# A Holistic Methodology for Optimizing Industrial Resource Efficiency

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## Abstract

**:**

## 1. Background

- developing methodologies for total site heat, mass, and power integration by considering potential heat and mass recovery technologies;
- incorporating sustainability and environmental criteria within the optimization framework;
- designing optimal hot water and hot oil loops;
- developing multi-period, multi-objective methodologies to address the eminent trade-offs among social, environmental, and financial drivers; and,
- giving priority to hybrid (conceptual–mathematical) methodologies to overcome the main drawback of mathematical approaches by including industrial and practical insights.

## 2. Problem Definition and Proposed Approach

**P**, (or clusters within each plant). Each site i has a set of water unit operations (demands:

**WAN**${}_{i,in}$, sources:

**WAN**${}_{i,out}$) and a set of thermal streams (hot:

**HS**${}_{i}$, cold:

**CS**${}_{i}$). Direct heat or mass exchanges are not allowed between sites (for practical reasons). Mass exchange is managed via the water network by incorporating several tanks which also handle cooling requirements. Heat exchange is managed via addition of several heat transfer vectors, such as steam cycle, ORC, heat pump, and water network. ORC and steam cycles can both be used to transfer heat by evaporating and condensing between sites while producing electricity where a pressure difference exists. The cooling system is modeled as part of the water network. Inter-site and inter-plant operations are essentially the same in terms of modeling (i.e., restricted exchanges of heat and resources except via a (de)centralized utility hub) which can both be addressed by the proposed superstructure.

## 3. Kraft Process

- burning of organic materials to produce water and CO${}_{2}$ which are more environmentally benign;
- recovering the energy content of the burnt organic materials in the hot flue gases to run turbo-generators or to satisfy the steam demands of the mill;
- restoration of inorganic chemicals in black liquor as chemical pulping agents; and
- recovery of by-products, e.g., tall oil and turpentine.

## 4. Data Extraction and Problem Formulation

- Only the temperature and maximum allowed inlet and outlet contaminations must be extracted from water unit operations, such as bleaching or washing. The proposed MILP superstructure [17] will consider all thermal stream possibilities within the water network.
- Successive heat exchangers without any stream splitting are combined into a single stream (e.g., three phases of a cold stream consisting of pre-heating, evaporation, and superheating are modeled as one stream). Phase changes are still considered with the corresponding heat load.
- Many process hot thermal streams in the current mill are part of the water network (i.e., being cooled down). Those with unknown (i.e., unmeasured) thermodynamic characteristics are replaced by their associated cooling water stream. This approach adds two water unit operations to the overall problem (i.e., a demand and a supply).

#### 4.1. Data Classification

**Cold process streams**: Nineteen (19) cold process streams exist in the mill (Table A2). Among these, the heat loads of the air pre-heater and black liquor heater are proportional to the size of the recovery boiler and hence were modeled as part of the black liquor furnace (Section 4.2.1).**Hot process streams**: Twenty (20) hot process streams are cooled in the mill (Table A3). After combining heat exchangers in series, fifteen (15) hot streams should be considered. As an example, the primary, secondary and inlet/outlet condensers in the evaporation section are modeled as 9.9 kg/s of saturated steam at 1.9 bar. Among these hot streams, five (5) represent several equipment cooling duties where temperatures of the hot sides are unknown (or uncertain), such as the bearing cooler, pulp machine cooler, and fan cooler. These heat exchangers were each modeled as two water unit operations, source and sink.**Waste thermal streams**: There are four (4) waste hot streams that can be recovered for heating purposes (Table A5).**Hot utility**: Highly concentrated black liquor is burnt in a recovery boiler to produce steam at 60 bar. The steam is passed through steam turbines to generate electricity. The process steam demands are satisfied using three pressure levels: high (10–12 bar), medium (5 bar), and low (1 bar) pressures (see Section 4.2.1).**Water unit operations**: Fourteen (14) water unit operations were extracted for this case study (Table A4, thirteen (13) demands and six (6) sources of water at various temperatures). One major issue in developing a mathematical model of water recycling is the availability of quantitative data on the contamination levels of water streams. To overcome this issue, several restrictions are discussed and imposed. In addition to the method described by Kermani et al. [17] (step 2), which is used to forbid or restrict specific mass exchanges, a level of quality is defined for each water unit operation (source/sink) using binary parameters. To address this, the following constraint was added to the model:$$\begin{array}{cccc}\hfill {\displaystyle \sum _{i\in {\mathbf{WAN}}_{out}}}{\dot{\mathbf{m}}}_{i,j}\xb7{\mathrm{q}}_{i}& \ge {\dot{\mathbf{m}}}_{j}\xb7{\mathrm{q}}_{j}\hfill & \hfill \phantom{\rule{1.em}{0ex}}& \forall j\in {\mathbf{WAN}}_{in}\hfill \end{array}$$▹ Direct recycling within each tank is forbidden.▹ The outlet of the pulp machine cannot be directly reused.▹ Consequently, the white water tank was modeled to recycle white water to the pulp machine.▹ The outlet of the vacuum pump cannot be recycled in the bleaching section.▹ The outlet of the cooling water cooler cannot be sent to wastewater disposal.▹ Freshwater cannot be used to dilute or (directly) cool wastewater.**Water network**: Freshwater is available at 20 ${}^{\circ}$C. Wastewater disposal is at 30 ${}^{\circ}$C. The water pathways through the plant are managed by three tanks, namely, treated warm water (28 ${}^{\circ}$C), raw warm water (52 ${}^{\circ}$C), and treated hot water (60 ${}^{\circ}$C). Their temperatures are due to the current operating conditions of the mill and are defined as variables in the optimization.

#### 4.2. Problem Formulation

**DG**cluster: Digester cluster, which includes the digester, washing, and recausticization units, and represents the process of breaking down wood chips for pulp production.**PM**cluster: Pulp machine cluster, which encompasses the pulp machine, bleaching, and ClO${}_{2}$ units and represents the industrial site for producing market-value pulp.**RB**cluster: Recovery boiler cluster, which encompasses evaporation, concentration, and recovery boiler units. It represents the steam production section and the process of regenerating chemicals for green liquor production.

#### 4.2.1. Recovery Boiler

#### 4.2.2. Steam Cycle

- Steam production can only happen at the highest pressure level.
- Turbines are placed between the highest pressure and subsequent lower pressures.

#### 4.2.3. Cooling Water System

#### 4.3. Solution Strategy

- Kermani [18] proposed an iterative three-step sequential solution strategy for targeting and designing HIWANs where problems
**P1**and**P2**were formulated as MILP models to target utility consumptions and provide potential thermal matches. Problem**P3**was proposed and formulated as a nonlinear programming (NLP) problem to optimize the operating conditions, i.e., temperatures and flows, in the HIWAN subject to thermal matches of problem**P2**and utility targets of problem**P1**. In addition, the heat recovery approach temperature (HRAT) in the water network was optimized by iteratively changing its value and selecting the best solution among all. Temperatures of water tanks could also be optimized as part of problem**P3**. - Kermani et al. [16] proposed a decomposition solution strategy and a novel superstructure for the optimal integration of ORCs into industrial processes addressing fluid selection, operating condition determination, and equipment sizing. The solution strategy uses a decomposition approach with the upper level handled by a GA in which the working fluid and its operating conditions are optimized. The lower level optimization applies a sequential solution strategy to solve the optimal ORC architecture and equipment sizes using a deterministic MILP model (similar formulation to problem
**P1**in [18]) and to provide a set of potential thermal matches by solving problem**P2**([33,34,35]).

**P1**can include ORC and steam cycle superstructures with fixed operating conditions to maintain linearity. Problem

**P2**is the heat load distribution (HLD) model and remains unchanged. To optimize the operating conditions of the ORC and steam cycle, GA is implemented in a similar way as presented in [16]. However, in addition to decision variables of ORC and steam cycle superstructures, HIWAN variables can be addressed, including water tank temperatures and HRAT. As the aim of the proposed methodology is not to provide a detailed design of HEN, problems

**P3**${}_{init}$ and

**P3**can be eliminated at this stage. Estimating the HEN cost is carried out as described in [16]. The objectives of the solution strategy are considered to be maximizing electricity production, minimizing freshwater consumption, and minimizing the annualized investment cost.

## 5. Preliminary Analysis

#### 5.1. Current Operating Conditions

#### 5.2. Thermal Integration

#### 5.3. ORC and Potential Working Fluids

- the critical temperature of working fluids is limited between 100–240 ${}^{\circ}$C;
- the global warming potential (GWP) of working fluids is limited to 200;
- working fluids with a flammability hazard [36] higher than 2 are excluded;
- fluids, such as R21 and R123 that are being phased out for environmental reasons are excluded.

## 6. Results and Discussion

**P1**and

**P2**ranging between 3–130 s. On average, 2000 evaluations could be performed in a 24-h time horizon. The objective function of problem

**P1**was selected to be the weighted total annualized cost (TAC) to better explore the trade-off between operating and investment costs [16]:

**P1**and

**P2**. Each instance of problem

**P1**had 1129–1359 binary variables and 7588–9053 constraints. In contrast, problem

**P2**consisted of 101–361 binary variables (i.e., potential thermal matches) and 1021–3012 constraints. The number of solutions in each generation of GA was fixed at 400 to reduce the number of mutations and crossovers while maintaining diversity within the Pareto frontier. In what follows, the last two generations (after 80,000 function evaluations) are combined and presented.

#### 6.1. Pareto Frontiers

- increased heat recovery among hot and cold process streams which reduced the steam demand of the processes, resulting in higher amount of steam available for the turbines. In addition, the condensation temperature at the outlet of turbines (consequently the pressure) was lower in these cases;
- higher pressure and temperature of the produced steam in the recovery boiler;
- better water management among clusters that resulted in reduced cooling duties and hence less heat sent to the environment which is valorized via ORC or the process itself; and,
- use of ORC to further increase the net electricity production.

#### 6.2. Analysis

#### 6.2.1. Visualization of all Solutions by Several Indicators

- The treated warm water tank temperature was mainly influenced by the return temperature of the cooling tower, i.e., it fluctuated around 26 ${}^{\circ}$C.
- For solutions with lower electricity production, the temperature of the treated hot water tank was in higher ranges (62–64 ${}^{\circ}$C). This is due to heat recovery using hot water loops among clusters. Furthermore, the freshwater flow was higher for these solutions which was due to higher cooling loads in the cooling tower and hence higher demand of make-up water.
- The steam production in the recovery boiler occurred at very high pressure levels (150–160 bar) for high power output. As mentioned in Section 4.2.1 this level of pressure does not pose any upgrade work and hence does not influence the investment cost of the system. For lower power outputs, the pressure was lower, and no ORC was integrated within the process (Figure 8).
- Higher electricity production required more stream matches and higher heat exchange areas indicating a highly integrated system.
- For high cooling loads, the temperature of cooling water was lower (around 35–40 ${}^{\circ}$C). The reason can be attributed to lower cost of heat exchangers in these cases due to higher approach temperatures.

#### 6.2.2. Extreme Points

#### 6.2.3. Cooling Utility, Freshwater Consumption, and Net Power Output

#### 6.3. Heat Integration and Heat Load Distribution

- Pareto frontier of the investment cost vs. the net power output: to position the selected solution with respect to all the solutions based on the values of the three objectives;
- parallel coordinates: similar to Figure 9, to highlight the value of other indicators of the selected solution with respect to all solutions;
- integrated grand composite curve: to illustrate how a steam cycle and/or ORC are integrated with other processes, and how heat is transferred among the three clusters;
- HLD: to find potential thermal matches prior to the HEN design. Several HLD configurations are available for any solution of problem
**P1**. For each of these configurations, large heat exchanges can be identified as potential opportunities for further economic, physical, and thermodynamic feasibility evaluation. This requires deep knowledge of the process and hence should be performed in collaboration with mill personnel. In this section, only the first solution of problem**P2**is presented. Furthermore, several heat recovery opportunities are extracted; however, the likelihood of implementation is not discussed here.

#### 6.3.1. Case I—No ORC Integration

**PM**cluster. This necessitates increased use of steam at higher pressure and consequently lower electricity production. Within each cluster, the HLD solutions show the potential connections among thermal streams and their associated heat loads (Figure 13). All these connections satisfy the energy and water targets of the solution of problem

**P1**. Multiple types of heat exchange can be distinguished by looking at the HLD results including new heat recovery opportunities by the use of a black liquor flash tank (hot stream) in the steaming vessel (

**DG**cluster: 5.48 MW${}_{th}$) and pre-heating water at the inlet of washing (

**DG**cluster: 4.48 MW${}_{th}$). Furthermore, low temperature heating demands such as the ClO${}_{2}$ heater in the bleaching section can be satisfied using hot water loops instead of consuming steam by transferring excess heat from the

**RB**cluster via water tanks.

#### 6.3.2. Case II—Maximum Electricity Production

**PM**cluster, while three condensation levels of the ORC supplied the heating requirements in this cluster.

**PM**cluster: 2.94 MW${}_{th}$). Furthermore, in the

**RB**cluster, opportunities exist in heat recovery between the condenser of the multi-effect evaporation and pre-heating the inlet of the concentration section (15.43 MW${}_{th}$ out of 16.22 MW${}_{th}$ demand) that must be evaluated by mill experts. It should be noted that in the current state of the mill, pre-heating is conducted by using steam while cooling is carried out using freshwater at 20 ${}^{\circ}$C. This heat recovery opportunity, alone, brings a reduction of 11.7% in steam demand while reducing freshwater consumption by 122.2 kg/s. Assuming that the reduced steam can be used to produce electricity with an efficiency of 24% (between 54.8 and 1 bar, conditions in the current state) and taking into account the water required to cool the condenser of the steam cycle, this simple heat recovery opportunity yields a payback time of 0.7 years. Analyzing the HLD encourages better assessment of reduction projects before detailed system design.

#### 6.3.3. Case III—ORC with Isobutene

## 7. Conclusions

**P3**to further optimize the temperature and flowrates of the HIWAN or in a comprehensive MINLP model as very good initialization points. A complex system such as an industrial mill cannot be fully designed by use of strict mathematical programming tools and requires human intervention at various stages to check, analyze, adapt, and improve the process. The proposed multi-stage approach in this paper offers this possibility with the help of various graphical tools at different stages. For improving the solution strategy, interesting future work can also focus on development of hybrid GAs which can account for human insight at various levels of the evolution towards improving the generation of solutions and accelerating the solution strategy. Implementing any of the solutions will affect the application of future energy efficiency measures or considerations and thus it is important to perform a holistic study which also includes potential changes or extensions to the system boundary by addressing network flexibility before making detailed designs.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$\mathsf{\Delta}{T}_{min}$ | heat exchanger minimum approach temperature |

adt | air-dried tons |

GA | genetic algorithm |

GWP | global warming potential |

HEN | heat exchanger network |

HIWAN | heat-integrated water allocation network |

HLD | heat load distribution |

HRAT | heat recovery approach temperature |

MER | minimum energy requirement |

MILP | mixed-integer linear programming |

MINLP | mixed-integer nonlinear programming |

NLP | nonlinear programming |

ORC | organic Rankine cycle |

TAC | total annualized cost |

## Appendix A. Kraft Pulp Mill Data

#### Appendix A.1. Water Tanks

Water Tank | Abbreviation | Current Temperature (${}^{\circ}$C) |
---|---|---|

Fresh water | FW | 20 |

Treated warm water | TWW | 28 |

Raw warm water | RWW | 52 |

Treated hot water | THW | 60 |

Waste water | WW | 30 |

#### Appendix A.2. Cold Process Streams

Section/Stream ID | Type * | ${\mathbf{T}}_{\mathit{in}}$[${}^{\circ}$C] | ${\mathbf{T}}_{\mathit{out}}$[${}^{\circ}$C] | Heat Load [kW] | Remarks |
---|---|---|---|---|---|

Digester | |||||

Chip bin heater | C | 20 | 55 | 3290 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Steaming vessel | C | 55 | 123 | 13,583 | |

Upper liquor heater | C | 122 | 150 | 4810 | |

Lower liquor heater | C | 146 | 160 | 5750 | |

Washer liquor heater | C | 126 | 165 | 4060 | |

Black liquor flash tank 1 | H | 128 | 128 | 5350 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Black liquor flash tank 2 | H | 93 | 93 | 9960 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Turpentine condenser | H | 123.25 | 60 | 1916 | $\mathsf{\Delta}{T}_{min}$/2 = 3, at 2.2 bar |

Bleaching | |||||

Steam mixer 1 | C | 70 | 75 | 1860 | |

Pulp heater | C | 75 | 77 | 2520 | |

Steam mixer 2 | C | 72 | 80 | 2630 | |

Steam mixer 3 | C | 73 | 87 | 3100 | |

ClO${}_{2}$ heater | C | 5 | 43 | 4183 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Pulp machine | |||||

Wash water heater | C | 66 | 88 | 1640 | |

Dryer | C | 42 | 95 | 26,510 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Room air pre-heater | C | 21 | 25 | 210 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Dryer exhaust - chimney | H | 92 | 68 | 4745 | |

Evaporators, concentrators, and recovery boiler | |||||

Evaporator heater (1st) | C | 119 | 139 | 33,390 | |

Concentrator heater | C | 106 | 111 | 16,220 | |

Boiler air pre-heater | C | 32 | 110 | 6240.6 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Black liquor heater | C | 111 | 129 | 1300 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

Stripping and ClO_{2} | |||||

Stripping column heater | C | 97 | 155 | 4457 | |

ClO2 heater before reactor | C | 65 | 75 | 3170 | $\mathsf{\Delta}{T}_{min}$/2 = 3 |

#### Appendix A.3. Hot Process Streams

#### Appendix A.4. Water Unit Operations

Section | From | To | Type | ${\mathbf{T}}_{\mathit{in}}$ [${}^{\circ}$C] | ${\mathbf{T}}_{\mathit{out}}$ [${}^{\circ}$C] | Heat Load [kW] |
---|---|---|---|---|---|---|

Evaporators (modeled as steam at 1.9 bar, 9.932 kg/s, $\mathsf{\Delta}{T}_{min}$/2 = 3) | ||||||

Primary condenser | FWT | FHD | W | 20 | 50 | 22,650 |

H | 119 | 55 | ||||

Secondary condenser | FWT | FHD | W | 20 | 30 | 2360 |

H | 119 | 30 | ||||

Inter/after condenser | FWT | FWT | W | 20 | 30 | 600 |

H | ||||||

Flash Heat Double (FHD) (modeled as steam at 0.25 bar, 4.628 kg/s, $\mathsf{\Delta}{T}_{min}$/2 = 3) | ||||||

Flash heat double cooler | - | RWWT | W | 46 | 54 | 9045 |

H | 65 | 65 | ||||

Non-condensable gas cooler | FWT | FWT | W | 21 | 25 | 460 |

H | 81 | 81 | ||||

Inter/After condenser | FWT | FWT | W | 1340 | ||

H | 30 | 30 | ||||

Recausticizing | ||||||

Green liquor cooler | FWT | FWT | W | 20 | 33 | 364 |

H | 93 | 30 | ||||

Bearing cooler | FWT | THWT | W | 20 | 31 | 385 |

H | 80 | 40 | ||||

Pulp Machine | ||||||

Water cooler | FWT | Press shower | W | 20 | 25 | 70 |

H | 120 | 105 | ||||

Cooler | FWT | Economizer | W | 20 | 36 | 1605 |

H | 46 | 30 | ||||

Stripping (modeled as steam at 1 bar, 1.983 kg/s, $\mathsf{\Delta}{T}_{min}$/2 = 3) | ||||||

Reflux condenser | FWT | RWWT | W | 20 | 60 | 4634 |

H | 101 | 81 | ||||

Recovery Boiler | ||||||

Main surface condenser | TWWT | THWT | W | 28 | 78 | 13,672 |

H | 89 | 88 | ||||

Auxiliary surface condenser | TWWT | THWT | W | 28 | 70 | 3700 |

H | 89 | 88 | ||||

Fan cooler | TWWT | THWT | W | 28 | 38 | 1346 |

H | 48 | 38 | ||||

Washing | ||||||

Cold blow cooler | FWT | FWT | W | 20 | 34 | 2930 |

H | 77 | 70 | ||||

Miscellaneous cooling | FWT | FWT | W | 20 | 26 | 3360 |

H | - | - |

Inlet Conditions | Unit | Outlet Conditions | ||||
---|---|---|---|---|---|---|

Flow [kg/s] | ${\mathbf{T}}_{\mathit{in}}$ [${}^{\circ}$C] | ${\mathbf{T}}_{\mathit{out}}$ [${}^{\circ}$C] | Flow [kg/s] | |||

3.7 | 20 | $-\u25b8$ | digester—chip bin vent | $-\u25b8$ | 60 | 3.7 |

69 | 60 | $-\u25b8$ | bleaching | |||

29.8 | 20 | $-\u25b8$ | ClO${}_{2}$—absorption | |||

6.7 | 20 | $-\u25b8$ | ClO${}_{2}$—shower | |||

33.3 | 20 | $-\u25b8$ | ClO${}_{2}$—indirect contact cooler (ICC) | |||

16.5 | 20 | $-\u25b8$ | ClO${}_{2}$—barometric condenser | |||

16.7 | 20 | $-\u25b8$ | recausticizing—vacuum pump | $-\u25b8$ | 36 | 16.7 |

6.7 | 60 | $-\u25b8$ | recausticizing—pressure disc filter | |||

48 | 20 | $-\u25b8$ | pulp machine—vacuum pump | $-\u25b8$ | 36 | 48 |

6.5 | 45 | $-\u25b8$ | pulp machine—shower | |||

578 | 71 | $-\u25b8$ | pulp machine—recycled white water | $-\u25b8$ | 66 | 666 |

69 | 60 | $-\u25b8$ | washing | |||

16 | 28 | $-\u25b8$ | smelt spout | $-\u25b8$ | 45 | 16 |

contaminated condensate | $-\u25b8$ | 85 | 22 |

#### Appendix A.5. Waste Thermal Streams

Section/Stream ID | ${\mathbf{T}}_{\mathit{in}}$ (${}^{\circ}$C) | ${\mathbf{T}}_{\mathit{out}}$ [${}^{\circ}$C] | Heat Load [kW] |
---|---|---|---|

Bleaching | |||

Alkaline bleach effluent | 82 | 35 | 14,852 |

Acid bleach effluent | 71 | 35 | 11,492 |

Pulp machine | |||

Dryer exhaust | 68 | 35 | 9643 |

Evaporators | |||

Combined condensate | 89 | 35 | 4608 |

#### Appendix A.6. Thermal Utilities

Utility | Pressure (bar) | Temperature (${}^{\circ}$C) |
---|---|---|

Steam #60 | 5.13 | 198 |

Steam #160 | 12 | 228 |

Freshwater | - | 20 |

## Appendix B. Assumptions and Solver Options

Solver Option | Value | Description (Mainly from Respective Solver’s Manual) | |
---|---|---|---|

Genetic Algorithm | |||

Population size | 400 | Number of initial population | |

Initialization type | unique_random | Creating random initial solutions but enforce uniqueness | |

Crossover type | multi_point_real 1 | Performing a variable switching crossover routing at 1 crossover point in the real valued genome of two designs | |

Crossover rate | 0.8 | Probability of the crossover event | |

Mutation type | bit_random | Performing mutation by flipping a random bit of a randomly chosen design variable | |

Mutation rate | 0.2 | Probability of the mutation event | |

Convergence type | metric_tracker | Converge if metric is below “percent_change” (0.01) for a given consecutive generations (10) | |

Fitness type | domination_count | below_limit = 1; Ranking based on number of dominations | |

Niching type | max_designs = 0.02 | encourage differentiation along the Pareto frontier. Minimum distance between any two points is set at 2% | |

num_designs = 400 | Limit the number of solutions that remain in each generation to 400 | ||

Number of evaluations | 60,000 | Maximum number of evaluations (a convergence criterion) | |

Number of generations | 100 | Maximum number of generations (a convergence criterion) | |

AMPL | |||

reset_initial_guesses | 1 | Reset variables to their initial values between different calls to solve command | |

presolve_eps | variable | Maximum difference between lower and upper bounds in constraint violations; 10${}^{-4}$ (P1) and 10${}^{-6}$ (P1) | |

presolve | 1 | Simplifying problem prior to the solver by fixing variables and dropping redundant constraints | |

P1 (CPLEX) | |||

mipgap | 5 10${}^{-3}$ | Relative tolerance for optimizing integer variables: | |

stop if abs((best bound) - (best integer)) < mipgap * (1 + abs(best bound)) | |||

integrality | 10${}^{-9}$ | Amount by which an integer variable can differ from the nearest integer and still be considered feasible. | |

timelimit | 120 | Time limit in seconds | |

P2 (CPLEX) | |||

mipgap | 10${}^{-2}$ | (see above) | |

integrality | 10${}^{-8}$ | (see above) | |

flowcuts | 1 | Aggressive use of flow cuts in solving MIP | |

mircuts | 1 | Moderate generation of MIP rounding cuts | |

dgradient | 2 | Pricing algorithm for dual simplex (2 = steepest-edge pricing) | |

timelimit | 60 | (see above) |

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**Figure 1.**Schematic of the proposed mathematical superstructure for combined heat, mass, and power integration in industrial processes.

**Figure 4.**Cold (

**a**) and hot (

**b**) grand composite curves of considered clusters for kraft case study, reflecting current consumption.

**Figure 7.**Visualization of key indicators of solution of the Pareto frontiers (color spectrum is based on electricity production column).

**Figure 12.**Results of case I: position on Pareto frontier (top left) and on parallel coordinates (top right), and integrated grand composite curves (bottom).

**Figure 13.**Heat load distribution of case I (circle sizes are proportional to the heat exchange rate).

**Figure 14.**Results of case II: position on Pareto frontier (top left) and on parallel coordinates (top right), and integrated grand composite curves (bottom).

**Figure 15.**Heat load distribution of case II (circle sizes are proportional to the heat exchange rate).

**Figure 16.**Results of case III: position on Pareto frontier (top left) and on parallel coordinates (top right), and integrated grand composite curves (bottom).

**Figure 17.**Heat load distribution of case III (circle sizes are proportional to the heat exchange rate).

**Table 1.**Parameters for recovery boiler [32].

Parameters | Unit | Value |
---|---|---|

Solid content of black liquor | % | 75 |

Adiabatic combustion temperature | ${}^{\circ}$C | 1500 |

Flue gas outlet temperature | ${}^{\circ}$C | 120 |

Boiler thermal efficiency | - | 0.888 |

Air to fuel ratio | 4.196 | |

Lower heating value of black liquor | kJ/kg | 12,250 |

The highest temperature that furnace can reach (radiation temperature) ${}^{*}$ | ${}^{\circ}$C | 1000 |

Temperature of preheated air at the furnace inlet | ${}^{\circ}$C | 110 |

Available heat for steam production (removing air pre-heating) | kJ/kg | 10,880.2 |

**Table 2.**Parameters for wet open recirculating cooling systems [25].

Parameters | Unit | Value |
---|---|---|

Wet bulb temperature | ${}^{\circ}$C | 18 |

Approach temperature | ${}^{\circ}$C | 8 |

Make-up water | m${}^{3}$/hr/MW${}_{th}$ | 2 |

Specific electricity consumption | kW/MW${}_{th}$ | 30 |

**Table 3.**Freshwater (20 ${}^{\circ}$C) consumers in the kraft mill (under the current operating conditions).

Section | Unit | Value [kg/s] |
---|---|---|

ClO${}_{2}$ plant | all water unit operations | 86.3 |

Recausticization | bearing cooler and vacuum pump | 25.0 |

green liquor cooler | 6.6 | |

Pulp machine | cooler and vacuum pump | 71.9 |

cooler and shower | 9.8 | |

Washing | miscellaneous cooling | 183.2 |

Digester | chip bin vent and turpentine condenser | 15.1 |

Evaporation | reflux and last effect condensers | 277.8 |

Concentrator | non-condensable gas and FHD coolers | 59.3 |

Recovery boiler | surface condenser | 86.1 |

Total | 821.1 |

Variables | Range | Unit | Type/Increment | Description/Remarks |
---|---|---|---|---|

$\kappa $ | [0:0.5] | - | continuous | Total annualized cost weight factor; the range is limited to 0.5 to emphasize reduction in operating cost (Equation (2)); |

${P}_{{}_{1}}^{st}$ | [50:160] | bar | step of 0.1 | Boiler pressure; the upper bound is limited to reported values for a typical steam power plant; |

${P}_{{}_{2}}^{st}$ | [9:14] | bar | step of 0.1 | High-pressure steam header |

${P}_{{}_{3}}^{st}$ | [3:8] | bar | step of 0.1 | Medium-pressure steam header |

${P}_{{}_{4}}^{st}$ | [0.5:2] | bar | step of 0.1 | Low-pressure steam header |

$\mathsf{\Delta}{T}_{{}_{1}}^{{}^{sup}}$ | [150:300] | ${}^{\circ}$C | continuous | Degree of superheating in the highest pressure level |

Based on the ORC superstructure proposed in [16] | ||||

${\zeta}_{{}_{1,fw}}^{ORC}$ | [0.25:1] | - | continuous | Pressure level 1 in ORC, ${P}_{{}_{1,fw}}^{ORC}={P}_{{}_{wf}}^{{}^{max}}(1-{\zeta}_{{}_{1,fw}}^{ORC})$, where ${P}_{{}_{wf}}^{{}^{max}}={P}_{wf,cr}$, |

${\zeta}_{{}_{2,fw}}^{ORC}$ | [0:1] | - | continuous | Pressure level 2 in ORC, ${P}_{{}_{2,fw}}^{ORC}={P}_{{}_{1,fw}}^{ORC}(1-{\zeta}_{{}_{2,fw}}^{ORC})$ |

${\zeta}_{{}_{3,fw}}^{ORC}$ | [0:1] | - | continuous | Pressure level 3 in ORC, ${P}_{{}_{3,fw}}^{ORC}={P}_{{}_{2,fw}}^{ORC}(1-{\zeta}_{{}_{3,fw}}^{ORC})$ |

${P}_{{}_{4,fw}}^{ORC}$ | [1:16] | bar | continuous | Lowest pressure level in ORC; for selected fluids and given water temperature 20–30 ${}^{\circ}$C |

${T}_{{}_{2,1}}^{{}^{trh,in,ORC}}$ | [−10:1] | ${}^{\circ}$C | integer | Degree of reheating relative to the temperature of pressure level 1; it is assumed that only first and second pressure levels are turbines inlets. |

$\mathsf{\Delta}{T}_{{}_{1}}^{{}^{sup,ORC}}$ | [0:20] | ${}^{\circ}$C | integer | Amount of superheating at highest pressure level p1 |

$\mathsf{\Delta}{T}_{{}_{2}}^{{}^{sup,ORC}}$ | [0:20] | ${}^{\circ}$C | integer | Amount of superheating at pressure level p2 |

$wf$ | [1:3] | - | integer | Working fluids for the case study; ammonia, R1234ze(Z), isobutene |

HRAT${}^{\mathrm{water}}$ | [1:10] | ${}^{\circ}$C | integer | HRAT for water streams; the contribution of water thermal stream to the overall HRAT is half of this value. |

${T}_{tww}^{\mathrm{water}}$ | [25:39] | ${}^{\circ}$C | step of 0.1 | Temperature of treated warm water tank |

${T}_{thw}^{\mathrm{water}}$ | [55:65] | ${}^{\circ}$C | step of 0.1 | Temperature of treated hot water tank |

${T}_{rww}^{\mathrm{water}}$ | [40:55] | ${}^{\circ}$C | step of 0.1 | Temperature of raw warm water tank |

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## Share and Cite

**MDPI and ACS Style**

Kermani, M.; Kantor, I.D.; Wallerand, A.S.; Granacher, J.; Ensinas, A.V.; Maréchal, F.
A Holistic Methodology for Optimizing Industrial Resource Efficiency. *Energies* **2019**, *12*, 1315.
https://doi.org/10.3390/en12071315

**AMA Style**

Kermani M, Kantor ID, Wallerand AS, Granacher J, Ensinas AV, Maréchal F.
A Holistic Methodology for Optimizing Industrial Resource Efficiency. *Energies*. 2019; 12(7):1315.
https://doi.org/10.3390/en12071315

**Chicago/Turabian Style**

Kermani, Maziar, Ivan D. Kantor, Anna S. Wallerand, Julia Granacher, Adriano V. Ensinas, and François Maréchal.
2019. "A Holistic Methodology for Optimizing Industrial Resource Efficiency" *Energies* 12, no. 7: 1315.
https://doi.org/10.3390/en12071315