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Hindawi Publishing CorporationJournal of Petroleum EngineeringVolume 2013 Article ID 709248 11 pageshttpdxdoiorg1011552013709248

Research ArticleModeling of Partially HydrolyzedPolyacrylamide-Hexamine-Hydroquinone Gel SystemUsed for Prole Modication os in the il ield

Upendra Singh Yadav and Vikas Mahto

Department of Petroleum Engineering Indian School of Mines Dhanbad 826004 India

Correspondence should be addressed to Upendra Singh Yadav yadavupendgmailcom

Received 25 September 2012 Accepted 11 November 2012

Academic Editor Serhat Akin

Copyright copy 2013 U Singh Yadav and V Mahtois is an open access article distributed under theCreativeCommonsAttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

e cross-linked polymer gel systems are being used increasingly to redirect or modify reservoir uid movement in the vicinity ofinjection wells for the purpose of permeabilityprole modication job in the oil eld due to their high temperature stability andcapability to provide rigid gel having high mechanical strength In this study a partially hydrolyzed polyacrylamide-hexamine-hydroquinonegel is used for the development of polymer gel systeme experimental investigation demonstrates that the gelationtime varies with polymer and crosslinker concentration and the temperature e mathematical model is developed with thehelp of gelation kinetics of polymer gel and using Arrhenius equation which relates the gelation time with polymer crosslinkerconcentrations and temperature e developed model is solved with the help of multivariate regression method It is observed inthis study that the theoretical values of gelation time have good agreement with the experimental values

1 Introduction

e reservoir heterogeneity permeability variations andpresence of fractures and fracture network in the reservoirare the main hurdles of the water ooding operations usedto enhance the oil recovery from matured oil elds Nor-mally during water ooding water sweeps through morepermeable sections of the reservoir leaving back oil in lowpermeability channels leading to low oil recovery and earlywater breakthrough is excessive water production fromthe producers leads to rise in handling and disposal costs andreduces the economic life of the well e polymer gels blockor reduce the permeability in high permeability channelsand divert the injected water through the low permeabilitysections which were not ooded or swept earlier leadingto improvement in oil recovery is technique is known asprole modication or permeability modication techniqueand the proper application of this technique is essential forthe success of water ooding projects in the oil elds [1ndash3]

Basically two types of polymers have been used for prolemodication jobs ese are polyacrylamides with dierentdegrees of hydrolysis and polysaccharide such as xanthan

biopolymer ese are cross linked with inorganic andorganic crosslinkers to produce a three-dimensional polymerstructure of the gel [4ndash7] e inorganic gel system based onthe crosslinking of the carboxylate groups on the partiallyhydrolyzed polyacrylamide chain (PHPA) with a trivalentcation like Cr (III) is crosslinking is believed to relyon coordination covalent bonding It should be mentionedthat Cr (III) based polymer gel system were reported to bestable at temperatures up to 300∘F [8ndash10] e organicallycrosslinked gels developed using phenol and formaldehydecrosslinkers are thermally stable under harsh environmentalconditions But these crosslinkers are not environmentfriendly To overcome the toxicity issues associated withformaldehyde and phenol the formaldehyde can be replacedwith less toxic derivatives like hexamethylenetetramineglyoxal paraformaldehyde acetaldehyde propionaldehydebutyraldehyde and so forth and phenol can be replaced withhydroquinone resorcinol pyrogallol phenyl salicylate and soforth [11ndash13] Other system is based on PEI crosslinker and acopolymer of acrylamide and t-butyl acrylate (PA-t-BA) PA-t-BA is a relatively lowmolecular-weight polymer is expected

2 Journal of Petroleum Engineering

O

C

H H

OH

OH

OH

OH

HO

HO

Hydroquinone Formaldehyde 2356-tetramethylol hydroquinone

OH

OH

4+

S 1

C C C C C C

C H C H C H

H H H H H H

O OO

Carboxylate Amide

Partially hydrolized polyacrylamide (PHPA)

Amide

+

OH

OH

OH

OH

HO

HO

2356-tetramethylol hydroquinone

NH2 NH2Ominus

Na+

R

R

N

H

H

OH

OHOH

OH

OH

HO

Water

Crosslinking 3-D gel structure

O

S 2

to provide rigid ringing gels Polyethyleneimine (PEI) cross-linking a copolymer of acrylamide and tert-butylacrylate(PAtBA) as water shutoff gels has been widely used in recentyears [14]

e gelation mechanism of organic crosslinkers is doneby covalent bonding which is much more stable thanthe ionic bonds Organic crosslinkers were introduced toobtained gels that can remain stable over a wide temperaturerange For high temperature (gt90∘C) reservoirs acrylamide-based copolymers with organic crosslinking agents such asphenol-formaldehyde and its derivatives can be used to forma gel with thermal stability and the gelation time is adjustable[15 16]

e different methods are presented in the literature forthe determination of the physical and chemical properties ofpolymer gel system such as bottle testingmethod sealed tubemethod dynamic shearmethod (rheometer) and static shearmethod (viscometer) Out of thesemethods the bottle testing

method is most suitable faster and inexpensive method tostudy the gelation kinetics [17]

Several models have been reported in the literature torelate the gelation time with temperature Jordan found thatthe gelation time of a specied system decreases as thetemperature is increased Plots of the logarithm of gelationtime versus the reciprocal of the absolute reaction temper-ature were found to be linear for the systems studied iscorrelation showed that the system apparently followed theHurd and Letteron model which assumed rate dependenceon only one species Hurd and Letteron studied the effect oftemperature on the formation of silicic acid gels and foundempirically that plot of the logarithm of the gelation timeversus the reciprocal of the absolute temperature linear eydeveloped an equation similar to the Arrhenius equationwhich relates gelation time and the temperature and supportthe linear relationship [15] But very few or raremodels relatethe gelation time with polymer and crosslinker concentration

Journal of Petroleum Engineering 3

Start

Input the values of constantsco-efficientsin the model

Input the values polymer crosslinker concentration and

Calculate the theoretical values of gelation time

Compare the experimental results of gelation time with the

End

Input experimental data in the

form of equation 15

Determine the constantco-efficients (a0 a1 a2 a3 and a4)

by multivariate regression method

equation16

temperature

theoretical values of gelation time

F 1 Flow chart for the solution of developed model

and temperature in case of polymer gel system used in the oilelds For the successful design of the prole modicationjob themathematicalmodel equation consists of polymer andcrosslinkers concentration as well as temperature is essential

e present paper involves bulk gelation studies of thepolymer gelant prepared from partially hydrolyzed polyacry-lamide (PHPA) andhexamine (HMTA)hydroquinone (HQ)e gelation time determined from the bulk gelation studiesat different temperatures is useful because its knowledge atreservoir temperature is required to nd out the depth up towhich the gel can be placed in the petroleum reservoir rocke gelation time and gel strengthmainly depend on polymerand crosslinker concentrations and reservoir temperaturewere also reported in this paper On the basis of the kinetics ofpolymer gel system the mathematical model for the gelationbehavior is also proposed which relates the gelation timewith polymer-crosslinkers concentrations and temperaturee theoretical values of gelation time obtained from theproposed model matches with the experimental data

2 GelationMechanism

e hexamine on hydrolysis yields formaldehyde which thencombines with hydroquinone and form 2356-tetramethylolhydroquinone Further partially hydrolyzed polyacrylamidereacts with 2356-tetramethylol hydroquinone and formsthree dimensional networks of polymer gel the different stepsof which are as follows

80 90 100 110 120

1

10

100

1000

10000

100000

1000000

Gel

atio

n t

ime

(hrs

)

Gelation temperature (C)

Experimental values at PHPA 11 wt

Theoretical values at PHPA 11 wt







HMTAHQ 0504 (wt)

pH 75

Gelation time (hrs)-

F 2 Plot of gelation temperature versus experimental and the-oretical values of gelation time at different polymer concentrationconstant crosslinker concentration (HMTAHQ 0504 wt) andpH 75

Step I In the initial step hexamine hydrolyses to yieldformaldehyde

10076491007649CH2100766510076656N4HMTA+ H2O+ Water⟶6OHndashCH2ndashOH

Methane diol+ 4NH3 (1)

OHndashCH2ndashOH⟶ HndashCH=OFormaldehyde

+ H2O+ water (2)

Step II Formaldehyde produced in Step I then react withhydroquinone to form a condensed structure known as2356-tetramethylolhydroquinone (see Scheme 1)Step IIIe condensedmolecule formed in Step II then reactswith PHPA to form the 3-dimensional gel structure whichhelps in prole modication jobs (see Scheme 2)

3 Development of Mathematical Model

e rate of gelation process for partially hydrolyzedpolyacrylamide-hexamine-hydroquinone system may bepresent as follows120572120572120572120572 + 120572120572120572120572 + 120572120572120572 120572 3D gel structure

119903119903120572120572 = minus119889119889120572120572120572120572119889119889119889119889= 119896119896120572120572120572120572

119886119886120572120572120572120572119887119887120572120572120572120572119888119888 (3)

where 119896119896 is the reaction rate constant 120572120572120572120572 120572120572120572120572 and 120572120572120572120572 denotesthe concentration of partially hydrolyzed polyacrylamide


T 1 Experimental values of gelation time at different polymer concentration temperature andpH75 (constant crosslinker concentrationHMTAHQ 0504 wt)

Sl No Polymer Crosslinkers Experimental values of gelation time(hrs)

eoretical values of gelation time(hrs)

Temperature(∘C)PHPA

(wt)HMTA(wt)

HQ(wt)

1 08 05 04 280 3288475

802 09 05 04 200 17838553 10 05 04 120 10331454 11 05 04 61 6291995 08 05 04 1743 1639435

906 09 05 04 823 8893227 10 05 04 49 5145658 11 05 04 293 3136819 08 05 04 87 848392

10010 09 05 04 41 46021511 10 05 04 31 26628212 11 05 04 153 16232613 08 05 04 453 454394

11014 09 05 04 23 24648915 10 05 04 13 14261916 11 05 04 7 8694117 08 05 04 28 251225

12018 09 05 04 14 13627819 10 05 04 8 6891720 11 05 04 5 480681

hexamine and hydroquinone and 119886119886 119887119887 and 119888119888 are the orderwith respect to 119860119860 119861119861 and 119862119862 respectively If the reactants arepresent in their stoichiometric ratios they will remain at thatratio throughout the reaction [19] us for reactants 119860119860 119861119861and 119862119862 at any time

119862119862119861119861119862119862119860119860=120573120573120572120572⟹ 119862119862119861119861 =

120573120573120572120572119862119862119860119860

119862119862119862119862119862119862119860119860=120574120574120572120572⟹ 119862119862119888119888 =

120574120574120572120572119862119862119860119860

(4)

where 120572120572 120573120573 and 120574120574 = reactant of species 119860119860 119861119861 and 119862119862 present inthe reaction respectively

119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119886119886 sdot 1007653100765312057312057312057212057211986211986211986011986010076691007669119887119887sdot 1007652100765212057412057412057212057211986211986211986011986010076681007668119888119888

= 11989611989610076531007653120573120573120572120572100766910076691198871198871007652100765212057412057412057212057210076681007668119888119888sdot 119862119862119860119860119886119886119886119887119887119886119888119888

(5)

e above equation can be also written as

119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119899119899 (6)

Taking integration both side wrt time we have

119889119889 =1(119899119899 minus 1) 119896119896119896

100768610076861119862119862119860119860119899119899minus1minus1119862119862119860119860119860119860119899119899minus110077021007702 (7)

Rearranging the above equation and putting the value of 119896119896and 119899119899

119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076871007687

119862119862119860119860119862119862119860119860119886119886 sdot 1198621198621198601198601198871198871007649100764912057312057312057312057212057210076651007665

119887119887 sdot 1198621198621198601198601198881198881007649100764912057412057412057312057212057210076651007665119888119888

minus119862119862119860119860119860119860

119862119862119860119860119860119860119886119886 sdot 1198621198621198601198601198601198601198871198871007649100764912057312057312057312057212057210076651007665119887119887 sdot 1198621198621198601198601198601198601198881198881007649100764912057412057412057312057212057210076651007665

11988811988810077031007703

(8)

Rearranging the above equation we get

119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076861007686119862119862119860119860

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888minus119862119862119860119860119860119860

11986211986211986011986011986011986011988611988611986211986211986111986111986011986011988711988711986211986211986211986211986011986011988811988810077021007702

(9)

where 119862119862119860119860119860119860 119862119862119861119861119860119860 and 119862119862119862119862119860119860 = initial concentrations of polymerhexamine amp hydroquinone

By generalizing the above equation it can be written as

119889119889 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888 (10)

e effect of temperature (119879119879 in degree kelvin) can also beincorporated in (8) and Arrhenius model [19] can be utilizedto connect 119896119896 with 119879119879 which is as follows

119896119896 = 119860119860 119896119896119896 10076521007652minus11986411986411988611988611987711987711987911987910076681007668 (11)






(wt)HMTA(wt)

HQ(wt)

1 08 05 03 312 3767173

802 09 05 03 230 20435283 10 05 03 134 11823934 11 05 03 68 7207915 08 05 03 207 1878085

906 09 05 03 91 10187797 10 05 03 553 5894698 11 05 03 333 3593439 08 05 03 101 971891

10010 09 05 03 553 52720811 10 05 03 34 30504512 11 05 03 19 18595613 08 05 03 50 520539

11014 09 05 03 253 2823715 10 05 03 143 1633816 11 05 03 8 9959717 08 05 03 32 287795

12018 09 05 03 143 15611619 10 05 03 83 9032920 11 05 03 63 55065

where 119864119864119886119886 is an apparent activation energy and 119877119877 is the gasconstant erefore the combination of (10) and (11) thenwe get

119905119905 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (12)

e above equation can be written as follows 119896119896 is theproportionality constant

119905119905 119905 1198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (13)

Taking natural logarithm and introducing the coefficients 119886119886119887119887 119888119888 then we get

ln 119905119905 119905 ln100768610076861198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 100765210076521198641198641198861198861198771198771198771198771007668100766810077021007702 (14)

ln 119905119905 119905 1198861198860 + 1198861198861 ln119862119862119860119860 + 1198861198862 ln119862119862119861119861 + 1198861198863 ln119862119862119862119862 +1198861198864119877119877 (15)

Taking antilog both sides and assume 119905119905 then we get

119905119905 119905 1198621198621198601198601198861198861 times 119862119862119861119861

1198861198862 times 1198621198621198621198621198861198863 times exp 100765210076521198861198860 +

119886119886411987711987710076681007668 (16)

Equation (16) is the general equation for the gelationbehavior of partially hydrolyzed polyacrylamide-hexamine-hydroquinone gel system e value of constant dependsupon the polymer and crosslinkers composition and temper-ature

4 Solution Procedure of the DevelopedModel

e mathematical model for gelation time consists of fourvariable parameters (119862119862119860119860 119862119862119861119861 119862119862119862119862 and 119877119877) and ve constants(1198861198860 1198861198861 1198861198862 1198861198863 and 1198861198864) For the determination of theseconstants ve simultaneous equations are generated by mul-tiplying the variables in both side of the model equation andutilizing the experimental data the ow diagram for solutionof proposed model is shown in Figure 1 Further theseequations are solved by multivariate regression method andvalues of the constants 1198861198860 1198861198861 1198861198862 1198861198863 and 1198861198864 are determinedAer putting these values in the model equation the gelationtime are calculated by varying the different parameters (119862119862119860119860119862119862119861119861 119862119862119862119862 and 119877119877) Finally these calculated values are comparedwith the actual values obtained from the laboratory work

5 Experimental Work

51 Material Used ematerials used for this work are par-tially hydrolyzed polyacrylamide hexamine hydroquinonesodium chloride hydrochloric acid and sodium hydroxidePartially hydrolyzed polyacrylamide is procured fromOil andNatural Gas Corporation LimitedMumbai India Hexamineis purchased from Otto Kemi Mumbai India and hydro-quinone is procured fromRanbaxy Fine Chemicals Ltd NewDelhi India Hydrochloric acid is purchased from CentralDrug house (P) Ltd New Delhi India Sodium chloride ispurchased from Nice Chemical Pvt Ltd Cochin India and






(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016

sodium hydroxide is purchased from S D Fine-Chem LtdMumbai India

52 Experimental Procedure Initially stock solution of par-tially hydrolyzed polyacrylamide was prepared in brine solu-tion and kept for aging at ambient temperature for 24 hrsand further fresh solution of hexamine and hydroquinonewere also prepared in brine e appropriate solution of par-tially hydrolyzed polyacrylamide hexamine hydroquinoneand brine were thoroughly mixed at room temperature bymagnetic stirrer e pH of the gelant solution was measuredby Century CP-901 digital pH meter and the pH of thegelant solution was adjusted by using 1N sodium hydroxideand 1N hydrochloric acid Finally the gelant solution wastransferred into small glass bottle and kept at the desiretemperature in the hot air oven (temperature ranges from80∘C to 120∘C) Due to the increased temperature and thecrosslinking reaction gel formation takes place e qualityof gel was visually inspected at regular intervals and gelationtime was noted Here the time for the formation of stiffrigidgel was only considered

6 Results and Discussions

e gelation behavior of the polymer gel system largelydepends on the polymer-crosslinker concentrations and the

temperaturee effects of these parameters on gelation timeare described below

61 Effect of Temperature on Gelation Time Different gellingsolutions were prepared with different concentrations ofpolymer and crosslinking agent at pH 75 and kept forgelation at different temperature e reaction rate betweenamide group and methylol group was accelerated by increas-ing temperature and the gelation time decreased Increasingthe gelation temperature results in a decrease in gelation timesince at higher temperature gels are formed in lesser timedue to rapid crosslinking as is depicted in Figures 2 and3 and Tables 1 2 3 4 and 5 A possible explanation forrapid cross-linking is either due to an increase in molecularmobility or formation of new cross-linking sites as a result ofgelation reaction It is a known fact that degree of hydrolysisof the polymer increases at elevated temperatures which inturn increases the number of cross-linking sites that is foundincreasing the reaction rate and decreasing the gelation time

62 Effect of Polymer Concentration on Gelation Time epolymer concentration has a signicant effect on the physicalproperties of gel e polymer concentration increases andgelation time decreases were shown in Figure 4e polymerconcentration ranges from 08 to 11 wt and constantconcentration of crosslinker (05 to 03 wt HMTA and 04to 03 wtHQ) at pH 75 are depicted in Tables 1 to 5 As the






(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917

polymer concentration increases it means more crosslinkingsites are available for the fast crosslinking reaction takes placeus the gel formation reaction increases which leads tothe decreases of gelation time is trend is expected to bethe same at all gelation temperatures under study us therequired time to obtain a non-owing polymer gel with atolerable strength decreasedwhen the polymer concentrationwas increased

63 Effect of Cross-Linker Concentration on Gelation TimeHexamine and hydroquinone crosslinkers are a multifunc-tional group which can build a complex network with amidegroups of partially hydrolyzed polyacrylamide and form a3-dimentional gel network structure Crosslinker concentra-tion has a signicant effect on the gel strengthe crosslinkerconcentration increases and gelation time decreases wereshown in Figure 5 e several samples were prepared toinvestigate the effect of crosslinker concentration on thenetwork strength Bottle testing results shown in Tables 1 to 5indicate that when the concentration of both crosslinker wasdecreased the gelation rate and gel quality is also decreasedIn other words when crosslinking agent concentration wasincreased the stage of polymer gel changed from a state ofowing gel to one of deformable non-owing gel becausecrosslinking sites are increased for the formation of gel inlesser time intervals

7 Model Discussion

Equation (12) shows the relation of gelation time withpolymer concentration cross linker concentrations andtemperature Here 119862119862119860119860 119862119862119861119861 and 119862119862119862119862 are polymers HMTAand hydroquinone concentrations respectively in gmlitreand temperature are taken in degree kelvin is equationindicates that the gelation time is inversely proportional tothe concentrations of polymer and crosslinking agent whichreects that the increasing the concentration of polymer andcrosslinking agent decreases the gelation time e proposedmodel for the study of the gelation behavior of partiallyhydrolyzed polyacrylamide-hexamine-hydroquinone poly-mer gel system is shown in (15)-(16) e values of theconstantscoefficients 1198861198860 1198861198861 1198861198862 1198861198863 and 1198861198864 are determined bymultivariate regression method

Equation (15) can be rewritten as follows

119910119910 119910 1198861198860 + 1198861198861 sdot 1199091199091 + 1198861198862 sdot 1199091199092 + 1198861198863 sdot 1199091199093 + 1198861198864 sdot 1199091199094 (17)

where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)

e above equation solved bymultivariate regressionmethodand the values of constants 1198861198860 1198861198861 1198861198862 1198861198863 and 1198861198864 are calculated






(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038

T 6 Comparison of gelation time of developed model and Arrhenius type equation

Temperature(∘C)

Experimental gelation time(hrs)

eoretical gelation time (hrs) by Arrheniustype equation Civan et al [18]ln(119905119905119905 119905 119905119905119905119905119905119905119905119905119905119905119905119905119905 (∘K) minus 1763044(08 wt PHPA 05 wtHMTA and 03

wt hydroquinone)

eoretical gelation time (hrs) byDeveloped Model

(08 wt PHPA 05 wtHMTA and03 wt hydroquinone)

80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554

e values of the constants 1198861198860 119886119886119905 119886119886119905 1198861198863 and 119886119886119905 are found tobe 177831 minus519301 minus100564 minus047246 and 892687612respectively and nally the gelation time is calculated fromthe following equation

119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861

minus1199051199050056119905 times 119905119905119905119905minus01199051199051199051199051199056

times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)

e value of 119877119877119905 is 099122 which shows the good agreementbetween experimental and theoretical values of gelation timeis study reveals that the developed model may be usedfor the study of gelation behavior of partially hydrolyzedpolyacrylamide-hexamine-hydroquinone gel system for itsapplication in prole modication obs e theoretical

values calculated from above equation are shown in Tables1ndash5 at different polymer-crosslinker concentration and tem-perature

71 Comparison between Developed Model and Civan etal [18] e developed model in the present study relatesstoichiometric relation between reactants involved in thegelation reaction as well as Arrhenius equation In thiscase gelation time is dependent on polymer and crosslinkerconcentration as well as temperature However model pro-posed by Civan et al is simply Arrhenius type equationwhich is dependent on temperature only Figure 3 shows thetheoretical values of gelation time for different concentrationof polymers It was found that there are several variations


00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs

1Gelation temparature (1K)

08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862

05 wt HMTA and 03 wt Hydroquinone

F 3 Plot for the temperature dependence of gelation timeaccording to Arrhenius-type equation

08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)

Polymer concentration (wt)

Experimental values at 80C

Theoretical values at 80C

Experimental values at 90CTheoretical values at 90C






F 4 Plot of polymer concentration versus experimental andtheoretical values of gelation time at different temperature constantcrosslinker concentration (HMTAHQ 0404 wt) and pH 75

0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)

Crosslinker concentration HMTAHQ (wt)











F 5 Plot of crosslinker concentration versus experimental andtheoretical values of gelation time at different temperature constantpolymer concentration (PHPA 09 wt) and pH 75

in the values of slopes and intercepts as well as 1198771198772 and mayhave different activation energy for different concentrationsof polymers e comparison of theoretical gelation timecalculated using Civan et al model and our developed modelat the concentration (08 polymer) are approximately thesame which is shown in Table 6 and have good agreementwith that particular experimental data But the developedmodel presents the same values of coefficients and activationenergy for whole experimental study and all data are tted inthat mathematical equation Hence it may be more realisticin nature

8 Conclusion

e following conclusions are drawn from the present study

(1) e gelation time of partially hydrolyzed poly-acrylamide-hexamine-hydroquinone gel systemdecreases with increasing the cross linker concen-tration and temperature

(2) On the basis of kinetics of gelation behavior themathematical model for the partially hydrolyzed


polyacrylamide-hexamine-hydroquinone gel systemis the following

119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)

(3) e values of constants 1198861198860 1198861198861 1198861198862 1198861198863 and 1198861198864 for thisstudy are found to be 177831 minus519301 minus100564minus047246 and 892687612 respectively

(4) e nal mathematical model for the present study isas follows

119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)

(5) A values show good agreement between experimentaland theoretical values of gelation time is studyreveals that the developed model may be used forthe study of gelation behavior of partially hydrolyzedpolyacrylamide-hexamine-hydroquinone gel systemfor its application in prole modication jobs

Nomenclature

119905119905119860119860 Concentration of partially hydrolyzedpolyacrylamide (PHPA) (gmliter)

119905119905119861119861 Concentration of hexamine (HMTA)(gmliter)

119905119905119905119905 Concentration of hydroquinone(gmliter)

119905119905 Gelation time (second)119879119879 Temperature (∘K119879119896119896119896 119896119896119896 119896119896 Reaction rateproportionality

constants119905119905119860119860119860119860 Initial concentrations of polymer119905119905119861119861119860119860 Initial concentrations of hexamine119905119905119905119905119860119860 Initial concentrations of

hydroquinone119864119864119886119886 Activation energy119877119877 Gas constant1198861198860119896 1198861198861119896 1198861198862119896 1198861198863 and 1198861198864 Constants119886119886119896 119886119886 and 119888119888 Reaction order with respect to 119860119860 119861119861

and 119905119905120572120572119896 120572120572 and 120574120574 Reactant of species 119860119860 119861119861 and 119905119905

present in the reaction respectively

Acknowledgment

e authors are very thankful to Council of Scientic andIndustrial Research (CSIR) New Delhi India for nancialassistance to carry out the research work

References

[1] Y Liu B Bai and YWang ldquoApplied technologies and prospectsof conformance control treatments in Chinardquo Oil and GasScience and Technology vol 65 no 6 pp 859ndash878 2010

[2] R Jain C S McCool D W Green G P Willhite and MJ Michnick ldquoReaction kinetics of the uptake of chromium

(III) acetate by polyacrylamiderdquo Society of Petroleum EngineersJournal vol 10 no 3 pp 247ndash255 2004

[3] C A Grattoni H H Al-Sharji C Yang A H Muggeridge andR W Zimmerman ldquoRheology and permeability of crosslinkedpolyacrylamide gelrdquo Journal of Colloid and Interface Science vol240 no 2 pp 601ndash607 2001

[4] A Moradi-Araghi ldquoA review of thermally stable gels foruid diversion in petroleum productionrdquo Journal of PetroleumScience and Engineering vol 26 no 1ndash4 pp 1ndash10 2000

[5] A Stavland and H C Jonsbraten ldquoNew insight into aluminumcitratepolyacrylamide gels for uid controlrdquo in Proceedings ofthe SPEDOE 10th Symposium on Improved Oil Recovery PaperSPEDOE 35381 pp 347ndash356 Tulsa Okla USA April 1996

[6] S L Bryant G P Borghi M Bartosek and T P Lock-hart ldquoExperimental investigation on the injectivity of phenol-formaldehydepolymer gelantsrdquo in Proceedings of the SPE Inter-national Symposium onOileld Chemistry Paper SPE 37244 pp335ndash343 Houston Tex USA February 1997

[7] H Jia W F Pu J Z Zhao and R Liao ldquoExperimental investi-gation of the novel phenol-formaldehyde cross-linking HPAMgel system based on the secondary cross-linking method oforganic cross-linkers and its gelation performance study aerowing through porous mediardquo Energy and Fuels vol 25 no 2pp 727ndash736 2011

[8] H Jia W F Pu J Z Zhao and F Y Jin ldquoResearch on thegelation performance of low toxic PEI cross-linking PHPAMgelsystems as water shutoff agents in low temperature reservoirsrdquoIndustrial and Engineering Chemistry Research vol 49 no 20pp 9618ndash9624 2010

[9] H T Dovan R D Hutchins and B B Sandiford ldquoDelayinggelation of aqueous polymers at elevated temperatures usingnovel organic crosslinkersrdquo in Proceedings of the SPE Interna-tional Symposium on Oileld Chemistry Paper SPE 37246 pp361ndash371 Houston Tex USA February 1997

[10] R D Hutchins H T Dovan and B B Sandiford ldquoFieldapplications of high temperature organic gels for water controlrdquoin Proceedings of the 10th Symposium of Improved Oil RecoveryPaper SPEDOE 35444 Tulsa Okla USA April 1996

[11] L Eoff D Dalrymple and D Everett ldquoGlobal eld resultsof a polymeric gel system in conformance applicationsrdquo inProceedings of SPE Russian Oil and Gas Technical Conferenceand Exhibition Paper SPE 101822 pp 280ndash285 MoscowRussia October 2006

[12] J Vasquez E D Dalrymple L Eoff B R Reddy and F CivanldquoDevelopment and evaluation of high-temperature confor-mance polymer systemsrdquo in Proceedings of the SPE InternationalSymposium on Oileld Chemistry Paper SPE 93156 HoustonTex USA February 2005

[13] G A Al-Muntasheri H A Nasr-El-Din and I A Hussein ldquoArheological investigation of a high temperature organic gel usedfor water shut-off treatmentsrdquo Journal of Petroleum Science andEngineering vol 59 no 1-2 pp 73ndash83 2007

[14] G A Al-Muntasheri ldquoA study of polyacrylamide-based gelscrosslinked with polyethyleneiminerdquo in Proceedings of the SPEInternational Symposium on Oileld Chemistry Paper SPE105925 Houston Tex USA February 2007

[15] S D Jordan D W Green E R Terry and G P Willhiteldquoe effect of temperature on gelation time for polyacry-lamidechromium (III) systemsrdquo Society of Petroleum EngineersJournal vol 22 no 4 pp 463ndash471 1982

[16] G A Al-Muntasheri H A Nasr-El-Din and P L J ZithaldquoGelation kinetic and performance evaluation of an organically


crosslinked gel at high temperature and pressurerdquo in Proceed-ings of the 1st International Oil Conference and Exhibition PaperSPE 104071 September 2006 Cancun Mexico

[17] M Simjoo M Vafaie Sei A Dadvand Koohi R Hashemi-nasab and V Sajadian ldquoPolyacrylamide gel polymer as watershut-off system preparation and investigation of physical andchemical properties in one of the iranian oil reservoirs condi-tionsrdquo Iranian Journal of Chemistry and Chemical Engineeringvol 26 no 4 pp 99ndash108 2007

[18] F Civan J Vasquez D Dalrymple L Eoff and B R ReddyldquoLaboratory and theoretical evaluation of gelation time datafor water-based polymer systems for water controlrdquo PetroleumScience and Technology vol 25 no 3 pp 353ndash371 2007

[19] O Levenspiel Chemical Reaction Engineering John Wiley ampSons New York NY USA 3rd edition 1999

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



O

C

H H

OH

OH

OH

OH

HO

HO

Hydroquinone Formaldehyde 2356-tetramethylol hydroquinone

OH

OH

4+

S 1

C C C C C C

C H C H C H

H H H H H H

O OO

Carboxylate Amide

Partially hydrolized polyacrylamide (PHPA)

Amide

+

OH

OH

OH

OH

HO

HO

2356-tetramethylol hydroquinone

NH2 NH2Ominus

Na+

R

R

N

H

H

OH

OHOH

OH

OH

HO

Water

Crosslinking 3-D gel structure

O

S 2

to provide rigid ringing gels Polyethyleneimine (PEI) cross-linking a copolymer of acrylamide and tert-butylacrylate(PAtBA) as water shutoff gels has been widely used in recentyears [14]

e gelation mechanism of organic crosslinkers is doneby covalent bonding which is much more stable thanthe ionic bonds Organic crosslinkers were introduced toobtained gels that can remain stable over a wide temperaturerange For high temperature (gt90∘C) reservoirs acrylamide-based copolymers with organic crosslinking agents such asphenol-formaldehyde and its derivatives can be used to forma gel with thermal stability and the gelation time is adjustable[15 16]

e different methods are presented in the literature forthe determination of the physical and chemical properties ofpolymer gel system such as bottle testingmethod sealed tubemethod dynamic shearmethod (rheometer) and static shearmethod (viscometer) Out of thesemethods the bottle testing

method is most suitable faster and inexpensive method tostudy the gelation kinetics [17]

Several models have been reported in the literature torelate the gelation time with temperature Jordan found thatthe gelation time of a specied system decreases as thetemperature is increased Plots of the logarithm of gelationtime versus the reciprocal of the absolute reaction temper-ature were found to be linear for the systems studied iscorrelation showed that the system apparently followed theHurd and Letteron model which assumed rate dependenceon only one species Hurd and Letteron studied the effect oftemperature on the formation of silicic acid gels and foundempirically that plot of the logarithm of the gelation timeversus the reciprocal of the absolute temperature linear eydeveloped an equation similar to the Arrhenius equationwhich relates gelation time and the temperature and supportthe linear relationship [15] But very few or raremodels relatethe gelation time with polymer and crosslinker concentration


Start





End


form of equation 15



equation16

temperature





2 GelationMechanism


80 90 100 110 120

1

10

100

1000

10000

100000

1000000

Gel

atio

n t

ime

(hrs

)










HMTAHQ 0504 (wt)

pH 75







+ H2O+ water (2)




119903119903120572120572 = minus119889119889120572120572120572120572119889119889119889119889= 119896119896120572120572120572120572

119886119886120572120572120572120572119887119887120572120572120572120572119888119888 (3)







(wt)HMTA(wt)

HQ(wt)

1 08 05 04 280 3288475

802 09 05 04 200 17838553 10 05 04 120 10331454 11 05 04 61 6291995 08 05 04 1743 1639435

906 09 05 04 823 8893227 10 05 04 49 5145658 11 05 04 293 3136819 08 05 04 87 848392

10010 09 05 04 41 46021511 10 05 04 31 26628212 11 05 04 153 16232613 08 05 04 453 454394

11014 09 05 04 23 24648915 10 05 04 13 14261916 11 05 04 7 8694117 08 05 04 28 251225

12018 09 05 04 14 13627819 10 05 04 8 6891720 11 05 04 5 480681


119862119862119861119861119862119862119860119860=120573120573120572120572⟹ 119862119862119861119861 =

120573120573120572120572119862119862119860119860

119862119862119862119862119862119862119860119860=120574120574120572120572⟹ 119862119862119888119888 =

120574120574120572120572119862119862119860119860

(4)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119886119886 sdot 1007653100765312057312057312057212057211986211986211986011986010076691007669119887119887sdot 1007652100765212057412057412057212057211986211986211986011986010076681007668119888119888

= 11989611989610076531007653120573120573120572120572100766910076691198871198871007652100765212057412057412057212057210076681007668119888119888sdot 119862119862119860119860119886119886119886119887119887119886119888119888

(5)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119899119899 (6)


119889119889 =1(119899119899 minus 1) 119896119896119896



119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076871007687

119862119862119860119860119862119862119860119860119886119886 sdot 1198621198621198601198601198871198871007649100764912057312057312057312057212057210076651007665

119887119887 sdot 1198621198621198601198601198881198881007649100764912057412057412057312057212057210076651007665119888119888

minus119862119862119860119860119860119860

119862119862119860119860119860119860119886119886 sdot 1198621198621198601198601198601198601198871198871007649100764912057312057312057312057212057210076651007665119887119887 sdot 1198621198621198601198601198601198601198881198881007649100764912057412057412057312057212057210076651007665

11988811988810077031007703

(8)


119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076861007686119862119862119860119860

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888minus119862119862119860119860119860119860

11986211986211986011986011986011986011988611988611986211986211986111986111986011986011988711988711986211986211986211986211986011986011988811988810077021007702

(9)



119889119889 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888 (10)


119896119896 = 119860119860 119896119896119896 10076521007652minus11986411986411988611988611987711987711987911987910076681007668 (11)






(wt)HMTA(wt)

HQ(wt)

1 08 05 03 312 3767173

802 09 05 03 230 20435283 10 05 03 134 11823934 11 05 03 68 7207915 08 05 03 207 1878085

906 09 05 03 91 10187797 10 05 03 553 5894698 11 05 03 333 3593439 08 05 03 101 971891

10010 09 05 03 553 52720811 10 05 03 34 30504512 11 05 03 19 18595613 08 05 03 50 520539

11014 09 05 03 253 2823715 10 05 03 143 1633816 11 05 03 8 9959717 08 05 03 32 287795

12018 09 05 03 143 15611619 10 05 03 83 9032920 11 05 03 63 55065


119905119905 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (12)


119905119905 119905 1198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (13)


ln 119905119905 119905 ln100768610076861198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 100765210076521198641198641198861198861198771198771198771198771007668100766810077021007702 (14)

ln 119905119905 119905 1198861198860 + 1198861198861 ln119862119862119860119860 + 1198861198862 ln119862119862119861119861 + 1198861198863 ln119862119862119862119862 +1198861198864119877119877 (15)


119905119905 119905 1198621198621198601198601198861198861 times 119862119862119861119861

1198861198862 times 1198621198621198621198621198861198863 times exp 100765210076521198861198860 +

119886119886411987711987710076681007668 (16)




5 Experimental Work







(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016













(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start





End


form of equation 15



equation16

temperature





2 GelationMechanism


80 90 100 110 120

1

10

100

1000

10000

100000

1000000

Gel

atio

n t

ime

(hrs

)










HMTAHQ 0504 (wt)

pH 75







+ H2O+ water (2)




119903119903120572120572 = minus119889119889120572120572120572120572119889119889119889119889= 119896119896120572120572120572120572

119886119886120572120572120572120572119887119887120572120572120572120572119888119888 (3)







(wt)HMTA(wt)

HQ(wt)

1 08 05 04 280 3288475

802 09 05 04 200 17838553 10 05 04 120 10331454 11 05 04 61 6291995 08 05 04 1743 1639435

906 09 05 04 823 8893227 10 05 04 49 5145658 11 05 04 293 3136819 08 05 04 87 848392

10010 09 05 04 41 46021511 10 05 04 31 26628212 11 05 04 153 16232613 08 05 04 453 454394

11014 09 05 04 23 24648915 10 05 04 13 14261916 11 05 04 7 8694117 08 05 04 28 251225

12018 09 05 04 14 13627819 10 05 04 8 6891720 11 05 04 5 480681


119862119862119861119861119862119862119860119860=120573120573120572120572⟹ 119862119862119861119861 =

120573120573120572120572119862119862119860119860

119862119862119862119862119862119862119860119860=120574120574120572120572⟹ 119862119862119888119888 =

120574120574120572120572119862119862119860119860

(4)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119886119886 sdot 1007653100765312057312057312057212057211986211986211986011986010076691007669119887119887sdot 1007652100765212057412057412057212057211986211986211986011986010076681007668119888119888

= 11989611989610076531007653120573120573120572120572100766910076691198871198871007652100765212057412057412057212057210076681007668119888119888sdot 119862119862119860119860119886119886119886119887119887119886119888119888

(5)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119899119899 (6)


119889119889 =1(119899119899 minus 1) 119896119896119896



119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076871007687

119862119862119860119860119862119862119860119860119886119886 sdot 1198621198621198601198601198871198871007649100764912057312057312057312057212057210076651007665

119887119887 sdot 1198621198621198601198601198881198881007649100764912057412057412057312057212057210076651007665119888119888

minus119862119862119860119860119860119860

119862119862119860119860119860119860119886119886 sdot 1198621198621198601198601198601198601198871198871007649100764912057312057312057312057212057210076651007665119887119887 sdot 1198621198621198601198601198601198601198881198881007649100764912057412057412057312057212057210076651007665

11988811988810077031007703

(8)


119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076861007686119862119862119860119860

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888minus119862119862119860119860119860119860

11986211986211986011986011986011986011988611988611986211986211986111986111986011986011988711988711986211986211986211986211986011986011988811988810077021007702

(9)



119889119889 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888 (10)


119896119896 = 119860119860 119896119896119896 10076521007652minus11986411986411988611988611987711987711987911987910076681007668 (11)






(wt)HMTA(wt)

HQ(wt)

1 08 05 03 312 3767173

802 09 05 03 230 20435283 10 05 03 134 11823934 11 05 03 68 7207915 08 05 03 207 1878085

906 09 05 03 91 10187797 10 05 03 553 5894698 11 05 03 333 3593439 08 05 03 101 971891

10010 09 05 03 553 52720811 10 05 03 34 30504512 11 05 03 19 18595613 08 05 03 50 520539

11014 09 05 03 253 2823715 10 05 03 143 1633816 11 05 03 8 9959717 08 05 03 32 287795

12018 09 05 03 143 15611619 10 05 03 83 9032920 11 05 03 63 55065


119905119905 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (12)


119905119905 119905 1198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (13)


ln 119905119905 119905 ln100768610076861198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 100765210076521198641198641198861198861198771198771198771198771007668100766810077021007702 (14)

ln 119905119905 119905 1198861198860 + 1198861198861 ln119862119862119860119860 + 1198861198862 ln119862119862119861119861 + 1198861198863 ln119862119862119862119862 +1198861198864119877119877 (15)


119905119905 119905 1198621198621198601198601198861198861 times 119862119862119861119861

1198861198862 times 1198621198621198621198621198861198863 times exp 100765210076521198861198860 +

119886119886411987711987710076681007668 (16)




5 Experimental Work







(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016













(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(wt)HMTA(wt)

HQ(wt)

1 08 05 04 280 3288475

802 09 05 04 200 17838553 10 05 04 120 10331454 11 05 04 61 6291995 08 05 04 1743 1639435

906 09 05 04 823 8893227 10 05 04 49 5145658 11 05 04 293 3136819 08 05 04 87 848392

10010 09 05 04 41 46021511 10 05 04 31 26628212 11 05 04 153 16232613 08 05 04 453 454394

11014 09 05 04 23 24648915 10 05 04 13 14261916 11 05 04 7 8694117 08 05 04 28 251225

12018 09 05 04 14 13627819 10 05 04 8 6891720 11 05 04 5 480681


119862119862119861119861119862119862119860119860=120573120573120572120572⟹ 119862119862119861119861 =

120573120573120572120572119862119862119860119860

119862119862119862119862119862119862119860119860=120574120574120572120572⟹ 119862119862119888119888 =

120574120574120572120572119862119862119860119860

(4)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119886119886 sdot 1007653100765312057312057312057212057211986211986211986011986010076691007669119887119887sdot 1007652100765212057412057412057212057211986211986211986011986010076681007668119888119888

= 11989611989610076531007653120573120573120572120572100766910076691198871198871007652100765212057412057412057212057210076681007668119888119888sdot 119862119862119860119860119886119886119886119887119887119886119888119888

(5)


119903119903119860119860 = minus119889119889119862119862119860119860119889119889119889119889= 119896119896119862119862119860119860

119899119899 (6)


119889119889 =1(119899119899 minus 1) 119896119896119896



119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076871007687

119862119862119860119860119862119862119860119860119886119886 sdot 1198621198621198601198601198871198871007649100764912057312057312057312057212057210076651007665

119887119887 sdot 1198621198621198601198601198881198881007649100764912057412057412057312057212057210076651007665119888119888

minus119862119862119860119860119860119860

119862119862119860119860119860119860119886119886 sdot 1198621198621198601198601198601198601198871198871007649100764912057312057312057312057212057210076651007665119887119887 sdot 1198621198621198601198601198601198601198881198881007649100764912057412057412057312057212057210076651007665

11988811988810077031007703

(8)


119889119889 =1

119896119896 119896(119886119886 119886 119887119887 119886 119888119888) minus 110076861007686119862119862119860119860

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888minus119862119862119860119860119860119860

11986211986211986011986011986011986011988611988611986211986211986111986111986011986011988711988711986211986211986211986211986011986011988811988810077021007702

(9)



119889119889 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888 (10)


119896119896 = 119860119860 119896119896119896 10076521007652minus11986411986411988611988611987711987711987911987910076681007668 (11)






(wt)HMTA(wt)

HQ(wt)

1 08 05 03 312 3767173

802 09 05 03 230 20435283 10 05 03 134 11823934 11 05 03 68 7207915 08 05 03 207 1878085

906 09 05 03 91 10187797 10 05 03 553 5894698 11 05 03 333 3593439 08 05 03 101 971891

10010 09 05 03 553 52720811 10 05 03 34 30504512 11 05 03 19 18595613 08 05 03 50 520539

11014 09 05 03 253 2823715 10 05 03 143 1633816 11 05 03 8 9959717 08 05 03 32 287795

12018 09 05 03 143 15611619 10 05 03 83 9032920 11 05 03 63 55065


119905119905 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (12)


119905119905 119905 1198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (13)


ln 119905119905 119905 ln100768610076861198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 100765210076521198641198641198861198861198771198771198771198771007668100766810077021007702 (14)

ln 119905119905 119905 1198861198860 + 1198861198861 ln119862119862119860119860 + 1198861198862 ln119862119862119861119861 + 1198861198863 ln119862119862119862119862 +1198861198864119877119877 (15)


119905119905 119905 1198621198621198601198601198861198861 times 119862119862119861119861

1198861198862 times 1198621198621198621198621198861198863 times exp 100765210076521198861198860 +

119886119886411987711987710076681007668 (16)




5 Experimental Work







(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016













(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(wt)HMTA(wt)

HQ(wt)

1 08 05 03 312 3767173

802 09 05 03 230 20435283 10 05 03 134 11823934 11 05 03 68 7207915 08 05 03 207 1878085

906 09 05 03 91 10187797 10 05 03 553 5894698 11 05 03 333 3593439 08 05 03 101 971891

10010 09 05 03 553 52720811 10 05 03 34 30504512 11 05 03 19 18595613 08 05 03 50 520539

11014 09 05 03 253 2823715 10 05 03 143 1633816 11 05 03 8 9959717 08 05 03 32 287795

12018 09 05 03 143 15611619 10 05 03 83 9032920 11 05 03 63 55065


119905119905 1199051

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (12)


119905119905 119905 1198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 1007652100765211986411986411988611988611987711987711987711987710076681007668 (13)


ln 119905119905 119905 ln100768610076861198961198961

119862119862119860119860119886119886119862119862119861119861119887119887119862119862119862119862119888119888times exp 100765210076521198641198641198861198861198771198771198771198771007668100766810077021007702 (14)

ln 119905119905 119905 1198861198860 + 1198861198861 ln119862119862119860119860 + 1198861198862 ln119862119862119861119861 + 1198861198863 ln119862119862119862119862 +1198861198864119877119877 (15)


119905119905 119905 1198621198621198601198601198861198861 times 119862119862119861119861

1198861198862 times 1198621198621198621198621198861198863 times exp 100765210076521198861198860 +

119886119886411987711987710076681007668 (16)




5 Experimental Work







(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016













(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(wt)HMTA(wt)

HQ(wt)

1 08 04 04 331 4115734

802 09 04 04 243 22326063 10 04 04 140 12917954 11 04 04 77 7874835 08 04 04 226 2051856

906 09 04 04 105 11130437 10 04 04 71 6440118 11 04 04 373 3925919 08 04 04 115 1061816

10010 09 04 04 61 57598911 10 04 04 37 33326912 11 04 04 23 20316213 08 04 04 56 568703

11014 09 04 04 30 30849615 10 04 04 17 17849716 11 04 04 10 10881217 08 04 04 36 314424

12018 09 04 04 17 17056119 10 04 04 9 9868720 11 04 04 7 6016













(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(wt)HMTA(wt)

HQ(wt)

1 08 04 03 370 4714855

802 09 04 03 286 25576043 10 04 03 168 14798394 11 04 03 84 9021165 08 04 03 266 2350542

906 09 04 03 1353 12750677 10 04 03 78 7377588 11 04 03 423 449749 08 04 03 133 1216383

10010 09 04 03 71 65983511 10 04 03 42 38178312 11 04 03 27 23273613 08 04 03 60 651488

11014 09 04 03 35 35340415 10 04 03 203 20448116 11 04 03 12 12465217 08 04 03 39 360194

12018 09 04 03 19 1953919 10 04 03 10 11305320 11 04 03 8 68917



7 Model Discussion




where

119910119910 119910 119910119910 119910119910119910 1199091199091 119910 119910119910119862119862119860119860119910 1199091199092 119910 119910119910119862119862119861119861

1199091199093 119910 119910119910119862119862119862119862 1199091199094 1199101119879119879

(18)







(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(wt)HMTA(wt)

HQ(wt)

1 08 03 03 451 6296609

802 09 03 03 362 34156373 10 03 03 216 197634 11 03 03 111 1204765 08 03 03 311 3139109

906 09 03 03 158 1702837 10 03 03 102 9852648 11 03 03 553 6006219 08 03 03 170 1624459

10010 09 03 03 82 88119811 10 03 03 58 50986412 11 03 03 30 31081513 08 03 03 86 870051

11014 09 03 03 66 57160415 10 03 03 243 2730816 11 03 03 15 16647117 08 03 03 45 481034

12018 09 03 03 23 2609419 10 03 03 14 1509820 11 03 03 10 92038


Temperature(∘C)



wt hydroquinone)



80 312 34366928 3766642690 207 18007746 18778207100 101 9768365 9717542110 50 5470794 5204664120 32 3155635 2877554


119905119905 119905 119905119905119860119860minus5119905119905930119905 times 119905119905119861119861


times 119890119890(1199051199051199051199051199053119905+(119905911990561199051199051199056119905119905119905119905119905119905119905119905(19)





00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










00

02

5

00

02

55

00

02

6

00

02

65

00

02

7

00

02

75

00

02

8

00

02

85

1

2

3

4

5

6

7

8

9

ln(g

elat

ion

tim

e) h

rs


08 wt PHPA R2= 098587

09 wt PHPA R2= 099223

1 wt PHPA R2= 099117

11 wt PHPA R2= 097862



08 085 09 095 1 105 11

10

100

1000

10000

100000

1000000

HMTAHQ 0404 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)











0303 0403 0404 0503 0504

10

100

1000

10000

100000

1000000

PHPA 09 (wt)

pH 75


Gel

atio

n t

ime

(hrs

)














8 Conclusion






119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119905119905 119905 1199051199051198601198601198861198861 times 119905119905119861119861

1198861198862 times 1199051199051199051199051198861198863 times 119890119890(1198861198860+(1198861198864119879119879119879119879 (20)



119905119905 119905 119905119905119860119860minus519301 times 119905119905119861119861


times 119890119890(177831+(892687612119879119879119879119879(21)


Nomenclature









Acknowledgment


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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