Non Isothermal CSTR Chemical Reaction Engineering I Aug Dec 2011 Dept. Chem. Engg., IIT-Madras

Overview Notation CSTR design equation (mass balance) Heat Balance Accounts for heat removal/addition Methodology given

Notation Usual notation applies. –F A = molar flow rate of A, F T = total molar flow rate –V = volume of reactor, Q = volumetric flow rate –T = temperature –x = conversion. –k = rate constant, C A = concentration of A –Ref = Reference temperature where the heat of reaction is given –  H = heat of reaction (exothermic reactions will have negative values) –Subscript “in” indicates inlet. E.g. F A-in is molar flow rate of A at the inlet. We consider only liquid phase reactions because they are the most common ones in CSTR

CSTR design equation- Solve Mass Balance and Energy Balance simultaneously Mass Balance Rate constant is Energy balance equation Heat released by reaction at operating conditions = Heat used to raise the feed to operating conditions The rest are just details. Heat released by reaction at operating conditions If C p doesn’t depend on temperature, it is given by What is  C p ?

Heat of Reaction If the reaction is given by e.g. Sulfuric acid + sodium hydroxide react and the heat of reaction is given “per one mole sulfuric acid reacted” (Although NaOH is a solid, we will consider the case where it is dissolved in water. Water is an inert material. We will also neglect the heat of dissolution, although it is actually high) And  H Ref is given per mol ‘A’ reacted, then

Heat of Reaction In a more general case, the specific heat capacity is a function of temperature. The heat of reaction at any temperature T is given by Example. Reaction A  B+C

Heat of Reaction In general, the Heat of reaction at any temperature would be a cubic equation in Temperature

Energy released by reaction / unit time = Number of moles reacted per unit time * Heat released per mole Energy Balance Equation Energy needed (/ unit time )to bring feed to a temperature T If C p is a constant, then If C p varies with temperature, then Note: To calculate  H T, we use C p of reactants and products. Data on inert present in the feed is not necessary To calculate ‘energy needed to bring feed to a temperature of T’, we need data on all materials (including inert) in feed.

Energy Balance Under steady state conditions This can be re-written as If C p is a constant, then it can be written as a linear equation Note: When we substitute actual values we find that “x vs T” is roughly linear even when C p is a function of T

Non-Isothermal Case If heat is removed (e.g. cooling coils), then energy balance becomes Heat removed by cooling coils = U A (T-T c ) where T c is the temperature of cooling fluids in the coils. Note: For endothermic reactions, with heat added by coils, the equation will be similar. Heat released by reaction at operating conditions = {Heat used to raise the feed to operating conditions + Heat removed by cooling coils} Heat ABSORBED by reaction at operating conditions = {Heat released by LOWERING the feed to operating conditions + Heat SUPPLIED by heating coils} Still, “x vs T” is a linear equation (or a roughly linear equation) for energy balance

Pictorial View ‘X vs T’: Energy Balance equation gives roughly a straight line Mass balance equations (for positive order reactions) gives a ‘non liner’ (i.e. curvy) line, which starts at X = 0 and ends at X = 1. Note: –For energy balance equation, there is no ‘inherent’ check to ensure that X will be between 0 and 1 –If the reaction order is 0, there is no inherent check to ensure that X will be between 0 and 1.

Choices 1.If the conversion desired (X) is known, then find V and T for adiabatic conditions 2.If Volume is known, find X and T 3.If Volume is known, and heat is removed to maintain the temperature below certain value (e.g. exothermic reaction), find the conversion 4.If Volume is known, and critical temperature (i.e. maximum allowed temperature) is known, find the conversion and the heat load (U A Del-T). 1.Solution: –If X is known, then using heat balance equation, find T Constant Cp: the linear equation can be solved easily. Variable Cp. The cubic ratios has to be solved, using a numerical method (e.g. fsolve in Matlab). –Using T and X, find V

Solutions 2. To find X and T, given V (adiabatic) : Solution: –Substitute for V in the mass balance equation –Solve for T and X simultaneously using numerical methods –Alternative: Graphically solve for T and X simultaneously i.e. Plot X vs T using energy balance equation alone for various assumed values of T Plot X vs T using mass balance equation alone, for various assumed values of T Find where these two lines intersect. That would give the X and T 3. If Volume is known, and heat is removed to maintain the temperature below certain value (e.g. exothermic reaction), find the conversion Solution: Use the same method as above, but the heat balance equation has one more term to accommodate heat removal

Solution 4. If Volume is known, and critical temperature (i.e. maximum allowed temperature) is known, find the conversion and the heat load (U A Del-T). Solution: T = maximum allowed temperature Using mass balance equation (since V is known and T is known), find X Using heat balance equation (now X and T are known), find the heat load: i.e. UA Del-T