Multivariate Linear Regression Model for Simulaneous Estimation of Debutaniser Products Compostion presentation by Obekpa R.G and Alabi S
- 1. MULTIVARIATE LINEAR REGRESSION MODEL FOR SIMULTANEOUS ESTIMATION OF DEBUTANISER PRODUCTS COMPOSITION Obekpa, R.G roseline261@gmail.com 08131807581 and *Alabi, S.B *sundayalabi@uniuyo.edu.ng 08063043106 Department of Chemical and Petroleum Engineering Faculty of Engineering, University of Uyo, Uyo, Akwa Ibom State, Nigeria NSE Annual Conference: SUNSHINE 2015 1
- 2. INTRODUCTION Debutaniser products composition and specification Top (Butane) Bottom (Pentane plus) 2.5% mole propane (max) 1.5% mole butane (max) 95% mole butane (min) 3.0% mole pentane (max) In order to maintain these compositions at their optimal values, it is necessary to measure them with high accuracy and fast response Available hardware measurement techniques Offline sample analysis in the laboratory Online product quality analyzers NSE Annual Conference: SUNSHINE 2015 2
- 3. Unfortunately, these instruments are plagued with measurement delay and as such, hinder effective feedback control of the column Challenges with available models Inability to predict all the required compositions of both the top and bottom product Project Objective Development of a linear regression model for the purposes of online prediction of any debutaniser top and bottom products composition. NSE Annual Conference: SUNSHINE 2015 3
- 4. MATERIALS Software Packages MINITAB for design of experiment MS EXCEL SPREADSHEET for data analysis HYSYS for modelling and simulation NSE Annual Conference: SUNSHINE 2015 4
- 5. METHODS Variable selection Definition of operating conditions Design of experiments Data acquisition/generation Model development and performance evaluation NSE Annual Conference: SUNSHINE 2015 5
- 6. RESULTS AND DISCUSSION 6 C3 top C4 top C5 top C4 bot C5 bot = 0.010229 0.855470 0.134460 0.031890 0.663670 + −0.00000003 − 0.00000005 … − 0.00000319 −0.0000272 − 0.00002842 … − 0.00000459 0.0000275 0.000002844 … 0.000004580 0.00000055 0.00032265 … 0.000007370 0.00000754 − 0.00034750 … 0.000000370 A B C D E F G H I J Where A = Feed flow rate (kg/hr) B = Feed temperature (oC) C = Feed pressure (kPa) D = Reflux flow rate (kg/hr) E = Bottom flow rate (kg/hr) F = Top pressure (kPa) G = Total number of trays H = Feed tray I = Bottom temperature (oC) J = Top temperature (oC)
- 7. Performance Indices of the Developed Model Predicted Outputs R2 Percentage Mean Relative Error (%) Total top propane 0.969 0.73 Total top butane 0.963 0.84 Total top pentane 0.963 9.66 Total bottom butane 0.416 2554.3 Total bottom pentane 0.960 3.33 NSE Annual Conference: SUNSHINE 2015 7
- 8. Interpolative and Extrapolative Performance Indices of the developed Model Predicted Outputs Percentage Mean Relative Error (%) Interpolation Extrapolation Total top propane 1.718 1.801 Total top butane 0.627 1.326 Total top pentane 5.755 8.150 Total bottom butane 6139.8 673.8 Total bottom pentane 3.580 14.43 NSE Annual Conference: SUNSHINE 2015 8
- 9. Graphical representation of interpolation ability of the developed model 9
- 10. Discussion The regression equations with high R2 and low PMRE showed that the observed outcomes are well replicated by the model, thus indicating high accuracy. The low R2 value of 0.416 and high PMRE of 2554.3 for bottom total butane equation indicates that the prediction accuracy level is low. Both evaluation techniques (R2 and PMRE) point out the fact that the regression equations are highly accurate with the exception of the bottom total butane. NSE Annual Conference: SUNSHINE 2015 10
- 11. CONCLUSIONS • The equations for top total propane, top total butane, top total pentane and bottom total pentane have high accuracies and generalisation abilities. • The proposed model can be used outside the range of data used for model development, as the resulting extrapolation errors are deemed reasonable for practical applications. NSE Annual Conference: SUNSHINE 2015 11
- 12. RECOMMENDATION The performance of the linear regression equation for the total bottom butane is very poor. Hence, in future work(s), linear equation of a higher order can be considered. Alternatively, a nonlinear model like artificial neural network which has been noted for its ability to model nonlinear systems with high accuracy can be considered. NSE Annual Conference: SUNSHINE 2015 12
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- 14. NSE Annual Conference: SUNSHINE 2015 14 Questions??