# New processes for recovery of acetic acid from waste water

## Abstract

This paper addresses an industrially important problem of acetic acid recovery from a waste water stream via reactive distillation. The presence of a three-phase regime on the column stages due to a liquid–liquid phase split between aqueous and organic phases is a typical characteristic of this process. A modern modeling approach is presented to detect the existence of potential phase splitting in this column. A good agreement of a phase splitting model with the literature data has been shown. A theoretical study for the recovery of acetic acid from its 30 wt% aqueous solution by esterification with *n*-butanol is presented. Alternate column structures were investigated and two structures rendering theoretically close to 100% conversion of acetic acid were identified. The dynamic simulations were performed on proposed structures to see transient responses wrt. to common process disturbances.

### Keywords

Phase splitting Homotopy continuation Reactive distillation Modeling and dynamic simulation Butyl acetate Esterification Acetic acid recovery### List of symbols

- HOLD
Molar liquid holdup on tray

*J*Jacobian matrix

- NC
Number of components

*R*Reaction ratio

*T*Temperature

*V*Volumetric liquid holdup on tray

*f*Function vector to be solved to 0

- fgab
Vapor sidedraw molar flowrate

- fgzu
External vapor feed molar flowrate

- flab
Liquid sidedraw molar flowrate

- flzu
External liquid feed molar flowrate

- liq
Internal liquid molar flowrate

*p*Pressure

- psp
Saturation pressure in the vapor phase

- vap
Internal vapor molar flowrate

*x*,*x*1,*x*2Mole fraction, liquid (global, phase 1, phase 2)

*y*Mole fraction, vapor phase

- zflzu
Mole fraction in external liquid feed

- zfgzu
Mole fraction in external vapor feed

### Greek letters

- Φ (or Fi)
Phase ratio

- γ1, γ2
Activity coefficient (phase 1, phase 2)

- θ
Solution vector

- λ
Continuation parameter

- ν
Stoichiometric coefficient

### Superscripts

- CRIT
Critical point of the miscibility gap

- PSA
Value given by the Phase Splitting Algorithm

- START
Reference state (starting point for continuation)

### Subscripts

- A, B, C
Example states in the phase diagram

*k*Tray number

*i*Component indices

*m*Variable indices (in the solution vector)

*s*Current step

## Introduction

The recovery of dilute acetic acid from its aqueous stream is a major concern for many petrochemical and fine chemical industries. Conventional distillation is highly uneconomical due to (a) the presence of a tangent pinch on the water end in the *y*–*x* diagram, that means high reflux ratio or high number of column stages to get pure products; and (b) large amount of water to be vaporized from dilute acid stream, which is impractical due to the high latent heat of vaporization of water. Recently, more advanced concepts based on azeotropic and extractive distillation have been proposed (Chien et al. 2004; Demiral and Yildirim 2003). Another very promising option is reactive distillation, where acetic acid is reacted off with a suitable alcohol in order to produce a valuable ester product at the one end of the column and the aqueous stream free of organic impurities at the other end of the column. In particular, esterification with *n*-butanol was proposed for this purpose (Saha et al. 2000). In that work, however, by trial and error experiments a maximum of up to 58% acetic acid conversion was achieved with a 100% excess of butanol in feed. In the present paper, using a model based approach, it can be observed that conversion close to 100% is possible for such a process.

*potential phase split*that can occur on many trays inside the column. To reliably predict the liquid–liquid phase split on the column trays in the course of a simulation run, an extra routine for the phase split calculations is required. The routine is based on homotopy continuation methods (Bausa and Marquardt 2000; Brüggemann et al. 2004; Steyer et al. 2005). The complexity introduced by the liquid–liquid phase split besides the existing complexity of a reaction–separation interaction makes the analysis of this process very challenging.

The article is organized in the following way: first an appropriate model is presented that carries out the simultaneous phase split calculations for a reactive distillation column. Model results showing very good agreement with literature data are presented afterwards. The phase split routine is used to design a heterogeneously catalyzed reactive distillation column for the acetic acid recovery process. Steady state simulation results are presented for six alternate configurations generated based on physical insights. After the process screening based on the conversion levels, two process configurations are proposed. Next, dynamic simulation results are presented. At the end, conclusions and future directions are discussed.

## Mathematical model

The classical approach treats the RD process as a pseudo-homogeneous system, where no phase splitting occurs in the liquid phase (Sundmacher and Kienle 2002; Taylor and Krishna 2000). However, for some systems, significant differences between states in the pseudo-homogeneous regime (no liquid phase splitting) and heterogeneous regime (with phase splitting) can be revealed (Bausa and Marquardt 2000; Brüggemann et al. 2004). As consequence, an appropriate model has to be used in order to better reflect the real system behavior. However, dynamic simulation of a (reactive) distillation column taking into account the potential appearance of a second liquid phase is a much more difficult task. The main challenge is to write a model, which switches between two model structures during the course of a simulation run. The switching is required when changes in the phase state on some trays occur. The model switching can be handled by considering that always there are two liquid phases present in the model and when the system leaves the heterogeneous regime, these two phases become identical having the same compositions. This way, there is no need to change the number of model equations when the system crosses the boundary between the homogeneous and heterogeneous region.

*the main model*, relatively close to the “classical” RD model (without phase splitting), which calculates at each step the global composition in liquid (*x*) and vapor (*y*) phases, temperature (*T*), internal liquid (liq) and vapor (vap) streams flowrates, for all distillation stages (column trays and condenser + decanter);*the phase splitting algorithm*, externally carried out in a separate procedure, called by the main model at each step, for all distillation stages; this algorithm gets from the main model the global compositions (*x*) and temperatures (*T*), together with some other parameters, giving back both liquid phases compositions (*x*1 and*x*2) and ratios (Φ).

### Main model

- 1.
All column trays and the decanter have constant liquid holdups.

- 2.
The vapor holdup on trays is neglected.

- 3.
The vapor and liquid phases are in equilibrium.

- 4.
The reaction takes place only in the liquid phases.

- 5.
The pressure drop along the column length was neglected.

*Component material balance:*

*R*is considered as the linear combination between the reaction rate in phase 1 and the reaction rate in phase 2, taking into account the phase split ratio Φ

_{k}. If the liquid phase splitting does not occur, then the compositions in both phases are equal and the reaction rates are identical. As remark, such a linear expression \([(1- \Phi_{k}) \times R(x1_{1,k},\ldots,x1_{{\rm NC},k}) + \Phi_{k} R(x2_{1,k},\ldots,x2_{{\rm NC},k})]\) can only be used when the uniform catalyst distribution in both liquid phases is considered.

*Summation condition for global liquid phase compositions:*

*Compositions in liquid phase 1 (externally calculated):*

*x*1

^{PSA}

_{k,i}represents the phase 1 composition, externally determined with the “Phase Splitting Algorithm”. The same annotation, PSA, is attached for compositions in liquid phase 2 and phase ratio, also given by the same procedure:

*Compositions in liquid phase 2(externally calculated):*

*Phase ratio (externally calculated):*

*Phase equilibrium:*

*Summation condition for vapor phase compositions:*

*Total material balance for the liquid phase:*

*Total material balance for the vapor phase:*

The model to be used later for steady state and dynamic simulations as said before is a heterogeneously catalyzed reactive disitllation column model with energy balances. This model has two major changes: (1) For the global reaction rate calulcation the phase split ratio has not to be taken into account and the assumption of a uniform catalyst distribution is not required. The reason for this is that the reaction rate is based on activities rather than mole fractions and that phase equilibrium implies equal activities in both liquid phases. (2) An energy balance replaces Eq. 9 and Eq. 8 has to be replaced by a total material balance for the liquid and vapor phases.

### Phase splitting algorithm

As mentioned before, the phase splitting algorithm runs almost independently, checking at each step the state of all distillation stages and returning to the main model the phases compositions and ratios. Of course, before running, it takes some mandatory information from the main model, including overall compositions, stages temperatures and other needed parameters (i.e., for the vapor–liquid (–liquid) equilibrium calculation, also some algorithm “tuning parameters”—as starting points for the internal continuation algorithm, for instance—and so on).

The phase splitting algorithm used in this work was originally presented by Bausa and Marquardt (2000) and subsequently modified by Steyer et al. (2005). It is a hybrid method using a-priori knowledge of phase diagram properties in order to tune-up the computational algorithm. The flash calculation is decomposed in two steps: a *preprocessing* step and the *computational* one.

In the first step, all heterogeneous regions of the system’s phase diagram at the specified pressure and boiling temperature are divided into convex regions and, for each region, one reference state inside it, (*x*^{START}, *x*1^{START}, *x*2^{START}, *y*^{START}, Φ^{START}, *p*^{START}, *T*^{START}), is stored—denoting here the overall composition, compositions in both liquid phases, vapor composition, phase ratio, pressure and temperature. Typically, this analyzing procedure may be carried out only once, before simulations and more, since the phase diagrams are investigated in an early phase of the process design, the information on the heterogeneous region(s) existence may be directly provided by user (at least for mixture with up to four components).

*x*

^{START},

*x*1

^{START},

*x*2

^{START}and Φ

^{START}) and ending at a desired two phase solution (

*x*,

*x*1,

*x*2 and Φ) if it exists. The homotopy run can be parameterized by a continuation parameter λ in the following manner:

On its turn, the homotopy continuation algorithm is based on a repetitive two-step process. First one, the *correction step*, solves the following equations:

*Mass balances (as constraints):*

*Activity difference equations (as necessary conditions):*

*The summation equation (as constraint):*

*k*” is provided, in order to increase the readability.

*predictor step*), a solution θ to Eqs. (11)–(13) for a new value of λ is estimated using

_{m}denoting an element of the solution vector. For the algorithm of Bausa and Marquardt (2000), θ contains 2NC mole fractions (

*x*1 and

*x*2) and one phase ratio (Φ).

The algorithm works by alternating prediction and correction steps while increasing λ from 0 to 1, effectively moving along the binodal surface in an effort to reach the desired *x* composition.

In systems with multiple binary pairs that exhibit phase splitting, multiple starting points for continuation have to be used in order to reach the correct solution (Bausa and Marquardt 2000). This is due to the fact that the straight line according to Eq. (10) connecting the starting point *x*^{START} with the desired composition *x* might cross over a region of one-phase behavior between the two-phase starting and ending points. As Bausa and Marquardt show in their paper, this approach is very successful in finding the correct solution very quickly, with a high reliability.

However, their original implementation has a big drawback: the solution vector θ has 2NC + 1 components even if the system degree of freedom is NC!, increasing this way the computational time for the solver. This is why a modified method, developed by Steyer et al. (2005) was used. The method’s principle is to parameterize the solution vector θ by introducing so-called phase partitioning coefficients, reducing the system order to NC, as the quoted authors proved in their work.

*J*denotes the Jacobian matrix of the remaining equation system (after model reduction), denoted here as

*f*. To avoid inverting the Jacobian matrix, the equivalent linear equation system has to be solved. Also, for a fast and reliable solution, the authors suggest that the Jacobian should be computed analytically since the equation system is highly non-linear due to the activity coefficient model.

## Model validation

Due to the lack of comprehensive experimental data, the model is validated by reproducing the results of Brüggemann et al. (2004). Brüggemann et al. have studied a batch distillation process in the heterogeneous regime, taking as example the laboratory column for butanol esterification to butyl acetate, previously presented by Venimadhavan et al. (1999).

- 1.
ternary non-reactive distillation (loading the column still pot with a mixture of 40% water, 20% butanol and 40% butyl acetate, with no catalyst load), at a constant reflux ratio (0.9);

- 2.
reactive distillation (filling the still pot with a binary mixture of 51% butanol and 49% acetic acid), homogeneously catalyzed with sulfuric acid, at a constant reflux ratio (0.9);

- 3.
reactive distillation (filling the still pot with a binary mixture of 51% butanol and 49% acetic acid), homogeneously catalyzed with sulfuric acid, at a variable-adaptive reflux ratio (0.9 and 0.99).

^{4}), on the right,

*t*is in (h). The right hand side picture is taken from Brüggemann et al. (2004).

For a homogeneously catalyzed RD column the phase split algorithm precisely detects the existence of two liquid phases. In the remainder, a heterogeneously catalyzed process will be considered.

## Alternate designs for acetic acid recovery by RD column

Its required to test for all the design alternatives, whether they are feasible to achieve the desired process goal. The desired goal in this work is to achieve a very high conversion of acetic acid (>99%). Not all the configurations will lead to the high conversion of acetic acid to butyl acetate. In order to check whether the configurations 1–6 achieve 99% conversion, ideally all of them have to be tested with various sets of design parameters in the entire solution space. In fact, this can be seen as an optimization problem with conversion of acetic acid set as a constraint or as a cost function to be maximized. The phase split routine to be used for the phase split detection on the column stages, however, does not allow the use of standard optimization tools. It was therefore necessary to use a simulation environment for this purpose. Designing all the configurations with a simulation tool is a tedious procedure. Through simulations we carried out limited feasibility tests for configurations 1–6. It has been found that configurations 1 and 6 can achieve the above desired goal. However, for configurations 2–5 no feasible solution was found.

Feed composition (mole fraction), BuOH:AcH is 2:1

Configurations 1–5 | Configuration 6 | ||
---|---|---|---|

Feed I | Feed II | ||

Feed (kmol/h) | 0.00675 | 0.0055 | 0.00125 |

| 0.0926 | 0.1137 | 0.0 |

| 0.1854 | 0.0 | 1.0 |

| 0.0 | 0.0 | 0.0 |

| 0.7220 | 0.8863 | 0.0 |

| 0.0 | 0.0 | 0.0 |

Configurational details

Configurations | 1 | 2 | 3 | 5 | 6 |
---|---|---|---|---|---|

AcH conversion (%) | 99 | 63.7 | 9.0 | 91.92 | 99 |

Reboiler duty (kW) | 0.1033 | 0.14 | 0.107 | 0.362 | 0.1244 |

Catalyst (kg/tray) | 0.00265 | 6.90 | 0.0027 | 0.8381 | 1.3637 |

Reactive stages | 8–21 | 12–21 | 12–21 | 12–21 | 9–21 |

Column stages | 22 | 22 | 22 | 22 | 22 |

Feed tray location | 8 | 11 | 11 | 11 | 9 and 21 |

Though configuration 1 and configuration 6 having very different column structures and reverse product streams, both are capable of providing close to 100% conversion of acetic acid. Configuration 1 yields 99% aqueous stream as a distillate and nearly a 50–50 mixture of butanol and butyl acetate as the bottoms. Downstream processing is required to separate the two organics. Configuration 6 yields a 98% water stream at the bottom and an organic stream containing 44% BuAc, 26% BuOH and 24% water is obtained as a distillate. Significant amount of side product di-butyl ether is also present in the distillate stream. Here again a downstream processing step is required to produce a high purity acetate stream.

## Dynamic simulations for the proposed configurations

In this section, dynamic simulation results are presented for the base case steady states with 99% conversion for configurations 1 and 6. Process responses are determined for ±5% step disturbances of the feed flow rate and the AcH composition in the feed.

### Configuration 1

The composition profiles show a very high sensitivity to the disturbances for configuration 1, as shown in Fig. 6. For instance, with an increase of 5% in feed flowrate, these profiles move like a traveling wave down in the stripping section leading to a serious drop in acetic acid conversion (from 99 to 38%, see Fig. 6d). The system moves toward a new steady state with totally different composition profiles in the reactive zone. As it can be seen in Fig. 6a and b, the non-reactive zone above the feed tray remains unaffected. Fig. 6c shows how the three-phase regime extends from a small region around the feed tray to about 75% of the reactive zone, without any effect in the upper part of the column.

### Configuration 6

## Conclusions

This work presented new features characterizing a modern modeling approach for RD processes, which include phase splitting calculation. By adapting a rapid, robust and reliable algorithm based on a homotopy-continuation method, the new model implementation was first validated and then put into value for a specific application, i.e., acetic acid recovery from the waste water. Two promising reactive distillation column structures were identified giving close to 100% conversion of acetic acid to a valuable ester product. The intringuing process behavior was revealed for the proposed column structures through a series of dynamic simulation runs—expansion and contraction of the three-phase regime along the column length is one of these phenomena, for example.

Important future directions are: (1) experimental validation of the proposed model, (2) integration of a reliable phase split routine within the standard optimization tool to obtain an economically optimal design and (3) control of the desired steady state using some suitable control strategy.

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