MPC MIMO State Space Control for Crude Oil Refining Process

Transcription

1 ISSN : International Science Press Volume 10 Number MPC MIMO State Space Control for Crude Oil Refining Process Juan Sebastián Useche a, Angélica Orjuela b and Darío Amaya c a-c Grupo de Aplicaciones Virtuales, Universidad Militar Nueva Granada. a U @unimilitar.edu.co, b U @ unimilitar.edu.co, c dario.amaya@ unimilitar.edu.co Abstract: The oil refining processes in the industry are one of the most cost, where energy consumption and product quality, affect the profitability. For this reason, it is looking to implement advanced control techniques, in order to improve the response times and reduce energy consumption. In the last years, it has begun apply the predictive controllers to these systems, seeking to improve the efficiency. With the help of simulation software is easier check the effectiveness of the controller and determine if their behavior is the desired. In this paper, the operation of a MCP MIMO controller is shown, based on Laguerre functions, applied to a crude oil distillation column, for controlling the concentration seven compounds, presenting the mathematical model of the plant. In obtaining model, the matrices in state space are calculated and based on this the development of a controller is proposed. Also, the implementation of Plant-controller scheme is performed and subsequent simulation to analyze the behavior of responses obtained and check the robustness of the controlled system. Keywords: Refinement, Multivariable, MPC, Optimization. 1. INTRODUCTION Distillation is the separation of substances, controlling the different boiling points of the components. Product quality and process efficiency represent the profitability to improve[1]. To optimize the schemes of oil refining, the methods use full knowledge of the plant and a robust mathematical development[2]. The predictive control is part of the most modern schemes have been implemented in the refining industry [3]. These controllers predict the behavior of the plant, using optimization algorithms which ensure a robust and stable operation [4]. The basic model prediction MPC (Model Predictive Control), is the most successful with the distillation of crude [5]. Control reduces energy consumption and improves product quality [6]. Optimization methods of the MPC controllers ensure the stability and convergence to the desired balance point[7]. For its implementation is necessary to know the complete mathematical model of the plant, to establish 143

2 Juan Sebastián Useche, Angélica Orjuela and Darío Amaya the appropriate restrictions and ensure that the prediction horizon can be reached at the desired operating point [8]. Some related papers to work are Tuning the Model Predictive Control of a Crude Distillation Unit, after performing controller tuning, the results showed a reduction in the computational cost [9]. Robust model predictive control of a pilot plant distillation column, It demonstrated that the proposed controller is efficient in preserve the stability of the plant, with different models and variations in the system [10]. Design of an adaptive predictive control strategy for crude oil atmospheric distillation process, where the results were better to work with centralized plants in comparison to one decoupled system[11]. This paper presents the design of a MIMO predictive control system for a crude oil distillation column, where seven different concentrations of compounds are controlled. The model in state space is discretized and calculations are performed to develop the controller using Laguerre functions. The responses are analyzed to determine the efficiency of these controllers. The principal contribution of this work is the design of a multivariable controller that keeps the seven concentrations of the compounds in the operating point. 2. MATERIALS AND METHODS 2.1. Model Crude Oil Distillation Column For a typical distillation column as shown in Figure 1, one proceeds to implement the equations (MESH), mass and energy balance for each state j and component i, in steady state [12]. Figure 1: Diagram of crude oil distillation Mass Balance (Equation M) Equation 1 is the general model to predict the mass flow of component i, in and out of the plate j.,,,,, 0 (1) (1 j NT, 1 i n) Phase equilibrium (Equation E) It is necessary to estimate the behavior of the substance verify states relation, described in equation 2.,,, (2) (1 j NT, 1 i n) 144

3 Sum of molar fraction (Equation S) MPC MIMO State Space Control for Crude Oil Refining Process The feed composition that corresponds to the product, expressed below. Enthalpy balance (Equation H), 1,, 1 (1 i n) (3) The equation 4 for heat balance is posed, considering the enthalpies, following some estimates.,,,, The relative volatility in each plate is considered constant as shown in equation 5., 0 (4) (5) The temperature of the liquid and vapor currents between the phases is the same, according to equation 6. (6) The flow rate of liquid and vapor is considered constant, as expressed in Equation 7.(7), V (7) In this case, the liquid-vapor flow into and out of each plate is constant, liquid-vapor retention is considered constant, according to the equation 8. Is assumed that no heat loss in the column structure., (8) The molar heat is considered constant and independent of fluid composition, also, the temperature variation of a plate to another is minimum by the above equation 9 is proposed. (9),,, According to the above considerations, the simplified model is shown in Equation 10.,,,, 0 (10) The mass balance for the plate j-1, is expressed in equation 11. (11) Writing the general form equation Substituting equations 11 and 12 in 10 2 (12),,,,, 0 (13) 145

4 The following values are set to simplify Juan Sebastián Useche, Angélica Orjuela and Darío Amaya, (14),, (15) Rewriting Equation 13 compactly, (16),, (17),,,,,,, 0 (18) Equation 19 represents the general model that predicts the temperature of each plate.,,,,,,,,,, 0 (19) Substituting equations 11 and 12 in 19 and ignoring the superscript, i is obtained,,,,,,,, 0 (20) The following equalities are established,, (21),,, (22),,, (23) Rewriting equation 20.,,,,,, 0 (24) The proposed model equations represent any component in a system of equations Nt (Nt is the number of plates). Performance data are taken of refinery Port-Harcourt[13], the characteristics of the components are described in Table 1, which are used to solve the equations 18 and 24. Table 1 Properties of Crude Oil STAGE FLOW (m3/h) Mole Fraction Kij Feed Gases Petrol Naphtha Kerosene Diesel Fuel Oil Residue

5 MPC MIMO State Space Control for Crude Oil Refining Process It is stressed that the proposed model poses obtaining seven products; most distillation processes have the objective of five State Space Matrices To obtain the model in state space, the following algorithm is used to complete the matrices. A is a tridiagonal matrix of order Nt, is calculated in the following order For i = 1 When i = Nt 1 For i = Nt 1,1 1,2, 1,, 1, 1,. The matrix, 7 is calculated considering intervals of 1 and 1 7 for the equation 28.,,,,, The output of the compounds in the matrix C[Nt,7] are expressed in equation 29.,,,,,,, 1 (23) The other values of the C matrix are zero MPC Controller using Laguerre Functions The MPC is performed using the development in [14]where it is made by Laguerre functions, the calculation of optimization matrices of [15]and obtaining the control matrix in[16]. The predictive control vector for a multivariable space states system generally is expressed by the following equation. (25) (26) (27) (22) (30) Each represents an independent vector for the control of a variable. It is composed of i predictions as shown in Equation (31) 147

6 Juan Sebastián Useche, Angélica Orjuela and Darío Amaya Independent control vectors are defined by Nc, which represents the control horizon and the length of the vector, at the instant k. Laguerre functions are used to obtain approximate values of the vector, expressing each element as a discrete polynomial function, rewriting the function as shown in Equation (32) Each element of the vector is part of network functions as equation 33. (33) The pole of Laguerre network is established by the value of, used to set the damping of the system and takes values in the interval from 0 to 1. To Laguerre functions is applied Z inverse transform as shown at 34, in order to obtain the network in the time domain. contains Laguerre functions in discrete time for. (34) The functioning of networks in discrete time satisfies the equation in differences shown below 1 (35) asexpressed in equation 36 is a matrix que agrupa los parámetros de y For the solution of the system, it is necessary to determine an initial condition for as shown in equation 37. (36) (37) The matrix is calculated by equation 38 with the system in state space, this matrix is required to calculate the prediction states. (38) The matrix is used for the prediction of the states and outputs of the plant, as expressed in the following equations. (39) 148

7 42. MPC MIMO State Space Control for Crude Oil Refining Process (40) Whereis a vector of coefficients of the system. Each element of the vector is expressed (41) The vector is obtained from the plant response within N prediction window as shown in the equation (42) and are the matrices of optimization and minimization, the calculation is expressed in equations 43 and 44 (43) (44) N p is the prediction horizon, is the matrix of reference signals, has a dimension of (i x N p), each element is obtained as shown in equation 45. The cost function is calculated by the prediction states, as stated below (45) 2 (46) represents the output vector which is equal to The control matrix is obtained according to the equation 47, by multiplying the matrices of minimization and optimization with initial conditions of Laguerre functions. 0 0 (47) 0 The elements are zero vectors withthe same dimension of 0, which serve for coupling the constants of multivariable control system.. The state space system with the included control is shown in equation RESULTS 1 (48) The plant is discretized with a holder of order 0, the matrices are order 65 by the number of column plates. The plate 1 is the concentration of Residue and the plate 65 Gases. Figure 2 shows the scheme of the plant - MPC. The plant is in space states with their matrices AD, BD and CD, using a sampling time equal to 10 seconds. The controller is the representation of equation 47, which is fed by a vector composed of the error signal from seven concentrations and the signal delay. The controller parameters are shown in Table

8 Juan Sebastián Useche, Angélica Orjuela and Darío Amaya Figure 2 Scheme of the plant controller Table 2 Controller parameters Parameter Value Control Horizon 65 Prediction Horizon 1200 Laguerre Poles 0.5 is the same order of the plant. is equal to the time response of plant to the unitary pulse. The poles values are where the system responded with improved stability and response time Figure 3 shows the behavior of the concentration of gases leaving the plate 65, has the highest stabilization time of the entire system with 3.5 hours. Figure 3: Gases (Blue) vs Set point (Black) Figure 4 shows the behavior of Petrol concentration on the plate 58, with a stabilization time of 2 hours. The control for the concentration of Naphtha, from the plate 43 is illustrated in Figure 5; the stabilization time is the fastest in the system with 30 minutes. In Figure 6 the behavior of the kerosene concentration in the plate 35 is observed with a stabilization time of 2 hours. Diesel controlled concentration shown in Figure 7, with a stabilization time of 2.5 hours in the output of the plate

9 MPC MIMO State Space Control for Crude Oil Refining Process Figure 4: Petrol (Blue) vs Set point (Black) Figure 5: Naphtha (Blue) vs Set point (Black) Figure 6: Kerosene (Blue) vs Set point (Black) Figure 7: Diesel (Blue) vs Set point (Black) 151

10 Juan Sebastián Useche, Angélica Orjuela and Darío Amaya Figure 8 shows that at 1.5 hours the concentration of fuel oil on the plate 12 is stabilized in the desired reference. 9. Figure 8: Fuel Oil (Blue) vs Set point (Black) The residue concentration is stabilized at 2 hours in the background of the column, as illustrated in Figure Figure 9: Residue (Blue) vs Set point (Black) The graphs obtained not have the same behavior; this is because the nonlinearity of the plant and the relation between the compounds, similarly the entry crude oil by the plate 40, causes disturbances in the concentrations of lower plates. 4. CONCLUSIONS From Laguerre functions, predictive controller design was performed. The results demonstrate its applicability to control seven different compounds, using the complete system, without using methods decoupling or order reduction. The MPC controllers have a more extensive mathematical development in comparison with traditional controllers, but has better stability and lower response times for the multivariable control. Laguerre functions reduce the computational cost for their recursiveness in mathematical operations, this making easier its implementation. In addition, the input parameters for optimization algorithms are lower compared to other methods of predictive control. Acknowledgments Special thanks to the Research Vice-rectory of the Universidad Militar Nueva Granada, for financing the project INV_ING_1911 titled Laboratorio Virtual para el Control del Proceso de Refinación del Petróleo con Realidad Aumentada y Realidad Virtual project, 2015 year. 152

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