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Aromatics lost to the purge set the cost optimum of the IDAES hydrodealkylation flowsheet under an assumed hydrogen limit

We minimized the total annualized cost of the open IDAES hydrodealkylation flowsheet and designed heat-exchanger networks for its optimum.

Thinh D. Ho | CheAI Research Inc. | Research article | October 2024

Abstract

We reproduced the open IDAES examples of toluene hydrodealkylation (HDA) and minimized the total annualized cost (TAC) of the distillation flowsheet with sourced 2023 prices (hydrogen on a 2021 basis). The published distillation model misses its column benzene balance by -0.026 %. With an added reactor-inlet limit H2/(benzene + toluene) ≥ 5, the TAC optimum for 370 t/yr of 99.0 mol % benzene is 642,926.6 USD/yr. Under our cost allocation, its largest controllable term is aromatics lost to the purge (108.6 kUSD/yr), because 48.4 % of the benzene leaves the cooling-water flash overhead. This holds in 29 of 37 converged sensitivity cases. With the limit on toluene alone, as its sources state it, the optimum falls by 12.5 % and capital becomes the largest term. A 298 K flash pays below an all-in refrigeration charge of 0.29 USD per kWh of cooling. The heat-exchanger networks found save only 0-14 % of the network cost.

1. Introduction

Toluene hydrodealkylation is the process that Douglas used to teach hierarchical conceptual design [1, 2]. Its gas recycle needs a purge, which removes the methane product together with some hydrogen and aromatics. The IDAES process modeling framework [3] distributes an equation-oriented HDA model in three example notebooks [4]. They minimize an operating cost with their own prices and do not show which cost term sets a TAC optimum.

Pinch analysis [5] and the stage-wise superstructure of Yee and Grossmann [6] design heat-exchanger networks (HENs), but the duties of this 370 t/yr plant are only tens of kilowatts. We asked which cost term sets the TAC optimum of the open model, and whether heat integration changes it. Under an assumed hydrogen-excess limit, aromatics lost to the purge set the optimum, and heat integration saves little because exchanger capital dominates.

2. Methods

We used idaes-pse 2.13.0, idaes-examples 2.10.0 and Ipopt 3.13.2. We reran each notebook against its published values and checked the atom and column benzene balances. The TAC is annualized capital plus utilities and raw materials, minus a purge fuel credit at the natural-gas price. Purchase costs come from the Seider-Seader-Lewin (SSLW) correlations [7] at 2023 prices, with a Lang factor of 4.74 and 10 % interest over 10 years. Utility prices follow [8]. We optimized ten decision variables for 370 t/yr of 99.0 mol % benzene and tested 20 Latin hypercube starts.

We took condenser purity from the overall outlet composition, raised the flash lower bound to 313.15 K (a 10 K approach to cooling water) and added the limit H2/(benzene + toluene) ≥ 5. Its sources state H2/toluene ≥ 5 for reactors at 34-35 bar [9, 10], so our form is an assumed, stricter heuristic.

Forty one-at-a-time cases varied prices, economic factors, targets and the hydrogen ratio, and some added a 0.614 bar loop pressure drop scaled from [11]. Each TAC was split into six controllable terms and an accounting residual. The aromatics term is

Carom,purge = tyr Σj = B, T Fj (Mjpj - pgasHHVj)

where Fj is the purge flow of benzene or toluene, Mj its molar mass and pj its price. HHVj is the higher heating value, pgas the gas price per joule and tyr the seconds per year.

We designed the HEN with a two-stage mixed-integer nonlinear program (MINLP) at ΔTmin = 10 K, tested on the SYNHEAT benchmark [12]. The exchangers span 0.035-22.6 m2 at base heat-transfer coefficients, but the SSLW correlation is valid only above about 10.6 m2, so two cost laws bracket their cost. Networks were re-costed with exact areas, and key numbers were re-derived independently.

3. Results

3.1 The column loses benzene

All three notebooks reproduce, and two flash asserts miss only within the scaled tolerance of Ipopt. The distillation model, however, loses 0.026 % of its benzene across the column in the simulation and 0.030 % in the optimization. Its total condenser keeps 0.4-4 % vapour, while its ports report the liquid composition on the total flow.

3.2 Benzene escaping the flash dominates the optimum

The TAC optimum is 642,926.6 USD/yr at a conversion of 0.9905, and the column is idle because the flash liquid already meets the purity target. The flash sits at its 313.15 K bound, and 48.4 % of the reactor benzene leaves it overhead (Figure 1). Recycled, it counts against the hydrogen limit.

Block flow diagram of the HDA flowsheet, with a dashed line for benzene leaving the flash overhead.
Figure 1. HDA flowsheet at the TAC optimum. The dashed path is the benzene that leaves the flash overhead, to be recycled or purged at fuel value.

Aromatics lost to the purge are the largest controllable term, 108.6 kUSD/yr net of the fuel credit. Capital (88.4 kUSD/yr) and hydrogen lost to the purge (20.8 kUSD/yr) follow (Figure 2). Separation energy is 1.2 kUSD/yr and never leads in a converged case (0.8-30.0 kUSD/yr). The published loop has no pressure drop. A 0.614 bar drop adds 98.6 kUSD/yr, mostly again as aromatics lost to the purge, and only 4.0 kUSD/yr as compression.

Stacked bars of controllable cost terms for six cases. Aromatics lost to the purge lead in the headline case.
Figure 2. Controllable TAC terms at the optimum of six cases, with the case TAC in kUSD/yr. The residual is omitted. The refrigerated case uses a tabulated refrigeration tariff.

3.3 The leading term depends on the hydrogen limit

Aromatics lost to the purge lead in 29 of the 37 converged sensitivity cases. Capital leads in six, among them low conversion caps and the refrigerated flash. Hydrogen lost to the purge leads at 11.34 USD/kg, and reactor-section heat with the notebook utility prices. The hydrogen limit binds in every case. The TAC is 534,006 USD/yr at a ratio of 3 and 867,116 USD/yr at 7. With the limit on toluene alone, the optimum is 562,501.9 USD/yr (12.5 % lower), and capital (77.3 kUSD/yr) becomes the largest term. Without any limit, the model runs near stoichiometric hydrogen.

A flash at 298 K loses 25.3 % of the benzene overhead instead of 48.4 %. This fixed design beats the headline if its 46.9 kW of cooling costs an all-in charge below 0.29 USD per kWh, 37 times the cooling-water price.

3.4 Heat integration saves little

At ΔTmin = 10 K, the 63.5 kW of hot process duty can supply all 44.5 kW of cold duty, so the minimum hot utility is zero (Figure 3a). Under the power cost law at base heat-transfer coefficients, one feed-effluent exchanger replaces the furnace and saves 8.2 % of the HEN cost. In this case the utility-only design spends 45.4 kUSD/yr on capital, about five times its utility cost (8.8 kUSD/yr). Over all six cases (Figure 3b), the networks found save 0-14 %, at most 7.0 kUSD/yr.

Composite curves with zero hot utility, and HEN costs of three designs in six cases.
Figure 3. (a) Composite curves at the zero-hot-utility target. (b) HEN cost of three designs for two cost laws and three heat-transfer levels.

4. Discussion

Under the assumed hydrogen limit, the flash-temperature multiplier (14,299 USD/yr per K) and the 298 K case both identify benzene escaping the flash as the cost lever. This agrees with Douglas's hierarchy, which fixes the recycle and purge structure first [1, 2]. In the IDAES model, however, the flash and not the column controls the purge loss.

The TAC span over ratios 3 to 7 (333 kUSD/yr) is of the same order as a hydrogen price rise from 1 to 11.34 USD/kg (396 kUSD/yr). A designer must choose the form and value of the limit with the same care as the prices.

Pinch targets give the energy limit [5], but here the capital trade-off [6] decides the network. The largest HEN saving is an order of magnitude below the purge term, so heat integration is unlikely to change the flowsheet decision. A designer should first evaluate a colder flash, an absorber or vapour recovery on the purge.

Balance checks, sign bounds on the duties and a run of the bare model exposed the condenser leak, the missing hydrogen limit and the zero loop pressure drop, which the notebook outputs did not show.

5. Limitations

The model has one reaction and no diphenyl formation, so high conversion carries no selectivity penalty and the column stays idle. A side-reaction extension needs a validated kinetic and selectivity model. The hydrogen limit is adapted from reactors at 34-35 bar and 873-973 K, whereas the IDAES reactor runs at 3.5 bar and 793 K. Likewise, the 0.614 bar loop drop is transferred from a 39.3 bar loop, not measured. Its effect would be smaller at industrial loop pressures, which we did not calculate. The condenser is only approximately vapour-free, because a zero-vapour equality did not converge.

On the cost side, utility correlations are extrapolated below their range. Hydrogen is on an unescalated 2021 basis, and the furnace efficiency is assumed. The 11.34 USD/kg price has no verified source. The term ranking reflects our cost allocation, because the residual changes between cases. Refrigeration is priced as a purchased utility with no chiller equipment, so the break-even is a lower bound and applies only to the fixed 298 K design. The model also has no absorber or purge recovery.

The HEN uses overall coefficients per service, not film coefficients. It was designed after the flowsheet, and its cost is not an equipment-by-equipment part of the flowsheet TAC. Both cost laws extrapolate below 10.6 m2, so the HEN costs are a bracket. No exact-cost HEN optimum is certified, and split networks are not covered. Piecewise-linear profiles add a discretization error to the approach checks.

Finally, the multistart is not a global certificate. Eleven of 20 starts converged, all to the same optimum, but only one of the 11 reached its sampled start. Three of the 40 sensitivity cases failed, and the sensitivity records omit the degrees of freedom. The whole-plant energy balance was not audited independently, and the one-run regeneration of all results was tested with short solver limits only.

6. Conclusions

The published IDAES HDA distillation model leaks benzene through vapour in its total condenser. Under an assumed reactor-inlet H2/(benzene + toluene) limit, aromatics lost through the flash overhead to the purge are the largest controllable cost of the TAC optimum. This holds in most sensitivity cases but depends on the form of the hydrogen limit. A colder flash is the design lever, and it pays below a break-even refrigeration charge. Heat integration is a threshold problem in which exchanger capital, not utility cost, decides the network.

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