Types of Reactor models available in the simulators (Hysys Chemical Reactors).

Design a system for heat transfer in association with the reactor, to sustain an exothermic or endothermic reaction s at its desired temperature level.

Determine if a reactor network should be considered.

Process simulators offer four kinds of reactor models

1.) a stochiometric model that permits the specification on reactant conversions and extents of reaction for one or more specified reactions

2.) a model for multiple phases (vapor, liquid and solid) in chemical equilibrium

3.) a kinetic model for a continuous-stirred –tank reactor (CSTR) that assumes perfect mixing of homogeneous phases (liquid or vapor).

4.) a kinetic model for a plug-flow tubular reactor (PFTR or PFR), for homogeneous phases (liquid or vapor) and assuming no backmixing (dispersion).

Early stages of process synthesis, reactor effluents and heat duties are needed.

For reactor models in simulators, it is necessary to provide R chemical reactions involving C chemical species:

is the chemical formula for species j and is the stoichiometric coefficient for species j in reaction i (negative for reactants, positive for products).

Fractional conversion, Xk of key reactant, k,

The extent of reaction i,

For the conversion of CO and H2 to CH3OH, assuming an initial feed of 100 kmol/hr of CO and 600 kmol/hr H2 and 70% conversion of CO (key component), calculate the molar flowrates of the three components in the reactor effluent.

= 0+70(1) = 70 kmol/hr, where

Reactions must be specified as series or parallel.

For parallel reactions, specify the extent of reaction for each reaction, which result in

General Stoichiometric Equation:

For a specific feed composition and final temperature and pressure, the product composition at chemical equilibrium can be computed by:

1.) chemical equilibrium constants (K-values): from Gibbs energy of reaction combined with material balance equations.

2.) the minimization of the Gibbs energy of the reacting system.

Chemical equilibrium constant, K

For gas solution:

The van’t Hoff equation relates K to temperature by

Integration and conversion to log10 gives:

For the gas-phase reaction of CO and H2 to form methanol over a temperature of 273 K to 773 K,

Chemical equilibrium curves can be represented by this equation.

The methanol synthesis reaction is catalyzed by copper-zinc oxide, at a pressure of 100 bar and temperature of 3000C. A large excess of hydrogen is used to absorb the relatively high heat of reaction.

At these conditions,

K = 0.0002202 ,

(1)

(2)

(3)

(4)

The equilibrium mole fractions are:Where X is the equilibrium fractional conversion of CO

Combining four equations to give a nonlinear equation in X and solving gives X = 0.7087

The total Gibbs energy, G is a minimum at constant temperature and pressure.

Advantages:

(1) the avoidance to formulate stoichiometric equations (only the possible products need to be specified)

(2)the ease of formulation for multiple phases and simultaneous phase equilibrium

For a single phase, Gibbs energy at specified T and P,

Ni is the mole number of component i,

Partial molar Gibbs energy of component i in the equilibrium state

Fractional conversion and equilibrium reactor models are useful in the early stages of process design (material and energy balance studies).

Reactor systems must be configured and sized

Power-law expression are used for regression of laboratory kinetic data.

The reaction rate coefficient is a function of temperature ( Arrhenius equation):

Laboratory kinetic data for the air-oxidation of SO2 to SO3 are fitted by the Langmuir-Hinshelwood equation:

For reactions catalyzed by catalyst particles:

Simplest kinetic reactor model:

1.) Perfectly mixed

2.) composition and temperature are uniform throughout the reactor volume and equal to the composition and temperature of the reactor effluent.

3.) There is a residence-time distribution

Consider the existence of multiple solutions

Composition of the fluid flowing as a plug, gradually changes down the length of the reactor, with no compositions or temperature gradients in the radial direction.

Mass and heat transfer rates are negligible in the axial direction.

Simulators:

One dimensional, plug flow models neglect axial dispersion.

No radial gradients of temp, composition or pressure.

Mass diffusion and heat conduction do not occur in the axial direction.

Adiabatic operation, a mole balance for limiting reactant A

The energy balance for adiabatic operation

Adiabatic operation is always considered first because it provides the simplest and least-expensive reactor. When reactions are highly exothermic or endothermic, desire to exercise some control over the temperature.

Methods include:a) Heat transfer to or from the reacting fluid, across a wall, to or from

an external cooling or heating agentb) An inert or reactive heat carrier or diluent in reacting fluidc) A series of reactor beds with a heat-exchanger for cooling or

heating between each pair of bedsd) Cold shot cooling or hot shot heating, where the combined feed is

split into two or more parts, one of which enters at the reactor entrance while the remaining parts enter the reactor at other locations.

Measure of the degree of exothermicity or endothermicity of a reaction is the adiabatic temperature rise (ATR)

Manufacture of phthalic anhydride, produced by the oxidation oforthoxylene with air in the presence of vanadium pentoxide catalyst.The reaction is carried out at 375oC and 1.2 atm, is highlyexorthermic with ATR 1170oC.Reactor resembles a vertical shell-and-tube heat exchanger.Hundreds of long tubes of small diameter, inside the shell, are packedwith catalyst through which reacting gas passes downwards.A heat transfer medium consisting of a sodium nitrite-potassiumnitrate fused salt circulates outside the tubes through the shell toremove the heat of reaction.

Styrene is produced by the catalytic dehydrogenation ofethylbenzene at 1.2 atm and 575oC.

The reaction is endothermic, with ATR -460oC.

If operated adiabatically, temperature of reacting fluiddecrease, reaction rate would be unable to compromise,resulting in a very large reactor volume.

To maintain a reasonable temperature, large amount of steamis added , preheated to 625oC before entering the reactor.

The steam is inert and easily recovered from the reactoreffluent by condensation.

The presence of steam reduced the reaction rate,

but the reactor can be operated adiabatically.

Sulfur trioxide, which is used to make sulfuric acid, is produced by catalytic oxidation of sulfur dioxide in air with vanadium pentoxide catalyst at 1.2 atm and 450oC.

Reaction is highly exothermic with an ATR 710oC.

The reactor system consists of four adiabatic reactor beds of same diameter but different height, in series with a heat exchanger between each pair beds.

The temperature rises adiabatically in each reactor bed, the hot reactor effluent is cooled in the heat exchanger positioned before the next bed.

When the ATR is higher, such as in the manufacture of ammonia from synthesis gas, the cold-shot design is recommended.

Desire to reduce the vessel volume to a minimum.

If z is the direction down to length of the reactor, the trajectory of the mass and energy balance equations for a single reaction in X (z) and T (z) space is adjusted to match the trajectory corresponding to the maximum reaction rate (X*, T*) (curved line) as closely as possible.

An exothermic reversible reaction in a PFR.

The rate of the reverse reaction increases more rapidly with increasing temperature than the rate of the forward reaction.

Reverse reaction is slow and the forward reaction fast at low temperatures.

For maximum rate of reaction, the temperature should be high at low conversions.

For maximum rate of reaction, the temperature should be low at high conversions.

Reaction rate for a sequence of fractional conversions, X, starting with X1= 0 is plotted against temperature, T.

Maximum rate corresponding to solid line passing through point B and C, maximum reaction rate decreasing with increasing fractional conversion.

The feed enters at temperature, TA with reaction rate at point A.

If the entering temperature cannot be increased, best to operate isothermally at TA

until the conversion at point C reached, follow optimal profile CB to the desired conversion.

If exit conversion is X4, the desired reactor temperature trajectory is solid line ACB with reactor exit temperature TB.

If the PFR operates at isothermal temperature TA, it follows trajectory ACD. Reaction rates are not at their maximum except at point C. Thus it requires a larger reactor volume.

For CSTR operation, the optimal temperature of operation for achieving X4 would be TB, to achieve maximum reaction rate.

Reactor feed temperature affect the stability of an autothermal reactor.

Autothermal reactor: reactor whose feed is preheated by its effluent.

For a reversible exothermic reaction, heat generation rate varies nonlinearly with the reaction temperature.

At low temp, rate of heat generation is limited by the low rate of the forward reaction.

At high temp, rate of reaction is limited by equilibrium.

The reaction rate exhibits a maximum value at intermediate temp.

The rate of heat removal is linear with the reaction temperature, as heat transfer by convection is dominant.

The intersection of the heat removal line (b) and heat generation line (a) leads to:

(O) the non-reacting state, (I) the ignition point and (S) the desired operating point.

Both non-reacting state and desired operating point, small positive pertubation in the reactor temp. leads to heat removal rate > heat generation rate, decreases reactor temperature. Oppositely, small negative pertubation of reactor temp. leads to heat generation > heat removal rate and thus increases the reactor temperature.

Temperature difference between Points I and S as the stability margin.

A design with increased rate of heat transfer (b’) have a lower stability margin.

Catalyst deactivation lead to loss of stability, as decreased catalyst activity leads to lower heat generation rates (a’).

Attainable region: the achievable compositions that may be obtained from a network of chemical reactors.

Consider the reaction below:

Reactions 1, 2 and 3 are first-order in A, B and B;

Reation 4 is second-order in A.

Attainable Region (AR) boundary compose of an arc representing a CSTR with bypass (curve C), A CSTR (point O) and A CSTR followed by a PFR (curve D).

The appropriate reactor configuration depends on the desired effluent concentration of A.

When 1 >CA>0.38 kmol/m3, maximum concentration B achieved by CSTR with bypass.

When CA<0.38 kmol/m3, maximum concentration B (CB = 1.25 x 10-4

kmol/m3) achieved by CSTR followed by a PFR configurations. Attainable Region: Helpful assistance in design of Optimal Reactor

Networks.

Feed of A: 1kmol/m3

For CSTRs and PFRs with or without mixing and bypass.

Step 1: Begin by constructing a trajectory for a PFR from the feed point, continuing to the complete conversion of A or chemical equilibrium.

The trajectory in CA-CB space is plotted in Figure 6.8a as curve in ABC. Component A is completely converted.

Step 2: When the PFR trajectory bounds a convex region, this constitutes a candidate attainable region (AR). The current limits are the boundary of the AR and the procedure terminates. A convex region is one in which all straight lines drawn from one point on the boundary to any other point on the boundary lie wholly within the region or on the boundary. If not, the region is nonconvex. When PFR trajectory is not convex, the next step is to determine if the AR can be extended beyond the trajectory curve.

In this example, PFR trajectory is not convex from A to B, so proceed to the next step to determine if the attainable region can be extended beyond the curve ABC.

Step 3:The PFR trajectory is expanded by linear arcs, representing mixing between the PFR effluent and the feed stream, extending the candidate attainable region. Note that a linear arc connecting two points on a composition trajectory is expressed by the equation:

c1 and c2 are vectors for two streams in the composition space, c* is the composition of the mixed stream. α is the fraction of the stream with composition c1.

The linear arcs are then tested to ensure that no rate vectors positioned on them point out of the AR. If there are such vectors, proceed to the next step.

A linear arc, ADB is added, extending the attainable region to ADBC. Since rate vectors computed along this arc are found to point out of the extended AR, proceed to next step.

Step 4: Since there are vectors pointing out of the convex hull, formed by the union between the PFR trajectory and linear mixing arcs, it is possible that a CSTR trajectory enlarges the attainable region. After placing the CSTR trajectory that extends the AR the most, additional linear arcs that represent the mixing of streams are placed to ensure that the AR remains convex.

•The CSTR trajectory is computed by solving the CSTR form of kinetic equation.•The CSTR trajectory that extends the AR most is that computed from the feed point, CA0, the largest concentration of A.•This is indicated as curve AEF which passes through point B.

•Since the union of the previous AR and the CSTR trajectory is not convex, a linear arc, AGO is augmented. This arc represents a CSTR with a bypass stream.

Step 5: A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory. If this PFR trajectory is convex, it extends the previous AR to form an expanded candidate AR.

The PFR trajectory, OHI, leads to a convex attainable region.

The boundaries of the region are (a) linear arc, AGO (represents CSTR with bypass stream), (b) the point O (represents a CSTR) and (c) the arc OHI (represents CSTR followed by a PFR in series.)

Maximum composition of B is obtained at point H, using a CSTR followed by a PFR.

A network of isothermal reactors is proposed to maximize the yield of maleic anhydride.

In the range 366 < T < 850 K, the rate coefficient k1 of the MA is larger than those of the competing reactions.

Composition space trajectory for PFR depends on the solution of the molar balances:

The temperature-dependent rate constants are computed using equation 6.49.

; vo = 0.0025 m3/s

; W = kg of catalyst

Since these trajectories are convex, the rate vectors computed along their boundaries are tangent to them, it is concluded that each trajectory bound the attainable region for its corresponding temperature.

Thus, a single PFR (or PBR) could provide the maximum amount of maleic anhydride.

At 800K, maximum concentration of maleic anhydride is 3.8 mol/m3. (required 4.5 kg of catalyst)

At 600K, it is 5.3 mol/m3. (required 1,400 kg of catalyst)

At 770K (trajectory can be constructed from equation (6.49) and the solution of molar balances), it is 4.0 mol/m3. (required 8 kg of catalyst)

Hence, less catalyst is required for higher operating temperatures of PFR.

Figure (a): Composition profile for maleic anhydride manufacture in an

isothermal PBR at 770 K, for all species as a function of bed length (proportional

to the weight of catalyst). Figure (b): Selectivity and yield of maleic anhydride.

4 mol/m310%

61%

The selectivity is poor

due to large amount of

CO2 and H2O produced.

Construct the attainable region (AR) for the steam reformingof methane at 1,050 K and use it to identify the networks thatprovide for the maximum compositions and selectivity of CO.

The following reactions, involving five species and threeelements, dominate in the steam reforming of methane:

Step 1:

Begin by constructing a trajectory for a PFRfrom the feed point continuing to thecomplete conversion of methane/ chemicalequilibrium.

PFR trajectory is computed by solving thekinetic equations for the reactions.

This leads to trajectory (1) (tracks thecompositions from the feed point (A) tochemical equilibrium point (B).

Step 2:

When then PFR trajectory bounds a convexregion, this constitutes a candidate attainableregion.

When the rate vectors at concentrationsoutside of the candidate AR do not point backinto it, the current limits are the boundary ofthe AR and the procedure terminates.

The PFR trajectory is not convex, so proceedto the next step.

Step 3:

The PFR trajectory is expanded by linear arcs.

Two linear arcs are introduced to form a convex hull , tangent to the PFR trajectory, connecting to the point B (line 2) (chemical equilibrium), and from the feed point to a point tangent to the PFR trajectory (line 3).

Rate trajectories point out of the convex hull, so proceed to the next step.

Step 4:

Since there are vectors pointing out of the convex hull, a CSTR trajectory may enlarge the attainable region.

Trajectory (4) augmented by two linear arcs, connecting the feed point to a point tangent to the CSTR trajectory (line 5) at point C.

Additional line (6) connecting the CSTR to the PFR trajectories at two tangent points.

Step 5:

A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory.

The PFR trajectory (line 7) leads to convex attainable region.

The boundaries of the region are: (a) the linear arc (line 5) from A to C (CSTR with bypass stream)

The point C (a CSTR)

Line 7 from C to B (CSTR followed by PFR in series).

The maximum composition of CO is obtained at point D using a CSTR and PFR in series.