can be made to happen by either increasing total pressure (P_T) or decreasing temperature which decreases the vapor pressure (PA)

Difference beween Equilibrium and Steady state

Steady state and Equilibrium:

Both steady state and equilibrium show a constant state of a system with time; the values of all the properties remain constant with time. Yet they are different; equilibrium represents a state, where all the forces are in balance and there is no net driving force, e.g. in thermal equilibrium temperature is same, while in steady state there is a constant driving force, e.g. in heat transfer at steady state there is a constant temperature difference.

In steady state the values of the property may change with position, e.g. plug flow reactor, but in equilibrium, there will be a single value for any property throughout the system like temperature, pressure, concentration. So, can we say uniform and steady state system will be a system in equilibrium? No, for example CSTR is a uniform steady state system, but is not at equilibrium because the reactants are converted into product continuously.
for example if we have a hot coffee placed in a room, it will cool down to room temperature eventually, i.e. equilibrium state no heat transfer. But if we put that coffee on a gas stove with heat such that its temperature is constant i.e. steady state heat transfer.

Dimensionless number and their importances

There are so many dimensionless numbers that we see in the chemical engineering. What is the importance of these dimensionless numbers and how they form? In dimensionless number we group the variable that affects a parameter. For example heat transfer coefficient h depends on viscosity, velocity, density, temperature, specific heat, thermal conductivity, length. How do these factors affect the heat transfer coefficient can be analysed through experiments but the number of experiments will be numerous. For each factor, we have to do a set of experiments and analyse its effect on heat transfer coefficient. We can group them in a dimensionless form which shows the ratio of two terms like forces, resistance etc. The equation can be written as a function of the dimensionless number and the exponent and constant can be taken from experimental results i.e. empirical correlations. Like the example of well known dimensionless number Reynolds number (dvρ/μ) gives the ratio of inertia forces and viscous forces. With the help of Re no we can find the type of flow whether it is laminar or turbulent. This no gives the effect of diameter, velocity, density and viscosity on type of flow. Every dimensionless number may not have its significance. This is a trial and error procedure to get meaningful dimensionless number.

Thermodynamics: Fugacity for solution

The fugacity for ideal solution either in liquid phase or gaseous phase can be calculated from the equations

where fi(circumflex) is the fugacity of species i in solution. For gaseous phase it is calculated form fugacity coefficient (𝜙) and its value is 1 for and ideal gas solution (Residual Property) while in the liquid phase (ideal solution) we use activity coefficient (𝛶) and  its value is 1 for an ideal liquid solution (Lewis Randall rule). when the two phases are in equilibrium their fugacity value of the species will be same in either phase. for low pressure systems, the gas phase can be assumed to be ideal and 𝜙 = 1. but we can consider the non ideal liquid solution that will lead to modified Raoult' law which includes the activity coefficient.

Heat Transfer: Insulation

Insulation is added to a system to decrease the rate of heat loss. In a system operating at steady state, if we increase the thickness of insulation, will it decrease the rate of heat loss?

For a steady state system, the heat in to the system should be equal to heat out of the system. So, by increasing the thickness of insulation will not decrease the heat loss. For example, if we are heating a copper disc with a 50 W heater, under steady state 50 W heat will be lost to the surrounding. If we add insulation on the sphere, the heat lost to the surrounding must be 50 W to make it steady. Then, heat loss has not been reduced. But by adding insulation we can increase the temperature of the system without losing more heat, i.e. if the temperature of the sphere was 40 °C with 50 W heat input earlier, by adding more insulation we can raise the temperature of sphere with same amount of heat input.