April 2024

Process Optimization

Optimization for the trigeneration of industrial waste

Many corporations are moving toward sustainable operations for their processes. One alternative pathway to reduce fossil fuels consumption in a processing plant is through harvesting waste heat from industrial waste through combined heat and power (CHP), or what is commonly known as cogeneration or polygeneration.

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Many corporations are moving toward sustainable operations for their processes. One alternative pathway to reduce fossil fuels consumption in a processing plant is through harvesting waste heat from industrial waste through combined heat and power (CHP), or what is commonly known as cogeneration or polygeneration. Apart from reducing the dependency on fossil fuels and, subsequently, the plant’s operating costs, the CHP scheme also helps to mitigate carbon dioxide (CO₂) emissions, which are major pollutants contributing to the greenhouse gas (GHG) effect. This waste-to-energy (WtE) pathway is an efficient way to supply thermal and electrical energy simultaneously for usage in the plant.

This article demonstrates a WtE project in a synthetic rubber plant where waste heat is harvested from the plant’s industrial waste. An optimization framework known as an automated targeting model (ATM) was used to simultaneously optimize the trigeneration potential and its waste inventory system. The ATM is linear in nature and may be executed easily using Excel and its Solver optimization toolbox.

The CHP system. 

A CHP (or cogeneration) system allows the generation of heat and power in a more efficient way. In general, it offers higher thermal efficiency over conventional facilities. For instance, conventional power generation has an efficiency lower than 50%, while that of cogeneration can achieve 90%.¹ A CHP facility is considered environmentally friendly due to its lower CO₂ emissions intensity per unit of power output. In the past few decades, many industrial processes have installed CHP facilities to improve energy efficiency.

The typical configuration of a steam system with a CHP scheme is shown in FIG. 1. As illustrated, very-high-pressure steam (VHPS) is generated in the steam boiler or heat recovery steam generator (HRSG) for power generation purposes and is then expanded through a non-condensing steam turbine to lower pressure levels as high-pressure steam (HPS), medium-pressure steam (MPS) and low-pressure steam (LPS). Electricity can then be produced in the form of cogeneration potential via turbo generators or shaft power via direct machine drivers due to the pressure reduction in the steam turbine across the header levels.

 

Conventional methods for evaluating cogeneration potential involve nonlinear models and are, therefore, discouraged. Several shortcut optimization methods based on process integration techniques have been proposed and have attracted increasing awareness in recent years. Process integration techniques have long been recognized as a systematic design method to enhance the energy efficiency of processing plants. This may be defined as a holistic approach to design and operation that emphasizes the unity of the process.^2,3 Process integration was developed in the 1970s as a systematic design tool for a heat recovery system and was later extended in the 1980s for use in other energy-intensive processes. In the 1990s and 2000s, process integration was extended into various waste minimization initiatives, such as water recovery, hydrogen networks and property integration.⁴ It can also be found in various chemical engineering design textbooks.^5,6

More recently, several process integration toolboxes have been developed for cogeneration targeting in a CHP system. One among them is the graphical tool of cogeneration pinch diagram⁷ (FIG. 2), which is a shortcut method that allows the identification of maximum cogeneration potential based on enthalpy values of the steam headers. Even though this graphical tool provides valuable insights for process designers, it suffers from inaccuracy issues and can be cumbersome. Therefore, algebraic and optimization toolboxes were later developed as alternatives to overcome the limitations of their graphical counterpart.⁸ The optimization toolbox of an ATM is particularly valuable due to its flexible nature in setting different objective functions, such as maximum cogeneration potential or cost optimization. As the ATM is a linear program (LP), it can be easily implemented using Excel via the optimization toolbox Solver add-in. An ATM has been demonstrated in evaluating different cogeneration schemes of a sulfuric acid recovery plant, as well as the simultaneous targeting of cogeneration potential and waste inventory.^9,10

 

In this article, the ATM was used to evaluate the trigeneration potential and CO₂ reduction for a WtE project in a synthetic rubber plant.

Methodology. 

A generic framework of the ATM for cogeneration targeting is shown in FIG. 3. The steps for using the ATM are:

1. Step 1: Level k steam headers are arranged in decreasing order based on their specific enthalpy (H_k)—the latter is a function of its steam pressure.
2. Step 2: At each level k, steam sources from external fuel (F_s, k ), waste (F_W, k ) and process stream demand (F_D, k ) are located.
3. Step 3: The net steam flowrate (F_STM, k) is determined at each level k from the difference between steam sources and demands. This is shown in Eq. 1:
          F_STM,k = F_s,k + F_W,k – F_D,k     Ɐk          (1)
   
   
4. Step 4: The steam cascade is formed by accumulating the net steam flowrate to the next level. The cumulated steam flowrates (δ_k ) across all levels are described in Eq. 2. To ensure a feasible steam cascade, no negative flowrates are allowed at any level, as described by Eq. 3:
   
          δ_k = δ_k–1 + F_STM,k      Ɐk          (2)
          δ_k ≥ 0       Ɐk                             (3)
   
   
5. Step 5: The extractable power cascade is used to determine the trigeneration potential. The extractable power (E_k ) of the steam turbine at each level k is determined by cascading E_k (kW) across all stream levels, as denoted in Eq. 4:
   
          E_k+1 = E_k + ƞ_k δ_k (H_k – H_k+1)           (4)
   
   where ƞ_k  is the isentropic efficiency of the steam turbine. The first entry of the extractable power cascade is always set to zero (Eq. 5), while the final entry (level n) dictates the total trigeneration potential (E_T) of the system (Eq. 6):
        
          E₁ = 0          (5)
   
          E_n = E_T         (6)

Economic evaluation. 

To determine the economic performance of the trigeneration system, the constraints described in Eqs. 1–6 should be used with the economic model that is discussed here. In particular, Eq. 7 shows that the total annualized cost (TAC, $/yr) of a trigeneration system is due to the capital costs of the boiler (TAC_Boil ), the steam turbine (TAC_Turb ) and the absorption chiller (TAC_Chil ), as well as the steam generation cost (C_GEN, $/hr) from fuel sources:

TAC = TAC_Boil + TAC_Turb + TAC_Chil + C_GEN AOT          (7)

where AOT is the annual operating time (hr/yr). TAC_Boil in Eq. 7 can be evaluated using Eq. 8, while TAC_Turb  is shown in Eq. 9. For the latter, the turbine capital cost is a function of the extractable power (E_k ). Both Eqs. 8 and 9 are linearized functions reported in literature:¹¹

TAC_Boil = 6,996 + 211.5 F_F                 (8)

TAC_Turb = 81,594 + 18.052 E_k           (9)

where F_F is the flowrate of fuel (tph).

Conversely, the cost of steam generation (C_Gen ) in Eq. 7 can be approximated following Eq. 10:¹¹

C_GEN = 1.3 CT_F LHV_F F_F            (10)

where CT_F ($/MJ) is the unit price of fuel. With a specified desired steam condition, LHV_F (MJ/kg) is the lower heating value of fuel. Note that this approximation includes 30% of other factors such as feedwater pumping power, sewer charges for boiler blowdown and environmental emissions control.¹¹ The steam generation (F_s,k ) can be evaluated by considering boiler efficiency (ƞ_Boil ), as outlined in Eq. 11:

F_s,k = (LHV_F  F_F  ƞ_Boil ) ⁄ H_s,k           (11)

The trigeneration potential indicated a reduced power consumption from the external utility supplier. Therefore, a positive economic indicator is the total savings and profit (TSP, $/yr), which comprises savings from a reduced external power purchase (C_P ), steam (C_s ) and industrial waste disposal (C_D ), as well as the profit from excess steam sales (C_XS ), as defined in Eq. 12. The savings from external power (C_P) can be attained using Eq. 13 based on the total cogeneration potential of the CHP system (E_T, calculated from Eq. 6).

TSP = C_P + C_s + C_xs + C_D         (12)

C_P = CT_P E_T AOT                        (13)

Savings from steam at a different level k can be determined using Eq. 14:

C_s = ∑_kCT_s,k F_s,k AOT          (14)

Savings from waste disposal is denoted in Eq. 15:

C_D = CT_D F_D AOT                 (15)

The excess steam produced from the trigeneration system may be sold, where profit can be generated, as expressed in Eq. 16:

C_xs = CT_XS F_XS AOT             (16)

In Eqs. 13–16, CT_D ($/t) and F_D (tph) are the unit disposal charge and flowrate of industrial waste, CT_P  ($/kWh) is the unit cost of power, CT_s,k ($/t) is the unit cost of steam at level k, and CT_XS ($/t) and F_XS (tph) are the unit selling price and the flowrate of excess steam.

The reduction of CO₂ (CDR, kg/hr) due to the implementation of a trigeneration system can be computed. In this context, the savings of both external fuel (CDR_F ) and power (CDR_P ) are considered. This is shown in Eq. 17:

CDR = CDR_F + CDR_P          (17)

The CDR_F is calculated using specific CO₂ emissions factors of the external fuel (S₁, kg/MJ), as shown in Eq. 18:

CDR_F = S₁ F_fs          (18)

The amount of external fuel saving (F_fs in Eq. 18) from trigeneration is calculated based on steam generation from waste combustion, as shown in Eq. 19 (revised from Eq. 15):

F_fs = (F_s,k × H_s,k ) / (η_f^BOILER × LHV_F )          (19)

Conversely, the CO₂ intensity of electricity generation (S₂, kg/kWh) may be used to calculate CDR_P, as expressed in Eq. 20:

CDR_P = S₂ E_T           (20)

CASE STUDY

A synthetic rubber plant in Malaysia produces acrylonitrile (AN) and butadiene (BD) as byproducts generated from the reactor. The current practice is to send these wastes via a third party for offsite disposal. As both AN and BD possess a good low heating value (LHV), a WtE project is being considered to harvest their energy. Apart from reducing waste disposal and handling costs, the WtE project will reduce natural gas usage for steam and electricity production in the plant. This is done through a polygeneration system, where the harvested energy can be used for heating, cooling and electrical power. Note: A thermally driven refrigeration system (an absorption cooling system) may be integrated to provide cooling for the plant: this system essentially becomes an environmentally friendly trigeneration system. The generation of chemical wastes is summarized in TABLE 1.

 

The plant’s utilities consist of electricity, LPS at 3 bar and 150°C, and chilled water at 10°C. Since the absorption chiller system requires LPS as heat input for the chiller, extra LPS will be required. The required LPS for the stripper and the electricity demand of the plant are provided on a 1-mos basis, while the extra LPS required for the chiller system is calculated using a coefficient of the system’s performance. The plant’s electricity and process steam demands are summarized in TABLE 2.

 

The proposed configuration of the trigeneration system is illustrated in FIG. 4. It is assumed that two boilers with different operating conditions will be utilized in the trigeneration process. The first boiler (Boiler A) will be installed to produce VHPS (30 bar, 400°C) by combusting waste chemicals. As VHPS (from the combustion of waste chemicals) is insufficient, additional VHPS will be supplied through the combustion of natural gas in Boiler B to fulfill process sink. The requirement of natural gas (F_F ) may be calculated using a revised form of Eq. 11. The steam is then let down to a lower pressure to provide process heating and to generate power. The assumptions made for the trigeneration system design are listed in TABLE 3, while the detail for steam is provided in TABLE 4.

 

Due to the fluctuating nature of weekly utility requirements, this work only considers the maximum and minimum demands to study the range of TAC and TSP. The ATM results for maximum and minimum production are summarized in FIG. 5. Based on Eq. 11, the VHP production with waste combustion is determined in the range of 6,644 kg/hr–6,930 kg/hr for the period of 4 wk. This helps to reduce the dependency of external fuel (natural gas) for the generation of LPS for the heating and absorption chiller. When the plant is not operated at its maximum capacity, extra generated LPS will be sold to a neighboring plant for additional revenue.

FIG. 5. Steam cascade diagram across 4 wk, with maximum (left) and minimum (right) plant utility.

 

The targeted trigeneration potential lies between 684 kW and 808 kW, and the minimum VHP steam flowrate (F_S ) is between 10,184 kg/hr and 13,580 kg/hr. Using Eq. 11, a total of 643 kg/hr–858 kg/hr of natural gas is required (F_F ) to provide the excess steam required. When the plant is operated at maximum utility demand, no excess steam is generated (F_XS = 0 kg/hr). Conversely, there is 14,269 kg/hr–17,771 kg/hr of excess steam generation when the production plant is operating at minimum utility demand.

Optimization can be achieved by minimizing TAC of the trigeneration system in Eq. 7, subject to constraints in Eqs. 3–6. An additional constraint is included where the optimization is subjected to the maximum available AN and BD for the week. In this case, the optimization was performed for the maximum utility demand scenario only (left column of FIG. 5). Note: The optimization also yields the maximum attainable TSP of the system. FIG. 6 shows an interface of Excel to carry out the optimization, using the Solver function. Cell B16 (TAC) is set to minimize as the objective function, while cell F4 (F_S ) is set as the changing variable.

FIG. 6. Snapshot of Excel’s interface showing the optimization approach for Week 1.

 

The results of the optimization across the 4 wk are shown in FIG. 7. Generally, both TAC and TSP profiles exhibit similar trends to the LPS demand of the plant. The minimum TAC attained ranges between $2.593 MM/yr and $3.378 MM/yr. The lowest TAC is obtained during Week 2 because the extractable power is the lowest (683.86 kW) during that week. Conversely, the TSP of the trigeneration system is computed to range from $11.33 MM/yr–$11.967 MM/yr. Week 3 yielded the highest TSP for the system due to large extractable power (756.98 kW) and the highest supply of waste (6,794.28 kg/hr). These profiles are expected due to the large contribution of weekly steam consumption to TAC (TAC_Boil and C_Gen ) and TSP (C_S and C_X,s ). However, an additional constraint must be considered during system or equipment design practices. The optimization should be conducted for maximum weekly capacity—i.e., largest flowrate of fuel gas (F_F ), cumulative extractable power of the steam turbine at level k (E_k^C ) and natural gas boiler duty. The CDR caused by the trigeneration system was calculated by taking S₁ (Eq. 18) as 56,100 kg/TJ and S₂ as 0.6648 kg/kWh (Eq. 20).¹³ As a result, approximately 15.02 kT/yr–16.19 kT/yr of CO₂ reduction can be attained with a trigeneration system for this plant.

FIG. 7. Profile of TAC and TSP across 4 wk.

Takeaways. 

In this article, an ATM was applied to optimize a trigeneration system, using industrial waste (AN and BD) generated in a synthetic rubber plant. The ATM was performed against maximum and minimum utility demands to compute the trigeneration potential. Based on the amount of waste generated under maximum utility demand scenarios, the minimum TAC and maximum TSP were computed across 4 wk. The lowest TAC was $2.593 MM/yr (Week 2), while the highest TSP was $11.967 MM/yr (Week 3). Key parameters in the analysis were maximum steam demand and waste (as fuel) supply.

Due to the reduction in natural gas consumption, optimization studies revealed that 15.02 kT/yr–16.19 kT/yr of CO₂ emissions can be mitigated. However, this article only provides a conceptual engineering design for project feasibility evaluation. For future studies, other aspects such as waste heat loss, government subsidies (feed-in tariff) and sensitivity analysis should be considered to validate the implementation of the system. This model can be extended to any plant that generates waste with a promising lower heating value. Besides reducing CO₂ emissions and improving waste management practices, this approach proves to be economically attractive for decision-makers. HP

REFERENCES

1. Ebrahimi, M., “Cogeneration cycles,” Power Generation Technologies, January 2023.
2. El-Halwagi, M. M., Sustainable design through process integration, Elsevier, 2012.
3. El-Halwagi, M. M. and D. C. Y. Foo, “Process synthesis and integration,” Encyclopedia of Chemical Technology, December 2014.
4. Foo, D., Process Integration for Resource Conservation (Green Chemistry and Chemical Engineering), CRC Press, July 17, 2012.
5. Smith, R., Chemical Process Design and Integration, 2nd Ed., John Wiley & Sons Inc., September 2016.
6. Seider, W. D., et al., Product and Process Design Principles: Synthesis, Analysis and Evaluation, 4th Ed., John Wiley & Sons Inc., May 2016.
7. El-Halwagi, M., “Targeting cogeneration and waste utilization through process integration,” Applied Energy, June 2009.
8. Ng, R. T. L., et al., “Targeting for cogeneration potential and steam allocation for steam distribution network,” Applied Thermal Engineering, February 2017.
9. Yeo, Z. M. and D. C. Y. Foo, “Evaluation of cogeneration potential for a sulfuric acid recovery (SAR) plant,” Process Integration and Optimization for Sustainability, November 2018.
10. Chua, X. Y. and D. C. Y. Foo, “Optimization of cogeneration system and fuel inventory with automated targeting model,” Clean Technologies and Environmental Policy, July 2021.
11. Bruno, J. C., F. Fernandez, F. Castells and I. E. Grossmann, “A rigorous MINLP model for the optimal synthesis and operation of utility plants,” Chemical Engineering Research and Design, March 1998.
12. Towler, G. and R. Sinnott, Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design, Elsevier, 2021.

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