Optimization control method for vacuum pressure swing adsorption carbon capture system based on model predictive control

Abstract

The invention discloses a model predictive control-based vacuum pressure swing adsorption carbon capture system optimization control method, which comprises the following steps of: performing an open-loop step experiment on a vacuum pressure swing adsorption carbon capture system by taking a cycle period as a unit step length to obtain a dynamic characteristic experiment curve of the vacuum pressure swing adsorption carbon capture system; according to data corresponding to the dynamic characteristic experiment curve, a discrete state space model representing the dynamic characteristics of the vacuum pressure swing adsorption carbon capture system is obtained through identification through a subspace identification method, the discrete state space model is amplified into an incremental state space model, and the incremental state space model is used for representing the dynamic characteristics of the vacuum pressure swing adsorption carbon capture system. Deriving the incremental state space model to obtain a prediction model; constructing a rolling optimization objective function of the prediction model, inputting the scheduling instruction into the prediction model, and designing a constrained MPC control algorithm based on the prediction model to obtain the MPC controller of the vacuum pressure swing adsorption carbon capture system; and the CO2 recovery rate and purity are precisely tracked and controlled through the MPC controller of the vacuum pressure swing adsorption carbon capture system. The technical problems that the CO2 recovery rate adjusting speed is low, the stability is poor and the CO2 purity deviates from the set value in a traditional control method can be solved, and meanwhile the anti-interference capacity and the multi-target optimization performance of the system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of industrial CO2 capture, and particularly to an optimized control method for a vacuum pressure swing adsorption carbon capture system based on model predictive control. Background Art

[0002] Carbon capture and storage (CCS) technology has become a key means to reduce industrial CO2 emissions. Among various carbon capture technologies, vacuum pressure swing adsorption (VPSA) technology has become an attractive carbon capture process due to its advantages such as low energy consumption, low corrosiveness to equipment, and suitability for separating medium and low concentration CO2.

[0003] However, the traditional VPSA system still faces the following technical bottlenecks in practical applications: 1. The traditional VPSA system usually operates with fixed process parameters (such as adsorption time, pressure, etc.), making it difficult to adapt to the increasing requirements for CO2 recovery rate. This fixed parameter mode cannot flexibly respond to changes in the flow rate and concentration of the feed gas, resulting in low system operation efficiency. 2. In actual industrial scenarios, fluctuations in the flue gas flow rate at the feed inlet are inevitable. These fluctuations will cause the system to deviate from the designed operating conditions, thereby affecting the stability of the CO2 capture rate, and may even cause the CO2 recovery rate to be lower than the minimum requirement, unable to meet the carbon capture target. 3. Currently, most control methods for VPSA systems still rely on empirical settings or simple PID control. These methods do not fully consider the dynamic characteristics of the system, the multivariable coupling relationship, and the influence of external disturbances, resulting in large fluctuations in the CO2 recovery rate, poor system operation stability, and difficulty in achieving efficient carbon capture effects. In addition, existing research usually only focuses on a single target (such as CO2 recovery rate), while ignoring the coupling relationship between variables. In actual operation, adjusting the duration of the adsorption step will cause fluctuations in CO2 purity while controlling the CO2 recovery rate. However, too low CO2 purity will limit its subsequent utilization (such as chemical raw materials or food-grade CO2). Traditional methods are difficult to effectively balance between CO2 recovery rate and CO2 purity, resulting in the inability to fully optimize the system performance. 4. Traditional control methods are usually difficult to effectively handle the constraint conditions (such as control variables, controlled variables) and external disturbances (such as flue gas flow rate fluctuations) during system operation, thereby destroying the stable performance of the system.

[0004] In summary, the deficiencies in the control method of the traditional VPSA system have become the main bottleneck restricting its performance improvement. Therefore, designing a multi-objective optimization control method that can adjust process parameters in real time, fully consider the dynamic characteristics and constraint conditions of the system, and effectively balance the CO2 recovery rate and CO2 purity has become the key to improving the performance of the VPSA carbon capture system. Summary of the Invention

[0005] Objective of the Invention: The present invention provides an optimized control method for a vacuum pressure swing adsorption carbon capture system based on model predictive control, which can solve the technical problems of slow adjustment speed and poor stability of CO2 recovery rate under traditional control methods, as well as the deviation of CO2 purity from the set value. At the same time, the anti-interference ability and multi-objective optimization performance of the system are improved.

[0006] Technical Solution: An optimized control method for a vacuum pressure swing adsorption carbon capture system based on model predictive control according to the present invention includes the following steps:

[0007] Step 1: Taking the cycle period as the unit step size, conduct an open-loop step experiment on the vacuum pressure swing adsorption carbon capture system to obtain the dynamic characteristic experiment curve of the vacuum pressure swing adsorption carbon capture system, where the control variables include the adsorption step duration and the intermediate pressure, the controlled variables include the CO2 recovery rate and purity, and the disturbance variable is the feed inlet flow rate;

[0008] Step 2: According to the data corresponding to the dynamic characteristic experiment curve, identify the discrete state space model representing the dynamic characteristics of the vacuum pressure swing adsorption carbon capture system through the subspace identification method, expand the discrete state space model into an incremental state space model, and then derive the prediction model from the incremental state space model;

[0009] Step 3: Construct the rolling optimization objective function of the prediction model, input the scheduling instruction into the prediction model, and design a constrained MPC control algorithm based on the prediction model to obtain the MPC controller of the vacuum pressure swing adsorption carbon capture system;

[0010] Step 4: Accurately track and control the CO2 recovery rate and purity through the MPC controller of the vacuum pressure swing adsorption carbon capture system, and effectively suppress the influence of the feed flue gas disturbance on the system.

[0011] Further, in Step 1, the vacuum pressure swing adsorption carbon capture system is a multi-bed multi-step periodic system, including feed adsorption, pressure relief, and vacuum desorption. Only product gas is produced during the vacuum desorption step when the system is operating; the CO2 recovery rate is defined as the ratio of the amount of CO2 captured from the raw gas in a cycle period to the total amount of CO2 in the raw gas; the CO2 purity is defined as the volume percentage of CO2 in the CO2 product gas separated and collected from the system; the calculation formulas for the CO2 recovery rate and purity are as follows:

[0012]

[0013] Where F product is the gas flow rate at the product gas outlet; y product,CO2 is the CO2 concentration in the gas at the product gas outlet; F feed is the gas flow rate at the feed inlet; y feed,CO2is the CO2 concentration in the inlet gas; t cycle is the duration of the VPSA carbon capture cycle.

[0014] Furthermore, in step 2, the information of the model data set is converted into a state-space expression, and its discrete state-space model expression is as follows:

[0015]

[0016] where u(k)=[u1(k), u2(k)] T , y(k)=[y1(k), y2(k)] T , d(k)=[d1(k)] T ; u(k) represents the control quantity; u1(k) represents the duration of the adsorption step in the k-th cycle; u2(k) represents the intermediate pressure in the k-th cycle; y(k) represents the controlled quantity; y1(k) represents the CO2 recovery rate in the k-th cycle; y2(k) represents the CO2 purity in the k-th cycle; d(k) represents the measurable disturbance; d1(k) represents the flue gas flow rate at the inlet in the k-th cycle; x0(k) represents the system state vector in the k-th cycle; A, B, C, D, E, and F all represent system characteristic matrices.

[0017] The state-space model expression in the form of an augmented matrix is as follows:

[0018]

[0019] where Δx0(k)=x0(k + 1)-x0(k), and Δx0(k) is obtained through state estimation by Kalman filtering; Δu(k)=u(k + 1)-u(k); Δd(k)=d(k + 1)-d(k); O represents the zero matrix; I y represents the identity matrix; the subscript aug represents the augmented matrix.

[0020] Furthermore, in step 2, the incremental state-space model is derived to obtain a prediction model, and the expression of the prediction model is as follows:

[0021] Y = δ $ x0(k)+δ8ΔU(k)+δ : Δd(k);

[0022]

[0023] where Y(k)=[y(k + 1|k) T , y(k + 2|k) T ,..., y(k + P|k) T T represents the change trajectory of the prediction of the controlled quantity within the prediction horizon P; ΔU = [Δu(k)​T , Δu(k + 1) T , …, Δu(k + M - 1) T T represents the incremental sequence of the control quantity within the control time domain M; P is the prediction time domain, M is the control time domain, and M ≤ P.

[0024] Furthermore, in step 3, the control objective function expression is as follows:

[0025] minJ = (Y G - Y) T Q y (Y G - Y) + ΔU T R8ΔU;

[0026] where Y G represents the target value matrix; Q y represents the error weight matrix; R8 is the control right matrix.

[0027] Furthermore, in step 3, set constraints on the adsorption step duration, intermediate pressure, adsorption step duration increment, intermediate pressure increment, CO2 recovery rate, and purity in the MPC controller of the vacuum pressure swing adsorption carbon capture system, and the expressions are as follows:

[0028]

[0029] Furthermore, in step 4, the MPC controller controls the CO2 recovery rate by the adsorption step duration, controls the CO2 purity by the intermediate pressure, and uses the flue gas flow rate at the feed port as its measurable disturbance.

[0030] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: By dynamically adjusting the adsorption step duration, the adjustment speed and stability of the CO2 recovery rate are significantly improved; Using the intermediate pressure control strategy, precise control of the CO2 purity is achieved, ensuring that the product gas quality meets industrial requirements; Through the multi-variable optimization ability of the MPC algorithm, an effective balance between the CO2 recovery rate and the CO2 purity is achieved, improving the overall performance of the system and effectively suppressing the influence of flue gas flow fluctuations on the system, enhancing the robustness of the system; By introducing constraint conditions, ensuring that the system operates within a safe range and the control output does not exceed the set range, improving the reliability and practicality of the system. The present invention is applicable to various vacuum pressure swing adsorption carbon capture systems and has broad application prospects and important industrial value. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a schematic diagram of the system structure of the present invention.

[0032] Figure 2 is a schematic diagram of the system cycle steps of the present invention.​

[0033] Figure 3 This is the system control block diagram of the present invention. Detailed implementation manners

[0034] An optimized control method for a vacuum pressure swing adsorption carbon capture system based on model predictive control includes the following steps:

[0035] Step 1: Taking the cycle period as the unit step length, conduct an open-loop step experiment on the vacuum pressure swing adsorption carbon capture system to obtain the dynamic characteristic experiment curve of the vacuum pressure swing adsorption carbon capture system, where the control variables include the adsorption step duration and the intermediate pressure, the controlled variables include the CO2 recovery rate and purity, and the disturbance variable is the feed inlet flow rate;

[0036] Step 2: According to the data corresponding to the dynamic characteristic experiment curve, through the subspace identification method, identify and obtain a discrete state space model representing the dynamic characteristics of the vacuum pressure swing adsorption carbon capture system, expand the discrete state space model into an incremental state space model, and then derive a prediction model from the incremental state space model;

[0037] Step 3: Construct a rolling optimization objective function for the prediction model, input the scheduling instruction into the prediction model, and based on the prediction model, design a constrained MPC control algorithm to obtain the MPC controller of the vacuum pressure swing adsorption carbon capture system;

[0038] Step 4: Through the MPC controller of the vacuum pressure swing adsorption carbon capture system, accurately track and control the CO2 recovery rate and purity, and effectively suppress the influence of the feed flue gas disturbance on the system.

[0039] The corresponding vacuum pressure swing carbon capture system is as Figure 1 shown. The main equipment of the system includes adsorption beds, vacuum pumps, and valves.

[0040] Taking the flue gas of a coal-fired power plant as the flue gas source of the carbon capture system, assuming that the flue gas pressure after pretreatment is 1.5 bar, the flue gas temperature is 303 K, the proportions of N2 and CO2 in the flue gas are 85 vol% and 15 vol% respectively, and the flue gas feed flow rate is 1.98 m 3 / h, the basic operating parameters of the VPSA carbon capture system are shown in Table 1.

[0041] Table 1 Basic operating parameters of the VPSA carbon capture system

[0042]

[0043]

[0044] In this embodiment, the VPSA carbon capture process adopts a two-bed six-step cycle dynamic simulation, asFigure 2 The following is a schematic diagram of the step cycle of the system, and the cycle steps are as follows:

[0045] (1) Pressurization: Valves VF and V1 are opened, and the flue gas enters BED1 through the feed port to pressurize it to the adsorption pressure PH.

[0046] (2) Adsorption: Valves VF, V1, V3, and VW are opened, and the flue gas enters BED1 from the feed port. At a relatively high adsorption pressure PH, a large amount of CO2 and a small amount of N2 are adsorbed inside the bed layer, and the unadsorbed N2 is discharged from the top of the bed layer through the exhaust port.

[0047] (3) Equal pressure drop: Valve VF is closed to stop feeding, valve VW is closed to stop exhausting, valve V4 is opened, connecting the high-pressure adsorption bed BED1 and the low-pressure adsorption bed BED2, and using the pressure difference to initially reduce the pressure of BED1.

[0048] (4) Pressure relief: Valve V4 is closed, V9 and VPURGE are opened, and vacuum pump #1 is started to reduce the pressure of BED1 to the intermediate pressure PI for pressure relief. Due to the pressure reduction, a large amount of N2 on the adsorption bed is desorbed from the adsorbent and discharged from the pressure relief port, improving the purity of CO2 in the adsorption bed layer.

[0049] (5) Vacuum desorption: Valve VPURGE is closed, V2 and VP are opened, and vacuum pump #2 is started to reduce the pressure of BED1 to the vacuum desorption pressure PL. Under the vacuum desorption pressure, most of the gas on the adsorbent is desorbed, and the desorbed gas is discharged from the product gas port. The adsorption bed layer is regenerated to prepare for the adsorption in the next cycle.

[0050] (6) Equal pressure increase: Valve VP is closed, and valve V4 is opened. At this time, BED2 performs the equal pressure drop step, and the high-pressure gas in BED2 is pressed into BED1 to initially increase the pressure of BED1.

[0051] Taking one cycle as a period, the CO2 recovery rate of the VPSA carbon capture system during one cycle of operation is calculated, and the calculation formula is as follows:

[0052]

[0053] The data set of the system is obtained through simulation, and its characteristics are analyzed. The adsorption step duration that has a significant impact on the CO2 recovery rate and is easy to adjust is selected as the control variable. Subsequently, an open-loop step experiment is carried out to obtain the dynamic characteristic curve of the VPSA carbon capture system. According to the experimental curve and the corresponding data, the discrete state space model of the system is identified by the subspace identification method, and the model is extended to an incremental state space model, and finally the prediction model is derived.

[0054] Specifically, the expression of its discrete state space model is as follows:

[0055]

[0056] where \(u(k)=[u_1(k),u_2(k)]\) T , \(y(k)=[y_1(k),y_2(k)]\) T , \(d(k)=[d_1(k)]\) T ; \(u(k)\) represents the control quantity; \(u_1(k)\) represents the duration of the adsorption step in the \(k\)-th cycle; \(u_2(k)\) represents the intermediate pressure in the \(k\)-th cycle; \(y(k)\) represents the controlled quantity; \(y_1(k)\) represents the CO₂ recovery rate in the \(k\)-th cycle; \(y_2(k)\) represents the CO₂ purity in the \(k\)-th cycle; \(d(k)\) represents the measurable disturbance; \(d_1(k)\) represents the flue gas flow rate at the feed inlet in the \(k\)-th cycle; \(x_0(k)\) represents the system state vector in the \(k\)-th cycle; \(A\), \(B\), \(C\), \(D\), \(E\), and \(F\) all represent system characteristic matrices.

[0057] The expression of the state space model in the form of an augmented matrix is as follows:

[0058]

[0059] where \(\Delta x_0(k)=x_0(k + 1)-x_0(k)\), and \(\Delta x_0(k)\) is obtained through state estimation by Kalman filtering; \(\Delta u(k)=u(k + 1)-u(k)\); \(\Delta d(k)=d(k + 1)-d(k)\); \(O\) represents the zero matrix; \(I\) y represents the identity matrix; the subscript aug represents the augmented matrix.

[0060] Deriving the incremental state space model gives a prediction model, and the expression of the prediction model is as follows:

[0061] \(Y=\delta\) $ \(x_0(k)+\delta_8\Delta U(k)+\delta\) : \(\Delta d(k)\);

[0062]

[0063] where \(Y(k)=[y(k + 1|k) T ,y(k + 2|k) T ,...,y(k + P|k) T T represents the change trajectory of the predicted controlled quantity within the prediction horizon \(P\); \(\Delta U=[\Delta u(k) T ,\Delta u(k + 1) T ,…,\Delta u(k + M - 1) T T represents the incremental sequence of the control quantity within the control horizon \(M\); \(P\) is the prediction horizon, \(M\) is the control horizon, and in this case, \(P = 10\), \(M = 2\). ​​

[0064] The control objective function expression for this case is as follows:

[0065] minJ = (Y G - Y) T Q y (Y G - Y) + ΔU T R8ΔU;

[0066] Wherein, Y G represents the target value matrix; Q y represents the error weight matrix; R8 represents the control right matrix.

[0067] Constraints are set for the adsorption step duration, the increment of the adsorption step duration, and the CO2 recovery rate. The expressions are as follows:

[0068]

[0069] The MPC control block diagram designed for this case is as Figure 3 shown, and the basic parameters and constraint settings of the MPC controller are shown in Table 2.

[0070] Table 2 MPC Controller Parameter Design

[0071]

[0072] In summary, the present invention proposes an optimized control method for a vacuum pressure swing adsorption carbon capture system based on model predictive control (MPC). This method realizes multi-objective optimized control of dynamically adjusting the adsorption step duration and intermediate pressure to control the CO2 purity, significantly improves the low-carbon performance of the system, and achieves an effective balance between the CO2 recovery rate and the CO2 purity. At the same time, through the multi-variable prediction and optimization capabilities of the MPC algorithm, the present invention effectively suppresses the influence of external disturbances such as flue gas flow fluctuations on the system operation, ensuring the flexibility and stability of the system under complex working conditions. In addition, the present invention fully considers the constraint conditions in the system operation, further improving the reliability and practicality of the system.

Claims

1. A vacuum pressure swing adsorption carbon capture system optimization control method based on model predictive control, characterized in that: The steps include: Step 1: Taking the cycle as the unit step length, an open-loop step experiment is performed on the vacuum pressure swing adsorption carbon capture system to obtain a dynamic characteristic experimental curve of the vacuum pressure swing adsorption carbon capture system, wherein the controlled quantity includes the adsorption step duration and the intermediate pressure, the controlled quantity includes the CO2 recovery rate and purity, and the disturbance quantity is the feed inlet flow rate; Step 2: According to the data corresponding to the dynamic characteristic experimental curve, a discrete state space model characterizing the dynamic characteristics of the vacuum pressure swing adsorption carbon capture system is identified by a subspace identification method, the discrete state space model is expanded into an incremental state space model, and then the incremental state space model is derived to obtain a prediction model; Step 3: construct a rolling optimization objective function of the prediction model, input the scheduling instruction into the prediction model, and design a constrained MPC control algorithm based on the prediction model to obtain the vacuum pressure swing adsorption carbon capture system MPC controller; Step 4: The MPC controller of the vacuum pressure swing adsorption carbon capture system is used to accurately track and control the CO2 recovery rate and purity, and effectively suppress the influence of the feed flue gas disturbance on the system.

2. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 1, the vacuum pressure swing adsorption carbon capture system is a multi-bed multi-step periodic system, including feed adsorption, pressure relief and vacuum desorption. When the system is running, product gas is produced only in the vacuum desorption step; CO2 recovery rate is defined as the ratio of the amount of CO2 captured from the feed gas in one cycle to the total amount of CO2 in the feed gas; CO2 purity is defined as the volume percentage of CO2 in the CO2 product gas separated and collected from the system; the calculation formula of CO2 recovery rate and purity is as follows: In the formula, F product is the gas flow rate of the product gas port; product,CO2 F is the CO2 concentration in the product gas outlet; feed is the gas flow rate at the feed inlet; y feed,CO2 is the CO2 concentration in the feed gas; t cycle is the duration of the VPSA carbon capture cycle.

3. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 2, the model data set information is converted into a state space expression. The discrete state space model expression is as follows: Where u(k)=[u1(k),u2(k)] T , y(k)=[y1(k),y2(k)] T ,d(k)=[d1(k)] T ; u(k) represents the controlled quantity; u1(k) represents the duration of the adsorption step of the kth cycle; u2(k) represents the intermediate pressure of the kth cycle; y(k) represents the controlled quantity; y1(k) represents the CO2 recovery rate of the kth cycle; y2(k) represents the CO2 purity of the kth cycle; d(k) represents the measurable disturbance; d1(k) represents the flue gas flow rate at the feed inlet of the kth cycle; x0(k) represents the system state vector of the kth cycle; A, B, C, D and E all represent system characteristic matrices.

4. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 2, the augmented matrix form state space model expression is as follows: Among them, Δx0(k)=x0(k+1)-x0(k), Δx0(k) is obtained by state estimation through Kalman filtering; Δu(k)=u(k+1)-u(k); Δd(k)=d(k+1)-d(k); O represents the zero matrix; represents the identity matrix; the subscript aug represents the augmented matrix.

5. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 2, the incremental state space model is derived to obtain a prediction model, and the prediction model expression is as follows: Y=δ # x0(k)+δ : ΔU(k)+δ < Δd(k); Where Y(k)=[y(k+1|k) T ,y(k+2|k) T ,...,y(k+P|k) T ] T Represents the change trajectory of the controlled quantity prediction in the prediction time domain P; ΔU=[Δu(k) T ,Δu(k+1) T ,…,Δu(k+M-1) T ] T Represents the incremental sequence of the control quantity in the control time domain M; P is the prediction time domain, M is the control time domain, and M≤P.

6. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 3, the control objective function expression is as follows: minJ=(Y I -Y) T Q K (Y I −Y)+ΔU T R : ΔU: Among them, Y I represents the target value matrix; Q K represents the error weight matrix; R : is the control rights matrix.

7. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 3, constraints on the duration of the adsorption step, the intermediate pressure, the increment of the duration of the adsorption step, the increment of the intermediate pressure, the CO2 recovery rate and the purity are set in the MPC controller of the vacuum pressure swing adsorption carbon capture system. The expressions are as follows:

8. The method for optimizing and controlling a vacuum pressure swing adsorption carbon capture system based on model predictive control according to claim 1, characterized in that: In step 4, the MPC controller uses the adsorption step duration to control the CO2 recovery rate, the intermediate pressure to control the CO2 purity, and the feed inlet flue gas flow rate as its measurable disturbance.

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