Self-optimizing control structure and dynamic behavior for CO2

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Process Systems Engineering

Self-optimizing control structure and dynamic behavior for CO2 compression and purification unit in oxy-fuel combustion application Kaile Liu, Bo Jin, Yunlei Zhao, and ZhiWu Liang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b00121 • Publication Date (Web): 30 Jan 2019 Downloaded from http://pubs.acs.org on February 3, 2019

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Industrial & Engineering Chemistry Research

Self-optimizing control structure and dynamic behavior for CO2 compression and purification unit in oxy-fuel combustion application Kaile Liu, Bo Jin*, Yunlei Zhao, Zhiwu Liang*

Joint International Center for CO2 Capture and Storage (iCCS), College of Chemistry and Chemical Engineering, Hunan University, Lushannan Road 1, Changsha, 410082, P.R. China *Corresponding author: [email protected] (B. Jin), [email protected] (Z. Liang)

Abstract CO2 compression and purification unit (CPU) using phase separation method is a promising option to obtain high purity CO2 products from oxy-fuel combustion power plants. For such CPU systems, self-optimizing control method is applied for the first time with the objectives of minimizing energy consumption and economic cost. Although the set of controlled variables is determined identically for self-optimizing control structures based on the targets of specific energy consumption (Case 1) and specific economic cost (Case 2), their control pairings are different. The optimized control structures are feasible for implementation of the operating targets with low energy and cost penalties. Case 1 would be the most suitable control strategy, because its absolute amplitude of variations for specific energy consumption and specific economic cost are only 14.02% and 10.29% of those for Case 2, respectively. The results provide a new solution to achieve energy-efficient and cost-effective operations for oxy-fuel combustion systems.

Keywords: CO2 capture; Oxy-fuel combustion; Process simulation; Self-optimizing control; Dynamic behavior

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1. Introduction Since CO2 emissions from power plants contribute to the serious problem of global warming, CO2 capture and storage (CCS) technology is proposed as an effective way to mitigate the severe impacts of these emissions on the environment. As one promising CCS technology, oxy-fuel combustion is attracting increased attention and is ready for commercial demonstration

1, 2

. In an

oxy-fuel combustion system, a CO2 compression and purification unit (CPU) is required to treat the produced flue gas with its 80-90 mol.% CO2. Using a phase separation approach, a CPU mainly compresses the flue gas and removes the impurities to obtain pure CO2 product. Compared to other CPU schemes, the partial condensation method with double flash separators (Fig. 1) is regarded as a promising option because auto-refrigeration operation with lower energy-economic penalties can be realized 3. However, energy consumption and economic cost derived from CPU operation would still degrade the thermodynamic and economic performance of the oxy-fuel combustion power plant. In order to achieve energy-efficient and economic-effective operation for the CPU, three approaches have been found in literature. The first solution is finding the desirable operating parameters via multi-variable optimization with minimization of energy-economic penalties 4. The second solution is to identify the source of thermodynamic irreversibility 5 or the cost formation process from raw materials to final products 6. The last solution focuses on control optimization that uncovers the roles that control structures, layers and loops play in energy performance

7

or,

alternatively, designing an advanced control structure with the optimized energy-economic targets. The first two aspects primarily concentrate on a steady-state operating point while lacking an entire operating cycle supervision experience on a real-time operation. Therefore, control structure optimization with efficient and economical targets would be a good choice to achieve favorable operation for a CPU system. Actually, as summarized in Table 1, several researchers have attempted to investigate the control behavior for CPU systems. Using the relative gain array (RGA) method, Atchariya et al. 8 identified the potential control structures for keeping CO2 product purity as the operating objective and analyzed the effects of uncertainty on control selection. Then, they further considered the operating objective of CO2 recovery rate in the newly designed control structure. As well, a dynamic model was built to test the reliability of the control structure and to investigate the


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dynamic behavior under disturbance rejection and set point tracking scenarios 9. Jin et al.4 proposed two control strategies (double temperature control and single temperature control) to achieve the operating targets of CO2 product purity, CO2 recovery rate and stream temperature. Furthermore, based on the well-established dynamic model, their dynamic characteristics were compared during flue gas flow rate and concentration change cases. On this basis, they further developed a dynamic exergy method 7, 10, 11 to reveal the functions that control components played on the real-time thermodynamic behavior, and then, to optimize the control and operation of the CPU system. Luyben 12 proposed a simple control structure without setting the objectives of CO2 product purity and CO2 recovery rate, and examined the reliability of the designed control system under some operating cases. From these control configurations, they mainly concentrated on designing a control structure to obtain the desired product quality (i.e. CO2 product purity and CO2 recovery rate), to achieve stable operation, and to identify the dynamic behavior under different operating conditions. However, to the best of our knowledge, no studies have been conducted to achieve the third solution where an advanced control structure is designed to minimize the energyeconomic penalties of the CPU system. Thus, more efforts are still required to obtain an optimized control structure for the energy-efficient and cost-effective operation of CPU systems. Table 1 Review of control configurations for CO2 compression and purification unit. MV b CV a

ΔP11 4

cCO2

ΔP119

TMCC

cCO2 CRR

VO

QMCC

WMCC

V CO2

Vv

R1,C

R2,C

Ref.

√ 8

√

TF1,exit

PF2

C

√

FCO2

T

PMC

√ √ √

9

√



LF1

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√ √

LF2

√

Ff √

TMCC LF1

√ √

LF2 TF1,exit

√

4

√

TF2,exit

√

FCO2 PF2

√

cCO2

√ √

CRR √

Ff √

TMCC

√

TF2,exit LF1 LF2

12

√ √ √

PF2

√

PC,2

a. Explanations for controlled variables (CVs): cCO2 (CO2 product purity), FCO2 (CO2 product flow rate), TF1,exit (exit temperature for first flash separator), T (temperature for the stream at the exit of first product compressor), PF1 (operating pressure for first flash separator), CRR (CO2 recovery rate), LF1, LF2 (liquid levels of first and secondary flash separators), Ff (flue gas flow rate), TMCC (temperature of multi-stage CO2 compressor), PF2(operating pressure for secondary flash separator), TF2,exit (exit temperature at the downstream of secondary


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flash separator), PC,2 (pressure of second product compressor). b. Explanations for manipulated variables (MVs): ΔP114 (pressure drop for valve at the downstream of first flash separator), ΔP119 (pressure drop for valve at the downstream of second flash separator), TMCC (exit temperature for multi-stage CO2 compressor), PMCC (discharge pressure for multi-stage CO2 compressor), VO (Splitter valve position), QMCC (cooling duty for multi-stage CO2 compressor), WMCC (brake power for multi-stage CO2 compressor), VCO2 (CO2 product valve position), Vv (vent gas valve position), R1,C (the speed of the first product compressor), R2,C (the speed of the two final product compressors).

Self-optimizing control means the process of finding a set of controllable variables which are the least sensitive to uncertainty and near-optimal operation when these variables remain unchanged

13.

Due to the fact that self-optimizing control

14

is a powerful tool to determine the

controlled variables for getting the desirable operations, it has been intensively applied to complicated process system engineering and energy conversion systems. In terms of CCS systems, the designs of self-optimizing controls for post-combustion and oxy-fuel combustion have been previously investigated. For post-combustion using monoethanolamine (MEA) as a solvent, Panahi et al.

15-17

employed the self-optimizing control design procedure to select the best

controlled variables, and then designed a control structure to maintain the process close to the most economically efficient operation in all operational regions. With respect to oxy-fuel combustion, Niva et al. 18-20 first applied the self-optimizing control method to the oxy-fuel boiler using a circulating fluidized bed, and identified the set of optimized controlled variables. Then, they used the partial relative gain array method to determine the pairings of control variables and manipulated variables for self-optimizing control structure but the dynamic validation for the designed control structure was absent. However, no self-optimizing controls for other subsystems (e.g. CPU) or full train oxy-fuel combustion systems have been investigated to improve their thermodynamic and economic properties during real-time operation. Toward that end, this work is the first to design new and advanced self-optimizing controls with the optimized energy-cost targets for the CPU subsystem in an oxy-fuel combustion power plant. Compared to the previous studies, the designed self-optimizing controls would realize the required operating objectives and the minimization of energy-economic targets simultaneously. More importantly, this research provides a new pathway to achieve energy and cost savings for CPU systems through control structure optimization and realizes the dynamic validations of the proposed self-optimizing controls for oxy-fuel combustion application. The findings would make



up the knowledge gap of how to optimize control strategies for CPU systems or even full train oxy-fuel combustion systems to implement energy-efficient and cost-effective operations. In this work, using a process model as the platform, degree of freedom analysis is first conducted to identify the inputs and outputs, while the minimization of specific energy consumption and specific economic cost are set as the objective functions. CO2 product purity (≥96 mol. %), CO2 recovery rate (≥90%), and stream temperature (>-56.6oC) are considered as the constraints, while five operating disturbances (nominal, flue gas flow rate and flue gas CO2 concentration) are used. In this way, all the values of objective functions under all the operating scenarios are obtained to determine the mean loss function for finding the suitable candidate controlled variables. Then, the RGA method is adopted to determine the control pairings and establish a self-optimizing control structure. Finally, the proposed self-optimizing control structure is confirmed through dynamic simulation, and the corresponding dynamic behaviors of process variables, energy consumption and economic cost are compared with that of a conventional control structure. 2. Self-optimizing control structure design In the design of self-optimizing control, the main steps include degree of freedom (DOF) analysis, definition of the optimal operation (objective function and constraints), determination of operating disturbance, candidate controlled variables, and loss assessment when disturbances and controlled variables remain unchanged. Here, in order to implement efficient-economical operation, two self-optimizing control structures based on the minimizations of specific energy consumption (Case 1) and specific economic cost (Case 2) are designed. 2.1 Process description Fig. 1 shows the process flow diagram of the studied CPU system 4. Flue gas compressed by a three-stage flue gas compressor with intercoolers (MCC) is sent into the cold box. For the cold box, two multi-stream heat exchangers (E1 and E2) and two flash separators (F1 and F2) are included. Flue gas is first cooled to -24.51oC and sent to the first flash separator (F1). The bottom stream containing at least 96 mol. % purity of CO2 is the first CO2 product flow, whilst the top stream is cooled continually to -54.69oC before entering into the second flash separator (F2) in which the rest of CO2 is obtained from the bottom as the second CO2 product flow. The vent gas


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from the separator top together with the two CO2 products is reheated in multi-stream heat exchangers. Finally, the two CO2 streams are mixed and compressed for storage or utilization.

Fig. 1 Process flow diagram of CO2 compression and purification unit4.

2.2 Case 1: Self-optimizing control based on specific energy consumption 2.2.1 Degree of freedom analysis Determining the number of steady-state DOFs is critical because it determines the number of steady-state controlled variables that need to be selected. In a complex process, the total number of degrees of freedom for the whole process can be calculated by determining the corresponding degrees of freedom for individual units

21-23

. Table 2 shows that the degrees of freedom for the

CPU system is 4, which indicates that four controlled variables need to be selected in the design of self-optimizing control. Table 2 Steady-state degrees of freedom analysis. Process unit

Number

DOFs

Each external feed stream

1

1

Splitter

0

0

Mixer

1

0

Compressor, turbine and pump

2

2

Adiabatic flash tank

2

0

Liquid phase reactor

0

0

Gas phase reactor

0

0



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heat exchanger

1

1

Tower (excluding heat exchanger)

0

0

Total number

4

2.2.2 Objective function and constraints Specific energy consumption, the ratio of total energy consumption (i.e. compression power consumptions from MCC and C) to total CO2 product flow rate, is selected as the objective function (J) and formulated in Eq. (1):

J

WMCC  WC FCO2

(1)

where, WMCC and WC means the power consumptions from MCC and C, while FCO2 stands for the flow rate of CO2 products. To implement the minimization of specific energy consumption, the following constraints should be subject to: C1: CO2 recovery rate ≥ 90% C2: CO2 product purity ≥ 96 mol. % C3: The temperature of S-8 stream > -56.6oC (CO2 three-phase critical point) As a consensus for CO2 capture technologies, C1 aims at recovering more CO2 to meet the environmental requirements and reduce CO2 emissions to the atmosphere 2, 24. C2 derives from the demand of CO2 transportation and storage, and this CO2 quality would realize acceptable energy consumption from compression and separation 25. C3 is determined by the nature of CO2 itself, in that the CO2 solidification and pipe blockage would occur when the stream temperature is lower than the three-phase freezing point 25, 26. 2.2.3 Operating disturbances Owing to the fact that raw flue gas is derived from the oxy-fuel combustion boiler island, flue gas flow rate and CO2 concentration would change with the variation of boiler operation. When the load changes in oxy-fuel combustion boiler island, the adjustment of fuel and oxygen flow rates would lead to the variation of the flue gas flow rate. Meanwhile, the change of combustion conditions in the burner would also directly affect the distribution of gas components in the flue gas. Hence, five process disturbance scenarios are considered as below. D1: No disturbances/nominal case D2: Flue gas flow rate + 5%


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D3: Flue gas flow rate -5% D4: The CO2 concentration in the flue gas +5% D5: The CO2 concentration in the flue gas -5% 2.2.4 Candidate controlled variables Since CO2 products should meet the quality requirements, the aforementioned three operating constraints (C1-C3) are directly used as the control variables. Additionally, from the above degree of freedom analysis (see 2.2.1), one more control variable is still needed to complete the set of controlled variables. Considering that the outlet temperatures of MCC and flash separators have great impacts on the product quality, one of them could be chosen as the last controlled variable and subjected to the following variation ranges. Therefore, two sets of controlled variables (C1-C3, C4 and C1-C3, C5) are determined as the candidate controlled variables for self-optimizing control design. C4: MCC outlet temperature: 25oC ≤ TMCC ≤ 50oC C5: F1 outlet temperature: -30oC ≤ TF1 ≤ -20oC 2.2.5 Optimization As listed in Table 3, the operating parameters after optimization under different disturbances are presented. Consistent with our previous study 4, flue gas flow rate change has little influence on CO2 product quality while the variation of flue gas CO2 concentration has significant impact. When CO2 concentration in flue gas decreases, CO2 product purity increases slightly while CO2 recovery rate decreases significantly. These results give some important information to further interpret the control structure selection and dynamic behavior for CPU system. Table 3 The optimized operating conditions under different operating disturbances. Parameter

D1

D2

D3

D4

D5

CO2 concentration in flue gas, mol.%

82.4

82.4

82.4

86.5

78.3

Flue gas flow rate, kg h-1

717186

750345

681327

717186

717186

CO2 recovery rate, %

93.85

93.85

93.85

95.73

91.77

CO2 product purity, mol.%

96.93

96.93

96.93

97.11

96.71

F1 outlet temperature, oC

-24.51

-24.51

-24.51

-24.51

-24.51


-53.85

-53.85

-53.85

-53.86

-53.85

MCC outlet pressure, bar

30

30

30

30

30



MCC outlet temperature, oC

35

35

Page 10 of 27

35

35

35

2.2.6 Loss evaluation Based on the optimized operating parameters, the reduction in specific energy consumption can be calculated under different operating disturbances to determine the final set of controlled variables. Here, the direct loss evaluation method

13

is selected and the loss function (L) is

presented as: L  J  u,d   J opt  u, d  . From the results of loss evaluation illustrated in Table 4, the pairings of C1 (CO2 recovery rate), C2 (CO2 product purity), C3 (S-8 stream temperature) and C4 (MCC outlet temperature) might be the proper set of controlled variables to achieve selfoptimizing control, because the lowest mean loss is obtained. Table 4 Loss, mean loss and ranking for the pairings of controlled variables under disturbances. Control pairings

D1

D2

D3

D4

D5

Lm

Rank

C1-C3, C4

0.018

0.018

0.018

0.017

0.017

0.018

1

C1-C3, C5

0.056

0.056

0.056

0.042

0.073

0.057

2

2.2.7 RGA analysis The RGA method

27

is employed to complete the pairing of controlled variables and

manipulated variables. Since the set of controlled variables for energy-efficient operation is determined, the available manipulated variables should be first identified. As shown in Table 5, four manipulated variables are considered for control pairings in the RGA analysis by excluding the variables that must be used for the other required operations. Table 5 List of manipulated and controlled variables. item

Controlled variables

item

Manipulated variables

C1

CO2 recovery rate

M1

∆P114

C2

CO2 product purity

M2

∆P119

C3

S-8 stream temperature

M3

MCC outlet pressure

C4

MCC outlet temperature

M4

MCC cooling duty

To finish the RGA analysis, the open-loop gain matrix for each operating scenario is first obtained from steady-state simulations. The gains of the controlled variables are calculated from the step changes on the manipulated variables. The step changes are implemented in such way that


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only one manipulated variable is changed at a time while keeping the rest of the manipulated variables at their nominal values (at the initial condition). In order to obtain stable control pairing, the magnitude of step changes should be carefully selected. In this study, the step changes performed on each manipulated variable are ±5% with respect to its nominal value. Hence, the gains for controlled variables are obtained from the changes of manipulated variables. An average of the process gains obtained from the step changes is used to build the nominal open loop gain matrix for each operating scenario. Then, the open-loop gain matrix is used to determine the final RGA matrix (Λ1). According to the rules of RGA

27

, the selected relative gain elements (λij)

between controlled variable (Ci) and manipulated variable (Mj) should be positive and close to unity. Therefore, the suggested control pairings for the self-optimizing control of CPU system are C1-M3, C2-M1, C3-M2 and C4-M4. 0.356 0.407 4.56E  3  0.242  0.716 1.51E  2 0.272 3.65E  3 Λ1    4.95E  2 0.629 0.321 1.10E  4    1.008   7.83E  3 4.11E  5 3.10E  4

2.3 Case 2: Self-optimizing control based on specific economic cost Because the difference between Case 1 and Case 2 lies in what kind of optimized objective function is chosen, the same design procedures can be applied for Case 2. For the identical process configuration, the degree of freedom for Case 2 is identified as 4. Based on the process configuration and operation safety, the total operating cost mainly consists of three components: electricity consumption from two compressors (MCC and C), cooling water consumptions from intercoolers in the MCC and Cooler, and feed flow (i.e. raw flue gas). Therefore, it is assumed that total operating costs mainly come from raw flue gas, power consumption and cooling water. However, it should be noted that the cost of raw flue gas can be ignored because the exhaust flue gas is the intermediate product between the upstream oxy-fuel boiler island system and CPU system.As formulated in Eq. (2), specific economic cost, defined as the ratio of total operating costs to total CO2 captured, is presented as objective functionJ.

J

(WMCC  WC )  pe  (QMCC  QC )  pw  V FCO2

(2)

where, pe and pw are the costs of electricity and water, which are 0.081$ (kW·h)-1 28 and 0.318$ m3 29;

QMCC and QC are the cooling duties required in the MCC and C; V is the amount of water



Page 12 of 27

consumed as cooling agent, which is estimated from temperature drop (20oC), specific heat capacity of water (4.2×103 J (kg·oC)-1) and density (998.2 kg m-3). In the minimization of specific economic cost, the same operating constraints of CO2 product purity (≥ 90%), CO2 recovery rate (≥ 96 mol.%) and S-8 stream temperature (> -56.6oC) should also be in place. Identically, five operating cases including nominal conditions, flue gas flow rate changes (±5%) and flue gas CO2 concentration changes (±5%) are considered as the operating disturbances, while the outlet temperatures of MCC and F1 might be selected as the possible candidate controlled variables. Table 6 shows the results for the desirable operating parameters obtained from optimization under the studied operating disturbances. Although different operating conditions are determined between Case 1 and Case 2, the influence of flue gas CO2 concentration is larger than that of flue gas flow rate. Table 6 The optimized operating condition under different disturbances. Disturbance

D1

D2

D3

D4

D5

CO2 concentration in flue gas, mol.%

82.4

82.4

82.4

86.5

78.3

Flue gas flow rate, kg h-1

717186

750345

681327

717186

717186

CO2 recovery rate, %

94.28

94.28

94.28

95.97

92.37

CO2 product purity, mol.%

96.86

96.86

96.86

97.10

96.63


-24.45

-24.45

-24.45

-24.72

-24.49


-55

-55

-55

-55

-55

MCC outlet pressure, bar

30.37

30.37

30.37

29.79

30.46

MCC outlet temperature, oC

48.17

48.17

48.17

50

40.30

Using the direct loss evaluation method13, the selection of controlled variables is determined in Table 7. Interestingly, the set of controlled variables (C1: CO2 product purity, C2: CO2 recovery rate, C3: S-8 stream temperature and C4: MCC outlet temperature) for Case 2 is identical to that of Case 1, even though their objective functions are different. This phenomenon might be ascribed to the fact that power consumption from MCC and C are the main components of the formation of specific energy consumption and specific economic cost in the CPU system. Table 7 Loss, mean loss and ranking for the pairings of controlled variables under disturbances. Control pairings

D1

D2

D3

D4

D5

Lmean

Rank

C1-C3, C4

0.17

0.17

0.17

1.50

0.33

0.47

1


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C1-C3, C5

0.92

0.92

0.92

2.13

1.33

1.24

2

Since the same process is studied, the identified controlled variables and manipulated variables that are summarized in Table 5 are used to determine the most promising control structures using the RGA analysis. From the array below, Λ2 and the criterion of RGA method, the control pairing of C1-M2, C2-M3, C3-M1 and C4-M4 is determined as the self-optimizing control structure for Case 2.

0 0.645 0.355   0.302 0.350 0.348 Λ2    0.698 4.53E  3 0.298   2.96E  15 5.20E  18 3.11E  18

0 0  0  1

2.4 Comparison of two self-optimizing control structures To understand the similarities and differences between the two designed self-optimizing controls, the double temperature control structure (i.e. two temperature cascade control loops TC_S18 and TC_S8 for S-8 and S-18 streams are configured and acted on two throttle valves LCV-114 and LCV-119, respectively) is chosen as the reference case 4. Fig. 2 presents the detailed control configurations for three control structures. In terms of similarity, flow rate control loops, level control loops and pressure control loops are identical in the regulatory control layers. Flue gas flow rate control loop (FC_FG) is achieved by adjusting the brake power of MCC, while CO2 product flow rate control loop (FC_CO2) is realized via regulating the valve opening of V-CO2. For the liquid levels of two flash separators, their controls (LC_F1 and LC_F2) are implemented through manipulating the valve positions in the downstream lines (LCV114 and LCV119). The vent gas valve (V-VENT) is used as the actuator in the pressure control loop (PC_F) to regulate system operating pressure. With respect to the differences in the three control structures, the key point is the components set up in the supervisory control layer to attain their objectives of CO2 product purity, CO2 recovery rate and S-8 stream temperature. Different from that of double temperature control structure in the reference case, a single temperature control structure is adopted in the two selfoptimizing control strategies. In the CO2 product purity control (CC_CO2), the secondary control signal is sent to the remote point of PC_F in the reference case and Case 2, while the signal is



transferred to the remote point of LC_F1 to manipulate the valve position of LCV114 for Case 1. The ratio of flue gas flow rate to CO2 product flow rate is regulated by the CO2 recovery control (CC_CRR) in the reference case, while the remote points of PC_F and LC_F2 are manipulated by CC_RR for Case 1 and Case 2, respectively. S-8 and S-18 stream temperatures are controlled by adjusting the valve opening positions of LCV119 and LCV114 in the reference case, but distinctively, only S-8 stream temperature control is achieved using the single valve opening position of LCV114 (Case 1) or LCV119 (Case 2) in the two self-optimizing control cases.

(a) Reference case: double temperature control structure 4 .

(b) Case1: self-optimizing control structure based on specific energy consumption.


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(c) Case 2: self-optimizing control structure based on specific economic cost. Fig. 2 Dynamic models for CPU systems configured with three different control structures.

3. Dynamic behavior for CPU configured with two self-optimizing controls Dynamic simulation is necessary to validate the feasibility of the proposed self-optimizing control structures. At first, the dynamic model was established in our previous study 4 is adopted to conduct the dynamic tests under two operating scenarios: flue gas flow rate change and flue gas concentration change. Then, the developed self-optimizing control strategies are configured in the dynamic model and compared to the reference case. Finally, the dynamic characteristics for these two controls during the studied operating conditions are obtained and discussed. 3.1 Flue gas flow rate change operating scenario A CPU system should be designed to accommodate flue gas flow rate changes, because they occur frequently in the integrated oxy-fuel combustion system. Therefore, flue gas flow rate changes between 100% and 80% with a ramp rate of 2%/min 30 are investigated here. As shown in Fig. 3, the flue gas flow rate changes from 100% at the 10th minute to 80% and up to 100% at the 30th minute. System pressure, S-8 temperature, CO2 product purity, and CO2 recovery rate are treated as the observed targets. From Fig. 4(a), system pressure has a slight change during the ramping up and down processes for the three control cases, and the variation of system pressure in the reference case is larger than in the two self-optimizing control cases. In Fig. 4(b), for all the



cases, temperatures are higher than the three-phase critical point and the variations follow the trend of flow rate change. The magnitude of reference case appears with the largest temperature decrement when compared to that in the other two cases. As illustrated in Figs. 4(c) ~ (d), CO2 product purity and CO2 recovery rate stay around their set points even though some fluctuations are involved.

Fig. 3 Flue gas flow rate change operating scenario.

Fig. 4 Dynamic responses of process variables under flue gas flow rate change case: (a) system pressure, (b) S-8 stream temperature, (c) CO2 product purity, and (d) CO2 recovery rate. 3.2 Flue gas concentration operating scenario


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As the flue gas concentration is affected by the operating condition of the oxy-fuel combustion boiler system, its variation should be investigated to clarify its effects on CPU operation. Here, as presented in Fig. 5, -1.5% and +1.5% ramping cases from the 10th minute to the 15th minute are performed, whilst other impurities (i.e. O2, Ar, N2, CO, SOx and NOx) are recalculated simultaneously to maintain the sum of the mole fractions equal to unity. The changes of system pressure, S-8 temperature, CO2 product purity and CO2 recovery rate with time are shown in Figs. 6(a) ~ (d). The change of CO2 concentration has a large influence on the system pressure. The variation of system pressure when CO2 concentration increases 1.5% is larger than that of 1.5% decrement for Case 1 and the reference case, while the variations for +1.5% and 1.5% are identical in Case 2. The S-8 stream temperature and CO2 product purity present the same trend as the CO2 concentration increase or decrease (see Fig.6(b) ~(c)). From Fig.6 (d), CO2 recovery rate shows an opposite trend to that of CO2 concentration, which is attributed to the fact that CO2 recovery rate is significantly affected by system pressure and operating temperature. As identified in previous studies 4, the influence of operating temperature is larger than that of system pressure. About the 42nd minute, the CO2 product purity in Case 1 drops rapidly (see Fig. 6(c)) when the CO2 concentration decreases 1.5%, because CO2 product purity is greatly affected by operating temperature. Finally, it should be noted that the lowest temperature for S-8 stream is still higher than the CO2 three-phase critical point (-56.6 °C), which indicates that the designed control systems are effective to achieve safe operation for the CPU system.



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Fig. 5 Flue gas concentration change operating scenario.

Fig. 6 Dynamic responses of process variables under flue gas concentration change case: (a) system pressure, (b) S-8 stream temperature, (c) CO2 product purity, and (d) CO2 recovery rate. Solid line is for +1.5% case while the dashed line is for -1.5% case.

From the above dynamic simulation results, the variations of all the operating parameters are within the acceptable ranges even though some process variables deviated from their set points. This situation demonstrates that the proposed two self-optimizing control structures could be used to realize the control and operation requirements for a CPU system. 4. Dynamic energy and economic performance Although the control structures and dynamic characteristics are determined, the energy and economic performance for two self-optimizing control structures during two operating scenarios should be discussed and compared. In order to quantitatively compare these three control structures, the relative amplitudes of variation (α) and the absolute amplitudes of variation (β) are introduced and formulated as the equations below.



xf  xi xi

     


(3) (4)

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where, x means the value of specific energy consumption/specific economic cost, depending on the case. Subscripts "i" and "f" stand for the initial and final operating state, and superscripts "+" and "-" represent the positive variation and negative variation, respectively. 4.1 Specific energy consumption From Fig.7, specific energy consumption appears with a tendency opposite to that of the flow rate change. This is derived from the flow rate control actions on the brake powers of the compressors. During the periods of 0-10th and 40-50th minutes, specific energy consumption for the three control cases is almost identical, which implies that the energy behavior could reach back to the initial state after the ramping down and up processes. Comparing the amount of variation in the three control cases, the rank is: Case 1> Case 2> reference case. Under the control intervention, Case 1 and Case 2 show lower energy consumption than did the reference case during all of the operating conditions. The results indicate that the proposed control schemes can achieve the objective of energy savings when flue gas flow rate changes.

Fig. 7 Specific energy consumption for three control cases under flue gas flow rate change operating scenario.

Fig. 8 reveals the effect of CO2 concentration change on specific energy consumption for three different control structures. When flue gas CO2 concentration increases at the 10th minute, specific energy consumption for Case 1 is lower than that of other two control methods while specific energy consumption for reference case begins to decrease. Starting from the 15th minute,



the specific energy consumption of the reference case begins to increase rapidly until it is close to Case 1 but lower than that of Case 2. For the decrement of flue gas CO2 concentration, Case 1 and Case 2 achieve almost the same specific energy consumption and it is lower than that of the reference case. It should be noted that the change trend of specific energy consumption for the reference case is opposite to that for Case 1 and Case 2. It is mainly derived from the variations of system pressure and operating temperature (see Fig. 6) caused by the control regulations, especially TC_S8, CC_CO2 and CC_CRR. Taking the +1.5% case for example, more power consumption is required to compress CO2 for all three control cases. Differently, the amount of CO2 product is increased for the reference case while it is almost unchanged for Case 1 and Case 2. In addition, the range of α for the three control cases is quite distinctive: [-0.03%, +0.10%] for Case 1, [-0.35%, +0.64%] for Case 2, and [-0.40%, +0.45%] for reference case. Therefore, Case 1 might be the most suitable control structure for the most desirable operation in a CPU system, because its β is the lowest among these three controls.

Fig. 8 Specific energy consumption for three control cases under flue gas concentration operating scenario: solid line for +1.5% case while dash line for -1.5% case.

4.2 Specific economic cost Fig. 9 and Fig. 10 illustrate the dynamic cost behavior of three control structures during flue gas flow rate and concentration change processes. It was found that similar evolutions occurred for the dynamic cost performance when compared to that of dynamic energy performance during


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an identical operating scenario. Specific economic costs for three control structures followed with the variation of flue gas flow rate, while appeared with different phenomena under the flue gas concentration change operating scenario. The reason for the similarity is related to the component of cost function. As shown in Eq. (2), cost function includes the cost of power consumption from compressors and the cost of cooling water for regulating the outlet temperature of the compressors. It can be seen that compressor power consumption as the primary component in the numerator of specific economic cost is actually the numerator of specific energy consumption. And very interestingly, this reason also results in self-optimizing control based specific economic cost (Case 2) not being the suitable case for cost behavior control. On the other hand, the β for Case 1 (0.14%) is 8.72 times and 5.65 times lower than that of Case 2 (0.98%) and the reference case (0.85%), respectively. Thus, self-optimizing based on energy target (Case 1) has better cost performance than that of self-optimizing control based on the cost target (Case 2).

Fig. 9 Specific economic cost for three controls under flue gas flow rate change operating scenario.



Fig. 10 Specific economic cost for three controls under flue gas concentration operating scenario: solid line for +1.5% case while dash line for -1.5% case.

5. Conclusion The paper aimed to develop self-optimizing control for a CO2 compression and purification unit (CPU) to achieve energy-efficient and economic-effective operations. At the beginning, based on the objective functions of specific energy consumption and specific economic cost, the sets of controlled variables were determined. Then, a relative gain array method was employed to match the desirable pairing of controlled variables and manipulated variables for finalizing the selfoptimizing control structures. To verify the designed control structures, dynamic simulation was carried out under the operating scenarios of flue gas flow rate change and flue gas concentration change. Finally, the dynamic behavior for two self-optimizing control strategies were identified and compared using the double temperature control structure as the reference case. These results provide deep insight into the control optimization for a CPU system to reach optimal energy-cost targeted operation. For self-optimizing control design, the sets of controlled variables are found to be identical for two self-optimizing control structures. The selected controlled variables are: CO2 product purity (C1), CO2 recovery rate (C2), S-8 stream temperature (C3) and temperature at outlet of three-stage flue gas compressor (C4). Meanwhile, the identified manipulated variables are: pressure drop for the valve at the downstream of the first flash separator (M1), pressure drop for the valve at the downstream of the second flash separator (M2), discharge pressure for three-stage flue gas compressor (M3), and temperature at the outlet of the three-stage flue gas compressor (M4). Although controlled and manipulated variables are identical, control pairings for two self-


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optimizing control structures are different. The control pairing for self-optimizing control based on specific energy consumption (Case 1) is C1-M3, C2-M1, C3-M2 and C4-M4, while for selfoptimizing control based on specific economic cost (Case 2) is C1-M2, C2-M3, C3-M1 and C4-M4. With respect to dynamic validation of self-optimizing controls, the dynamic behavior of two self-optimizing controls is quite similar. The main reason might be the similarities of control structure and objective function. In terms of control structure, the difference between the two selfoptimizing controls lies in the fact that their configurations of CO2 product purity, CO2 recovery rate and S-8 stream temperature in the supervisory control layer are distinct while their regulatory control layers are identical. The primary constituent for objective functions in both self-optimizing controls is compression power consumption. The dynamic behavior of both controls during flue gas flow rate change is different from that during flue gas concentration change, while their energy-economic performance varies similarly. Self-optimizing control based on specific energy consumption would be the desirable control strategy for a CPU system to realize energy-efficient and cost-effective operation, since the lowest energy-cost performance is obtained during dynamic operations, when compared to that of the reference case and self-optimizing control based on specific economic cost. Acknowledgment The authors gratefully acknowledge the financial support of the National Key R&D program of China (Grant 2018YFB0605302), National Natural Science Foundation of China (Grants21808050 and 21536003), Natural Science Foundation of Hunan Province in China (Grant 2018JJ3061), and Fundamental Research Funds for the Central Universities (Grant 531107050907).

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Self-optimizing control structure and dynamic behavior for CO2

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