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Question : Alkanolamines are used in scrubbers to clean streams contain...

Alkanolamines are used in scrubbers to clean streams containing acid gases. Extension of existing applications to new situations involving carbon capture and sequestration of CO_{2} for environmental reasons will lead to increased demand for these substances. The reaction of ammonia (A) with ethylene oxide (EO) in aqueous solution produces monoethanolamine (MEA), diethanolamine (DEA), and triethanolamine (TEA). The reactions for stepwise formation of these products are

 

NH_{3}+C_{2}H_{4}O\rightarrow NH_{2}C_{2}H_{4}OH

 

r_{1}=k_{1}(A)(EO) (1)

 

NH_{2}C_{2}H_{4}OH+C_{2}H_{4}O\rightarrow NH(C_{2}H_{4}OH)_{2}

 

r_{2}=k_{2}(MEA)(EO) (2)

 

NH(C_{2}H_{4}OH)_{2}+C_{2}H_{4}O\rightarrow N(C_{2}H_{4}OH)_{3}

 

r_{3}=k_{3}(DEA)(EO) (3)

 

Viewed from the perspective of ethylene oxide, these reactions are competitive; by contrast, from the perspective of the amines, they are consecutive. Consider a research scale batch reactor operating at 60^{\circ}C and 20 bar to maintain all species in the liquid phase. Actual production of these commodity products on a large scale would be conducted in flow reactors, as described in Illustration 9.5. The rate laws are of the mixed second-order form (first-order in each reactant), with hypothetical rate constants k_{1},k_{2} and k_{3} equal to 1, 0.4, and 0.1 L\cdot mol^{-1}/min, respectively.MEA and DEA are both high-volume chemicals, while TEA is less in demand. The distribution of alkanolamine products obtained under the specified conditions can be influenced by controlling the initial mole ratio of EO to A and the time of reaction.

(a) Solutions of ammonia and ethylene oxide are prepared independently and heated to the reaction temperature. At time zero the solutions are blended rapidly in a batch reactor to obtain a solution that is 1M in ammonia and 2.4M in ethylene oxide. Determine the concentrations of all five reactant and product species present at times from 0 to 15 min when reactions (1) to (3) take place under isothermal conditions.

(b) What would be the anticipated effects of using a lower mole ratio of ethylene oxide to ammonia (but holding the initial concentration of ammonia at 1M) in the initial charge to the reactor?

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(a) Because these reactions take place at constant volume (liquid phase), the progress of these coupled reactions can be tracked using either three extents of reaction per unit volume or three suitable species concentrations. This solution employs the former progress variables. The concentrations of all species are expressed in these terms as follows:

 

A=A_{0}-\xi _{1}^{\ast } (A)

 

EO=EO_{0}-\xi _{1}^{\ast }-\xi _{2}^{\ast }-\xi _{3}^{\ast } (B)

 

MEA=\xi _{1}^{\ast }-\xi _{2}^{\ast } (C)

 

DEA=\xi _{2}^{\ast }-\xi _{3}^{\ast } (D)

 

TEA=\xi _{3}^{\ast } (E)

 

The three independent rates of reaction per unit volume are then

 

\frac{d\xi _{1}^{\ast }}{dt}=k_{1}(A)(EO)=k_{1}(A_{0}-\xi _{1}^{\ast })(EO_{0}-\xi _{1}^{\ast }-\xi _{2}^{\ast }-\xi _{3}^{\ast }) (F)

 

\frac{d\xi _{2}^{\ast }}{dt}=k_{2}(MEA)(EO)=k_{2}(\xi _{1}^{\ast }-\xi _{2}^{\ast })(EO_{0}-\xi _{1}^{\ast }-\xi _{2}^{\ast }-\xi _{3}^{\ast }) (G)

 

\frac{d\xi _{3}^{\ast }}{dt}=k_{3}(DEA)(EO)=k_{3}(\xi _{2}^{\ast }-\xi _{3}^{\ast })(EO_{0}-\xi _{1}^{\ast }-\xi _{2}^{\ast }-\xi _{3}^{\ast }) (H)

 

with initial conditions \xi _{1}^{\ast }=\xi _{2}^{\ast }=\xi _{3}^{\ast }=0 at t=0 This system of coupled, nonlinear differential equations may be integrated numerically by any suitable computer routine, such as the ode15 or ode23 commands in Matlab. The results for the extents of reaction per unit volume then lead to the plots of the evolution of the concentrations of all reactant and product species shown in Figure I5.6.

 

Examination of the various plots in Figure I5.6 reveals that the concentration of MEA goes through a maximum (0.54 M) at 0.8 min and that the peak corresponding to this maximum is relatively narrow. By contrast, the peak corresponding to the plot of the concentration of DEA is very broad, with concentrations of this species varying only slightly (near 0.6 M) during the period from 5 to 10 min.

 

(b) If a lower mole ratio of EO to ammonia were employed in a batch trial, one is still likely to observe a maximum in the concentration of MEA at short times, but the location of the maximum will occur at a longer time and at a higher concentration than that for the base case. The product mixture at times greater than 15 min will contain less TEA than in the base case. As for ethylene oxide and ammonia, their concentrations will each decline less rapidly than in the base case.

 

 

 

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