Predicting Propylene Loss With Inferential Model

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2014-01-01

Predicting Propylene Loss With Inferential ModelDevelopment Using Design Of Experiments (doe)And Historical DataJeffrey Allen WheelerUniversity of Texas at El Paso, [email protected]

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PREDICTINGPROPYLENELOSSWITHINFERENTIALMODELDEVELOPMENT

USINGDESIGNOFEXPERIMENTS(DOE)ANDHISTORICALDATA

JEFFREYALLENWHEELER

DepartmentofIndustrial,ManufacturingandSystemsEngineering,IMSE

Approvals:

__________________________________________

Tzu‐Liang(Bill)Tseng,Ph.D.,Chair

________________________________________________YitongLin,Ph.D.

________________________________________________EricD.Smith,Ph.D.

____________________________________

CharlesAmbler,Ph.D.DeanoftheGraduateSchool

Copyright©

By

JeffreyAllenWheeler

2014

PREDICTINGPROPYLENELOSSWITHINFERENTIALMODELDEVELOPMENT

USINGDESIGNOFEXPERIMENTS(DOE)ANDHISTORICALDATA

BY

JEFFREYALLENWHEELER,B.S.CHEMICALENGINEERING

THESIS

PresentedtotheFaultyoftheGraduateSchoolof

TheUniversityofTexasatElPaso

InPartialFulfillment

OftheRequirement

fortheDegreeof

MASTEROFSCIENCE

DepartmentofIndustrial,ManufacturingandSystemsEngineering,IMSE

THEUNIVERSITYOFTEXASATELPASO

August2014

iv

ACKNOWLEDGEMENTS

My love and gratitude go tomywife, StefnyWheeler. Her support through

this chapter inmyeducation allowedme to accomplish thismilestone. Her

loveandpatientskeptmeafloatthroughthisjourney.Myparents,foralways

supporting me through tough times. In addition, thanks would like to be

extended to the IMSE department at the University of Texas at El Paso.

Withouttheassistanceofthedepartment,thisresearchwouldnotbepossible.

Thanks are also extended to the personnel at Enterprise Products. Their

supportintheiremployees’questforhighereducationallowsmetoconduct

andanalyzereallifeindustrialapplications.

v

ABSTRACT

Inferential models are a highly researched topic as the science of digital

automation becomesmore prevalent as information is in abundance. Well‐

developed inferredmodels canaugment theuseofanalyzers in steadystate

processingandhighlycorrelatedonescanevenreplaceonlineanalytics.The

use of design of experiments (DOE) inferredmodelswith historical process

dataandarigorousplantsimulatorcanreducethecasestudydurationwhile

achievingahighdegreeofaccuracy.Thispaperusessurfaceresponseandfull

factorialmodelsasthefirststepinmodeldevelopment,andthenusesactual

historical plant data to create a well‐defined inferred property. The main

effect interactions need to be analyzed and identified to determine their

statisticalsignificance.Thisstepisimportantbecausetheinteractionfactors

willnotbeleftoutofthefinalmodelifsignificant.Thoroughanalysisshows

the identifiedmodel to be robust but exhibits orthogonality in the uncoded

units equation. The model was reduced to the main effects to remove

orthogonality. Once complete a strong model was identified with good

success and application. After identification, themodelwas tweaked to the

historicaldataforbetteraccuracy.Thismethodprovessuccessfulinreducing

vi

plant step tests and case study durations to develop a good cost effective

correlatedmodel.

vii

TABLEOFCONTENTS

ACKNOWLEDGEMENTS ...................................................................................... iv

ABSTRACT ........................................................................................................... v

TABLE OF CONTENTS ......................................................................................... vii

LIST OF TABLES .................................................................................................. ix

LIST OF FIGURES .................................................................................................. x

CHAPTER 1: INTRODUCTION ............................................................................... 1

1.1 MOTIVATION ............................................................................................ 1

1.2 OBJECTIVE ................................................................................................ 2

1.3 FOCUS OF THE STUDY ............................................................................... 2

1.4 CONTRIBUTIONS ....................................................................................... 2

CHAPTER 2: PROBLEM STATEMENT ..................................................................... 4

CHAPTER 3: LITERATURE REVIEW ........................................................................ 9

CHAPTER 4: METHODOLOGY ............................................................................. 11

CHAPTER 5: CASE STUDY ................................................................................... 15

5.1 HISTORICAL DATA PROCESSING ............................................................... 16

viii

5.2 DESIGN OF EXPERIMENTS (DOE) SET UP .................................................. 18

5.3 DEPENDENT COLLINEARITY ...................................................................... 23

5.4 DEPENDENT DOE SETUP .......................................................................... 24

CHAPTER 6: RESULTS AND CONCLUSIONS ......................................................... 26

6.1 CASE STUDY RESPONSE RESULTS ............................................................ 26

6.2 ANOVA ANALYSIS ................................................................................... 27

6.3 HISTORICAL DATA FINE TUNING ............................................................. 36

6.4 CONCLUSIONS ........................................................................................ 40

CHAPTER 7: FUTURE RESEARCH ........................................................................ 42

WORKS CITED ................................................................................................... 43

APPENDICES ...................................................................................................... 47

LEGEND FOR PROCESS FLOW DIAGRAMS ...................................................... 47

ADDITIONAL GRAPHS .................................................................................... 48

FINAL MODEL ................................................................................................ 55

COMPLETE MINITAB OUTPUT ........................................................................ 60

FULL FACTORIAL ............................................................................................ 69

VITA .................................................................................................................. 83

ix

LISTOFTABLES

Table 1: Summary for Literature Review ........................................................... 10

Table 2: Manipulated Variables ........................................................................ 17

Table 3: Manipulated Variable Factor Table ...................................................... 20

Table 4: 2K Dependent Variables ....................................................................... 25

Table 5: Case Study Results ............................................................................... 26

Table 6: Coded 2K Regression Model ................................................................. 31

Table 7: Uncoded 2K Regression Model ............................................................. 32

Table 8: Orthogonalty Test Results ................................................................... 33

Table 9: Linear Regression Model ..................................................................... 35

Table 10: Final Equation in Matrix Form ............................................................ 40

Table 11: Legend for Process Flow Diagrams ..................................................... 47

x

LISTOFFIGURES

Figure 1: Typical Distillation Column ................................................................... 4

Figure 2: Batch MISO Control Configuration ........................................................ 6

Figure 3: Continuous MISO Control Configuration ............................................... 6

Figure 4: Methodology Flow Sheet .................................................................... 13

Figure 5: DeC2 Column ...................................................................................... 16

Figure 6: Ethane Histogram ............................................................................... 17

Figure 7: Feed Histrogram Plot .......................................................................... 18

Figure 8: Overhead Pressure Histogram Plot .................................................... 18

Figure 9: Economizer Flow Histogram ............................................................... 22

Figure 10: Side Condenser Flow Histogram ....................................................... 23

Figure 11: Overhead Temperaure Histogram Plot ............................................. 24

Figure 12: Cooling Exchanger Delta P ................................................................ 25

Figure 13: Probability Plot of Response ............................................................. 27

Figure 14: Normal Plot of Effects ....................................................................... 28

Figure 15: Normal Plot of the Standard Effects .................................................. 29

Figure 16: Normal Probability Plot of the Residuals .......................................... 29

Figure 17: Residual vs Fits ................................................................................. 29

xi

Figure 18: Normal Plot of Effects (Dependent) ................................................. 30

Figure 19: Coded R2 Fitness Check ..................................................................... 31

Figure 20: Uncoded R2 Fitness Check ................................................................. 33

Figure 21: Main Effects Plot w/o Pressure MV .................................................. 34

Figure 22: Uncoded Reduced Fitness Check ....................................................... 35

Figure 23: Raw Inferential ................................................................................. 36

Figure 24: Smoothed Inferential ........................................................................ 37

Figure 25: Final Graph Segment 1 ...................................................................... 38



Figure 28: R2 Regression .................................................................................... 39

Figure 29: Ethane Goodness of Fit Plot .............................................................. 48

Figure 30: Ethane Normality Plot ...................................................................... 48

Figure 31: Feed Goodness of Fit Plot ................................................................. 49

Figure 32: Feed Normality Plot .......................................................................... 49

Figure 33: Overhead Pressure Goodness of Fit .................................................. 50

Figure 34: Pressure Normality Plot .................................................................... 50

Figure 35: Side Condenser Flow Histogram ....................................................... 51

xii

Figure 36: Overhead Temperature Normality Plot ............................................. 51

Figure 37: Overhead Temperaure Normality Plot .............................................. 52

Figure 38: Normal Plot of the Effects, α = 0.01 .................................................. 52

Figure 39: Effects Plot w/o Pressure .................................................................. 53

Figure 40: Liquid to Vapor Propylene Relationship ............................................ 53

Figure 41: Uncoded R2 Regression w/o Pressure ............................................... 54

1

CHAPTER1:INTRODUCTION

Todaythereisalotofeffortputforthwithensuringthatproductqualityisof

thehigheststandardinthehydrocarbonprocessingindustry(HPI). Pushing

the processing units harder and closer to the edge of equipment design is

extremelydesirableasproductmarginsdictateuptime.Partofthattaskisto

tighten the operational dead band around the product specification.

Operating costs and products give away impact the bottom dollar of the

company.

1.1Motivation

Online process analyzers, typically gas chromatographs (GC), are extremely

expensive. The total installed costs for a single unit typical run into the

hundredsof thousandsofdollars. Thisdoesnot includethesupportstaff to

ensure that the GC stays online and accurate. GCs were the standard

measurement when the process measurement could not keep up. Digital

technology has increased the resolution and repeatability of process

measurement making information readily available and in abundance.

Statistical modeling has been a growing field with the birth of digital

2

technology and has accomplished great success with less capital and

operationalcosts.

1.2Objective

Theobjectiveofthisresearchistodevelopamodeltopredictpropylene(C3=)

contentintheoverheadofadeethanizercolumn.Theultimategoalistohave

amodelcorrelatewellenoughtoplaceinclosedloopregulatorycontrol.Once

developed,themodelneedstobetestedbyobservingthehistoricaldataand

thesampledresults.

1.3FocusoftheStudy

Many independent variables control the distillation in deethanizer columns.

Themain independent variables for this study are feed concentration, feed

flow,columnpressure,economizerflow,vapordrawandsidecondenserflow.

In previousmethodologies, the interaction terms are not analyzed and it is

wellknowthatchemicalprocessingishighlycollinear[1].

1.4Contributions

This study will use a robust simulated process along with actual historical

process data to aid in the developing inferred models. The simulation will

3

contribute by determining any process measurement variable that is not

withinrangeorcorrectcalibration. Italsoreduced thecasestudyduration.

The research contribution will be another methodology to analyze process

inferentials.Thiswillcreateamorerobustequationwhileminimizingcapital

costsandoperatingcostsovertime.

4

CHAPTER2:PROBLEMSTATEMENT

In the chemical processing industry, the workhorse of the process is the

distillation column. When analyzed, the matrix comes out to a 5x5 of

Manipulated Variables (MVs) vs. Controlled Variables (CVs) [2]. The typical

MVsareDistillateProduct(D),BottomsProduct(B),Reflux(R),ReboilerHeat

Input(Qr),CondencerHeatRemoval(Qc). TheCVsforthetypicaldistillation

columnaretheDistillateComposition(Xd),BottomsComposition(Xb),Reflux

Drum Level (Lr), ColumnBottom Level (Lb) and Column Pressure (P). See

Figure1.Forfiguresymgologyseeappendix.

Figure1:TypicalDistillationColumn

5

Thetypicalcolumnmentionedutilizescomputerizedregulatorycontroloften

referred to a distributed control system (DCS). The MVs are adjusted to

ensure that the CVs are operating between the operating limits. Outside

disturbances such as feed composition changes, and material temperatures

cancauseupsetsinthesteadystateprocess.Usually,upsetssuchastheseare

not seen in the correspondingCVswithout significantdelay timedue to the

nature of the process. The regulatory controllers (alsoMVs) are considered

Single‐inSingle‐out(SISO)design.ThemainissueoftheSISOdesignisdueto

the high correlation between the MVs and CVs in the process [1]. These

controllersactindependentlyaccordingtotheirconfiguration.

AnemergingfieldinprocesscontroliscalledAdvancedProcessControl(APC).

Therearetwomainclassifications:

1. AdvancedRegulatoryControl(ARC)

2. AdvancedMultivariableControl(AMC)

ARC is a controller design that utilizes Multi‐in Single‐out (MISO) control.

This often contains a linear equation, referred to as an inferential, that

computestheprocessvariable(PV)usingmultipleknowninputsandadjusts

the final output (OP) to the desired set point (SP). In this case, the batch

6

process measurement is a process where a sample is taken to the lab and

analyzedthenacorrection(bias)isappliedtoapredatedpredictionterm,see

Figure2.

Figure2:BatchMISOControlConfiguration

The second application of the ARC takes a steady state online process

measurement and applies it to the model continuously, augmenting the

analyzer’srecordedvalue,seeFigure3.

Figure3:ContinuousMISOControlConfiguration

AMC is aMulti‐inMulti‐out (MIMO)methodology that utilizes coupledMVs

andCVs in amatrix tomoveall theMVsoptimizing theprocess toward the

CVs.MIMOistypicallyastate‐spacedynamicmodelthatrecordsCVresponse

7

comparedperMVmove. TheCV in theMIMOmethodcouldbean inferred

propertymodelasdiscussedinthisresearch.Thispaperwillnotexplorethe

MIMOconfigurationorthedynamicresponseofthesystem.

BothMIMO andMISO processes can utilize inferentialmodels. Inferentials

reduceprocessdeadtimefromdisturbancetoprocessmeasurementandare

highlysoughtafterbecausetheycanproviderobustcontrolatamuchlower

costthananonlinesampler.Thesearesometimereferredtoas“softsensors”

[3] [4]. This paper explores a new methodology of coupling Design of

Experiment (DOE) analysis with historical process data and a rigorous

simulated plant model to develop inferential models for MISO or MIMO

applications.Thisequationcanbeseenasaninputvariablematrix(B)inthe

state‐space model of multivariable process control equation (1). The

associatedmodelis:

8

(1)

(2)

Where:

x ≡ l‐dimension vector of state variables u ≡ m‐dimension vector of manipulated variables

y ≡ n‐dimension vector of output variables d ≡ k‐dimension vector of disturbance variables

A(state),B(input),C(Output),andΓarethematricesforthecorresponding

vectors.[5]

9

CHAPTER3:LITERATUREREVIEW

Literature reviewed for this design explored many different inferential

developmentmethodologies. The commonunderlying factorwas a need to

develop better input models for the desired control system. The two step

procedure proposed by Amirthalingam, Sung, & Lee utilized historical data

generatedbyasimulatorandthenusedtestdatafromthatsamesimulatorto

develop the inferential. After using Partial Least Squares (PLS) regression,

they adjusted themodel gains to the historical data to place the inferential

controlonline[6].Theirmethodprovednobetterthantheregulatorymodel

of the original simulator. Zhou, Liu, Huang, & Zhang used an aggregate

bootstrapmodelalongwithPLStodistinguishbetweenvaryingcrudefeedsto

determine thekersoenedrypoint. They tested theirmethodologyutilizinga

simulated case and applying it effectively to an industrial application, again

using PLS regression [7]. There is also the reasearch done by a couple of

teams focusing on neural networks (NN). Hu, Zhao, and Liang use an

autoregressiveexogenous(ARX)‐NNthatutilizedPLSaswell.Theirproposed

modelwas determined to be robust and concise for inferential applications

[8].Shang,Yang,Huang,andLyualsouseanArtifical‐NNdesigninthedeep

learningtechniquetoassistinthemodel’sidentification.Theirmodelproved

10

sucessful in its ability to analyze massive amounts of data and process it

accuratelytopredictactualsampledvalues[4].NNareagreattooltoassistin

nonlinear models. As mentioned, this paper focuses on DOE model

identification.Asummarytableisprovidedseetable

Table1:SummaryforLiteratureReview

Authors Years Methodology Focus

Amirthalingam,

Sung, & Lee 2000

Two step

procedure,

(Simulated)

Historical Data,

Plant Test data,

PLS, Simulated

Stochastic

system model

Zhou, Liu,

Huang, & Zhang 2012

Aggregate

bootstrap, PLS,

Simulated,

Industrial

Application

Inferential

Estimation of

Kerosene

Hu, Zhao, and

Liang 2012

Autoregressive

exogenous

(ARX)‐NN, PLS,

Simulated

Nonlinear

MIMO contol

Shang, Yang,

Huang, and Lyu 2014

ANN, deep

learning,

Industrial

application

Soft Sensors on

deep learning

11

CHAPTER4:METHODOLOGY

This paper explores the use of historical data and a rigorous dynamic

simulationtoassessthevalueofaDOEmodelforinferredpropertyprediction

in an online plant environment. One way this method differs from the

literature reviewed is that themodel identifiedwillutilizeDOEmethods for

thefinalequation.UsingeitherDOEtechniquesFactorialorSurfaceResponse

canyieldahigherdegreeofaccuracythroughmaineffectinteractionanalysis.

The surface response analysis will be used first because a larger order

polynomialisdesiredinthe[‐1,1]codedrange.Alargerorderpolynomialis

moreeffective inreducingcollinearity[9]. Theproposedequationwasthen

checkedagainsthistoricalplantdataforvalidity.Afterfine‐tuningthemodel’s

gainsandevaluatingthemodel’s,accuracywithhistoricaldata,themodelcan

then be placed on the DCS for further PV processing and model tuning.

Eventually,thegoalistoestablishthemodelinanonlineplantenvironmentin

closedloopadvancedinferredregulatorycontrol.

12

Assumingthattherigoroussimulationisaccuratetoplanttestdataandfully

functional,themethodologyisasfollows:

Phase1

o Generate system step responses, iterative process with historical

dataandsimulationmodel

o PerformDOEexperiment(SimulatedModel)

o ConductANOVAanalysis

Phase2

o Adjustmodelgainstomatchplantdata

o Checkregressionvalidity

o Comparepredictedvaluevsplantdata

Tobetterunderstandthestepsandphasesofthemethodology,seeFigure4.

13

Choose manipulated variables to model,

(as many as possible)

Gather data and filter

Perform DOE Experiment

Is a rigorous simulation available?

Identify highly valued

target process variable

Yes

Check Historical data vs.

simulation

No

Converge Simulation

Does the simulation match

historical data

Generate Responses from

Simulation

Yes All responses developed?

Yes

No

Perform Step Test

No

Generate step responses from historical data

Generate step responses from historical data

Regress model vs. historical data

Adjust gains accordingly

Investigate data discrepancies

Install on system and observe

Lead‐Lad Filtering

Figure4:MethodologyFlowSheet

Thefirstphaseintheproposedmethodologyistoutilizeplantdataandbasic

statistics to develop the step responses and rule out any outliers. The first

step,historicaldatafiltering,isfollowedbythecasestudy,DOEcomputations,

andtheANOVAanalysis.Thesecondphaseusesthedatafromthefirstphase

to fine tune the model. This is done by checking the gains found in the

historicaldataagainstthepredictedgainsdevelopedfromthecasestudy.

The followingequationswill beused for theDOEanalysis [10]. Inorder to

fullyperformthesumofsquaresanalysis,firstcalculatethecontrast:

14

…. 1 1 … 1 (3)

Furthermore,theeffectsandthenthesumofsquares:

… …. (4)

Minitab™willbeusedtoperformthesecomputations.

15

CHAPTER5:CASESTUDY

The tower chosen for this example is a deethanizer (DeC2) column in a

propane propylene splitter operation, see Figure 5. It is important for the

towertominimizethepropylenelosses,asitisthedesiredkeycomponentfor

polymer production. This column was chosen due to the use of online

analytics. They will aid in either proving or disproving the proposed

methodology by tracking the model with the online analyzer through

historicaldata.

Pleasenotethatthefollowingdataisasimplifiedversionduetoproprietary

information. The flowdiagram, factorstepsizes, factor table,andsimulated

caseinformationarecompanyownedinformation.

5.1His

Inorde

the MV

gathere

capture

to dete

could b

storicalDa

ertoaccur

Vs must b

edforthre

edaccurat

ermine the

be due to

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eemonths

tely. The

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plant sta

Figure

essing

erminethe

ed and hi

satone‐ho

datawas

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rtup, shut

16

5:DeC2Colu

eappropr

istorized,

ourinterva

filteredt

1] step si

tdown,m

umn

riatesteps

see Table

alstoensu

oremove

izes. The

eter calib

sizeforth

e 1. Pl

urethatst

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e outlayin

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heDOEdes

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tepsizesw

thenanaly

ng data po

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were

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e, or

17

incorrect ranges etc. Only themaster control algorithms in cascade loops

werechosenfortheMVs.SeeTable2

Table2:ManipulatedVariables

Ethaneinthefeedwasmodeledasanindependentandwillbeconsideredasa

feedforward(FF)forthemodel.Ethanehasahugeimpactontheoperationof

theunitcausingpropylenerecoverytobediminished.Afterdataprocessing,

the following histograms, Figures 6, 7, 8 with the use of Minitab™ were

developedtodeterminethedata’sutility.

Figure6:EthaneHistogram

Factor Service Units

A Ethane Concentration %

B Feed BPD

C Overhead Pressure PSIG

D Vapor Draw Lbs/Hr

E Economizer Flow BPD

F Side Condenser Flow BPD

250

200

150

100

50

0Ethane Concentration

Freq

uenc

y

Loc -0.8089Scale 0.4803N 2105

Histogram of Ethane ConcentrationLognormal

18

Figure7:FeedHistrogramPlot

Figure8:OverheadPressureHistogramPlot

5.2DesignofExperiments(DOE)setup

After the historical data was processed, the DOE factors were developed.

Usingthehistograms,thebinwiththegreatestfrequencyusedforonefactor

levelandthenastandarddeviationupordown,dependingonthevariablefor

140

120

100

80

60

40

20

0Feed

Freq

uenc

y

StDev 790.8N 2105

Histogram of FeedNormal

300

250

200

150

100

50

0Overhead Pressure

Freq

uenc

y

Shape 3089Scale 0.07367N 2105

Histogram of Overhead PressureGamma

19

theotherfactorlevel.Onereplicatewaschosenduetotherepeatabilityofthe

simulation.TheresultingmatrixisrepresentedinTable3.

20

Table3:ManipulatedVariableFactorTable

Ethane Feed Overhead Pressure Vapor Draw Economizer Flow Side Condenser Flow

‐1 1 1 1 1 ‐1

1 ‐1 ‐1 1 ‐1 ‐1

1 1 1 1 ‐1 1

‐1 ‐1 ‐1 ‐1 1 ‐1

1 1 1 1 1 1

‐1 1 1 1 1 1

1 1 ‐1 1 ‐1 1

1 1 1 ‐1 ‐1 ‐1

‐1 1 ‐1 ‐1 1 1

1 1 ‐1 1 ‐1 ‐1

1 ‐1 ‐1 1 1 ‐1

‐1 ‐1 1 ‐1 1 1

‐1 1 ‐1 1 ‐1 ‐1

1 1 1 ‐1 1 ‐1

‐1 1 1 ‐1 ‐1 1

1 ‐1 1 1 1 1

1 ‐1 ‐1 1 ‐1 1

1 ‐1 ‐1 ‐1 ‐1 1

1 1 ‐1 ‐1 ‐1 1

‐1 ‐1 ‐1 ‐1 1 1

1 1 ‐1 1 1 1

1 1 1 1 ‐1 ‐1

1 ‐1 ‐1 1 1 1

1 1 1 ‐1 1 1

1 ‐1 1 1 1 ‐1

1 1 ‐1 ‐1 ‐1 ‐1

‐1 1 ‐1 1 1 1

1 ‐1 1 ‐1 ‐1 ‐1

1 1 1 ‐1 ‐1 1

‐1 ‐1 1 1 ‐1 1

‐1 1 1 ‐1 1 ‐1

1 ‐1 ‐1 ‐1 ‐1 ‐1

1 1 1 1 1 ‐1

1 ‐1 ‐1 ‐1 1 ‐1

‐1 ‐1 1 1 ‐1 ‐1

‐1 1 ‐1 1 1 ‐1

1 ‐1 1 ‐1 ‐1 1

‐1 ‐1 ‐1 ‐1 ‐1 ‐1

‐1 ‐1 ‐1 1 ‐1 1

‐1 ‐1 ‐1 ‐1 ‐1 1

‐1 1 ‐1 ‐1 ‐1 ‐1

1 ‐1 1 ‐1 1 1

‐1 1 ‐1 ‐1 1 ‐1

‐1 1 1 ‐1 1 1

‐1 1 1 1 ‐1 ‐1

‐1 ‐1 1 ‐1 ‐1 1

‐1 1 1 ‐1 ‐1 ‐1

‐1 1 ‐1 ‐1 ‐1 1

1 1 ‐1 ‐1 1 ‐1

1 ‐1 1 1 ‐1 ‐1

‐1 1 ‐1 1 ‐1 1

‐1 ‐1 ‐1 1 1 1

1 ‐1 1 1 ‐1 1

‐1 ‐1 1 1 1 ‐1

‐1 ‐1 1 ‐1 1 ‐1

‐1 ‐1 1 ‐1 ‐1 ‐1

‐1 ‐1 ‐1 1 ‐1 ‐1

1 1 ‐1 ‐1 1 1

1 ‐1 1 ‐1 1 ‐1

‐1 1 1 1 ‐1 1

‐1 ‐1 ‐1 1 1 ‐1

‐1 ‐1 1 1 1 1

1 1 ‐1 1 1 ‐1

1 ‐1 ‐1 ‐1 1 1

21

ThreeoftheMVfactorsdidnotfitanyprobabilitydensityfunctionpreviously

shown.

5.2.1VaporDraw

Thevapordrawhistoricaldatawasthoroughlycheckedagainstthesimulation

and the vertices picked did not converge in the simulation. Often, there is

two‐phase flow through that meter which affects the measurement.

Therefore,theverticeschosenwerebasedontheresponsefromthemodelin

aregionthatthesimulationconverged.Ideally,thespanandrangeoftheflow

indicationmustbecorrected.Thishasweightedimplicationsonthehistorical

data that can be biased according to discrepancies between themodel and

historicaldata.

5.2.2EconomizerFlow

The economizer flow did not have enough data to determine variable

operatingranges. Thenormaloperatingrangebinandthenthenexthighest

occurringfrequencybinwereselected,seeFigure10.

22

Figure9:EconomizerFlowHistogram

5.2.3SideCondenserFlow

Thesidecondenser flowalsodidnot fitaprobabilitydensity function. This

meter’scalibrationwaswrongforthetimerangeselectedandlaterchanged

tomatchthesimulatedmodel.Historicaldataforalaterperiodused,andthe

bin with the highest frequency and one standard deviation higher were

chosen,seeFigure11.

900

800

700

600

500

400

300

200

100

0Economizer Flow

Freq

uenc

y

Histogram of Economizer Flow

23

Figure10:SideCondenserFlowHistogram

5.3DependentCollinearity

Component concentration in amixture is set by temperature and pressure.

Without being able to independently manipulate the accumulator

temperature, another simulation must be run to determine if interaction

variable are needed between the temperature, pressure, and the

concentration variables. Historical data was used to determine the [‐1, 1]

indices as previously conducted for the MVs. Figure 9 is the histogram

developed.

100

80

60

40

20

0Side Condenser Flow

Freq

uenc

y

Histogram of Side Condenser Flow

24

Figure11:OverheadTemperaureHistogramPlot

5.4DependentDOEsetup

Knowing that composition is set by pressure and temperature, the second

DOEdesignwasdevelopedon two levels. Theoverheadaccumulatorof the

vessel demonstrated consistent pressure drop across the exchangers. The

samepressureas thecolumnpressure for the factordesignwasusedminus

the drop, see Figure 12. The samemethod used previously mentioned for

determiningtheotherfactorverticeswasusedforthetemperaturevariable.

Table4showsthefactordesignincodedunits.Again,onereplicatewaschose

due to the repeatability of the simulation. The Soave‐Redlich‐Kwong (SRK)

[11]EquationofState(EOS)intheAspenHYSYSmodelwasusedtodetermine

the effect of temperature and pressure on propylene in the overhead

accumulatoroftheDeC2tower.

300

250

200

150

100

50

0Overhead Temperature

Freq

uenc

y

StDev 4.555N 2101

Histogram of Overhead TemperatureNormal

25

Figure12:CoolingExchangerDeltaP

Table4:2KDependentVariables

Service Low Verities High Vertices

Accumulator Pressure ‐1 1

Accumulator Temperature ‐1 1

1 2001 4001 6001 8001 10001

Delta P

Time (Hours)

Delta P Across Cooling

26

CHAPTER6:RESULTSANDCONCLUSIONS

6.1CaseStudyResponseResults

Table5representstheresultsfromthecasestudy.

Table5:CaseStudyResults

Ethane Feed Overhead Pressure Vapor Draw Economizer Flow Side Condenser Flow Overhead Proplyene

‐1 ‐1 ‐1 ‐1 ‐1 ‐1 0.4064

1 ‐1 ‐1 ‐1 ‐1 ‐1 0.093

‐1 1 ‐1 ‐1 ‐1 ‐1 0.3998

1 1 ‐1 ‐1 ‐1 ‐1 0.0847

‐1 ‐1 ‐1 ‐1 ‐1 ‐1 0.4063

1 ‐1 ‐1 ‐1 ‐1 ‐1 0.0932

‐1 1 ‐1 ‐1 ‐1 ‐1 0.3996

1 1 ‐1 ‐1 ‐1 ‐1 0.0846

‐1 ‐1 ‐1 1 ‐1 ‐1 0.4486

1 ‐1 ‐1 1 ‐1 ‐1 0.1542

‐1 1 ‐1 1 ‐1 ‐1 0.4424

1 1 ‐1 1 ‐1 ‐1 0.146

‐1 ‐1 ‐1 1 ‐1 ‐1 0.4485

1 ‐1 ‐1 1 ‐1 ‐1 0.1544

‐1 1 ‐1 1 ‐1 ‐1 0.4422

1 1 ‐1 1 ‐1 ‐1 0.1462

‐1 ‐1 ‐1 ‐1 1 ‐1 0.4001

1 ‐1 ‐1 ‐1 1 ‐1 0.0844

‐1 1 ‐1 ‐1 1 ‐1 0.3933

1 1 ‐1 ‐1 1 ‐1 0.0759

‐1 ‐1 ‐1 ‐1 1 ‐1 0.3999

1 ‐1 ‐1 ‐1 1 ‐1 0.0846

‐1 1 ‐1 ‐1 1 ‐1 0.3931

1 1 ‐1 ‐1 1 ‐1 0.0761

‐1 ‐1 ‐1 1 1 ‐1 0.4427

1 ‐1 ‐1 1 1 ‐1 0.1457

‐1 1 ‐1 1 1 ‐1 0.4364

1 1 ‐1 1 1 ‐1 0.1373

‐1 ‐1 ‐1 1 1 ‐1 0.4426

1 ‐1 ‐1 1 1 ‐1 0.146

‐1 1 ‐1 1 1 ‐1 0.4362

1 1 ‐1 1 1 ‐1 0.1376

‐1 ‐1 ‐1 ‐1 ‐1 1 0.4008

1 ‐1 ‐1 ‐1 ‐1 1 0.0848

‐1 1 ‐1 ‐1 ‐1 1 0.3941

1 1 ‐1 ‐1 ‐1 1 0.0763

‐1 ‐1 ‐1 ‐1 ‐1 1 0.4006

1 ‐1 ‐1 ‐1 ‐1 1 0.085

‐1 1 ‐1 ‐1 ‐1 1 0.3938

1 1 ‐1 ‐1 ‐1 1 0.0765

‐1 ‐1 ‐1 1 ‐1 1 0.4433

1 ‐1 ‐1 1 ‐1 1 0.1464

‐1 1 ‐1 1 ‐1 1 0.4371

1 1 ‐1 1 ‐1 1 0.1379

‐1 ‐1 ‐1 1 ‐1 1 0.4433

1 ‐1 ‐1 1 ‐1 1 0.1466

‐1 1 ‐1 1 ‐1 1 0.437

1 1 ‐1 1 ‐1 1 0.1382

‐1 ‐1 ‐1 ‐1 1 1 0.3945

1 ‐1 ‐1 ‐1 1 1 0.0763

‐1 1 ‐1 ‐1 1 1 0.3877

1 1 ‐1 ‐1 1 1 0.0676

‐1 ‐1 ‐1 ‐1 1 1 0.3945

1 ‐1 ‐1 ‐1 1 1 0.0765

‐1 1 ‐1 ‐1 1 1 0.3875

1 1 ‐1 ‐1 1 1 0.0679

‐1 ‐1 ‐1 1 1 1 0.4377

1 ‐1 ‐1 1 1 1 0.1379

‐1 1 ‐1 1 1 1 0.4312

1 1 ‐1 1 1 1 0.1294

‐1 ‐1 ‐1 1 1 1 0.4376

1 ‐1 ‐1 1 1 1 0.1383

‐1 1 ‐1 1 1 1 0.4311

1 1 ‐1 1 1 1 0.1297

27

6.2ANOVAAnalysis

The data was checked to see if the responses from the case study were

normallydistributed,SeeFigure13P‐Value<α.

Figure13:ProbabilityPlotofResponse

After the normality check, the response surface analysis was performed to

determine ifahigherorderpolynomialwasachievable. Minitab™threwout

the quadratic terms and subsequently only the 2K factorial design was

analyzed for the rest of the case study, see appendix for response surface

analysis.First,theeffectsplotwasdevelopedduetothedegreesoffreedom.

This determines which of the main effects and interaction effects were

significantFigure14.Thiswasconductedwithanα=0.05.

0.80.60.40.20.0-0.2

99.9

99

9590

80706050403020

10

5

1

0.1

Overhead Proplyene

Perc

ent

Mean 0.2648StDev 0.1572N 64AD 6.526P-Value <0.005

Probability Plot of Overhead PropyleneNormal

28

Figure14:NormalPlotofEffects

While it is difficult to see all the significant effects and their interactions

distinguishedbythegraph,allofthemaininteractionsweresignificant(A,B,

C,D,E,F)andthefollowinginteractioneffectsweresignificantaswell;AB,AC,

AD,AE,AF,BD,BE,BF,CD,DE,DF,EF,ABD,ADE,ADF.Theanalysiswasalso

run with an α = 0.01 to check a higher degree of confidence. The only

differencewasthethree‐interactioneffectADFwasnolongersignificant,see

appendix. The remaining computations were taken at α = 0.05. After

removingtheinsignificantinteractioneffectsFigure15wasobtained.Figure

16representsthenormalprobabilityplotoftheresidualsandFigure17isthe

residualsvsfits.Noteallofthesegraphsrepresentthestatisticsforthecoded

factoranalysis.

0.10.0-0.1-0.2-0.3

99.9

99

9590

80706050403020

105

1

0.1

Effect

Perc

ent

A AB BC CD DE EF F

Factor Name

Not SignificantSignificant

Effect Type

ADFADEABD

EF

DFDECD

BFBE

BD

AFAE

ADAC

ABFE

D

C

BA

Normal Plot of the Effects(response is Overhead Propylene, Alpha = 0.05)

Lenth's PSE = 0.0000140625

29

Figure15:NormalPlotoftheStandardEffects

Figure16:NormalProbabilityPlotoftheResiduals

Figure17:ResidualvsFits

50000-5000-10000-15000-20000

99

95

90

80

70

60504030

20

10

5

1

Standardized Effect

Perc

ent

A AB BC CD DE EF F

Factor Name


Effect Type

ADF

ADEABD

EF

DF

DE

CDBFBE

BD

AFAE

AD

AC

AB

FE

D

C

B

A

Normal Plot of the Standardized Effects(response is Overhead Propylene, Alpha = 0.05)

0.000150.000100.000050.00000-0.00005-0.00010-0.00015-0.00020

99.9

99

9590

80706050403020

10

5

1

0.1

Residual

Perc

ent

Normal Probability Plot(response is Overhead Propylene)

0.50.40.30.20.1

0.00010

0.00005

0.00000

-0.00005

-0.00010

-0.00015

-0.00020

Fitted Value

Res

idua

l

Versus Fits(response is Overhead Propylene)

30

The following two factorial design was done to test the dependency of the

independentvariablepressureandthedependentvariabletemperatureinthe

overhead accumulator drum. None of themain effects at these levelswere

observedtobesignificant,seeFigure18.Thiswasleftoutofthesubsequent

analysis.

Figure18:NormalPlotofEffects(Dependent)

Withall theP‐Values less thanα fromtheANOVAanalysis,seeappendix for

Minitaboutput.Alltheremainingtermsintheequationareallsignificant.

Theresultinglinearequationisasfollowsinmatrixform,Table6:

0.040.030.020.010.00-0.01

99

95

90

80

7060504030

20

10

5

1

Effect

Perc

ent

A PressureB Tempreature

Factor Name


Effect Type

Normal Plot of the Effects(response is Propylene, Alpha = 0.05)

Lenth's PSE = 0.005175

Thiseqquationyie

T

eldsaR2g

C

Table6:Code

raphofpr

Figure19:Co

Terms

Constant

a

b

c

d

e

f

ab

ac

ad

ae

af

bd

be

bf

cd

de

df

ef

abd

ade

adf

31

d2KRegressi

redictedv

odedR2Fitne

Coe

2.65E

‐1.54E

‐3.75E

2.03E

2.61E

‐3.66E

‐3.36E

‐4.77E

9.22E

4.66E

‐6.11E

‐6.61E

7.03E

‐3.59E

‐2.97E

2.03E

7.34E

9.84E

2.97E

‐3.91E

‐4.84E

‐1.72E

ionModel

sactualva

essCheck

ef

E‐01

E‐01

E‐03

E‐05

E‐02

E‐03

E‐03

E‐04

E‐05

E‐03

E‐04

E‐04

E‐05

E‐05

E‐05

E‐05

E‐05

E‐05

E‐05

E‐05

E‐05

E‐05

alue,Figur

re19:

32

When regressed in uncoded units the following linear equation is yielded,

Table7:

Table7:Uncoded2KRegressionModelTerm Coef

Constant 1.84E+00

Ethane ‐2.13E+00

Feed ‐9.31E‐06

Pressure ‐2.93E‐04

Vapor Draw ‐6.45E‐04

Economizer Flow ‐1.23E‐04

Side Cond Flow ‐7.20E‐05

Ethane*Feed 8.57E‐06

Ethane*Pressure 2.12E‐04

Ethane*Vapor Draw 1.38E‐03

Ethane*Economizer Flow 5.91E‐05

Ethane*Side Cond Flow ‐2.45E‐05

Feed*Vapor Draw 1.17E‐08

Feed*Economizer Flow ‐1.28E‐09

Feed*Side Cond Flow ‐1.13E‐09

Pressure*Vapor Draw 1.35E‐07

Vapor Draw*Economizer Flow 7.97E‐08

Vapor Draw*Side Cond Flow 5.27E‐08

Economizer Flow*Side Cond Flow 6.52E‐09

Ethane*Feed*Vapor Draw ‐1.34E‐08

Ethane*Vapor Draw*Economizer Flow ‐9.54E‐08

Ethane*Vapor Draw*Side Cond Flow ‐3.65E‐08

WiththecorrespondingR2graphofpredictedvsactualvalue,Figure20:

Thisgr

conduc

ANOVA

display

observe

XMAT1_1

XMAT1_2 *

XMAT1_3 *

XMAT1_4 *

XMAT1_5 *

XMAT1_6 *

XMAT1_7 *

XMAT1_8 *

XMAT1_9 *

XMAT1_10 *

XMAT1_11 *

XMAT1_12 *

XMAT1_13 *

XMAT1_14 *

XMAT1_15 *

XMAT1_16 *

XMAT1_17 *

XMAT1_18 *

XMAT1_19 *

XMAT1_20 *

XMAT1_21 *

XMAT1_22 *

aphsugge

ctedandth

A analysis

ystheresu

edmatrix

1 XMAT1_2 XMAT1_3 XMAT

0

0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

Fi

eststhato

hedatawa

was use

ultsfromth

displayed

TT1_4 XMAT1_5 XMAT1_6 XM

0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

0 0

igure20:Unc

rthogonal

asorthogo

ed to dete

heorthog

dshowsth

Table8:OrthMAT1_7 XMAT1_8 XMAT1_9

0

0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

33

codedR2Fitn

lityexists

onal.The

ermine if

onaltest,

hatthedat

hogonaltyTesXMAT1_10 XMAT1_11 XMAT

0

0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

nessCheck

inthedat

resulting

f orthogon

seeappen

tasetwas

stResultsT1_12 XMAT1_13 XMAT1_14

0

0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

a.Further

designm

nality exi

ndixforpr

orthogon

XMAT1_15 XMAT1_16 XMA

0

0 0

0 0

0 0

0 0

0 0

0 0

ranalysis

atrixfrom

sts. Tab

rocedure.

al.

AT1_17 XMAT1_18 XMAT1_19

0

0 0

0 0 0

0 0 0

0 0 0

was

mthe

le 8

The

9 XMAT1_20 XMAT1_21

0

0 0

34

Itwasobservedthattheoverheadpressurehadanon‐significantvalueduring

the surface response test. Another factorial analysis was run without the

pressuremaineffectandthenreduceddowntothemodel’ssignificantterms.

Once regressed, the data also exhibited orthogonality, see appendix for

information.

Another factorial analysis was conducted to a find a regressionmodel that

wasplainer.Thiswasdonebyremovingalltheinteractionterms.Figure21

maineffectsplotwithoutinteractiontermsshowsallthetermsaresignificant.

Please note that once the interaction termswere removedpressurewas no

longerasignificantmaineffect.

Figure21:MainEffectsPlotw/oPressureMV

Thefollowingregressionmodel,inmatrixformisobtained,Table9,AlsoSee

Figure22.Thisisinuncodedunits.

500-50-100-150-200-250

99

95

90

80

70

60504030

20

10

5

1

Standardized Effect

Perc

ent


Effect Type

Side Condenser Flow

Economizer Flow

Vapor Draw

Feed

Ethane

Normal Plot of the Standardized Effects(response is Overhead Propylene, Alpha = 0.05)

Thedat

determ

Thefin

tawasgra

minetheac

aluncode

1.0593

Figur

S

aphedand

ctualbiast

dsimulate

4 ∗ 9.

re22:Uncod

Table9:LineTerm

Constan

Ethane

Feed

Vapor Dra

Economizer

ide Condense

dthebiass

tobetterfi

edequatio

33 ∗

35

edReducedF

earRegressio

nt 8

‐1

‐9

aw 5

Flow ‐5

er Flow ‐5

seemedto

fitthedata

onis:

.00052

0.6035 (5

FitnessCheck

onModelCoef

.69E‐01

1.06E+00

9.33E‐06

.22E‐04

5.23E‐05

5.17E‐05

obeshifte

aresulting

21 ∗ 5

5)

k

edupand

ginC=0.6

5.23 ∗

wassolve

6035.

5.17

edto

∗

36

6.3HistoricalDataFineTuning

Theactualanalyzervalueisconvertedfromliquidphasetovaporphaseusing

ASPENTechHYSYS and the SRKEOS. This stepmust be conductedbecause

the model predicts the loss in propylene leaving the system in the vapor

streamnot as reflux back to the column. This prediction of overhead vapor

propylenevsoverheadliquidpropyleneisgraphed.Therelationshipislinear,

seeappendixforgraph.Utilizingthismodel,thepredictioncanbackcalculate

the propylene losses from historical data. A time shift was applied, fifteen

hours, to account for the process dead time. The equation trackswell, see

Figure23.

Figure23:RawInferential

Next,themodelgainsvs.historicaldataarechecked.Thishelpsgetthepeaks

and valleys more in line. The trends indicated that all of the gains were

1 21 41 61 81

Propylene Concentration

Time (in Hours)

Actual Vs Predicted

Predicted Value

Actual value

37

approximately correct except for the vapor draw; this was an order of

magnitude off. After that the inferential equation, it can be smoothed and

tunedusingthecoefficients,orgains,oftheequation,seeFigure24.Uponfull

implementationof theequation, (notconducted in thisstudy) thePVcanbe

post processed using time processing lead‐lag filters on the DCS. This will

accountforthedeadtimeintheprocessandhelpfilteroutnoise.

Figure24:SmoothedInferential

Figure 25‐27 are the resulting inferential graphs after the historical data

analysishasbeen conducted. The large spikes in thepredictedvalue in the

followinggraphscouldbearesultofanunwantedprocesscondition. There

are fiveprocess inputs so oneof the inputswasnot reading correctly. The

large spikes in the actual value can most likely be attributed to analyzer

calibrationoranalyzerfailure.Specificallythelastgraphhasalargevariation

1 51

Propylen

e Concentration

Time (in Hours)

Actual Vs Predicted

Predicted Value

Actual value

38

frompredictedtoactual.Itwasidentifiedthattheanalyzerwasnotcalibrated

was off and from around hour 30 to its calibration around hour 100. In

general,theequationstrack.Figure28istheresultingcorrelationregression

showing a goodness fit of about 70%. One item of not is these are not

sequentialsegments.

Figure25:FinalGraphSegment1


1 51 101 151


Time (in Hours)

Actual Vs Predicted

Predicted Value

Actual value

1 51 101 151


Time (in Hours)

Actual Vs Predicted

Predicted Value

Actual value

39


Figure28:R2Regression

1 51 101

Propylen

e Concentration

Time (in Hours)

Actual Vs Predicted

Predicted Value

Actual value

R² = 0.6867

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Actual Value

Predicted Value

Actual Vs Predicted

40

Table10isthefinalequation:

Table10:FinalEquationinMatrixFormTerm Coef

Constant 1.000000

Cc2 Ethane ‐0.850000

F Feed ‐0.000009

V Vapor Draw 0.000250

E Economizer Flow ‐0.000010

S Side Condenser Flow ‐0.000052

Term

Abrev

0.85 ∗ 9 ∗ .00025 ∗ 1 ∗ 5.2 ∗ 1 (6)

6.4Conclusions

Typically,processdataistakenascorrectandacasestudyisconducted.The

use of a simulation upfront aided in identifying areas where the historical

process datawas incorrect. In addition, the use of simulated andhistorical

data can reduce the case study length. DOE provides great utility for

analyzingsystemsinamultivariableinputsituation.Factorialanalysisand/or

responsesurfaceshouldbethefirststepinanysituationwhenconductingan

experiment if the outcome is expected to be a linear or quadratic equation.

Identification of possible interaction terms is critical to themodel even if it

leads to a puremain effects linear equation. One identified issuewith this

analysis is that thehistoricaldatacanbecompromiseddueto the limitation

andassumptionsofthemeasurementdevicesandranges. Whenpossible,a

41

hypothetical model should be scrutinized against to historical data

periodicallyinordertoincreaseaccuracy.

42

CHAPTER7:FUTURERESEARCH

Factorial design and surface response models do not pick up any type of

dynamic response in the model. Utilizing factorial design and/or surface

responsemodelwithstate‐spacedynamicmodelingcouldgreatlyincreasethe

responseofthecontrolsystem.Interactingindependentvariablesneedtobe

identifiedon thematrix toensure thecalculationsareas robustaspossible.

Afterimplementationoftheinferredmodel,itcanthenbetestedtodetermine

thedynamicsforthefullstate‐spacemodelinclosedloopMIMOcontrol.

43

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46

Minitab™ Disclaimer:

"MINITAB® and all other trademarks and logos for the Company's products and services are the exclusive property of Minitab Inc. All other marks referenced remain the property of their respective owners. See minitab.com for more information."

Legend

dforProccessFlow

Table

APP

Diagram

e11:Legendf

47

PENDICES

s

forProcessF

S

FlowDiagramms

48

AdditionalGraphs

HistoricalDataFilteringGraphs

Ethane

Figure29:EthaneGoodnessofFitPlot

Figure30:EthaneNormalityPlot

99.99

99

95

80

50

20

5

1

0.01Ethane Concentration

Perc

ent

Goodness of F it Test

LognormalA D = 4.329 P-V alue < 0.005

Probability Plot for Ethane Concentration

Lognormal - 95% CI

99.99

99

95

80

50

20

5

1

0.01Ethane Concentration

Perc

ent

StDev 0.2565N 2105AD 54.705P-Value <0.005

Probability Plot of Ethane ConcentrationNormal

49

Feed

Figure31:FeedGoodnessofFitPlot

Figure32:FeedNormalityPlot

99.99

99

95

80

50

20

5

1

0.01Feed

Per

cen

t


NormalA D = 1.698 P-V alue < 0.005

Probability Plot for Feed

Normal - 95% CI

99.99

99

95

80

50

20

5

1

0.01Feed

Perc

ent

StDev 790.8N 2105AD 1.698P-Value <0.005

Probability Plot of FeedNormal

50

OverheadPressure

Figure33:OverheadPressureGoodnessofFit

Figure34:PressureNormalityPlot

99.99

99

95

80

50

20

5

1

0.01Overhead Pressure

Perc

ent


GammaA D = 19.405 P-V alue < 0.005

Probability Plot for Overhead Pressure

Gamma - 95% CI

99.99

99

95

80

50

20

5

1

0.01Overhead Pressure

Perc

ent

StDev 4.072N 2105AD 17.766P-Value <0.005

Probability Plot of Overhead PressureNormal

51

SideCondenserFlow

Figure35:SideCondenserFlowHistogram

OverheadTemperature

Figure36:OverheadTemperatureNormalityPlot

100

80

60

40

20

0Side Condenser Flow

Freq

uenc

y

Histogram of Side Condenser Flow

2520151050-5-10

99.99

99

95

80

50

20

5

1

0.01

Overhead Temperature

Per

cen

t


NormalA D = 18.934 P-V alue < 0.005

Probability Plot for Overhead Temperature

Normal - 95% CI

52

Figure37:OverheadTemperaureNormalityPlot

AdditionalANOVAgraphs

Figure38:NormalPlotoftheEffects,α=0.01

2520151050-5-10

99.99

99

95

80

50

20

5

1

0.01

Overhead Temperature

Perc

ent

Mean 6.459StDev 4.555N 2101AD 18.934P-Value <0.005

Probability Plot of Overhead TemperatureNormal

0.10.0-0.1-0.2-0.3

99.9

99

9590

80706050403020

105

1

0.1

Effect

Perc

ent

A AB BC CD DE EF F

Factor Name


Effect Type

ADEABD

EF

DF

DE

CD

BFBE

BD

AFAE

AD

AC

AB

FE

D

C

B

A

Normal Plot of the Effects(response is Overhead Proplyene, Alpha = 0.01)

Lenth's PSE = 0.0000140625

53

Figure39:EffectsPlotw/oPressure

Figure40:LiquidtoVaporPropyleneRelationship

10000-1000-2000-3000-4000-5000-6000-7000

99

95

90

80

70

60504030

20

10

5

1

Standardized Effect

Perc

ent

A EthaneB FeedD V apor DrawE Economizer F lowF Side C ondenser F low

Factor Name


Effect Type

BD

AFAE

AD

AB

FE

D

B

A

Normal Plot of the Standardized Effects(response is Overhead Proplyene, Alpha = 0.05)

y = 2.2403x + 0.0421R² = 0.9863

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.02 0.04 0.06 0.08 0.1 0.12

Liquid to Vapor Proplyene

Figure441:Uncoded

54

R2Regressioonw/oPress

ure

55

FinalModel

Full2kfactorialdesigntable:

Ethane Feed Overhead Pressure Vapor Draw Economizer Flow Side Condenser Flow Overhead Proplyene

‐1 ‐1 ‐1 ‐1 ‐1 ‐1 0.4064

1 ‐1 ‐1 ‐1 ‐1 ‐1 0.093

‐1 1 ‐1 ‐1 ‐1 ‐1 0.3998

1 1 ‐1 ‐1 ‐1 ‐1 0.0847

‐1 ‐1 ‐1 ‐1 ‐1 ‐1 0.4063

1 ‐1 ‐1 ‐1 ‐1 ‐1 0.0932

‐1 1 ‐1 ‐1 ‐1 ‐1 0.3996

1 1 ‐1 ‐1 ‐1 ‐1 0.0846

‐1 ‐1 ‐1 1 ‐1 ‐1 0.4486

1 ‐1 ‐1 1 ‐1 ‐1 0.1542

‐1 1 ‐1 1 ‐1 ‐1 0.4424

1 1 ‐1 1 ‐1 ‐1 0.146

‐1 ‐1 ‐1 1 ‐1 ‐1 0.4485

1 ‐1 ‐1 1 ‐1 ‐1 0.1544

‐1 1 ‐1 1 ‐1 ‐1 0.4422

1 1 ‐1 1 ‐1 ‐1 0.1462

‐1 ‐1 ‐1 ‐1 1 ‐1 0.4001

1 ‐1 ‐1 ‐1 1 ‐1 0.0844

‐1 1 ‐1 ‐1 1 ‐1 0.3933

1 1 ‐1 ‐1 1 ‐1 0.0759

‐1 ‐1 ‐1 ‐1 1 ‐1 0.3999

1 ‐1 ‐1 ‐1 1 ‐1 0.0846

‐1 1 ‐1 ‐1 1 ‐1 0.3931

1 1 ‐1 ‐1 1 ‐1 0.0761

‐1 ‐1 ‐1 1 1 ‐1 0.4427

1 ‐1 ‐1 1 1 ‐1 0.1457

‐1 1 ‐1 1 1 ‐1 0.4364

1 1 ‐1 1 1 ‐1 0.1373

‐1 ‐1 ‐1 1 1 ‐1 0.4426

1 ‐1 ‐1 1 1 ‐1 0.146

‐1 1 ‐1 1 1 ‐1 0.4362

1 1 ‐1 1 1 ‐1 0.1376

‐1 ‐1 ‐1 ‐1 ‐1 1 0.4008

1 ‐1 ‐1 ‐1 ‐1 1 0.0848

‐1 1 ‐1 ‐1 ‐1 1 0.3941

1 1 ‐1 ‐1 ‐1 1 0.0763

‐1 ‐1 ‐1 ‐1 ‐1 1 0.4006

1 ‐1 ‐1 ‐1 ‐1 1 0.085

‐1 1 ‐1 ‐1 ‐1 1 0.3938

1 1 ‐1 ‐1 ‐1 1 0.0765

‐1 ‐1 ‐1 1 ‐1 1 0.4433

1 ‐1 ‐1 1 ‐1 1 0.1464

‐1 1 ‐1 1 ‐1 1 0.4371

1 1 ‐1 1 ‐1 1 0.1379

‐1 ‐1 ‐1 1 ‐1 1 0.4433

1 ‐1 ‐1 1 ‐1 1 0.1466

‐1 1 ‐1 1 ‐1 1 0.437

1 1 ‐1 1 ‐1 1 0.1382

‐1 ‐1 ‐1 ‐1 1 1 0.3945

1 ‐1 ‐1 ‐1 1 1 0.0763

‐1 1 ‐1 ‐1 1 1 0.3877

1 1 ‐1 ‐1 1 1 0.0676

‐1 ‐1 ‐1 ‐1 1 1 0.3945

1 ‐1 ‐1 ‐1 1 1 0.0765

‐1 1 ‐1 ‐1 1 1 0.3875

1 1 ‐1 ‐1 1 1 0.0679

‐1 ‐1 ‐1 1 1 1 0.4377

1 ‐1 ‐1 1 1 1 0.1379

‐1 1 ‐1 1 1 1 0.4312

1 1 ‐1 1 1 1 0.1294

‐1 ‐1 ‐1 1 1 1 0.4376

1 ‐1 ‐1 1 1 1 0.1383

‐1 1 ‐1 1 1 1 0.4311

1 1 ‐1 1 1 1 0.1297

56

AnalysisofVarianceforOverheadPropylene(codedunits)

Source DF Seq SS Adj SS Adj MS F P Main Effects 6 1.55612 1.55612 0.25935 77632558.84 0.000 A 1 1.51004 1.51004 1.51004 4.52004E+08 0.000 B 1 0.00090 0.00090 0.00090 270072.58 0.000 C 1 0.00000 0.00000 0.00000 7.90 0.007 D 1 0.04359 0.04359 0.04359 13048539.84 0.000 E 1 0.00086 0.00086 0.00086 257192.71 0.000 F 1 0.00072 0.00072 0.00072 215996.04 0.000 2-Way Interactions 12 0.00146 0.00146 0.00012 36434.94 0.000 A*B 1 0.00001 0.00001 0.00001 4350.84 0.000 A*C 1 0.00000 0.00000 0.00000 162.81 0.000 A*D 1 0.00139 0.00139 0.00139 416736.58 0.000 A*E 1 0.00002 0.00002 0.00002 7150.34 0.000 A*F 1 0.00003 0.00003 0.00003 8368.62 0.000 B*D 1 0.00000 0.00000 0.00000 94.71 0.000 B*E 1 0.00000 0.00000 0.00000 24.74 0.000 B*F 1 0.00000 0.00000 0.00000 16.88 0.000 C*D 1 0.00000 0.00000 0.00000 7.90 0.007 D*E 1 0.00000 0.00000 0.00000 103.32 0.000 D*F 1 0.00000 0.00000 0.00000 185.63 0.000 E*F 1 0.00000 0.00000 0.00000 16.88 0.000 3-Way Interactions 3 0.00000 0.00000 0.00000 26.61 0.000 A*B*D 1 0.00000 0.00000 0.00000 29.23 0.000 A*D*E 1 0.00000 0.00000 0.00000 44.95 0.000 A*D*F 1 0.00000 0.00000 0.00000 5.66 0.022 Residual Error 42 0.00000 0.00000 0.00000 Total 63 1.55758 Estimated Effects and Coefficients for Overhead Propylene (coded units) Term Effect Coef SE Coef T P Constant 0.2648 0.000007 36654.99 0.000 A -0.3072 -0.1536 0.000007 -21260.37 0.000 B -0.0075 -0.0038 0.000007 -519.69 0.000 C 0.0000 0.0000 0.000007 2.81 0.007 D 0.0522 0.0261 0.000007 3612.28 0.000 E -0.0073 -0.0037 0.000007 -507.14 0.000 F -0.0067 -0.0034 0.000007 -464.75 0.000 A*B -0.0010 -0.0005 0.000007 -65.96 0.000 A*C 0.0002 0.0001 0.000007 12.76 0.000 A*D 0.0093 0.0047 0.000007 645.55 0.000 A*E -0.0012 -0.0006 0.000007 -84.56 0.000 A*F -0.0013 -0.0007 0.000007 -91.48 0.000 B*D 0.0001 0.0001 0.000007 9.73 0.000 B*E -0.0001 -0.0000 0.000007 -4.97 0.000 B*F -0.0001 -0.0000 0.000007 -4.11 0.000 C*D 0.0000 0.0000 0.000007 2.81 0.007 D*E 0.0001 0.0001 0.000007 10.16 0.000 D*F 0.0002 0.0001 0.000007 13.62 0.000 E*F 0.0001 0.0000 0.000007 4.11 0.000 A*B*D -0.0001 -0.0000 0.000007 -5.41 0.000 A*D*E -0.0001 -0.0000 0.000007 -6.70 0.000 A*D*F -0.0000 -0.0000 0.000007 -2.38 0.022

57

Orthogonaltest

TheProcedureisasfollows:

Runfactorialdesignanalysis

StoreDesignmatrixinworksheet

Copythematrixintocolumns

Create columns for the stored data equal to the degrees of freedom

minustheerrorplus1

Perform a correlation test and look in the report sheet for any non‐

zeroes

Correlations: XMAT1_1, XMAT1_2, XMAT1_3, XMAT1_4, XMAT1_5, XMAT1_6, ... XMAT1_1 XMAT1_2 XMAT1_3 XMAT1_4 XMAT1_5 XMAT1_6 XMAT1_7 XMAT1_2 * XMAT1_3 * 0.000 XMAT1_4 * 0.000 0.000 XMAT1_5 * 0.000 0.000 0.000 XMAT1_6 * 0.000 0.000 0.000 0.000 XMAT1_7 * 0.000 0.000 0.000 0.000 0.000 XMAT1_8 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_9 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_10 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_11 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_12 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_13 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_14 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_15 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_16 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_17 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_18 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_19 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_20 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_21 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_22 * 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_8 XMAT1_9 XMAT1_10 XMAT1_11 XMAT1_12 XMAT1_13 XMAT1_14 XMAT1_9 0.000 XMAT1_10 0.000 0.000 XMAT1_11 0.000 0.000 0.000 XMAT1_12 0.000 0.000 0.000 0.000 XMAT1_13 0.000 0.000 0.000 0.000 0.000 XMAT1_14 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_15 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_16 0.000 0.000 0.000 0.000 0.000 0.000 0.000

58

XMAT1_17 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_18 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_19 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_20 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_21 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_22 0.000 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_15 XMAT1_16 XMAT1_17 XMAT1_18 XMAT1_19 XMAT1_20 XMAT1_21 XMAT1_16 0.000 XMAT1_17 0.000 0.000 XMAT1_18 0.000 0.000 0.000 XMAT1_19 0.000 0.000 0.000 0.000 XMAT1_20 0.000 0.000 0.000 0.000 0.000 XMAT1_21 0.000 0.000 0.000 0.000 0.000 0.000 XMAT1_22 0.000 0.000 0.000 0.000 0.000 0.000 0.000

ANOVAandEffectsforLinearModel(uncodedunits)

Estimated Effects and Coefficients for Overhead Propylene (coded units) Term Effect Coef SE Coef T P Constant 0.2648 0.000627 422.12 0.000 Ethane -0.3072 -0.1536 0.000627 -244.83 0.000 Feed -0.0075 -0.0038 0.000627 -5.98 0.000 Vapor Draw 0.0522 0.0261 0.000627 41.60 0.000 Economizer Flow -0.0073 -0.0037 0.000627 -5.84 0.000 Side Condenser Flow -0.0067 -0.0034 0.000627 -5.35 0.000 S = 0.00501907 PRESS = 0.00177901 R-Sq = 99.91% R-Sq(pred) = 99.89% R-Sq(adj) = 99.90% Analysis of Variance for Overhead Propylene (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 5 1.55612 1.55612 0.31122 12354.50 0.000 Ethane 1 1.51004 1.51004 1.51004 59943.45 0.000 Feed 1 0.00090 0.00090 0.00090 35.82 0.000 Vapor Draw 1 0.04359 0.04359 0.04359 1730.46 0.000 Economizer Flow 1 0.00086 0.00086 0.00086 34.11 0.000 Side Condenser Flow 1 0.00072 0.00072 0.00072 28.64 0.000 Residual Error 58 0.00146 0.00146 0.00003 Lack of Fit 26 0.00146 0.00146 0.00006 2549.49 0.000 Pure Error 32 0.00000 0.00000 0.00000 Total 63 1.55758 Estimated Coefficients for Overhead Propylene using data in uncoded units Term Coef Constant 0.868671

59

Ethane -1.05934 Feed -9.32842E-06 Vapor Draw 0.000521969 Economizer Flow -5.23438E-05 Side Condenser Flow -5.16587E-05

60

CompleteMinitabOutput

ResponseSurface

—————6/2/20149:21:20PM———————————————————— Welcome to Minitab, press F1 for help. Retrieving project from file: '\\Client\H$\Grad School info\Thesis Work\thesis work.MPJ'

ResponseSurfaceRegression:PropyleneversusA,B,C,D,E,FThe following terms cannot be estimated, and were removed. A*A B*B C*C D*D E*E F*F The analysis was done using coded units. Estimated Regression Coefficients for Propylene Term Coef SE Coef T P Constant 0.264830 0.000012 22601.192 0.000 A -0.153605 0.000012 -13108.987 0.000 B -0.003755 0.000012 -320.434 0.000 C 0.000020 0.000012 1.734 0.090 D 0.026098 0.000012 2227.302 0.000 E -0.003664 0.000012 -312.700 0.000 F -0.003358 0.000012 -286.564 0.000 A*B -0.000477 0.000012 -40.671 0.000 A*C 0.000092 0.000012 7.867 0.000 A*D 0.004664 0.000012 398.042 0.000 A*E -0.000611 0.000012 -52.139 0.000 A*F -0.000661 0.000012 -56.406 0.000 B*C -0.000014 0.000012 -1.200 0.237 B*D 0.000070 0.000012 6.001 0.000 B*E -0.000036 0.000012 -3.067 0.004 B*F -0.000030 0.000012 -2.534 0.015 C*D 0.000020 0.000012 1.734 0.090 C*E 0.000014 0.000012 1.200 0.237 C*F 0.000014 0.000012 1.200 0.237 D*E 0.000073 0.000012 6.267 0.000 D*F 0.000098 0.000012 8.401 0.000 E*F 0.000030 0.000012 2.534 0.015 S = 0.0000937401 PRESS = 8.569615E-07 R-Sq = 100.00% R-Sq(pred) = 100.00% R-Sq(adj) = 100.00%

61

Analysis of Variance for Propylene Source DF Seq SS Adj SS Adj MS F P Regression 21 1.55758 1.55758 0.07417 8440725.38 0.000 Linear 6 1.55612 1.55612 0.25935 29514833.97 0.000 A 1 1.51004 1.51004 1.51004 1.71846E+08 0.000 B 1 0.00090 0.00090 0.00090 102677.89 0.000 C 1 0.00000 0.00000 0.00000 3.01 0.090 D 1 0.04359 0.04359 0.04359 4960875.86 0.000 E 1 0.00086 0.00086 0.00086 97781.14 0.000 F 1 0.00072 0.00072 0.00072 82118.73 0.000 Interaction 15 0.00146 0.00146 0.00010 11081.94 0.000 A*B 1 0.00001 0.00001 0.00001 1654.13 0.000 A*C 1 0.00000 0.00000 0.00000 61.90 0.000 A*D 1 0.00139 0.00139 0.00139 158437.53 0.000 A*E 1 0.00002 0.00002 0.00002 2718.46 0.000 A*F 1 0.00003 0.00003 0.00003 3181.63 0.000 B*C 1 0.00000 0.00000 0.00000 1.44 0.237 B*D 1 0.00000 0.00000 0.00000 36.01 0.000 B*E 1 0.00000 0.00000 0.00000 9.41 0.004 B*F 1 0.00000 0.00000 0.00000 6.42 0.015 C*D 1 0.00000 0.00000 0.00000 3.01 0.090 C*E 1 0.00000 0.00000 0.00000 1.44 0.237 C*F 1 0.00000 0.00000 0.00000 1.44 0.237 D*E 1 0.00000 0.00000 0.00000 39.28 0.000 D*F 1 0.00000 0.00000 0.00000 70.57 0.000 E*F 1 0.00000 0.00000 0.00000 6.42 0.015 Residual Error 42 0.00000 0.00000 0.00000 Total 63 1.55758 Obs StdOrder Propylene Fit SE Fit Residual St Resid 1 1 0.406 0.406 0.000 0.000 0.78 2 2 0.093 0.093 0.000 -0.000 -1.52 3 3 0.400 0.400 0.000 -0.000 -0.04 4 4 0.085 0.085 0.000 0.000 0.37 5 5 0.406 0.406 0.000 0.000 2.26 R 6 6 0.093 0.093 0.000 -0.000 -0.95 7 7 0.400 0.400 0.000 0.000 0.86 8 8 0.085 0.085 0.000 -0.000 -2.26 R 9 9 0.449 0.449 0.000 -0.000 -1.11 10 10 0.154 0.154 0.000 0.000 1.11 11 11 0.442 0.442 0.000 -0.000 -0.37 12 12 0.146 0.146 0.000 0.000 0.62 13 13 0.449 0.449 0.000 -0.000 -0.70 14 14 0.154 0.154 0.000 0.000 0.62 15 15 0.442 0.442 0.000 -0.000 -0.53 16 16 0.146 0.146 0.000 0.000 0.86 17 17 0.400 0.400 0.000 0.000 0.37 18 18 0.084 0.084 0.000 -0.000 -0.04 19 19 0.393 0.393 0.000 -0.000 -1.19 20 20 0.076 0.076 0.000 0.000 1.11 21 21 0.400 0.400 0.000 -0.000 -0.21 22 22 0.085 0.085 0.000 -0.000 -0.21 23 23 0.393 0.393 0.000 -0.000 -1.03 24 24 0.076 0.076 0.000 0.000 1.69 25 25 0.443 0.443 0.000 -0.000 -0.12 26 26 0.146 0.146 0.000 0.000 0.04 27 27 0.436 0.436 0.000 0.000 1.19 28 28 0.137 0.137 0.000 -0.000 -1.19 29 29 0.443 0.443 0.000 -0.000 -0.45

62

30 30 0.146 0.146 0.000 0.000 0.12 31 31 0.436 0.436 0.000 0.000 0.29 32 32 0.138 0.138 0.000 -0.000 -0.37 33 33 0.401 0.401 0.000 0.000 1.03 34 34 0.085 0.085 0.000 -0.000 -0.70 35 35 0.394 0.394 0.000 0.000 0.45 36 36 0.076 0.076 0.000 0.000 0.12 37 37 0.401 0.401 0.000 0.000 0.45 38 38 0.085 0.085 0.000 -0.000 -0.86 39 39 0.394 0.394 0.000 -0.000 -0.70 40 40 0.076 0.076 0.000 0.000 0.70 41 41 0.443 0.443 0.000 -0.000 -2.10 R 42 42 0.146 0.146 0.000 0.000 2.02 R 43 43 0.437 0.437 0.000 0.000 0.21 44 44 0.138 0.138 0.000 -0.000 -0.86 45 45 0.443 0.443 0.000 -0.000 -1.11 46 46 0.147 0.147 0.000 0.000 0.78 47 47 0.437 0.437 0.000 0.000 0.62 48 48 0.138 0.138 0.000 -0.000 -0.04 49 49 0.395 0.395 0.000 -0.000 -0.95 50 50 0.076 0.076 0.000 0.000 0.53 51 51 0.388 0.388 0.000 -0.000 -0.95 52 52 0.068 0.068 0.000 0.000 0.62 53 53 0.395 0.394 0.000 0.000 0.37 54 54 0.076 0.077 0.000 -0.000 -0.37 55 55 0.388 0.388 0.000 -0.000 -1.52 56 56 0.068 0.068 0.000 0.000 1.77 57 57 0.438 0.438 0.000 0.000 1.28 58 58 0.138 0.138 0.000 -0.000 -0.62 59 59 0.431 0.431 0.000 0.000 1.52 60 60 0.129 0.130 0.000 -0.000 -1.60 61 61 0.438 0.438 0.000 0.000 0.21 62 62 0.138 0.138 0.000 0.000 0.04 63 63 0.431 0.431 0.000 0.000 1.19 64 64 0.130 0.130 0.000 -0.000 -1.52 R denotes an observation with a large standardized residual. Estimated Regression Coefficients for Propylene using data in uncoded units Term Coef Constant 0.264830 A -0.153605 B -0.00375469 C 2.03125E-05 D 0.0260984 E -0.00366406 F -0.00335781 A*B -4.76563E-04 A*C 9.21875E-05 A*D 0.00466406 A*E -6.10937E-04 A*F -6.60938E-04 B*C -1.40625E-05 B*D 7.03125E-05 B*E -3.59375E-05 B*F -2.96875E-05 C*D 2.03125E-05 C*E 1.40625E-05 C*F 1.40625E-05

63

D*E 7.34375E-05 D*F 9.84375E-05 E*F 2.96875E-05 Predicted Response for New Design Points Using Model for Propylene Point Fit SE Fit 95% CI 95% PI 1 0.406341 0.0000550 (0.406230, 0.406452) (0.406121, 0.406560) 2 0.093116 0.0000550 (0.093005, 0.093227) (0.092896, 0.093335) 3 0.399803 0.0000550 (0.399692, 0.399914) (0.399584, 0.400022) 4 0.084672 0.0000550 (0.084561, 0.084783) (0.084453, 0.084891) 5 0.406128 0.0000550 (0.406017, 0.406239) (0.405909, 0.406347) 6 0.093272 0.0000550 (0.093161, 0.093383) (0.093053, 0.093491) 7 0.399534 0.0000550 (0.399423, 0.399645) (0.399315, 0.399754) 8 0.084772 0.0000550 (0.084661, 0.084883) (0.084553, 0.084991) 9 0.448684 0.0000550 (0.448573, 0.448795) (0.448465, 0.448904) 10 0.154116 0.0000550 (0.154005, 0.154227) (0.153896, 0.154335) 11 0.442428 0.0000550 (0.442317, 0.442539) (0.442209, 0.442647) 12 0.145953 0.0000550 (0.145842, 0.146064) (0.145734, 0.146172) 13 0.448553 0.0000550 (0.448442, 0.448664) (0.448334, 0.448772) 14 0.154353 0.0000550 (0.154242, 0.154464) (0.154134, 0.154572) 15 0.442241 0.0000550 (0.442130, 0.442352) (0.442021, 0.442460) 16 0.146134 0.0000550 (0.146023, 0.146245) (0.145915, 0.146354) 17 0.400072 0.0000550 (0.399961, 0.400183) (0.399853, 0.400291) 18 0.084403 0.0000550 (0.084292, 0.084514) (0.084184, 0.084622) 19 0.393391 0.0000550 (0.393280, 0.393502) (0.393171, 0.393610) 20 0.075816 0.0000550 (0.075705, 0.075927) (0.075596, 0.076035) 21 0.399916 0.0000550 (0.399805, 0.400027) (0.399696, 0.400135) 22 0.084616 0.0000550 (0.084505, 0.084727) (0.084396, 0.084835) 23 0.393178 0.0000550 (0.393067, 0.393289) (0.392959, 0.393397) 24 0.075972 0.0000550 (0.075861, 0.076083) (0.075753, 0.076191) 25 0.442709 0.0000550 (0.442598, 0.442820) (0.442490, 0.442929) 26 0.145697 0.0000550 (0.145586, 0.145808) (0.145478, 0.145916) 27 0.436309 0.0000550 (0.436198, 0.436420) (0.436090, 0.436529) 28 0.137391 0.0000550 (0.137280, 0.137502) (0.137171, 0.137610) 29 0.442634 0.0000550 (0.442523, 0.442745) (0.442415, 0.442854) 30 0.145991 0.0000550 (0.145880, 0.146102) (0.145771, 0.146210) 31 0.436178 0.0000550 (0.436067, 0.436289) (0.435959, 0.436397) 32 0.137628 0.0000550 (0.137517, 0.137739) (0.137409, 0.137847) 33 0.400722 0.0000550 (0.400611, 0.400833) (0.400503, 0.400941) 34 0.084853 0.0000550 (0.084742, 0.084964) (0.084634, 0.085072) 35 0.394066 0.0000550 (0.393955, 0.394177) (0.393846, 0.394285) 36 0.076291 0.0000550 (0.076180, 0.076402) (0.076071, 0.076510) 37 0.400566 0.0000550 (0.400455, 0.400677) (0.400346, 0.400785) 38 0.085066 0.0000550 (0.084955, 0.085177) (0.084846, 0.085285) 39 0.393853 0.0000550 (0.393742, 0.393964) (0.393634, 0.394072) 40 0.076447 0.0000550 (0.076336, 0.076558) (0.076228, 0.076666) 41 0.443459 0.0000550 (0.443348, 0.443570) (0.443240, 0.443679) 42 0.146247 0.0000550 (0.146136, 0.146358) (0.146028, 0.146466) 43 0.437084 0.0000550 (0.436973, 0.437195) (0.436865, 0.437304) 44 0.137966 0.0000550 (0.137855, 0.138077) (0.137746, 0.138185) 45 0.443384 0.0000550 (0.443273, 0.443495) (0.443165, 0.443604) 46 0.146541 0.0000550 (0.146430, 0.146652) (0.146321, 0.146760) 47 0.436953 0.0000550 (0.436842, 0.437064) (0.436734, 0.437172) 48 0.138203 0.0000550 (0.138092, 0.138314) (0.137984, 0.138422) 49 0.394572 0.0000550 (0.394461, 0.394683) (0.394353, 0.394791) 50 0.076259 0.0000550 (0.076148, 0.076370) (0.076040, 0.076479) 51 0.387772 0.0000550 (0.387661, 0.387883) (0.387553, 0.387991) 52 0.067553 0.0000550 (0.067442, 0.067664) (0.067334, 0.067772) 53 0.394472 0.0000550 (0.394361, 0.394583) (0.394253, 0.394691)

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54 0.076528 0.0000550 (0.076417, 0.076639) (0.076309, 0.076747) 55 0.387616 0.0000550 (0.387505, 0.387727) (0.387396, 0.387835) 56 0.067766 0.0000550 (0.067655, 0.067877) (0.067546, 0.067985) 57 0.437603 0.0000550 (0.437492, 0.437714) (0.437384, 0.437822) 58 0.137947 0.0000550 (0.137836, 0.138058) (0.137728, 0.138166) 59 0.431084 0.0000550 (0.430973, 0.431195) (0.430865, 0.431304) 60 0.129522 0.0000550 (0.129411, 0.129633) (0.129303, 0.129741) 61 0.437584 0.0000550 (0.437473, 0.437695) (0.437365, 0.437804) 62 0.138297 0.0000550 (0.138186, 0.138408) (0.138078, 0.138516) 63 0.431009 0.0000550 (0.430898, 0.431120) (0.430790, 0.431229) 64 0.129816 0.0000550 (0.129705, 0.129927) (0.129596, 0.130035)

ResidualPlotsforPropylene


InteractionPlotforPropylene

SurfacePlotofPropylenevsB,A

SurfacePlotofPropylenevsC,A

SurfacePlotofPropylenevsD,A

SurfacePlotofPropylenevsE,A

SurfacePlotofPropylenevsF,A

SurfacePlotofPropylenevsC,B

SurfacePlotofPropylenevsD,B

SurfacePlotofPropylenevsE,B

SurfacePlotofPropylenevsF,B

SurfacePlotofPropylenevsD,C

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SurfacePlotofPropylenevsE,C

SurfacePlotofPropylenevsF,C

SurfacePlotofPropylenevsE,D

SurfacePlotofPropylenevsF,D

SurfacePlotofPropylenevsF,E

ResponseOptimizationParameters Goal Lower Target Upper Weight Import Propylene Minimum 0 0 1 1 1 Global Solution A = 1 B = 1 C = -1 D = -1 E = 1 F = 1 Predicted Responses Propylene = 0.0675531 , desirability = 0.932447 Composite Desirability = 0.932447

OptimizationPlot

GeneralLinearModel:PropyleneversusA,B,C,D,E,FFactor Type Levels Values A fixed 2 -1, 1 B fixed 2 -1, 1 C fixed 2 -1, 1 D fixed 2 -1, 1 E fixed 2 -1, 1 F fixed 2 -1, 1 Analysis of Variance for Propylene, using Adjusted SS for Tests

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Source DF Seq SS Adj SS Adj MS F P A 1 1.51004 1.51004 1.51004 58911.00 0.000 B 1 0.00090 0.00090 0.00090 35.20 0.000 C 1 0.00000 0.00000 0.00000 0.00 0.975 D 1 0.04359 0.04359 0.04359 1700.66 0.000 E 1 0.00086 0.00086 0.00086 33.52 0.000 F 1 0.00072 0.00072 0.00072 28.15 0.000 Error 57 0.00146 0.00146 0.00003 Total 63 1.55758 S = 0.00506286 R-Sq = 99.91% R-Sq(adj) = 99.90%


ResponseSurfaceRegression:OverheadProversusEthane,Feed,...The following terms cannot be estimated, and were removed. Ethane*Ethane Feed*Feed Overhead Pressure*Overhead Pressure Vapor Draw*Vapor Draw Economizer Flow*Economizer Flow Side Condenser Flow*Side Condenser Flow The analysis was done using uncoded units. Estimated Regression Coefficients for Overhead Propylene Term Coef SE Coef T P Constant 1.34786 0.117806 11.441 0.000 Ethane -1.21170 0.010476 -115.663 0.000 Feed 0.00000 0.000004 1.039 0.305 Overhead Pressure -0.00064 0.000411 -1.549 0.129 Vapor Draw -0.00019 0.000030 -6.407 0.000 Economizer Flow -0.00007 0.000020 -3.184 0.003 Side Condenser Flow -0.00006 0.000019 -3.246 0.002 Ethane*Feed -0.00001 0.000000 -40.671 0.000 Ethane*Overhead Pressure 0.00021 0.000027 7.867 0.000 Ethane*Vapor Draw 0.00064 0.000002 398.042 0.000 Ethane*Economizer Flow -0.00006 0.000001 -52.139 0.000 Ethane*Side Condenser Flow -0.00007 0.000001 -56.406 0.000 Feed*Overhead Pressure -0.00000 0.000000 -1.200 0.237 Feed*Vapor Draw 0.00000 0.000000 6.001 0.000 Feed*Economizer Flow -0.00000 0.000000 -3.067 0.004 Feed*Side Condenser Flow -0.00000 0.000000 -2.534 0.015 Overhead Pressure*Vapor Draw 0.00000 0.000000 1.734 0.090 Overhead Pressure*Economizer Flow 0.00000 0.000000 1.200 0.237 Overhead Pressure* 0.00000 0.000000 1.200 0.237 Side Condenser Flow Vapor Draw*Economizer Flow 0.00000 0.000000 6.267 0.000

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Vapor Draw*Side Condenser Flow 0.00000 0.000000 8.401 0.000 Economizer Flow*Side Condenser Flow 0.00000 0.000000 2.534 0.015 S = 0.0000937401 PRESS = 8.569615E-07 R-Sq = 100.00% R-Sq(pred) = 100.00% R-Sq(adj) = 100.00% Analysis of Variance for Overhead Propylene Source DF Seq SS Adj SS Adj MS Regression 21 1.55758 1.55758 0.074170 Linear 6 1.55612 0.00012 0.000020 Ethane 1 1.51004 0.00012 0.000118 Feed 1 0.00090 0.00000 0.000000 Overhead Pressure 1 0.00000 0.00000 0.000000 Vapor Draw 1 0.04359 0.00000 0.000000 Economizer Flow 1 0.00086 0.00000 0.000000 Side Condenser Flow 1 0.00072 0.00000 0.000000 Interaction 15 0.00146 0.00146 0.000097 Ethane*Feed 1 0.00001 0.00001 0.000015 Ethane*Overhead Pressure 1 0.00000 0.00000 0.000001 Ethane*Vapor Draw 1 0.00139 0.00139 0.001392 Ethane*Economizer Flow 1 0.00002 0.00002 0.000024 Ethane*Side Condenser Flow 1 0.00003 0.00003 0.000028 Feed*Overhead Pressure 1 0.00000 0.00000 0.000000 Feed*Vapor Draw 1 0.00000 0.00000 0.000000 Feed*Economizer Flow 1 0.00000 0.00000 0.000000 Feed*Side Condenser Flow 1 0.00000 0.00000 0.000000 Overhead Pressure*Vapor Draw 1 0.00000 0.00000 0.000000 Overhead Pressure*Economizer Flow 1 0.00000 0.00000 0.000000 Overhead Pressure*Side Condenser Flow 1 0.00000 0.00000 0.000000 Vapor Draw*Economizer Flow 1 0.00000 0.00000 0.000000 Vapor Draw*Side Condenser Flow 1 0.00000 0.00000 0.000001 Economizer Flow*Side Condenser Flow 1 0.00000 0.00000 0.000000 Residual Error 42 0.00000 0.00000 0.000000 Total 63 1.55758 Source F P Regression 8440725.38 0.000 Linear 2237.71 0.000 Ethane 13377.89 0.000 Feed 1.08 0.305 Overhead Pressure 2.40 0.129 Vapor Draw 41.05 0.000 Economizer Flow 10.14 0.003 Side Condenser Flow 10.54 0.002 Interaction 11081.94 0.000 Ethane*Feed 1654.13 0.000 Ethane*Overhead Pressure 61.90 0.000 Ethane*Vapor Draw 158437.53 0.000 Ethane*Economizer Flow 2718.46 0.000 Ethane*Side Condenser Flow 3181.63 0.000 Feed*Overhead Pressure 1.44 0.237 Feed*Vapor Draw 36.01 0.000 Feed*Economizer Flow 9.41 0.004 Feed*Side Condenser Flow 6.42 0.015 Overhead Pressure*Vapor Draw 3.01 0.090 Overhead Pressure*Economizer Flow 1.44 0.237 Overhead Pressure*Side Condenser Flow 1.44 0.237 Vapor Draw*Economizer Flow 39.28 0.000

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Vapor Draw*Side Condenser Flow 70.57 0.000 Economizer Flow*Side Condenser Flow 6.42 0.015 Residual Error Total Overhead Obs StdOrder Propylene Fit SE Fit Residual St Resid 1 1 0.406 0.406 0.000 0.000 0.78 2 2 0.093 0.093 0.000 -0.000 -1.52 3 3 0.400 0.400 0.000 -0.000 -0.04 4 4 0.085 0.085 0.000 0.000 0.37 5 5 0.406 0.406 0.000 0.000 2.26 R 6 6 0.093 0.093 0.000 -0.000 -0.95 7 7 0.400 0.400 0.000 0.000 0.86 8 8 0.085 0.085 0.000 -0.000 -2.26 R 9 9 0.449 0.449 0.000 -0.000 -1.11 10 10 0.154 0.154 0.000 0.000 1.11 11 11 0.442 0.442 0.000 -0.000 -0.37 12 12 0.146 0.146 0.000 0.000 0.62 13 13 0.449 0.449 0.000 -0.000 -0.70 14 14 0.154 0.154 0.000 0.000 0.62 15 15 0.442 0.442 0.000 -0.000 -0.53 16 16 0.146 0.146 0.000 0.000 0.86 17 17 0.400 0.400 0.000 0.000 0.37 18 18 0.084 0.084 0.000 -0.000 -0.04 19 19 0.393 0.393 0.000 -0.000 -1.19 20 20 0.076 0.076 0.000 0.000 1.11 21 21 0.400 0.400 0.000 -0.000 -0.21 22 22 0.085 0.085 0.000 -0.000 -0.21 23 23 0.393 0.393 0.000 -0.000 -1.03 24 24 0.076 0.076 0.000 0.000 1.69 25 25 0.443 0.443 0.000 -0.000 -0.12 26 26 0.146 0.146 0.000 0.000 0.04 27 27 0.436 0.436 0.000 0.000 1.19 28 28 0.137 0.137 0.000 -0.000 -1.19 29 29 0.443 0.443 0.000 -0.000 -0.45 30 30 0.146 0.146 0.000 0.000 0.12 31 31 0.436 0.436 0.000 0.000 0.29 32 32 0.138 0.138 0.000 -0.000 -0.37 33 33 0.401 0.401 0.000 0.000 1.03 34 34 0.085 0.085 0.000 -0.000 -0.70 35 35 0.394 0.394 0.000 0.000 0.45 36 36 0.076 0.076 0.000 0.000 0.12 37 37 0.401 0.401 0.000 0.000 0.45 38 38 0.085 0.085 0.000 -0.000 -0.86 39 39 0.394 0.394 0.000 -0.000 -0.70 40 40 0.076 0.076 0.000 0.000 0.70 41 41 0.443 0.443 0.000 -0.000 -2.10 R 42 42 0.146 0.146 0.000 0.000 2.02 R 43 43 0.437 0.437 0.000 0.000 0.21 44 44 0.138 0.138 0.000 -0.000 -0.86 45 45 0.443 0.443 0.000 -0.000 -1.11 46 46 0.147 0.147 0.000 0.000 0.78 47 47 0.437 0.437 0.000 0.000 0.62 48 48 0.138 0.138 0.000 -0.000 -0.04 49 49 0.395 0.395 0.000 -0.000 -0.95 50 50 0.076 0.076 0.000 0.000 0.53 51 51 0.388 0.388 0.000 -0.000 -0.95 52 52 0.068 0.068 0.000 0.000 0.62 53 53 0.395 0.394 0.000 0.000 0.37

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54 54 0.076 0.077 0.000 -0.000 -0.37 55 55 0.388 0.388 0.000 -0.000 -1.52 56 56 0.068 0.068 0.000 0.000 1.77 57 57 0.438 0.438 0.000 0.000 1.28 58 58 0.138 0.138 0.000 -0.000 -0.62 59 59 0.431 0.431 0.000 0.000 1.52 60 60 0.129 0.130 0.000 -0.000 -1.60 61 61 0.438 0.438 0.000 0.000 0.21 62 62 0.138 0.138 0.000 0.000 0.04 63 63 0.431 0.431 0.000 0.000 1.19 64 64 0.130 0.130 0.000 -0.000 -1.52 R denotes an observation with a large standardized residual.

ResidualPlotsforOverheadPropylene

FullFactorial

—————6/3/20146:56:01PM————————————————————Welcome to Minitab, press F1 for help.

FullFactorialDesignFactors: 6 Base Design: 6, 64 Runs: 64 Replicates: 1 Blocks: 1 Center pts (total): 0 All terms are free from aliasing.

FactorialFit:OverheadPropyleneversusA,B,C,D,E,FEstimated Effects and Coefficients for Overhead Propylene (coded units) Term Effect Coef Constant 0.2648 A -0.3072 -0.1536 B -0.0075 -0.0038 C 0.0000 0.0000

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D 0.0522 0.0261 E -0.0073 -0.0037 F -0.0067 -0.0034 A*B -0.0010 -0.0005 A*C 0.0002 0.0001 A*D 0.0093 0.0047 A*E -0.0012 -0.0006 A*F -0.0013 -0.0007 B*C -0.0000 -0.0000 B*D 0.0001 0.0001 B*E -0.0001 -0.0000 B*F -0.0001 -0.0000 C*D 0.0000 0.0000 C*E 0.0000 0.0000 C*F 0.0000 0.0000 D*E 0.0001 0.0001 D*F 0.0002 0.0001 E*F 0.0001 0.0000 A*B*C 0.0000 0.0000 A*B*D -0.0001 -0.0000 A*B*E 0.0000 0.0000 A*B*F -0.0000 -0.0000 A*C*D 0.0000 0.0000 A*C*E 0.0000 0.0000 A*C*F 0.0000 0.0000 A*D*E -0.0001 -0.0000 A*D*F -0.0000 -0.0000 A*E*F -0.0000 -0.0000 B*C*D 0.0000 0.0000 B*C*E 0.0000 0.0000 B*C*F 0.0000 0.0000 B*D*E -0.0000 -0.0000 B*D*F -0.0000 -0.0000 B*E*F -0.0000 -0.0000 C*D*E -0.0000 -0.0000 C*D*F 0.0000 0.0000 C*E*F 0.0000 0.0000 D*E*F 0.0000 0.0000 A*B*C*D 0.0000 0.0000 A*B*C*E 0.0000 0.0000 A*B*C*F 0.0000 0.0000 A*B*D*E -0.0000 -0.0000 A*B*D*F -0.0000 -0.0000 A*B*E*F 0.0000 0.0000 A*C*D*E 0.0000 0.0000 A*C*D*F -0.0000 -0.0000 A*C*E*F -0.0000 -0.0000 A*D*E*F 0.0000 0.0000 B*C*D*E -0.0000 -0.0000 B*C*D*F -0.0000 -0.0000 B*C*E*F -0.0000 -0.0000 B*D*E*F 0.0000 0.0000 C*D*E*F -0.0000 -0.0000 A*B*C*D*E -0.0000 -0.0000 A*B*C*D*F -0.0000 -0.0000 A*B*C*E*F -0.0000 -0.0000 A*B*D*E*F 0.0000 0.0000 A*C*D*E*F 0.0000 0.0000 B*C*D*E*F 0.0000 0.0000 A*B*C*D*E*F -0.0000 -0.0000

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S = * PRESS = * Analysis of Variance for Overhead Propylene (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 6 1.55612 1.55612 0.25935 * * A 1 1.51004 1.51004 1.51004 * * B 1 0.00090 0.00090 0.00090 * * C 1 0.00000 0.00000 0.00000 * * D 1 0.04359 0.04359 0.04359 * * E 1 0.00086 0.00086 0.00086 * * F 1 0.00072 0.00072 0.00072 * * 2-Way Interactions 15 0.00146 0.00146 0.00010 * * A*B 1 0.00001 0.00001 0.00001 * * A*C 1 0.00000 0.00000 0.00000 * * A*D 1 0.00139 0.00139 0.00139 * * A*E 1 0.00002 0.00002 0.00002 * * A*F 1 0.00003 0.00003 0.00003 * * B*C 1 0.00000 0.00000 0.00000 * * B*D 1 0.00000 0.00000 0.00000 * * B*E 1 0.00000 0.00000 0.00000 * * B*F 1 0.00000 0.00000 0.00000 * * C*D 1 0.00000 0.00000 0.00000 * * C*E 1 0.00000 0.00000 0.00000 * * C*F 1 0.00000 0.00000 0.00000 * * D*E 1 0.00000 0.00000 0.00000 * * D*F 1 0.00000 0.00000 0.00000 * * E*F 1 0.00000 0.00000 0.00000 * * 3-Way Interactions 20 0.00000 0.00000 0.00000 * * A*B*C 1 0.00000 0.00000 0.00000 * * A*B*D 1 0.00000 0.00000 0.00000 * * A*B*E 1 0.00000 0.00000 0.00000 * * A*B*F 1 0.00000 0.00000 0.00000 * * A*C*D 1 0.00000 0.00000 0.00000 * * A*C*E 1 0.00000 0.00000 0.00000 * * A*C*F 1 0.00000 0.00000 0.00000 * * A*D*E 1 0.00000 0.00000 0.00000 * * A*D*F 1 0.00000 0.00000 0.00000 * * A*E*F 1 0.00000 0.00000 0.00000 * * B*C*D 1 0.00000 0.00000 0.00000 * * B*C*E 1 0.00000 0.00000 0.00000 * * B*C*F 1 0.00000 0.00000 0.00000 * * B*D*E 1 0.00000 0.00000 0.00000 * * B*D*F 1 0.00000 0.00000 0.00000 * * B*E*F 1 0.00000 0.00000 0.00000 * * C*D*E 1 0.00000 0.00000 0.00000 * * C*D*F 1 0.00000 0.00000 0.00000 * * C*E*F 1 0.00000 0.00000 0.00000 * * D*E*F 1 0.00000 0.00000 0.00000 * * 4-Way Interactions 15 0.00000 0.00000 0.00000 * * A*B*C*D 1 0.00000 0.00000 0.00000 * * A*B*C*E 1 0.00000 0.00000 0.00000 * * A*B*C*F 1 0.00000 0.00000 0.00000 * * A*B*D*E 1 0.00000 0.00000 0.00000 * * A*B*D*F 1 0.00000 0.00000 0.00000 * * A*B*E*F 1 0.00000 0.00000 0.00000 * * A*C*D*E 1 0.00000 0.00000 0.00000 * * A*C*D*F 1 0.00000 0.00000 0.00000 * * A*C*E*F 1 0.00000 0.00000 0.00000 * *

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A*D*E*F 1 0.00000 0.00000 0.00000 * * B*C*D*E 1 0.00000 0.00000 0.00000 * * B*C*D*F 1 0.00000 0.00000 0.00000 * * B*C*E*F 1 0.00000 0.00000 0.00000 * * B*D*E*F 1 0.00000 0.00000 0.00000 * * C*D*E*F 1 0.00000 0.00000 0.00000 * * 5-Way Interactions 6 0.00000 0.00000 0.00000 * * A*B*C*D*E 1 0.00000 0.00000 0.00000 * * A*B*C*D*F 1 0.00000 0.00000 0.00000 * * A*B*C*E*F 1 0.00000 0.00000 0.00000 * * A*B*D*E*F 1 0.00000 0.00000 0.00000 * * A*C*D*E*F 1 0.00000 0.00000 0.00000 * * B*C*D*E*F 1 0.00000 0.00000 0.00000 * * 6-Way Interactions 1 0.00000 0.00000 0.00000 * * A*B*C*D*E*F 1 0.00000 0.00000 0.00000 * * Residual Error 0 * * * Total 63 1.55758

EffectsPlotforOverheadPropyleneAlias Structure I A B C D E F A*B A*C A*D A*E A*F B*C B*D B*E B*F C*D C*E C*F D*E D*F E*F A*B*C A*B*D A*B*E A*B*F A*C*D A*C*E A*C*F A*D*E A*D*F A*E*F B*C*D B*C*E B*C*F B*D*E B*D*F

73

B*E*F C*D*E C*D*F C*E*F D*E*F A*B*C*D A*B*C*E A*B*C*F A*B*D*E A*B*D*F A*B*E*F A*C*D*E A*C*D*F A*C*E*F A*D*E*F B*C*D*E B*C*D*F B*C*E*F B*D*E*F C*D*E*F A*B*C*D*E A*B*C*D*F A*B*C*E*F A*B*D*E*F A*C*D*E*F B*C*D*E*F A*B*C*D*E*F * NOTE * Could not graph the specified residual type because MSE = 0 or the degrees of freedom for error = 0.

—————6/4/20148:04:50PM———————————————————— Welcome to Minitab, press F1 for help. Retrieving project from file: '\\Client\H$\Grad School info\Thesis Work\thesis work 3 - MAIN.MPJ'

Resultsfor:Worksheet2

FactorialFit:OverheadPropyleneversusA,B,C,D,E,FEstimated Effects and Coefficients for Overhead Propylene (coded units) Term Effect Coef SE Coef T P Constant 0.2648 0.000007 36654.99 0.000 A -0.3072 -0.1536 0.000007 -21260.37 0.000 B -0.0075 -0.0038 0.000007 -519.69 0.000 C 0.0000 0.0000 0.000007 2.81 0.007 D 0.0522 0.0261 0.000007 3612.28 0.000 E -0.0073 -0.0037 0.000007 -507.14 0.000

74

F -0.0067 -0.0034 0.000007 -464.75 0.000 A*B -0.0010 -0.0005 0.000007 -65.96 0.000 A*C 0.0002 0.0001 0.000007 12.76 0.000 A*D 0.0093 0.0047 0.000007 645.55 0.000 A*E -0.0012 -0.0006 0.000007 -84.56 0.000 A*F -0.0013 -0.0007 0.000007 -91.48 0.000 B*D 0.0001 0.0001 0.000007 9.73 0.000 B*E -0.0001 -0.0000 0.000007 -4.97 0.000 B*F -0.0001 -0.0000 0.000007 -4.11 0.000 C*D 0.0000 0.0000 0.000007 2.81 0.007 D*E 0.0001 0.0001 0.000007 10.16 0.000 D*F 0.0002 0.0001 0.000007 13.62 0.000 E*F 0.0001 0.0000 0.000007 4.11 0.000 A*B*D -0.0001 -0.0000 0.000007 -5.41 0.000 A*D*E -0.0001 -0.0000 0.000007 -6.70 0.000 A*D*F -0.0000 -0.0000 0.000007 -2.38 0.022 S = 0.0000577994 PRESS = 3.258050E-07 R-Sq = 100.00% R-Sq(pred) = 100.00% R-Sq(adj) = 100.00% Analysis of Variance for Overhead Propylene (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 6 1.55612 1.55612 0.25935 77632558.84 0.000 A 1 1.51004 1.51004 1.51004 4.52004E+08 0.000 B 1 0.00090 0.00090 0.00090 270072.58 0.000 C 1 0.00000 0.00000 0.00000 7.90 0.007 D 1 0.04359 0.04359 0.04359 13048539.84 0.000 E 1 0.00086 0.00086 0.00086 257192.71 0.000 F 1 0.00072 0.00072 0.00072 215996.04 0.000 2-Way Interactions 12 0.00146 0.00146 0.00012 36434.94 0.000 A*B 1 0.00001 0.00001 0.00001 4350.84 0.000 A*C 1 0.00000 0.00000 0.00000 162.81 0.000 A*D 1 0.00139 0.00139 0.00139 416736.58 0.000 A*E 1 0.00002 0.00002 0.00002 7150.34 0.000 A*F 1 0.00003 0.00003 0.00003 8368.62 0.000 B*D 1 0.00000 0.00000 0.00000 94.71 0.000 B*E 1 0.00000 0.00000 0.00000 24.74 0.000 B*F 1 0.00000 0.00000 0.00000 16.88 0.000 C*D 1 0.00000 0.00000 0.00000 7.90 0.007 D*E 1 0.00000 0.00000 0.00000 103.32 0.000 D*F 1 0.00000 0.00000 0.00000 185.63 0.000 E*F 1 0.00000 0.00000 0.00000 16.88 0.000 3-Way Interactions 3 0.00000 0.00000 0.00000 26.61 0.000 A*B*D 1 0.00000 0.00000 0.00000 29.23 0.000 A*D*E 1 0.00000 0.00000 0.00000 44.95 0.000 A*D*F 1 0.00000 0.00000 0.00000 5.66 0.022 Residual Error 42 0.00000 0.00000 0.00000 Total 63 1.55758 Unusual Observations for Overhead Propylene Overhead Obs StdOrder Propylene Fit SE Fit Residual St Resid 4 4 0.084700 0.084603 0.000034 0.000097 2.07R 8 8 0.084600 0.084787 0.000034 -0.000187 -4.00R 41 41 0.443300 0.443403 0.000034 -0.000103 -2.20R 53 53 0.394500 0.394403 0.000034 0.000097 2.07R

75

R denotes an observation with a large standardized residual. Least Squares Means for Overhead Propylene Mean SE Mean A -1 0.41843 0.000010 1 0.11122 0.000010 B -1 0.26858 0.000010 1 0.26108 0.000010 C -1 0.26481 0.000010 1 0.26485 0.000010 D -1 0.23873 0.000010 1 0.29093 0.000010 E -1 0.26849 0.000010 1 0.26117 0.000010 F -1 0.26819 0.000010 1 0.26147 0.000010 A*B -1 -1 0.42171 0.000014 1 -1 0.11546 0.000014 -1 1 0.41516 0.000014 1 1 0.10699 0.000014 A*C -1 -1 0.41851 0.000014 1 -1 0.11111 0.000014 -1 1 0.41836 0.000014 1 1 0.11134 0.000014 A*D -1 -1 0.39700 0.000014 1 -1 0.08046 0.000014 -1 1 0.43987 0.000014 1 1 0.14199 0.000014 A*E -1 -1 0.42149 0.000014 1 -1 0.11550 0.000014 -1 1 0.41538 0.000014 1 1 0.10695 0.000014 A*F -1 -1 0.42113 0.000014 1 -1 0.11524 0.000014 -1 1 0.41574 0.000014 1 1 0.10721 0.000014 B*D -1 -1 0.24256 0.000014 1 -1 0.23491 0.000014 -1 1 0.29461 0.000014 1 1 0.28724 0.000014 B*E -1 -1 0.27221 0.000014 1 -1 0.26478 0.000014 -1 1 0.26496 0.000014 1 1 0.25737 0.000014 B*F

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-1 -1 0.27191 0.000014 1 -1 0.26446 0.000014 -1 1 0.26526 0.000014 1 1 0.25769 0.000014 C*D -1 -1 0.23873 0.000014 1 -1 0.23873 0.000014 -1 1 0.29089 0.000014 1 1 0.29097 0.000014 D*E -1 -1 0.24247 0.000014 1 -1 0.29452 0.000014 -1 1 0.23499 0.000014 1 1 0.28734 0.000014 D*F -1 -1 0.24219 0.000014 1 -1 0.29419 0.000014 -1 1 0.23528 0.000014 1 1 0.28767 0.000014 E*F -1 -1 0.27188 0.000014 1 -1 0.26449 0.000014 -1 1 0.26511 0.000014 1 1 0.25784 0.000014 A*B*D -1 -1 -1 0.40039 0.000020 1 -1 -1 0.08472 0.000020 -1 1 -1 0.39361 0.000020 1 1 -1 0.07620 0.000020 -1 -1 1 0.44304 0.000020 1 -1 1 0.14619 0.000020 -1 1 1 0.43670 0.000020 1 1 1 0.13779 0.000020 A*D*E -1 -1 -1 0.40018 0.000020 1 -1 -1 0.08476 0.000020 -1 1 -1 0.44280 0.000020 1 1 -1 0.14624 0.000020 -1 -1 1 0.39383 0.000020 1 -1 1 0.07616 0.000020 -1 1 1 0.43694 0.000020 1 1 1 0.13774 0.000020 A*D*F -1 -1 -1 0.39981 0.000020 1 -1 -1 0.08456 0.000020 -1 1 -1 0.44245 0.000020 1 1 -1 0.14592 0.000020 -1 -1 1 0.39419 0.000020 1 -1 1 0.07636 0.000020 -1 1 1 0.43729 0.000020 1 1 1 0.13805 0.000020

EffectsPlotforOverheadPropyleneAlias Structure I A B

77

C D E F A*B A*C A*D A*E A*F B*D B*E B*F C*D D*E D*F E*F A*B*D A*D*E A*D*F

NormplotofResidualsforOverheadPropylene

ResidualsvsFitsforOverheadPropylene

ResidualHistogramforOverheadPropylene

ResidualsvsOrderforOverheadPropyleneResultsfor:Worksheet4

FullFactorialDesignFactors: 2 Base Design: 2, 4 Runs: 4 Replicates: 1 Blocks: 1 Center pts (total): 0 All terms are free from aliasing.

FactorialFit:PropyleneversusPressure,TemperatureEstimated Effects and Coefficients for Propylene (coded units) Term Effect Coef Constant 0.077775 Pressure -0.003450 -0.001725 Temperature 0.037450 0.018725 Pressure*Temperature 0.003450 0.001725 S = * PRESS = *

78

Analysis of Variance for Propylene (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 2 0.00141440 0.00141440 0.00070720 * * Pressure 1 0.00001190 0.00001190 0.00001190 * * Temperature 1 0.00140250 0.00140250 0.00140250 * * 2-Way Interactions 1 0.00001190 0.00001190 0.00001190 * * Pressure*Temperature 1 0.00001190 0.00001190 0.00001190 * * Residual Error 0 * * * Total 3 0.00142631 Least Squares Means for Propylene Mean Pressure -1 0.07950 1 0.07605 Temperature -1 0.05905 1 0.09650 Pressure*Temperature -1 -1 0.06250 1 -1 0.05560 -1 1 0.09650 1 1 0.09650

EffectsPlotforPropyleneAlias Structure I Pressure Temperature Pressure*Temperature

GeneralRegressionAnalysis:PropyleneversusA,B,C,D,E,FRegression Equation Propylene = 0.26483 - 0.153605 A - 0.00375469 B + 2.03125e-005 C + 0.0260984 D - 0.00366406 E - 0.00335781 F Coefficients Term Coef SE Coef T P Constant 0.264830 0.0006329 418.466 0.000 A -0.153605 0.0006329 -242.716 0.000 B -0.003755 0.0006329 -5.933 0.000 C 0.000020 0.0006329 0.032 0.975 D 0.026098 0.0006329 41.239 0.000 E -0.003664 0.0006329 -5.790 0.000 F -0.003358 0.0006329 -5.306 0.000

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Summary of Model S = 0.00506286 R-Sq = 99.91% R-Sq(adj) = 99.90% PRESS = 0.00184195 R-Sq(pred) = 99.88% Analysis of Variance Source DF Seq SS Adj SS Adj MS F P Regression 6 1.55612 1.55612 0.25935 10118.1 0.000000 A 1 1.51004 1.51004 1.51004 58911.0 0.000000 B 1 0.00090 0.00090 0.00090 35.2 0.000000 C 1 0.00000 0.00000 0.00000 0.0 0.974507 D 1 0.04359 0.04359 0.04359 1700.7 0.000000 E 1 0.00086 0.00086 0.00086 33.5 0.000000 F 1 0.00072 0.00072 0.00072 28.2 0.000002 Error 57 0.00146 0.00146 0.00003 Total 63 1.55758 Fits and Diagnostics for Unusual Observations No unusual observations

FullFactorialDesignFactors: 6 Base Design: 6, 64 Runs: 64 Replicates: 1 Blocks: 1 Center pts (total): 0 All terms are free from aliasing. Design Table Run A B C D E F 1 - - - - - - 2 + - - - - - 3 - + - - - - 4 + + - - - - 5 - - + - - - 6 + - + - - - 7 - + + - - - 8 + + + - - - 9 - - - + - - 10 + - - + - - 11 - + - + - -

80

12 + + - + - - 13 - - + + - - 14 + - + + - - 15 - + + + - - 16 + + + + - - 17 - - - - + - 18 + - - - + - 19 - + - - + - 20 + + - - + - 21 - - + - + - 22 + - + - + - 23 - + + - + - 24 + + + - + - 25 - - - + + - 26 + - - + + - 27 - + - + + - 28 + + - + + - 29 - - + + + - 30 + - + + + - 31 - + + + + - 32 + + + + + - 33 - - - - - + 34 + - - - - + 35 - + - - - + 36 + + - - - + 37 - - + - - + 38 + - + - - + 39 - + + - - + 40 + + + - - + 41 - - - + - + 42 + - - + - + 43 - + - + - + 44 + + - + - + 45 - - + + - + 46 + - + + - + 47 - + + + - + 48 + + + + - + 49 - - - - + + 50 + - - - + + 51 - + - - + + 52 + + - - + + 53 - - + - + + 54 + - + - + + 55 - + + - + + 56 + + + - + + 57 - - - + + + 58 + - - + + + 59 - + - + + + 60 + + - + + + 61 - - + + + + 62 + - + + + + 63 - + + + + + 64 + + + + + +

FactorialFit:OverheadPropyleneversusEthane,Feed,...Estimated Effects and Coefficients for Overhead Propylene (coded units)

81

Term Effect Coef SE Coef T P Constant 0.2648 0.000627 422.12 0.000 Ethane -0.3072 -0.1536 0.000627 -244.83 0.000 Feed -0.0075 -0.0038 0.000627 -5.98 0.000 Vapor Draw 0.0522 0.0261 0.000627 41.60 0.000 Economizer Flow -0.0073 -0.0037 0.000627 -5.84 0.000 Side Condenser Flow -0.0067 -0.0034 0.000627 -5.35 0.000 S = 0.00501907 PRESS = 0.00177901 R-Sq = 99.91% R-Sq(pred) = 99.89% R-Sq(adj) = 99.90% Analysis of Variance for Overhead Propylene (coded units) Source DF Seq SS Adj SS Adj MS F P Main Effects 5 1.55612 1.55612 0.31122 12354.50 0.000 Ethane 1 1.51004 1.51004 1.51004 59943.45 0.000 Feed 1 0.00090 0.00090 0.00090 35.82 0.000 Vapor Draw 1 0.04359 0.04359 0.04359 1730.46 0.000 Economizer Flow 1 0.00086 0.00086 0.00086 34.11 0.000 Side Condenser Flow 1 0.00072 0.00072 0.00072 28.64 0.000 Residual Error 58 0.00146 0.00146 0.00003 Lack of Fit 26 0.00146 0.00146 0.00006 2549.49 0.000 Pure Error 32 0.00000 0.00000 0.00000 Total 63 1.55758 Estimated Coefficients for Overhead Propylene using data in uncoded units Term Coef Constant 0.868671 Ethane -1.05934 Feed -9.32842E-06 Vapor Draw 0.000521969 Economizer Flow -5.23438E-05 Side Condenser Flow -5.16587E-05 Least Squares Means for Overhead Propylene Mean SE Mean Ethane 0.4700 0.4184 0.000887 0.7600 0.1112 0.000887 Feed 19160 0.2686 0.000887 19965 0.2611 0.000887 Vapor Draw 1200 0.2387 0.000887 1300 0.2909 0.000887 Economizer Flow 2960 0.2685 0.000887 3100 0.2612 0.000887 Side Condenser Flow 5040 0.2682 0.000887 5170 0.2615 0.000887

EffectsPlotforOverheadPropylene

82

Alias Structure I Ethane Feed Vapor Draw Economizer Flow Side Condenser Flow

NormplotofResidualsforOverheadPropylene

ResidualsvsFitsforOverheadPropylene

ResidualHistogramforOverheadPropylene

ResidualsvsOrderforOverheadPropylene

ProbabilityPlotofRESI1

83

VITA

JeffWheelerwasborninElPasoTexasonDecember151982.Heearnedhis

BachelorofScienceinChemicalEngineeringinthespringof2007fromNew

MexicoStateUniversity. He thenbeganworkingprofessionally forWestern

Refining in El Paso as a Process Engineer. Jeff thenmoved to California in

pursuitofanemploymentopportunitywithalargeoilrefineronlytoreturnto

ElPasoin2010. ThisthiswherehebeganhiscareerinProcessControland

automation.Itwasthenwhenhebeganlearningaboutstatisticalmodelingof

chemicalprocesses. Jeffwasprovidedanopportunitytoworkforagrowing

midstream company where he works today in process control, Enterprise

Products. When moving to Mont Belvieu Texas he met his wife, Stefny

Wheeler, and enjoys life learning about the ever‐growing process control

industry and many different industrial applications. Currently, his main

research interests are in the Advanced Process Control and Safety

InstrumentedSystemfieldsofControlEngineering.

Permanentaddress: 5007N.TravisSt.

Liberty,TX77575

Thisthesiswasresearched,composedandtypedbyJeffA.Wheeler

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