iv 4 discontinuous batch chemical reactors polym

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorA discontinuous or batch reactor has no fluid streams flowing through.The total feed is introduced before start, and no withdrawal is made until the reaction has reached the degree of completion desired.The mathematical model results from mass balances for all species

FILS Chemical ReactorsThe Discontinuous/Batch Reactor

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorThe Characteristic EquationRewriting the dynamic mass balance


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorUsing the Mean Value Theorem of Integral Calculus Single Reaction Chemical Process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorThe Characteristic Equation Reaction time Initial conditionsPerformanceOperating conditions


EMBED Equation.DSMT4

0

XA

EMBED Equation.2

_1136556541.unknown

_1141541287.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorMultiple reactions chemical processesRewriting the dynamic mass balanceReaction rate with respect to AjEquivalent reaction rate for i reaction


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorHolds for every term of the sumThe extent of reaction i, kmolThe vector of extents of all reactions, kmol


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorThe Characteristic Equation and the Volume of ReactionA) The volume of reaction is constant during the chemical process1) Single reaction chemical process 2) Multiple reactions chemical process The volumic extent of reaction i, kmol m-3The vector of volumic extents of all reactions, kmolm-3


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorThe Characteristic Equation and the Volume of ReactionB) The volume of reaction is variable during the chemical process1) Single reaction chemical process 2) Multiple reactions chemical process The mass extent of reaction i, kmol kg-1The vector of mass extents of all reactions, kmolkg-1


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorIrreversible chemical processes(the equilibrium constant has very large values, thus the reverse reaction is negligible)


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Single reaction chemical processIrreversible first order chemical processesA) The volume of reaction is constant during the chemical processB) The volume of reaction is variable during the chemical processImportant Conclusion!! The volume behavior does not affect the performance


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a first-order irreversible reaction The initial concentration does not affect the performance of the first order processes


0

t

Slope = k

0

EMBED Equation.2

_1136555125.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a first-order irreversible reaction


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible second order elementary chemical processesA) The volume of reaction is constant during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA > 1Constant volume case


Slope= EMBED Equation.DSMT4

0

Slope= EMBED Equation.DSMT4

0

t

Intercept= EMBED Equation.DSMT4

EMBED Equation.2

0

t

EMBED Equation.2

0

_1136793315.unknown

_1136793612.unknown

_1136793690.unknown

_1136793342.unknown

_844337312.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA >1Constant volume case


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA = 1Constant volume case


0

EMBED Equation.2

0

Slope=k

1/CA0

t

0

t

0

Slope = kCA0

EMBED Equation.2

_843518772.unknown

_844342799.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA = 1Constant volume case


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible second order elementary chemical processesB) The volume of reaction is variable during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA > 1Variable volume case


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible second order elementary chemical processesB) The volume of reaction is variable during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible second-order elementary reactions, MBA = 1Variable volume case


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible second order chemical processesA) The volume of reaction is constant during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible second order chemical processesB) The volume of reaction is variable during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible trimolecular type third-order reactions A) The volume of reaction is constant during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible third-order elementary reactions, MBA > 1 , MDA > 1Constant volume caseDrawbackIncreasing MBA and/or MDA results in large quantities of B & D remained unreacted


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible trimolecular type third-order reactions B) The volume of reaction is variable during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorCommon plot for a irreversible third-order elementary reactions, MBA > 1 , MDA > 1Variable volume caseDrawbackIncreasing CA0 results in faster reactions, but large reactants quantities remaine unreacted


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible third-order reactions of particular type A) The volume of reaction is constant during the chemical process


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible third-order reactions of particular type B) The volume of reaction is variable during the chemical processThis case is homework


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Empirical rate equations of nth order The reactions with order n >1 can never go to completion in finite time (but this is a characteristic of first order chemical processes).For orders n < 1, this rate form predicts that the reactant concentration will fall to zero and then become negative at some finite time


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Empirical rate equations of nth order


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Reactions of Shifting Order A) Shift from low to high as the reactant concentration drops at high CA (or k2CA1) - the reaction rate is of zero order with rate constant k1/k2.at low CA (or k2CA1) - the reaction is of first order with rate constant k1.


CA

t

rA

k2 / k1

CA

First order

Zero order

Zero order

First order

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Reactions of Shifting Order B) Shift from high to low as the reactant concentration drops(two competing reactions of different orders) at low CA - the reaction rate is of zero order with rate constant k1.at high CA- the reaction is of first order with rate constant k2.


CA

t

rA

CA

First order

Zero order

Zero order

First order

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Autocatalytic Reactions One of the products of reaction acts as a catalystThe total number of moles of A and R remains unchangedThere is a maximum, due to the antagonic effects


0

0

t

1

XA

Low rate

High rate

Low rate

Progress in time

Parabolic

Start with some R present

0

0

rA

1

CA = CR

CA/CA0

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Autocatalytic Reactions


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Discontinuous/Batch ReactorReversible chemical processes(The complete conversion is never achieved, due to the thermodynamic barriers)


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation First-order Reversible Reaction At equilibriumThe mass balance applying the differential form of the characteristic equation


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation First-order Reversible Reaction


EMBED Equation.2

t

EMBED Equation.2

_1141633689.unknown

_1141633833.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Second-order Reversible Reactions (V=ct) At equilibriumThe integral form of the characteristic equation


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Second-order Reversible Reactions (V=ct)


EMBED Equation.2

t

EMBED Equation.2

_1141641061.unknown

_1236323676.unknown

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Second-order Reversible Reactions (V=ct) At equilibriumThe integral form of the characteristic equation


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Second-order Reversible Reactions (V=ct) The solving procedure remains the same; care should be taken when computing the roots of the equilibrium equation.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Second-order Reversible Reactions (Vct) The integral form of the characteristic equation


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Multiple reactions chemical processes


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible Reactions in Parallel (V=ct)The integration of equations gives


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible Reactions in Parallel (V=ct)


CA0

CA

CS

CR

0

0

t

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible Reactions in Series (V=ct)The integration of equations gives


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The DC Reactor Solving the Characteristic Equation Irreversible Reactions in Series (V=ct)


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsPolymer molecular weight distribution (MWD) is one of the most important polymer properties that dictate the physical, mechanical, and rheological properties of industrial polymers.

These are commonly used:

Molecular weight averagesAverage/mean molecular numberAverage/mean molecular mass

Polydispersity - ratio of mean molecular mass and mean molecular number


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsThere are cases of two polymers of different chain length distribution having identical molecular weight averages.

Sometimes, a slight variation in high or low molecular weight fractions of polymer causes a significant difference in the polymers enduse properties.

In practice, it is desired to predict or control the entire chain length distribution instead of molecular weight averages.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsIn modern industrial polymerization processes, polymerization process conditions are designed and operated to produce the polymers of desired molecular weight properties with minimum variance from their target values.

The requirement is that the relations between the polymers molecular weight properties and reaction conditions be quantitatively established.

A detailed polymerization process model can be utilized for such purposes.

If the main goal is to predict and control polymer molecular weight distribution in a given polymerization process, it will be necessary to have available an appropriate computational method to predict the chain length distribution during the progress of reaction.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsWhen a polymerization kinetic model is available, molecular weight averages and MWD can be calculated by: numerical integration of the polymer population balance equations using a moment generating function z-transform continuous variable transformation the method of molecular weight moments Markov chain approaches integrating an instantaneous chain length distribution to a desired conversion fitting a pre-specified chain length distribution function with molecular weight averages Monte Carlo simulation techniques, for free radical polymerization discrete weighted Galerkin methods, with expansion of a chain length distribution into certain orthogonal polynomials.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsBatch near-isothermal bulk polymerization of 150oC The reaction temperature reaches 150oC after about 60 min, during which period, the monomer conversion is quite low.This operation as a near isothermal operation.As expected, the molecular weight averages reach their stationary values when the monomer conversion exceeds about 50%.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsWeight chain length distribution for near-isothermal polymerization at 150oC Notice that after 3 h of reaction, the chain length distribution is almost time invariant.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsThe reactor temperature set point is changed from 150oC to 180oC at t = 120 min With an increase in the reactor temperature, the polymer molecular weight decreases slightly and the polydispersity increases slightly.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsWeight chain length distribution for non-isothermal polymerization Although the polymer chain length distribution curves look quite similar, there is a distinct diffe-rence in the final chain length distributions bet-ween the two cases


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*Polymerization in Batch ReactorsDifferential and cumulative chain length distributions for near-isothermal and nonisothermal polymerizations The temperature variations yield a subtle but clear difference in the chain length distributions of the two polymers a difference in the enduse properties.If the polymer chain length distribution can be computed with a kinetic model, it is possible to discern the difference in the polymer molecular weight properties, otherwise difficult to do with molecular weight averages only.


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Semi-Continuous ReactorA semi-continuous or fed-batch reactor has a stream of fluid flowing into the reactor and no stream leaving it.One reactant is introduced before start, the other at given intervals, and no withdrawal is made until the reaction has reached the degree of completion desired.A) Fed Batch - Mathematical model Single/Multiple reactions


XA(t)

Perfect mixed medium

V(t)

CA(t)

*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Semi-Continuous ReactorA) Fed Batch - Mathematical model Single/Multiple reactionsk = the index of the current feedj = the index of species


*FILS Chemical ReactorsThe Discontinuous/Batch Reactor*The Semi-Continuous ReactorB) One reactant fed/removed continuously Mathematical model


iv 4 discontinuous batch chemical reactors polym

Documents

chemical processb

order chemical processesa

dc reactor

reverse reaction

mass extent of reaction

ajequivalent reaction

volumic extent of reaction

sumthe extent of reaction