reactive absorption & non-equilibrium absorption

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses Reactive Absorption & Non-equilibrium Absorption Senior Design CHE 396 By Chemical Concepts Clint McElroy Jeromy Miceli Mike Viirre Chris Woltz

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Page 1: Reactive Absorption & Non-equilibrium Absorption

CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Reactive Absorption & Non-equilibrium Absorption

Senior Design CHE 396

By Chemical ConceptsClint McElroyJeromy Miceli

Mike ViirreChris Woltz

Prof. Andreas Linninger

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Table of Content

Introduction____________________________________________________________1

Section IOverview of Physical Absorption_____________________________________2Isothermal Example Problem_________________________________________7Heat Effects______________________________________________________9Solvent Losses___________________________________________________11Estimation of Solvent Losses________________________________________12Example Problem: Absorption of Acetone with Acetic Acid_______________16Design Decisions_________________________________________________18

Section IIIntroduction to Reactive Absorption___________________________________19Process Operation_________________________________________________21The Rate Equation for Mass Transfer and Reaction_______________________22References_______________________________________________________25

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

IntroductionAbsorption is the unit operation where one or more components of a gas stream are removed by being taken up (absorbed) in a nonvolatile liquid (solvent). Physical absorption and reactive absorption are the both readily used in industry today. Physical absorption, the most common of the two, can be modeled in a number of ways. The 1st being the isothermal case, the 2nd being the non-isothermal case, and finally the 3rd being the case of an non-isothermal absorber including solvent losses. Each of these cases, including a detailed sample calculation of the isothermal case, will be looked at in greater detail.

Reactive absorption involves a liquid phase reaction that effects the liquid mass transfer coefficient of the solvent. There are several advantages and disadvantages when considering a reactive absorption unit. These advantages and disadvantages along with a brief introduction on mass transfer will be included following physical absorption.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Overview of Physical AbsorptionAbsorption is the unit operation where one or more components of a gas stream are removed by being taken up (absorbed) in a liquid solvent. Absorption can be either physical or chemical. In physical absorption the gas is removed because it has a greater solubility in the solvent than in other gases. In other words, the gas solute has a greater affinity to be in the liquid phase. In chemical absorption the solute reacts with the solvent and remains in solution. The reaction can either be reversible or irreversible. Reversible reactions are often favored because the solvent can be regenerated, unlike irreversible reactions, where the resulting liquid must be disposed of. A simple absorption system is shown below in Figure 1.

Figure 1: Absorption Process

A brief overview of physical absorption will now be given to introduce the basic principles and assumptions used when considering such a process.

In three component systems it is often assumed that

1. Carrier gas is insoluble.2. Solvent is nonvolatile.3. The system is isothermal and isobaric.

The Gibbs phase rule yields three degrees of freedom for the following three component vapor/liquid system. Setting the temperature and pressure as constant, one degree of freedom remains. Equilibrium data is usually represented by plotting solute compositions in the vapor versus solute compositions in the liquid phase or by using Henry’s law.

pB = HBxB (1)

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Absorber

j

StripperAbsorber

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Henry’s law relates the partial pressure of B in the vapor (pB) to the mole fraction of B in the liquid (xB) by using Henry’s constant (HB) for the particular system. Since partial pressure is defined as

yB = pB / ptot (2)

Henry’s law becomes

yB = (HB / ptot)xB (3)

Since H is roughly independent of the total pressure, as pressure is increased, the mole fraction in the vapor phase decreases. In other words, at greater pressures the gas solute is absorbed more into the liquid phase. Henry’s law constants depend on temperature and are only valid for low concentrations of B or very dilute solutes.

The derivation of the operating lines for absorption are accomplished by material balances around the top of the column. Again, these calculations are developed assuming isothermal/isobaric operation, negligible heat of absorption, insoluble carrier gas, and a nonvolatile solvent. Figure 2 is a representation of an absorber where L and G are the solvent and carrier gas flow rates, respectively.

Figure 2: Absorber

For very dilute solutions (<1% solute), overall flow rates can be used, and mass or mole fractions can be used for operating equations and equilibria. However, overall flow rates

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yj+1

j

V,y1 L,x0

V,yN+

1

L,xN

N

j

1

yj+

1

xj

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

of gas and liquid in concentrated mixtures cannot be considered because a significant amount of solute may be absorbed, which would change gas and liquid flow rates and give a curved equilibrium line. For now, interest lies in simple ideal absorber design.

Mole ratios are used as a basis for calculating mass balances around portions of the absorber. The mole ratios X and Y are defined in the following way.

Y= and X= (4a)

These mole ratios are also related to mole fractions by

Y = and X = (4b)

The mass balance around the top of the column and stage j gives

Yj+1G + X0L = XjL + Y1G (5)

or

Moles B in/hr = moles B out/hr

Solving for Yj+1 we obtain the operating line for absorption

(6)

This is a straight line with slope L/G and intercept . Plotting Y vs X

equilibrium data and the operating line gives a McCabe-Thiele type of graph for an absorber. The following steps are taken when developing a graphical solution for an absorption problem:

1. Plot Y versus X equilibrium data (convert from fractions to ratios).2. Values of X0, YN+1, Y1 and L/G are known. Point (X0,Y1) is on operating line, since it

represents passing streams.3. Slope is L/G. Plot operating line.4. Starting at stage 1, step off stages: equilibrium, operating, equilibrium, ect.

In designing an absorber, or in solving absorption problems, usually YN+1, X0, and G are known, and L is to be found for a given Y1. In other words, the solvent flow rate necessary to achieve a desired absorption is to be calculated. Operating lines for four different absorbent flow rates are shown in Figure (6.9 p284 Seader), where each operating line passes through the terminal point, (Y1, X0), at the top of the column, and corresponds to a different liquid solvent rate and corresponding slope, L/G.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

To achieve the desired value of Y1, the solvent flow rate L must lie in the range of (operating line 1) to Lmin (operating line 4). The value of the solute concentration in the outlet liquid, XN depends on L by a material balance on the solute for the entire absorber. From equation (5), for j=N,

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

(7)or

(8)

The value of Lmin corresponds to a value of XN (leaving the bottom of the tower) in equilibrium with YN+1, the solute concentration in the feed gas. It takes an infinite number of stages for this equilibrium to be achieved. An expression for Lmin can be derived as follows.

For the solute at stage N, the equilibrium relationship can be expressed as

(9)

Solving equation (9) for XN and substituting the result into equation (8) gives

(10)

For dilute-solute conditions, where Yy and Xx, equation (10) becomes

(11)

Furthermore, if the entering liquid contains no solute, that is, X00, equation (11) becomes

=GKN(fraction of solute absorbed) (12)

This equation is reasonable because it would be expected that Lmin would increase with increasing G, K-value, and fraction of solute absorbed.A graphical derivation of Lmin is also possible. As stated before, the value of Lmin

corresponds to a value of XN in equilibrium with YN+1. Since this is an equilibrium stage (at stage YN+1), as well as a point on the operating line, the operating line extends from the point (Y1, X0) to the equilibrium curve at YN+1. The slope of this line, and hence Lmin, can be determined from these two points.

The selection of the actual operating solvent flow rate is based on some multiple of Lmin, typically from 1.1 to 2. A value of 1.5 is typically used. In Figure (6.9 p284 Seader), operating lines 2 and 3 correspond to 2.0 and 1.5 times Lmin, respectively. As the operating line moves from 1 to 4, the number of required equilibrium stages, N, increases

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

from zero to infinity. Thus, a trade-off exists between L and N, and an optimal value of L exists.

To illustrate this method a sample problem will now be discussed.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Case Study:

Isothermal Example Problem

Absorption is to be used to recover acetone from a gas mixture. Readily available acetic acid will be used as the solvent. The inlet gas contains 5 mole % acetone and 95 mole % methane. Using a basis of calculation of 100 mol/s of gas feed and assuming isothermal conditions at 1 atm, determine the number of equilibrium stages required to recover 90% of the acetone. Equilibrium data for the acetone acetic acid system is readily available.

The equation for the operating line is

10% of acetone remains in exit gas steam

(5 moles in)(.1 recovered) = .5 moles in exit gas stream

The mole ratios at the top of the operating line are

X0=0 and Y1= = =.00526

The known mole ratio at the bottom of the operating line is

YN+1= =.0526

The equilibrium curve is generated from the vapor liquid equilibrium data given, by first converting the mole fractions to mole ratios (y,x ), then plotting Y vs X. The molar flow rate of the carrier gas G is given in the problem as

G = 95

(L/G)min is found as the slope of the operating line from point (Y1,Xo) to the intersection with the equilibrium curve at YN+1.

From graph, (L/G)min = 2.973 so, Lmin = (2.973)(95) = 282.4

Lactual = 1.5 Lmin = 423.6 and (L/G)actual = 4.460

A solution for Lmin can also be found using the analytical method outined above. Equation (10) gives the relationship between Lmin and KN. KN values can be found in the literature, or from equation (9). The value for YN+1 is known, and the XN stream is in equilibrium with the YN+1 stream.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

KN=

This value is very close to the one found using the graphical method.

Plot the operating line from (Y1,Xo) with a slope of (L/G)min and step off stages to determine the number of equilibrium stages needed. From the figure below it is seen that about five equilibrium stages will be necessary to recover 90% of the acetone.

This is the theoretical number of stages required. The actual number of stages is found from the relation Nactual = Ntheoretical / Eo where Eo is the stage efficiency. Therefore the actual number of stages for a stage efficiency of 25% is

Nactual = 5/.25 = 20

So 20 equilibrium stages are needed to absorb 90% of the acetone from the inlet gas stream.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Heat EffectsOne of the most important considerations when designing a gas-absorption column is to determine whether or not to consider temperature effects. These temperature effects can directly influence the solubility of the solute gas and are due to heat effects. Heat effects to consider when designing a gas-absorber are:

1) The heat of solution of the solute that entails the heat of condensation, heats of mixing, and heats of reaction.

2) The heat of vaporization or condensation of the solvent.3) The exchange of sensible heat between the gas and liquid phases.4) The loss of sensible heat from the fluids to internal or external cooling coils or to the

atmosphere via the tower walls.

There are various conditions that give rise to heat effects. The 1st being a considerable heat of solution and the 2nd being a large amount of solute absorbed in the liquid phase. The 2nd consideration can be achieved by high pressures in the absorber, low liquid flow rate (L/G is small), and when the solute has a high solubility. When the solute is absorbed rapidly, the equilibrium line tends to be curved upward towards the solute rich end of the absorber. If the solvent is volatile and the rich gas is not saturated with respect to the solvent, the solvent may evaporate near the bottom of the absorber and condense near the top causing the operating line and the equilibrium lines to approach each other somewhere in the column. This is known as a pinch point in the column. The pinch point increases the height and the number of trays needed to absorb a certain amount of solute in the solvent.

Operating variables such as pressure, temperature, L/G ratios also effect the performance of a gas-liquid absorber. These will be discussed in more detail below.

Raising the operating pressure of the absorber tends to increase the separation efficiency considerably. For example: the absorption of methanol from water-saturated air showed that when the pressure was increased by a factor of two, the solvent was able to absorb two times the concentration of methanol that could be tolerated in the feed gas while still achieving the end concentration in the gas.

The temperature of the fresh solvent has little to no effect on the degree of absorption. However, the temperature and humidity of the rich gas do effect the absorption process. Cooling and consequent dehumidification of the feed gas to an absorption tower can be very beneficial. High humidity or relative saturation with the solvent limits the capacity of the gas phase to take up latent heat and does not favor absorption. If heat effects are present, a dehumidification system may be beneficial and should be further investigated.

High liquid-to-gas ratios (L/G ratios) tend to result in less strongly developed temperature profiles because of the high heat capacity of the liquid phase. As the L/G ratio increases, the operating lines move farther away from the equilibrium line and more solute is absorbed in each stage of the absorber. However, more heat is liberated in each stage and

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

the temperature of each stage rises, shifting the equilibrium line upward. On the other hand, as L/G decreases, the temperature maximum moves to the top of the tower and inhibits the solvents ability to absorb the solute.

As discussed above, an absorber may form a pinch point when the solvent is volatile and the solute is saturated with respect to the solvent. This in turn effects the number of trays in the tower. Some solutions to reducing the number of plates are:

1) increasing the solvent flow rate2) strategically placed coolers in the tower3) dehumidifying the inlet gas4) raising the operating pressure

The number of stages in an absorber is very important in terms of costing the absorber and running the absorber. Decreasing the number of stages in turn decreases the cost of the absorber. However, the above suggestions cost may outweigh the expense of the trays.

Equipment considerations are also important when designing an absorber unit. If the solute concentration in the feed gas is large and the heat of solution of the solute is large, cooling coils should be considered. In most cases, heat liberation is largest towards the bottom of the tower where more absorption takes place. In this situation, cooling coils may only be needed at the bottom of the tower. Coggan & Bourne found that a 12-plate tower with two strategically placed interstage coolers tripled the amount of ammonia feed concentration for given off-gas specifications. More separation was possible in this unit than with a simple column of 100 stages with no coolers.

There are a variety of ways in which a designer would go about approaching heat effects. Depending on the job in consideration, a designer may:

1) add internal or external heat-transfer surface to remove heat from the absorber2) treat the process as isothermal, where the temperature of the liquid is the same

everywhere in the absorber and the feed gas is sufficiently dilute3) employ the classical adiabatic model, which assumes the heat of solution only shows

up as sensible heat in the liquid phase and the solvent vaporization is negligible4) use semi-theoretical shortcut methods derived from rigorous calculations5) employ rigorous design procedures requiring the use of a computer

For preliminary screening, the simpler cases may be sufficient (such as the above example), but for a final absorber design, one should consider the rigorous approach. Next we will discuss the more rigorous design procedure in the form of the matrix method. This method will take into account all of the above heat effects including solvent losses.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Solvent lossesIn the example we made many assumptions. Many are valid, such as the column operating at constant pressure. However, there are many assumptions that are not completely accurate and could harm the validity of our work. One of these assumptions is that the solvent will not interact with the gas stream and be taken away by this stream. If the solvent is water this is not really important, but if the solvent is anything other than water, we want to account for possible solvent losses. The reason for this could be economic (recovery of a valuable product or reactant) or environmental (removal of a harmful impurity).

A good approximation to these losses can be found in Douglas (Douglas, 79). At lower pressures we can assume that the fugacities of all species can be neglected. This means that we can simplify our equilibrium relations to simply

PtyS = SPSxS

With a good recovery of solute we can assume that the only liquid in the top of the column is that of the solvent

xS 1

If the solvent chosen has many of the same properties as the solute then the activity of the solvent will be almost unity

S = 1

Going back to the first equation we obtain

yS = PS/PT

Hence, a quick estimate of solvent losses can be had by

While this provides a fairly simple model at which to obtain the value of solvent losses it is not a satisfactory solution for real world conditions. What if we don’t recover at or above 99%? What if we don’t operate the column isothermally? If we are truly interested in what is happening inside the column, we need a more rigorous method to explain the absorber. This method, known as the matrix method (Wankat), utilizes a multivariate Newtonian convergence to attain the flows and temperatures of every stage in the column. The basis of this method is described below:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Estimation of Solvent LossesFor more concentrated solutions, absorbers and strippers are usually not isothermal, total flow rates are not constant, and solutes may not be independent. For this reason, a much better approximation of the actual operation of the absorber is a stage by stage calculation of the absorber using a matrix method as described by Wankat (Wankat, 497). We first start with mass balances from the bottom of the absorber and number going upward according to the following diagram:

Calculating Solvent Losses Assuming Non-Isothermal Conditions and Non-Constant Flow Rates

The General method of solving the absorber stage by stage is to first set up the mass balances. The mass balance for stage 1 is:

(15-45)where

(15-46)

and the component flow rates are and . These equations are repeated for each component.For stage N the mass balance is

(15-47)where

, (15-48)

To solve the mass balances, a different matrix for each component must be made and solved independently. The general solution for each of the matrices is:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

(8-23)

For a general stage j within the absorber, the mass balance for any component is:

()

The unknown vapor compositions, yj and yj-1 can be replaced using the equilibrium expressions:

and

(15-55a)

(15-55b)

(15-55c)

where we have identified the terms A, B and C for the tridiagonal matrix. The total stream heat capacities can be determined from individual component heat capacities. For ideal mixtures this is

(15-56)

For the next trial we hope to have (Ej)k+1 = 0. If we define(15-57)

then the equations for the Tj can be written as

(15-58)

This matrix can be inverted using a computer algorithm. The result will be all of the Tj values. The check for convergence is by defining a T. This T can typically be defined as approximately 10-2 to 10-3. The check is:

(15-59)

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

If for all stages the convergence of Tj is achieved then the problem is solved. If (15-59) is not satisfied, determine new temperatures using (15-54).

(15-54)

This method can best be visualized in the form of a flow diagram as below (Wankat):

The major drawback to this method is the fact that the n n coefficient matrix depends upon the number of stages. Of course, the number of stages is usually the thing you are looking for in order to obtain a desired composition. Therefore, you must guess the

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

number of stages and calculate the flows and compositions based on this number. If the number you chose was not sufficient you must chose a higher one and repeat the process.

This tedious method obviously lends itself better to computer calculations than hand calculations. Below is one iteration of the procedure using acetic acid as the solvent, methane as a carrier gas and acetone as the solvent.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Case Study:

Example Problem: Absorption of Acetone with Acetic Acid

An absorber with 3 equilibrium stages is operating at 1 atm of pressure. The feed is 100 mol/hr of a 95 mol% methane, 5 mol% acetone mixture which enters at 56C. The solvent is pure acetic acid at 100 mol/hr and 30C. Find the outlet compositions assuming an insulated column.

Solution: As a first guess lets assume the entire column is at the highest possible temperature of 56C. We will also make some initial guesses about the liquid and vapor flow rates:

L4=100 V3=95 (mole/hr)L3=101 V2=97L2=102 V1=98L1=103 V0=100

Let's first find the K values for the individual components:

KAcetone(56) = 0.1106 , KAcid(56)= 0.9967 , KMethane(56)=200

We can now construct the mass matrices for the individual components:

The inverse of the M matrix multiplied by the D matrix yields the solution matrix to l . Where, as mentioned before . Once the l matrix is determined we can solve for the new L values and check to see how closely they agree with the old L values. If they are not within some value that can be chosen to be approximately 10-3 or so. Let's proceed:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

compared to our initial guesses of .

For these values , where , is higher than the allowable limits so we

must use our new approximation of L at every stage to get new component balance matrices for the components. This was done three more times and the following flow rates were obtained:

Now that the mass balance has been solved we must now solve the energy equations to obtain the new temperature at each stage. This involves a new single tridiagonal matrix whose coefficients depend upon the specific heats of liquid and gas at each stage. These values are found from equations 15-56 and the cp functions are given in literature.

With these values the energy matrix can be formulated:

The following values for delta T were obtained:

These T values are not within the T value so we must take these new estimates of the temperature and calculate new K values for all of the components on all of the stages. Then we must perform new mass balances on each component as shown above. Once the new mass balance is obtained we get a new temperature and see if this temperature is within T of the old temperature. Once this is done the column has been solved. This procedure needed five more iterations to obtain the following results:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Amount of Acetone recovered in Solvent: 3.7 mol/h (74%)Amount of Acetic Acid lost in gas stream: 7.9 mol/h (7.9%)

The following temperature profile was obtained:

Stage TemperatureV3 30V2 40.2V1 48.3V0 56

Design Decisions

This clearly shows that temperature changes within the column are certainly not negligible. These figures also give conclusive proof that solvent losses are an extremely important aspect when designing a column. In our case we were operating in a fairly narrow temperature range so the most important factor for this column is the pressure of the structure.

When two atmospheres of pressure were used in this same 3-stage column it was possible to recover 84% of the acetone and lose only 3.4% of the acid. One solution would be to install a compressor to achieve these higher purity levels, however the pressure is but one of the design variables. While it would be great to operate at 10 atm and require only on theoretical stage, this is not practical. The best combination of variables, unfortunately, must be found by trial and error. Hold the pressure constant and perturb the number of

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stages or the flow rate. Do you get the desired recovery? What is the highest recovery for the lowest price?

This can be a time consuming process, but overall, the probable design result would be to keep the costly solvent flow rate lower by increasing the number of stages and hope that this will be sufficient without adding a compressor. The above example was carried out with three stages simply to show how the computation could be carried out by hand. However, a much better separation would be achieved with 10 or 15 stages.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Introduction to Reactive AbsorptionMass transfer in absorbers is explained using the two-film theory. The boundary between the gas phase and the liquid phase is presumed to consist of a gas film adjacent to a liquid film. Flow in both of these films is assumed to be laminar or stagnant. The main-body gas phase and liquid phase are assumed to be completely mixed in turbulent flow so that no concentration gradient exists in the main body of either phase. The solute concentration in the gas film at the interface is assumed to be in equilibrium with the solute concentration in the liquid film at the interface. There is a solute concentration gradient across both the gas film and the liquid film.

The rate of mass transfer from the main-body gas phase through the gas film is given by:

N kG ( p – p’ )

Where kG is the gas phase mass transfer coefficient and p and p’ are the pressures in the bulk gas and gas film respectively.

Similarly, the solute transferred per unit time through the liquid film to the main-body liquid phase is given by:

N kL ( x’ – x )

Where (x’ – x ) represents the concentration driving force for mass transfer from the liquid film to the bulk liquid phase, and kL is the liquid phase mass transfer coefficient.

Mass transfer theory considers that the gas-film and liquid-film resistances are in series. Overall mass transfer coefficients for both phases are defined as :

m= slope of equilibrium curve

The overall transfer coefficient depends partly on the nature of the gas film and partly on the nature of the liquid film.

In reactive absorption, a fluid-fluid reaction takes place between a gas phase and a liquid phase. At the same time, mass transfer from the gas to the liquid phase is also occurring. To be able to completely understand reactive absorption, one must first gain some understanding of the kinetics of fluid-fluid reactions. A detailed discussion into the theory of such is well beyond the scope of this paper. Literature on this subject can be found in most books on chemical reaction kinetics such as (Levenspiel,1999 ).

Absorption occurs through mass transfer. Therefore any factors that have any effect on the overall mass transfer coefficient will affect the rate of absorption. Many times the presence of a chemical reaction can influence the mass transfer rate. One must consider the impacts of chemical equilibrium and reaction kinetics on the absorption rate in

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addition to accounting for the effects of gas solubility, diffusivity, and system hydrodynamics.

There is no sharp dividing line between pure physical absorption and absorption controlled by the rate of a chemical reaction. Most cases fall in an intermediate range in which the rate of absorption is limited both by the resistance to diffusion and by the finite velocity of the reaction.

Consider an absorber with a reaction occurring in the liquid phase. Since the reaction is in the liquid phase, the gas-phase rate coefficient KG is not affected. If the reaction is extremely fast and irreversible, the rate of absorption may be governed completely by the resistance to diffusion in the gas phase. Therefore the absorption rate can be estimated by knowing the gas-phase rate coefficient KG. The liquid-phase rate coefficient KL is strongly affected by fast chemical reactions and generally increased with increasing reaction rate.

The highest possible absorption rates will occur under conditions in which the liquid-phase resistance is negligible and the equilibrium back pressure of the gas over the solvent is zero. This condition can be attained if KL is very large. Frequently, even though reaction consumes the solute as it is dissolving, thereby enhancing both the mass-transfer coefficient and the driving force for absorption, the reaction rate is slow enough that the liquid-phase resistance must be taken into account. This may be due to an insufficient supply of a second reagent or to an inherently slow chemical reaction. What this all boils down to is that the liquid-phase rate coefficient KL in the presence of a chemical reaction normally is larger than the value found when only physical absorption occurs. To account for the effects of chemical reaction, the liquid enhancement factor, E is introduced.

E =

Process Operation

Pressure Constraints

Reactive absorption is best run at high pressures. The high pressure will force more gas into the liquid phase and consequently a better reaction conversion will be attained. However, to operate at high pressures requires the use of a compressor, which is usually the most expensive unit in a plant design.

Temperature Considerations

In physical absorption it is best to operate at low temperatures to promote the gas to go to the liquid phase and to avoid solvent losses to the vapor phase. In reactive absorption one would want to operate at low enough temperatures to allow for absorption of the gas to the liquid, but if the kinetics governing the reaction are not favorable at this temperature

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we have to weigh the possibilities of operating at a higher. The burden is on the engineer to choose a solvent that reacts with the solute at low enough temperatures.

Finding a Suitable Flowrate

Flooding issues, like those in physical absorption dominate this topic. We obviously want to operate below the flooding velocity of the gas. However, in chemical absorption if the is essentially irreversible and the equilibrium partial pressure of the solute is zero, then the countercurrent and co-current absorber require the same number of stages (McCabe, 730). This is advantageous because co-current operation eliminates the flooding concerns. We can have very high flow rates for both the gas and solvent streams and still attain very good separations.

Applicability and Limitations

Reactive absorption is typically used when physical absorption is not able to attain the proper separation desired. Here are some pros and cons with reactive absorption:

Advantages of using reactive absorption

1) a reaction in the liquid phase reduces the equilibrium partial pressure of the solute over the solution, which greatly increases the driving force for mass transfer

2) Absorption plus reaction increases the mass transfer coefficient by introducing a greater effective interfacial area since absorption can now take place in the nearly stagnant regions as well as in the liquid holdup

3) Chemical absorption usually has a much more favorable equilibrium relationship than physical absorption (solubility of most gases is very low)

Disadvantages of using reactive absorption

1) the Murphee plate efficiency is often quite low (10% is not unusual)2) the suitable solvent stream may not be available in the current process or the

solvent stream may be very expensive3) heat of reaction introduces non-isothermal conditions which may require cooling

coils (increase in capital costs)4) additional costly separation unit may be required

The Rate Equation for Mass Transfer and ReactionThe basic reaction in reactive absorption is:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

Solute (gas liquid) + solvent ( ) product (s or or g)

Here we have three factors to consider: what happens in the gas film, in the liquid film, and in the main body of the liquid as shown in the figure below:

From a discussion on the kinetic theory of fluid-fluid reactions with simultaneous mass transfer ( Levenspiel, 1999 ) , it turns out that there are eight basic cases for which reactive absorption can occur.

Case A: Instantaneous reaction with low concentration of soluteCase B: Instantaneous reaction with high concentration of soluteCase C: Fast reaction in liquid film, with low concentration of soluteCase D: Fast reaction in liquid film, with high concentration of soluteCase E and F: Intermediate rate with reaction in the film and in the main body of

the liquidCase G: Slow reaction in the main body but with film resistanceCase H: Slow reaction, no mass transfer resistance

These eight cases can best be visualized by the diagram below:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

The general rate equation for fluid-fluid reaction with simultaneous chemical reaction is:

-rA=

gas film liquid film bulk liquid resistance resistance resistance

where:

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

a = interfacial areaH = Henry’s constantCB = solute concentrationE = liquid enhancement factor

The liquid enhancement factor E is extremely important when dealing with reactive absorption systems. It is introduced into the rate expression to adjust the liquid mass transfer coefficient and takes into account reaction conditions.

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CHE-396 Senior Design Reactive Absorption and Estimation of Solvent Losses

References

1. Douglas, J.M., "Conceptual Design of Chemical Engineering," McGraw-Hill, New York, 1988.

2. King, C.J., "Separation Processes," McGraw-Hill, New York, 1971. 3. Perry, R.H. and Green, "Perry's Chemical Engineer's Handbook," New York, 1997.

4. Reid, R.C., Prausnitz, J.M. and B.E. Poling, "Properties of gases and liquids," McGraw-Hill, New York, 1987.

5. Seader, J.D., and Henley, E.J., "Separation Process Principles," John Wiley & Sons, New York, 1998.

6. Strigle, R.F., "Packed Tower Design and Applications," Gulf Publishing, Houston, 1994.

7. Wankat, P.C. "Equilibrium Staged Separations," Prentice Hall, Englewood Cliffs, New Jersey, 1998

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