MODELLING OF MULTICOMPONENT DISTILLATION FOR OPTIMIZATION AND ON-LINE CONTROL SHORT-CUT MODEL AND MODEL ADAPTATION

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1 Journal of Chemical Technology Nikolay and Kozarev Metallurgy, 50, 3, 2015, MODELLING OF MULTICOMPONENT DISTILLATION FOR OPTIMIZATION AND ON-LINE CONTROL SHORT-CUT MODEL AND MODEL ADAPTATION University of Chemical Technology and Metallurgy 8 Kl. Ohridski, 1756 Sofia, Bulgaria kozarev@uctm.edu Received 12 February 2015 Accepted 03 April 2015 ABSTRACT Some aspects of the multicomponent distillation modelling are analysed and discussed. A highly simplified noniterative mathematical model is offered for calculation of the top and bottom product compositions. It can be successfully adapted to a working distillation column on the base of easy obtainable measurement data related to the lower or upper cut points of the products. Being extremely fast, the model can be used for optimisation of the mode of operation and on-line control of crude oil separation and other multicomponent distillation processes. Keywords: multicomponent distillation, short-cut model, model adaptation, optimal mode of operation, on-line control. INTRODUCTION Crude oil distillation is a basic process in crude oil refining.it is a multistage two phase continuous process of simultaneous mass and heat transfer [1-3]. That is why distillation columns are quite complicated industrial units in respect to mathematical modelling and control even in the case when a two-component mixture is to be separated.the process complexity becomes much higher for multicomponent separation processes. Crude oil is an exceedingly complex mixture, containing a large number of chemical substances, ranging from methane to compounds with many carbon atoms [4]. In practice, a true boiling point distillation curve (TBP curve) is used to represent the crude oil composition as a relationship between the percentage distilled and the temperature, reached at its separation [5]. A common practice [6, 7] is to represent the crude oil composition as a mixture of real and pseudo components. This reduces the number of crude oil components. Nevertheless, it typically remains bigger more than forty. The crude oil distillation processes are characterised with high energy consumption. In addition, the energy price is high, and is steadily increasing. On the other hand, the energy saving is directly connected to the more and more serious problem of air pollution. The lower energy consumption is, the better the air quality becomes. So, the process optimisation in respect to energy conservation is very important. Any change in operation conditions, such as feed flow rate and its composition, as well as standard requirements for product composition and properties specifications, involves changes in the mode of operation. It is well known that distillation columns are quite inertial industrial units. That is why, all operative interventions should be realised as a series of consistent small steps, directed to the new steady state of the process. Of course, the effects of those steps on the product compositions and properties should be quickly and exactly estimated. Different rigorous mathematical models have been developed and are in use for modelling and computer simulation of distillation columns. Since those models are complicated and difficult for use, they are applied mostly for design but not for process optimisation or 273

2 Journal of Chemical Technology and Metallurgy, 50, 3, 2015 when in need of fast process parameters estimation. Therefore, significant efforts are recently made to develop and apply short-cut models [8-12, 13] for optimisation and successful on-line control of distillation columns. GENERAL IDEA A simple distillation column is presented on Fig. 1. Here F, D, R and B are the mass flow rates of the feed, top product, reflux and the bottom flow, correspondingly. If the feed components are ordered from the lightest to the heaviest one, the feed composition can be expressed by xx FF = xx FF (1), xx FF (2), xx FF (nn), (mm) where xx FF, mm = 1, 2, nn, i is the cumulative mass fraction of the first m components. The feed flow is divided into two flows - the top product D and the residue B. In case of ideal separation, the top product composition xx DD = xx (1) DD, xx (2) DD, xx (kk) DD (2) is represented by the straight line AB on Fig. 2.The bottom flow composition is then (1) xx BB = xx BB (kk+1), xx BB (kk+2), xxbb (nn) (3) C In real conditions, three groups of components (Fig. 2) can be distinguished: Some of the lightest components of the feed (group 1) with cumulative mass fraction values up to a 1 will be completely separated. They will belong clearly to the top product D. Some of the heaviest components of the feed (group 3) with cumulative mass fraction values higher than a 2 will be completely separated too, but they will leave the column as a part of the bottom product B. The remaining (group 2) components (a 1 < mass fraction values in the feed a 2 ) will exist in both the top product and the bottom product. Since the group 1 components are completely separated, the slope of the straight line AB is defined by the ratio kk = FF DD (4) The individual mass fraction values of group 3 components in the top product are equal to zero, hence their cumulative mass fraction values in the top product are equal to 1. Finally, the cumulative mass fraction values of the group 2 components in the top product are represented by the curve MN on Fig. 2. As mentioned above, the slope of the linear part depends on the feed flow rate F and the top product flow rate D. At given combination of F and D, the reflux R (Fig. 3) affects the positions of points M and N. The increasing of reflux flow rate causes points M and N to move towards each other, and vice versa. R DD, xx D FF, xx F BB, xx B Fig. 1. A simple distillation column. Fig. 2. Feed and top product compositions. 274

3 N 2 N 1 M 2 M 1 Fig. 3. Feed and top product composition. MATHEMATICAL MODEL Based on the above considerations, the mathematical model can by described in the following way: xx DD = kkxx FF ffffff xx FF aa 1 (5) If the model parameter has been evaluated, the other parameter, t, can be found by expressions (7) and (8) (6) dddd DD dddd FF = kk ffffff xx FF = aa 1 (7) hence ττ = (1 kkaa 1 ) kk (8) Fig. 4 represents the compositions of the top product and the residue for a 1 = 0.1and D = 0.2 F. The top product composition is calculated by the model described above, while the bottom product composition is found from the material balance. The first premise for application of the described model is to define the feed flow composition. Different algorithms and software products [6, 7] are available and can be used for crude oil characterization. As a result the feed of the column is represented as a multicomponent mixture of real and pseudo components. For each of them, the mass fraction and also the boiling temperature, the average molecular mass, the density and other important properties are evaluated. If component m is the lightest one in the bottom flow, parameter a 1 is equal to the cumulative mass fraction of component m -1. So, to define the parameter a 1 it Fig. 4. Compositions of the products vs the feed composition. is necessary the lower cut-point of the bottom flow to be experimentally estimated. MODEL ADAPTATION The model (5) - (8) is a principle one. In order to be practically run it should be a priory adapted to the column which the model will be applied to. Experimental data or results of rigorous model simulations are to be used for that purpose. What is necessary to be done is: 1. To carry out a real or numerical experiment based on a rigorous model for planned combinations of the feed flow rate, the top product flow rate and the reflux flow rate. 2. To estimate the lower cut-point of the bottom product and hence, the value of the model parameter a 1 for each combination. 3. To work out a satisfactory approximation aa 1 = ff(ff, DD, RR) (9) The model described above was adapted to data, Fig. 5. Model accuracy. 275

4 Journal of Chemical Technology and Metallurgy, 50, 3, 2015 generated by use of the HYSIM simulator. The comparison of experimental and modelled bottom product composition is shown on Fig. 5. Obviously, the proposed model demonstrates a good accuracy. MODELLING AND SIMULATION OF SIDE PROD- UCTS DISTILLATION COLUMNS Simple distillation columns (Fig. 1) can still be seen as a part of some distillation systems. Their function in such cases is to separate part of the lightest crude oil fraction. In addition, being a pre-processor, they play the role of a buffer regarding the main distillation column, stabilising its operation. Many distillation systems for crude oil separation include only the main distillation unit where the full crude oil separation is carried out. A three side products distillation column is shown on Fig. 6. The side products kerosene, LGO and HGO are drawn as bottom products of the strippers S 1, S 2 and S 3. A distillation column with side products can be represented as a series of consecutive simple columns. Their number is equal to N SP +1, where N SP is the number of the side products. The three side products (Fig. 6) column can be decomposed into a series of simple columns - sections as shown on Fig. 7. Each one of the upper three sections operates as a condenser providing liquid reflux F, X F 1 D 1 2 D 2 Residue 3 D 3 P 1 HGO Fig. 7. Decomposed three side products distillation column. R i, i=2,3,4 for the next section downwards. Each one of the lower three sections provides net feed D i, i=1,2,3 for the next section upwards. The net feed D i is defined by the difference between the vapour flow Vi from section i and the liquid reflux from section upwards R i+1. At given operating conditions F, P i, i=1,2,3,4, all of the internal flows D i can be [2] calculated. The model adaptation is similar to that fora simple column described above. NSP +1 adaptive relationships are to be worked out, such as aa 1,ii = ff ii (FF, PP 1, PP 2, PP 3, PP 4, RR), ii = 1,2, N SSSS + 1 (10) It was mentioned above that the crude oil characterisation supplies information about many important properties of all crude oil components. Provided the product compositions have been calculated, the necessary product properties [14] such as cut-points, density, average boiling point, average molecular mass, etc., can be calculated as well. 4 P 2 LGO R C P 4 Gasoline P 3 Kerosene CONCLUSIONS Fig. 6. Side productsdistillation column. The proposed short-cut model for simulation of multicomponent distillation columns is simple and fast. Its adaptation needs easy obtainable data. Therefore, the model can be used for investigation, optimisation and on-line control of distillation columns and distillation systems. A very important feature of the model is that increasing the number of components does not make the model difficult or slow. In the same time, the more the components are, the higher the model accuracy is. 276

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