Model to Monitor, Predict and Control Impulse Input Response of Distillate and Reflux Ratio of A Distillation Column

Transcription

1 Applied Science Reports E-ISSN: / P-ISSN: DOI: /PSCP.ASR App. Sci. Report. 13 (1), 2016: 29-2 PSCI Publications Model to Monitor, Predict and Control Impulse Input Response of Distillate and Reflux Ratio of A Distillation Column Ukpaka C.P Department of Chemical/Petrochemical Engineering, Rivers State University of Science and Technology, Nkpolu, P.M.B. 5080, Port Harcourt, Nigeria Corresponding author chukwuemeka2@yahoo.com Paper Information Received: 11 October, 2015 Accepted: 29 November, 2015 Published: 20 January, 2016 Citation Ukpaka CP Model to Monitor, Predict and Control Impulse Input Response of Distillate and Reflux Ratio of A Distillation Column. Applied Science Reports, 13 (1), Retrieved from (DOI: /PSCP.ASR ) A B S T R A C T This work is focused on the development of mathematical model that can monitor, predict and simulate the relationship between distillate and reflux ratio using impulse application of response. The response application used was, impulse in conjunction with development of model on the interior tray, reflux drum and reboiler component. The general equation developed in the interior tray, reflux drum and reboiler component was correlated with the impulse response to evaluate the distillate and reflux ratio control action. The system was tested by applying impulse parameters and the result obtained indicates the behavior as presented in this research work. The control response is useful in monitoring the distillate and reflux ratio in a distillation column PSCI Publisher All rights reserved. Key words: Predict, Control Impulse, Distillate, Reflux Ratio, Distillation Column Introduction In this research work, the following components are useful which includes; distillation column, mathematical model, distillate product, reflux ratio, as well as the application of the response characteristics. Distillation column is often considered as the most significant unit and most commonly used in separation processes in terms of chemical application as well as separating feed streams and for the purpose of purification of final and intermediate product from the streams and for the purpose of purification of final and intermediate product from the streams (Ukpaka and Farrow, 2009; Henry, 2011; Ogoni Ukpaka, 200 and Satish, 200). The many objectives of a distillation unit is the ability to separate a mixture of components with the application of heat into different products of more than two or more, with different chemical compositions. The distillation column is made up of the following component s, entering of the feed in to the distillation column which contains the trays, the mechanisms of distillate components and the bottom components. For the distillate components will have the condenser, storage tank, Reflux and distillate product separator with the reflux flow containing a control valve. In the bottom distillate it contains the reboiler, heater with a control valve as well as recovery of the bottom product as the residual product which may be useful for other application (Amadi et al. 2007; Ukpaka, et al. 2008; Joan and Camelo 2009; Ukpaka, and Nnadi, 2008). The separation takes place in a vertical column where heat is introduced to a reboiler at the bottom and removed from condenser at the top. A stream of vapor produced in the reboiler rises through the column and is forced into contact with a liquid stream from the condenser flowing downwards in the column. The volatile (light) components are enriched in the vapors phase whereas the less volatile (heavy) components are enriched in the liquid phase (James, 2008). The distillate products: The distillate products are achieved as stated above. The mechanism to achieve the distillate products is known as the application of fractional distillation. The mechanism involve separation of the distillate product based on the boiling points: Flux ratio, control, control responses ( Ukpaka and Ndor, 2013; Ukpaka, et al and Warrant et al, 1992) Reflux Ratio: As stated above, as the feed is heated through the reboiler, the more volatile component evaporates up the column, and the condensed in the condenser, from the condenser the condensed products enters into the reflux storage tanks, from the reflux storages tank some of the product is recycled back into the fractionators. The recycled product is known

2 as (Reflux) while the remaining products comes out as distillate product. Therefore, Reflux ratio is the ratio of reflux flow to that of distillate flow. Control of a distillation unit: The control of a distillation unit is a very importance since it have a significant impact on the improvement of theproduct from the unit, also proper control of the unit will help to improve the efficiency of the distillation unit by reducing the energy consumed, there will be protecting of the environmental resources. Distillation control is a challenging problem due to the following factors: Process non-linearity, substantial coupling of manipulated variables, no stationary behavior and severe disturbances From the research works done by other researchers on the control of a distillation unit it is found that control has the major impact on the quality of product, energy usage and plant through put on those industries, also effective control of a distillation unit is the best way to reduce the operation cost of an existing unit since distillation processes requires large amount of energy (Ukpaka, 2011). Control of response: There are various types of response, some of these are: Step input response: There are functions those changes instantaneously from one level to another. If the step size is equal to one (1), then it is called a unit step function, Ramp inputs: these are functions that changes linearly with time, Impulse: This is a Dirac delta function on infinitely high pulse whose width is zero and area is unity e.g. infection of a finite amount of energy into process in an infinitesimal length of time, Sinusoidal input: these are input that vary periodically, Pulse: Pulse is a function that begins and ends at the same level, it is the sum of one positive step function made at time zero and one negative step function made DL minutes later BL is a delay or dead time, and exponential input (Ogoni and Ukpaka 200) Since distillation columns are important separation techniques in the chemical process industries around the world. Improved distillation control should be attained; the purpose of this research work is to improve the control of a distillation unit to achieve maximum quality of product, by attaining proper control of the distillate and reflux, by developing a mathematical model to control the distillation unit. The aim of the study is to develop a mathematical model that will predict, control and monitor the dynamic response of a distillation unit under extreme transient conditions, and to demonstrate the usefulness of the model for various control response of the column, the calculated result will be compared with those obtained experimentally for a multi component system. Objectives: Product quality control: Both the products from the top and bottom have to be controlled to obtain the specified percentage of compositions at the top and bottom product. Material balance control: The column control system must cause the average sum of the distillate and tail streams to be exactly equal to the average feed rate; also, the resulting adjustments in process flow must be smooth and gradual to avoid upsetting either the column or downstream process equipment fed by the column.constraints: For safe satisfactory operation of the column, certain constraints must be observed for example: The column should not flood and column pressure drop should be high enough to maintain effective. The dynamic mode for a distillation unit is to be studied by introducing step changing in reflux rate also measuring the distillate and reflux concentration, studying of the interaction of variables and selecting the best control parameters by carrying a tuning procedures using different control equipment. Distillation is an important process in chemical engineering, hence, need to be improved to increase efficiency, to enhance quality product, if this is not done, then, product of low quality may be achieved even though the need arise to produce product that have high quality than what is been produced in the past, this is because in separation of a mixture of component with slightly different volatility may overlap thereby reducing the quality of the product, therefore, the distillation unit have to be controlled and monitor properly. This study unlike others will enable us develop a mathematical model to control and monitor the distillation unit, with the aim to get quality of the product. Materials And Methods The mathematical model to be developed in this section will include the mass and energy balance equations of the feed stream the trays, the reboiler the condenser, and the reflux tank that is responsible for the distillate and reflux that goes back into the fractionators, the feed to be consider for this job is the Nigerian crude oil. Development of mathematical Model Assumptions used in this modeling The feed stream considered as stated above is the Nigerian crude oil which contains more than two components. The column preserve is assumed to be at steady state for each thing but changes linearly throughout the unit. The vapor hold up is negligible. The unit has a singular period input and two product streams, which are the over head or top product and the bottom or heavy product. At each tray and the reboiller the vapor phase is assumed to be in equilibrium with the liquid phase The equation of state used to represent the vapor liquid equilibrium is that of soave-peddlish-among (SRK). Enthalpies are estimated using ideal enthalpy data and enthalpy departure functions. The reboiler is treated as an ideal stage 30

3 Murphree tray efficiency are used for the modeling of the trays because they are assume d to be non ideal. Hydraulic time constant approach is used to treat the dynamics of the liquid tray. Heat transfer dynamics of the condenser are not considered The heat transfer dynamics of reboiler are treated using first-order lag. The column has total condenser and partial reboiler Flow rate model with first order lags to represent value dynamics Tray temperatures are used to infer overhead and bottom compositions for control. The heat transfer dynamics of the tray temperatures measurements are modeled using first order stage Sensible heat change at each tray of the column is assumed to be small enough to be rejected (Satish, 2000). Vapour/Lipid Equilibrium Figure 1. Simple Distillation Column The figure 1 above has a single feed stream and double product stream which comprises of the top and bottom product. At each tray of the fractionators the liquid composition is in equilibrium state with the vapor composition. In this distillation unit we have the following component:the feed or inlet, the trays, the reboiler, the condenser, and the reflux drum For a multi-component mixture such as crude oil, the vapor liquid equilibrium (VLE) between these components can be represented by: v = l, where l is the fugacity of the vapour component and l is the fugacity of the liquid component. Expressing the fugacity in terms of fugacity coefficient y y - - (1) Where and and fugacity coefficient of vapour and liquid fugacity are estimated using Reddish kwong equation of state. Using Redlich Kwong equation of state fugacity coefficient can be represented as 31

4 Y ci = K ij X ij (2) Where K = vaporization equilibrium ratio and is defined as Kij = Also for a multicomponent system the relative volatility is defined as: α nj = (3) Where α nj = the relative volatility of component n and j The above vapor liquid equilibrium equations above (VLE) are solved on each tray. For us to have a linear dynamic model, these equations have to be linearized at each tray around its steady state operating conditions. Using numerical techniques for the lirearization of the equations above, we have ij = [( ) ( ) ( ) ( ) ] - () This equation is solved using numerical techniques. The equations are linear but solving these equations for each tray needs a long amount of computational period, to reduce the amount of computational time an inside-out algorithm is used. The modified version of the K B method is used for a multi-component distillation unit and it is given as: ln (K Bi ) = A j (5) Using the basic rules of vapor liquid equilibrium for a given tray n and components it can be shown that K B is given by ln (KB) = (6) to calculate the parameters A and B the linear vapor liquid equilibrium equations are solved at two temperatures close to the tray temperature T and T + ΔT, ΔT being small. Using equation (5) and (6) the parameters are calculated as B i = ( ) (7 ) A i = yy ln(k ijt ) (8) Linear Modeling Using the input-out method as shown in the figure below V n L n-1 Feed Input F n Z n Stage (n) Heat input or removal DH n V n+1 L n (Y n+1 ) X n Figure 2. Component of mass balance of inflow and outflow system 32

5 Mass balance equation for stage n is given as F n + V n+1 + L n-1 = V n + L n (9) The component balance for stage n is given as F n Z n + V n+1 Y n+1 + L n-1 X n -1 = V n Y n + L n X n (10) Linear Modeling for the interior tray Using the input-output method, for nth tray the mass balance equation is: Rate of mass into the system Rate of mass out - of the system = Rate of accumulation of mass Mathematically L n V n-1 -L n -V n = (11) Equation (11) is the material balance equation of n th tray at un-steady state for us to develop the model for the trays, we have to make the system a steady state system therefore = (12) Then equation (11) becomes, n + 1 V n-1 L n- V n = (13) For the energy balance equation = h n + 1 L n +1 h n L n + V n-1 V n H (1) Becomes + = h n + 1 L n+1 h n L n + V n-1 H n-1 V n H n - (15) Is the sensible heat change on each trays, this term can be negligible for a multicomponent distillation column. Then equation 3.15 becomes = h n + 1 L n + 1 h n L n + V n-1 H n-1 V n H n (16) Substituting equation (13) into (9) we have, (h n+1 + V n-1 L n -V n ) = h n+1 h n L n - V n 1 H n-1 - V n H n - - (17) Simplify equation (17) we have Vn = (18) The liquid and vapor enthalpies are obtained from ideal enthalpy data using departure function (Satish, 2000), these departure functions are estimated using (SRK) equation of state. (Satish, 2000) thus the enthalpy equation for each component in liquid and vapor are given as n, l = on, l + Dh nl (19) n, l = on, l + DH nl (20) Where: n, l = The ideal liquid enthalpy component l Dh nl = This represent the departure of liquid enthalpy of component l at tray n from an ideal solution. 33

6 This statement is applicable for vapor enthalpy. For a multicomponent liquid and vapor stream are assumed to be ideal solution, therefore the liquid and vapor stream enthalpies are given respectively as h l = x ln ln (21) H l = ln ln (22) To obtain a linear mode for the deproparnizer the non-linear equations at each tray are linearized around the steady state operating conditions on each tray, the linearized equations are; For the mass balance equation, the linear model is = n+1 + n-1 - n - n (23) For the energy balance linear equation H is given as n = Model for the reflux drum or accumulator For the accumulator the material balance equations are = (2) The component material balance is = Y n V n (L R + D) X ACC (25) The Reflux drum is considered to be in an ideal stage, also it is assumed that the cooling water is not considered as part of the distillation unit, thereafter the energy balance equation is not put into consideration. The linear model for the reflux drum is given by - R + = (26) - R (27) Also the component balance for the linear model is given as = (Vn) - ( ) (28) Dividing through equation 3.28 by M ACC we have = ( ) - ( ) (29) = ( ) (30) Modeling of the Reboiler For the reboiler the energy and material balance equation are necessary, they are given as: = L i V o B (31) The component material balance, is given as, For energy balance, V o = = X I L I Y REB V 0 X REB B (32) Also assuming that reboiler is in it ideal state, the resulting modeled equation is 3

7 - I + O + = (33) I - O - = (3) = (x 1 x REB ) 1 + (L1) - r( - (LI VO) ( ) (35) Dividing through equation (35) by REB we have = I ( ) - ( ) - ( ) -(36) Table 1. mathematical models developed for the distillation column summarized for the different functions 1. The interior trays = L n+1 + V n+1 L n V n While the energy balance equation is V n = 2. The reflux drum or accumulator = V n L R D 3. The Reboiler = L n V O B While the energy balance equation is, Vo = Table 2. gives a list of the linear models in distillation unit. Interior tray = n+1 + n+1 - n- n For the reflux drum or accumulator For the reboiler For the energy balance equation ( ) n = = - - The mass balance equation is = - - While the energy balance equation is = Solutions to modeled equations In this section we are going to use various mathematical tools to solve the modeled equations. Solution to modeled equation for the interior tray: We have ; = L n+1 + V n+1 L n -V n (36) Assuming a constant molar overflow, where the mixture has a constant heat of vaporization and that sensible heat of mixing effect are negligible (Hery Z. Kister, 1992). L n+1 = Ln = L (37) Where L = Liquid flow rate into the distillation column Also V n+1 = V n = V (38) Substituting equation (38) and (2) into equation (11) we have Each tray is assumed to be a CSTR with a hydraulic time constant t tray, hence equation ( )becomes = (39) t = (L n+1 + V n+1 ) (L n + V n ) (0) Where = Liquid hold up on stage n t= Time 35

8 L n, V n = Input liquid and vapour flow rates L n+1, V n+1 = Output liquid and vapour flow rates From equation (0) we have Let = L n+1 + V n+1 L n -V n (1) = (L n+1 L n ) + (V n+1 V n ) (2) Substituting equation (0) and (1) into equation (2), we have, = L n + V n (3) Using laplace transform to solve equation (3) we have = SL n(s) L (o) () L n = L n(s) (5) V n = V n(s) (6) Substituting equation (3), () and (5) into equation (6) we have t (SL n(s) L (o) = L n(s) + V n(s) (7) tsl n(s) = L n(s) + V n(s) (8) TsL n(s) L n(s) = V n(s) (9) L n(s) (ts-1) = V n(s) (50) Ln(s) = (51) Equation (51) is the Laplace transform equation Ln(s)= Where L n(s) = Output response V (s) = Input response K = Gain = 1 Solution to the modeled equation for the reflux drum From equation (10) we have = - D (52) Where V n = Vapour flowrate L R = Liquid flowrate D = Distilat flow rate = dm = LR (53) Dividing through equation (10) by D we have = (5) = (55) But R = Reflux = (56) Substituting equation (56) into equation (55) we have = - R (57) 36

9 = (R + 1) (58) Let t = (59) Substituting equation (59) into (58) we have t If = (R + 1) is normalized to be a function mass dependent That is in terms of unit = x (60) Where equation (60) represent density per unit time Therefore we have, t = x - (R + 1) (61) t = M acc (R + 1) (61) let y = M acc and R + 1 = Y Therefore t y-u (61 = sy (s) y (o) y = y (s) ( 62) u = u (s) Substituting equation (62) into equation (61) we have t(sy (s) Y (o) = Y (s) U (s) tsy (s) = Y (s) Y (s) tsy (s) Y (s) = - U (s) Y (s) tsy (s) = U (s) Y(s) (1-tS) = U(s) Y(s) = - Solution to modeled equation for the reboiler the material balance equation for the reboiler is = - B (6) For the top product in a distillation unit the vapour going into the condenser is given tobe V = L + D (65) Where V = Vapour flow rate L = Liquid flow rate back into the distillation n unit D = Distillate flow rate Substituting equation (65) into equation (6) we have = L n -L D-B (66) Assuming a constant molar overflow L n + L Rearranging equation (66) we have 37

10 = (L n -L) D B = L- D- B (67) But Relux = R = Therefore L = RD (68) Substituting equation (67) into (68) we have = RD D B = D(R-1) B (69) Dividing through equation (69) by D we have = (R 1) (70) Let = τ Equation (70) becomes τ = (R 1) - If is normalized to be a function of mass dependent = x (71) τ = (R 1) - x = (R 1) M REB Let M REB = Y and (R-1) = U τ = U-Y (72) Applying Laplace transform to equation (72) we have = SY (s) Y (o) U = U (s) (73) Y = Y (s) Substituting equation (73) into equation (72) we have τ(sy (s) Y (o) ) = U (s) Y (s) Using boundary condition Y (o) = 0 τ(sy (s) ) = U (s) Y (s) τsy (s) + Y (s) = U (s) Y (s) (τs + 1) = U (s) Y(s) = (73) Control Response The response consider at this point is the impulse input response Impulses This is a dirac delta function, an infinitely high pulse whose width is zero and area is unity e.g. infection of a finite amount of energy into a process in an infinitesimal length of time V (s) = A 38

11 Applying different control response to the interior tray Impulse Y (s) = But for impulse response U (s) = Y( t) KA (7) Applying Different Control Response to the Reflux Drum Impulse For impulse input response U (s) = A But Y (s) = Therefore Y (s) = (75) Taking inverse laplace transform of equation (75) we have Y (t) = KA (76) Applying different control response to the reboiler Impulse Response For impulse response U (s) = A But Y (s) = Therefore Y (s) = Taking inverse laplace transform of equation (75) we have Y (t) = KA (77) Results And Discussion This presence the results obtained from the developed modeled equation. The results obtained from this modeled equation are gotten by testing the models with experimental data. The first part of this chapter shows the results of step input for the feed tray Table 3 Area(m 2 ) Time(seconds) Residence time(seconds) Using impulse response the plot in figure 3a,b,c,d is gotten, From the graph it is shown that for ramp input response the output y (t) increase with increase in time, but at time equal to 6.5s the output tend to drop and at time above 6.5s the output rate is increased. Also for equal time range (0 to 10s) and varying area we have different value of output rate, we can also see that increase in area also result to increase in output response from the figure above. This behavior is due to the properties of the crude, some of these properties are the viscosity of the crude oil, and the sulphur content of the crud, the presence of salt in the crud is also a major contributing factor for the behavior of the output response. 39

12 Impulse Response For The Feed Tray 5 PLOT OF AGAINST 10 PLOT OF AGAINST 1 PLOT OF AGAINST 20 PLOT OF AGAINST Figure 3.a,b,c,d : Graph of impulse response against time for the feed tray. Testing of modelled equation for the reflux drum. The figures below shows the result for tested models with different input parameters with varying area as follows, when the area is two meter square (2m 2 ), f when the area is four meter square (m 2 ) when the area is six meter square (6m 2 ) and when the area is eight meter square (8m 2 ). The figures below presents the graphs for step input response, ramp input, impulse input, pulse input and exponential input for the reflux drum Plot For Impulse Input For The Reflux Drum: The plot below represent a plot of output against time using impulse input function. PLOT OF AGAINST 2 PLOT OF AGAINST PLOT OF AGAINST 6 PLOT OF AGAINST Figure. a,b,c,d: Graph of impulse input against time for the reflux drum. From the graph it is shown that for impulse input response the output y (t) decrease with increase in time, but at time equal to 8.3s the output deviate from the impulse input function as presented in Figure a,b,c,d. Also for equal time range (0 to 10s) and varying area we have different value of output rate, we can also see that increase in area also result to increase in output response from the figure above. the behavior is due to the properties of the crude, some of this properties are the 0

13 viscosity of the crude oil, the sulphur content of the crud, the presence of salt in the crud is also a major contributing factor for the behavior of the output response. Testing of Modelled Equation for the Reboiller The figures below shows the result for tested models with different input parameters with varying area as follows, when the area is two meter square (2m 2 ), f when the area is four meter square (m 2 ) when the area is six meter square (6m 2 ) and when the area is eight meter square (8m 2 ). The figure below presents the graphs for step input response, ramp input, impulse input, pulse input and exponential input Plot for Impulse Input for the Reboiller The plot below represent a plot of output against time using impulse input function. PLOT OF AGAINST 2 PLOT OF AGAINST PLOT OF AGAINST 6 PLOT OF AGAINST Figure 5.a,b,c,d:Graph of impulse input against time for the reboiller. From the graph it is shown that for impulse input response the output y (t) decrease with increase in time, but at time equal to 8.3s the output deviate from the ramp input function as shown in Figure 5a,b,c,d. Also for equal time range (0 to 10s) and varying area we have different value of output rate, we can also see that increase in area also result to increase in output response from the figure a,b,c,and d above. the behavior is due to the properties of the crude, some of this properties are the viscosity of the crude oil, the sulphur content of the crud, the presence of salt in the crud is also a major contributing factor for the behavior of the output response Conclusion The main points concluded from the present study are summarized as follows: Area is a major factor that influences the kind of control response to be used in the distillation column. The residence time also influence output rate of the column. The type of control response applied in the distillation of unit determines if there will be an increase or decrease in the output rate with respect to time. References Amadi SA, Ukpaka CP, Akpa J, Dune KK Evaluating the effective corrosion rate and control in a Nitrogenous fertilizer plant in Nigeria, Journal of Research in Engineering, vol. 2, no. 2, pp Henry Z. Kister2011. Distilattion Design, Mc Graw-hill Incorporated, pp 28 5 James OM Perry's chemical engineering handbook 8 th edition published by McGraw-Hill Company. Joan R, Camelo B Chemical Engineering, 3 th edition published by McGraw-Hill Company. Ogoni HA, Ukpaka, PC.200. Instrumentation, Process Control and Dynamics 1 st edition, Library of congress cataloging in publication data pp Satish E Chemical Engineering, th edition published by McGraw-Hill Company. Pp

14 Ukpaka CP, Amadi SA, Njobuenwu DO Modeling the localized corrosion cell caused by differential aeration and its effective protection mechanism,journal of Modeling, Simulation and Control (AMSE), vol.69, no.2, pp Ukpaka CP, Eno O, Farrow TS Modeling the effect of physical parameter: Euler and Stanton Number on the Temperature Fields and Velocity of gas distribution on a Steam heater Tube, A Multidisciplinary Environ. Agric. Science & Techno. vol.1, no.1, pp Ukpaka CP, Farrow ST Development of model for temperature distribution on fin material during ethanol production. Nigerian Journal of Research and Production, vol.1, no.1, pp (2009). Ukpaka CP, Ndor VM The Flow characteristics of fluid (hexane) and its effectiveness on orifice plate using pneumatic proportional control.. Journal of Engineering and Technology Research, vol.5, no 5, pp Ukpaka CP, Nnadi VG.2008a.Smokeless Flare Modeling of an associated gas in a production oil flied, Journal of Modelling, Simulation and Control (AMSE), vol. 69, no.1, pp Ukpaka CP Application of Algorithm of Range-Kutta method in microbial entrained oil recovery in Oil wells of Niger Delta in Nigeria. International Journal of Current Research, vol..3, no. 12 pp Warrant M, Julian CS, Peter H Unit operations of chemical engineering 5 th edition, published by the Mc Graw-hill international editions, pp