# Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes

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## Abstract

**:**

## 1. Introduction

#### 1.1. Economic Benefit from Integrated Scheduling and Control

- (i)
- Rapid fluctuations in dynamic product demand;
- (ii)
- Rapid fluctuations in dynamic energy rates;
- (iii)
- Dynamic production costs;
- (iv)
- Benefits of increased energy efficiency;
- (v)
- Necessity of control-level dynamics information for optimal production schedule calculation.

#### 1.2. Previous Work

#### 1.2.1. Integrating Process Dynamics into Scheduling

#### 1.2.2. Reactive Integrated Scheduling and Control

#### 1.2.3. Responsiveness to Market Fluctuations

#### 1.3. Purpose of This Work

## 2. Phases of Progressive Integration

#### 2.1. Phase 1: Fully Segregated Scheduling and Control

#### 2.2. Phase 2: Reactive Closed-Loop Segregated Scheduling and Control

#### 2.3. Phase 3: Open-Loop Integrated Scheduling and Control

#### 2.4. Phase 4: Closed-Loop Integrated Scheduling and Control Responsive to Market Fluctuations

#### 2.5. Mathematical Formulation

## 3. Case Study Application

#### 3.1. Process Model

- Constant volume;
- Well mixed;
- Constant density.

#### 3.2. Scenarios

- (A)
- Process disturbance $({C}_{A})$;
- (B)
- Demand disturbance;
- (C)
- Price disturbance.

## 4. Results

#### 4.1. Scenario A: Process Disturbance

#### 4.2. Scenario B: Market Update Containing Demand Fluctuation

#### 4.3. Scenario C: Market Update Containing New Product Selling Prices

## 5. Conclusions

#### Directions for Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ISC | integrated scheduling and control |

SSC | segregated scheduling and control |

MINLP | mixed-integer nonlinear programming |

NLP | nonlinear programming |

CSTR | continuous stirred tank reactor |

MIDO | mixed-integer dynamic optimization |

MILP | mixed-integer linear programming |

NMPC | nonlinear model predictive control |

ASU | air separation unit |

MMA | methyl methacrylate reactor |

FBR | fluidized bed reactor |

RTN | resource task network |

HIPS | high impact polystyrene reactor |

ASU | cryogenic air separation unit |

SISO | single-input single-output |

PFR | plug flow reactor |

PWA | piecewise affine |

DR | demand response |

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**Figure 1.**Phase 1: Open-loop scheduling determined once per day with no consideration of process dynamics. Closed-loop control implemented to follow the schedule.

**Figure 2.**Phase 2: Dual-loop segregated scheduling and control. Scheduling is recalculated reactively in the presence of process disturbances above a threshold or updated market conditions. Closed-loop control implements the schedule in the absence of disturbances.

**Figure 3.**Phase 3: Open-loop scheduling determined once per day with consideration of process dynamics and control structure in the form of grade transition information. Closed-loop control implemented to follow the schedule.

**Figure 4.**Phase 4: Closed-loop combined scheduling and control responsive to both process disturbances and updated market information.

**Table 1.**Economic benefit of integrated scheduling and control (ISC) over segregated scheduling and control (SSC) (CSTR: continuously stirred tank reactor; MMA: methyl methacrylate; DR: demand response; FRB: fluidized bed reactor; RTN: resource task network; ASU: air separation unit; HIPS: high-impact polystyrene; PFR: plug flow reactor; SISO: single-input single-output; MIMO: multiple-input multiple-output).

Author | Shows Benefit of ISC over SSC | Batch Process | Continuous Process | Example Application (s) |
---|---|---|---|---|

Baldea et al. (2015) [15] | X | CSTR | ||

Baldea et al. (2016) [16] | X | MMA | ||

Baldea (2017) [17] | X | DR chemical processes and power generation facilities | ||

Beal (2017) [18] | X | CSTR | ||

Beal (2017) [19] | X | CSTR | ||

Beal (2017a) [20] | X | CSTR | ||

Cai et al. (2012) [21] | X | Semiconductor production | ||

Capon-Garcia et al. (2013) [6] | X | 2 different batch plants (1-stage, 3-product & 3-stage, 3-product) | ||

Chatzidoukas et al. (2003) [22] | X | X | gas-phase polyolefin FBR. | |

Chatzidoukas et al. (2009) [23] | X | X | catalytic olefin copolymerization FBR | |

Chu & You (2012) [24] | X | MMA | ||

Chu & You (2013) [25] | X | CSTR | ||

Chu & You (2013a) [26] | X | polymerization with parallel reactors & 1 purification unit (RTN) | ||

Chu & You (2013b) [27] | X | X | 5-unit batch process | |

Chu & You (2013c) [28] | X | X | sequential batch process | |

Chu & You (2014) [29] | X | batch process (reaction task, filtration task, reaction task) | ||

Chu & You (2014a) [30] | X | 8-unit batch process | ||

Chu & You (2014b) [31] | X | X | 8-unit batch process | |

Dias et al. (2016) [32] | X | MMA | ||

Du et al. (2015) [33] | X | CSTR & MMA | ||

Flores-Tlacuahuac & Grossmann (2006) [34] | X | CSTR | ||

Flores-Tlacuahuac (2010) [8] | X | Parallel CSTRs | ||

Gutiérrez-Limón et al. (2011) [35] | X | CSTR | ||

Gutiérrez-Limón et al. (2016) [36] | X | CSTR & MMA | ||

Gutiérrez-Limón & Flores-Tlacuahuac (2014) [37] | X | CSTR | ||

Koller & Ricardez-Sandoval (2017) [38] | X | CSTR | ||

Nie & Bieglier (2012) [7] | X | X | flowshop plant (batch reactor, filter, distillation column) | |

Nie et al. (2015) [39] | X | X | polymerization with parallel reactors & 1 purification unit | |

Nystrom et al. (2005) [40] | X | industrial polymerization process | ||

Nystrom et al. (2006) [4] | X | industrial polymerization process | ||

Patil et al. (2015) [41] | X | CSTR & HIPS | ||

Pattison et al. (2016) [42] | X | X | ASU model | |

Pattison et al. (2017) [10] | X | ASU model | ||

Prata (2008) et al. [43] | X | medium industry-scale model | ||

Terrazas-Moreno et al. (2008) [44] | X | MMA (with one CSTR) & HIPS | ||

Terrazas-Moreno & Flores-Tlacuahuac (2007) [45] | X | HIPS & MMA | ||

Terrazas-Moreno & Flores-Tlacuahuac (2008) [9] | X | HIPS & MMA | ||

You & Grossmann (2008) [46] | X | medium and large polystyrene supply chaiins | ||

Zhuge & Ierapetritou (2012) [47] | X | CSTR & PFR. | ||

Zhuge & Ierapetritou (2014) [48] | X | simple and complex batch processes | ||

Zhuge & Ierapetritou (2015) [49] | X | SISO & MIMO CSTRs | ||

Zhuge & Ierapetritou (2016) [50] | X | X | CSTR & MMA |

Authors | Product Price Disturbance | Product Demand Disturbance | Process Variable Disturbance | Other Disturbances |
---|---|---|---|---|

Baldea et al. (2016) [16] | X | X | ||

Baldea (2017) [17] | X | |||

Cai et al. (2012) [21] | X | |||

Chu & You (2012) [24] | X | |||

Du et al. (2015) [33] | ||||

Flores-Tlacuahuac (2010) [8] | X | |||

Gutiérrez-Limón et al. (2016) [36] | X | |||

Kopanos & Pistikopoulos (2014) [56] | X | |||

Liu et al. (2012) [57] | X | X | ||

Patil et al. (2015) [41] | X | |||

Pattison et al. (2017) [10] | X | X | ||

Touretzky & Baldea (2014) [58] | Weather & energy price | |||

You & Grossmann (2008) [46] | X | |||

Zhuge & Ierapetritou (2012) [47] | X | |||

Zhuge & Ierapetritou (2015) [49] | X |

Parameter | Value |
---|---|

V | 100 m${}^{3}$ |

${E}_{A}/R$ | 8750 K |

$\frac{UA}{V\rho {C}_{p}}$ | 2.09 s${}^{-1}$ |

${k}_{0}$ | $7.2\times {10}^{10}$ s${}^{-1}$ |

${T}_{f}$ | 350 K |

${C}_{A0}$ | 1 mol/L |

$\frac{\Delta {H}_{r}}{\rho {C}_{p}}$ | −209 $\mathrm{K}\text{}{\mathrm{m}}^{3}\text{}{\mathrm{mol}}^{-1}$ |

q | 100 m${}^{3}$/h |

Product | ${\mathit{C}}_{\mathit{A}}$ | Max Demand | Price | Storage Cost |
---|---|---|---|---|

(mol/L) | (m${}^{3}$) | ($/m${}^{3}$) | ($/h/m${}^{3}$) | |

1 | 0.10 | 1000 | 22 | 0.11 |

2 | 0.30 | 1000 | 29 | 0.1 |

3 | 0.50 | 1000 | 23 | 0.12 |

Starting | Final Product | ||
---|---|---|---|

Product | 1 | 2 | 3 |

1 | 0 | 0.50 | 0.833 |

2 | 0.50 | 0 | 0.50 |

3 | 0.417 | 0.833 | 0 |

Scenario | Time | Disturbance | ||
---|---|---|---|---|

(h) | Product 1 | Product 2 | Product 3 | |

A | 2.2–3.8 | |||

B | 3.1 | +0 ${\mathrm{m}}^{3}$ | +200 ${\mathrm{m}}^{3}$ | +0 ${\mathrm{m}}^{3}$ |

C | 2.1 | +0 $/m^{3} | $-9$ $/m^{3} | +6 $/m^{3} |

Phase | Description | Profit | Production ${(\mathbf{m}}^{3})$ | |||
---|---|---|---|---|---|---|

($) | (%) | Product 1 | Product 2 | Product 3 | ||

1 | Segregated, Fixed Schedule | 3114 | ($-38\%$) | 367 | 858 | 908 |

2 | Segregated, Reactive Schedule | 3942 | ($-21\%$) | 317 | 900 | 992 |

3 | Integrated, Fixed Schedule | 4983 | (+0%) | 308 | 1000 | 983 |

4 | Integrated, Reactive Schedule | 7103 | (+43%) | 308 | 1000 | 983 |

Phase | Description | Profit | Production $({\mathbf{m}}^{3})$ | |||
---|---|---|---|---|---|---|

($) | (%) | Product 1 | Product 2 | Product 3 | ||

1 | Segregated, Fixed Schedule | 6033 | ($-19\%$) | 367 | 967 | 908 |

2 | Segregated, Reactive Schedule | 7446 | (+0.1%) | 133 | 1200 | 908 |

3 | Integrated, Fixed Schedule | 7441 | (+0%) | 317 | 1000 | 992 |

4 | Integrated, Reactive Schedule | 8676 | (+17%) | 308 | 1200 | 800 |

Phase | Description | Profit | Production $({\mathbf{m}}^{3})$ | |||
---|---|---|---|---|---|---|

($) | (%) | Product 1 | Product 2 | Product 3 | ||

1 | Segregated, Fixed Schedule | 3758 | ($-16\%$) | 367 | 967 | 908 |

2 | Segregated, Reactive Schedule | 4879 | (+9%) | 967 | 367 | 908 |

3 | Integrated, Fixed Schedule | 4466 | (+0%) | 317 | 1000 | 992 |

4 | Integrated, Reactive Schedule | 5662 | (+27%) | 1000 | 317 | 992 |

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## Share and Cite

**MDPI and ACS Style**

Beal, L.D.R.; Petersen, D.; Pila, G.; Davis, B.; Warnick, S.; Hedengren, J.D.
Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes. *Processes* **2017**, *5*, 84.
https://doi.org/10.3390/pr5040084

**AMA Style**

Beal LDR, Petersen D, Pila G, Davis B, Warnick S, Hedengren JD.
Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes. *Processes*. 2017; 5(4):84.
https://doi.org/10.3390/pr5040084

**Chicago/Turabian Style**

Beal, Logan D. R., Damon Petersen, Guilherme Pila, Brady Davis, Sean Warnick, and John D. Hedengren.
2017. "Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes" *Processes* 5, no. 4: 84.
https://doi.org/10.3390/pr5040084