paraffin wax deposition and fouling

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— ;55 — 1.7.3 Dimensionless Expressions it is convenient to introduce the following diensionless constants: + U U — + = .....(A7.3.2) V W .1. = I i ri f’-. T — .i W u* I u = C TW /pwY ;‘hore w rez’ers to values at y = o, i.e. at the wall, u is the shearing stress velocity and v the kineratic viscosity. Eçuaiors A7.1.3, h7.1.4, A7.2.i and A7.2.2 can now be expressed in diensioniess forz as follows: •fqW p 4 u Vw:Iw/Pw) /Pi dy’ + (du / y EU : .....(A7.3.7) — .2÷ .÷2 (ciu /c.y ) 2 ÷ + / 2 ++\ EU = n u y — exp —n u y .....(A7.3.8) W
— A36 — A74 Velocity Distribution if I’luid Properties are Constant Doissler used velocity distribution data for flow without heat transfer to evaluate the constants K and n. Assuming T = Tw and constant physical properties, a substitution for cu/rw in equation A73.5 gives: (1) Away from wall + + y + u = in —- - u1 .....(A7.4.i) where y is the lowest of y for which the equation applies and u is the value o u at y1. From experimental data Deissier found K = 0.3 u — (2) Close to wall y ÷ dy + (4 2 + + 2 + + l+n u y 1-exp(—n u y) J From experimental data Deissler found n = 0.124. At small y (< 5) the equation reduces to + + u = y .....(A7.4.3 Equations A7.4.1 and A7.4.3 are the same as in the Universal Velocity Profile. Deissler found his data to Lit very well with these equations if ttaay from the wall” was considered when y26, at which point u = 12.82. A75 ueratur Distribution if Fluid ProDorties are Constant Assuming q = q,,, and = 1 in the dimensionless form of the heat flux equation A7.3.6, results in the following equation: A dT’ l=ç.+ __) sucsti;ution for the dimensionless eddy diffusivity gives:
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1 ci 0 Ilc (i) s_ri P4 4) •,-1 0
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ACKC’bJLED3E.:ENTS should like to
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46 iixperimental Results 461 IntroJ
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APPNNDICES 1. PHYSICal PRSPHTIES Oi
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the major unresolved problem in hea
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and time, fouling factors are usual
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o F-I 0 U J ,ij cn J ‘I—I F3 Fl
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—5— vary from less than 1 per c
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2.2.3 Solubility refined paraffin w
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-.9— whica is well novc condition
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— -ii — deposit. Tronov statej
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— 13 remain in solution and the p
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- iuctoov and dorov concluded hat t
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— 17 — a deporsiion ce:Ll in a
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— 19 - toat sur:ace. hjsima.a ot
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— 2 - S * .. -, ‘.: ,- - .-,-
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and surface proueriez reapectlvely_
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- 25 - loading to a random process
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y - F’J CD:’ C) x— Dcpoit thi
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0 C 15O— 200 From ref 2 of wax eo
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0 o3 Tb 3D 0•0 L D 2 •O— Fg.2
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2 I In 0 Tot -D -D U 16H 16 20, In
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C CE) CL) CE) () .: rJ\: - . c: CD
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400 function of roughness factor. m
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— 2o — 3. i3:\CGRDU ND TO TI PR
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3.5 Conclusions decreases At the in
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L - A sz: CF Fo:;:NG BY SOLUTIONS O
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was designed to cut off the steam s
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• saLLy measures were tacen. oa:D
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— 34 .4 ‘mrii:ntal Solution The
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sections were ke-:t the same. fosi:
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sectaon 4- at eajt tests sections h
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These fluctuations were not reduced
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ii ID XXX 9 C-) 0 (N x S x xx< 7r-
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12— -; 11L. s 10E - 9: ‘3) 0 Ru
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(1) U) C’) C) Cl) It) 0 0 0 0 ox
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f-iq. 1.0-3.5.— Hecit trcinsfcr r
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I--i Fig. f.6.3.7. I ;ut transfer r
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0 C’) R — [feat transfer resist
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characteristc does exist and is tyt
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The ziuewor in the circulation syst
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The calibrations o the tesperature
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the solution and water o::a;es thro
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‘-- 5,5 wocrinentsl Resuts with f
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two hours, the deposits were observ
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wcr: on ara:zic: c.eposc.tion consi
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-- II 1 L1 SOLUIIOIJ C;IFCU1_/:[ION
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SCAR FE 1 DEPOSITION PLATE - - 0 C)
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M—AMOUNI DEPOSITED (mg) T1 0_i c)
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C) 0 0 0 Li.] CD - 3 0 3 0 h Iii (E
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- II -fl M—AMOUNT DEPOSITED (rng)
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91 9) :< C) --z 9] mc-) .;J -i ru
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.1 1• ci E 0 Ci) c) — nj
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- . O, O, I— —,-, fouling studi
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profiles at different Reynolds numb
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L Run . (°c) used to calculate tem
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Due to a concentration gradient the
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1 I C. (1.2.2.2 \1L. I .OC[FY V [A[
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V 40 - 0 C—, lt! -— o. ---—-
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Li FIG. G.2.3./. TEMPERAI URE v RAD
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— 1 7.0 0 --Tc.=10.0°C 50 140
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— -- — -——— — -—Tb =
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Z_o_—o-- 50 l0 - yX—--X— —-
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I:302 00 50 Ito -0——— ---—-
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I 50 ;) 30c’/ / C —------------
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FIG. 6. 4.1. AN IDEEAL TEMPERATURE
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— 63 — 7. DISCUSSIOI 7.1 Introd
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— 65 — through it decreases gra
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For breakdown and removal to occur
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— 69 — the large fouling studie
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Increased flowrate and temperature
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— 72 — 8. ICOi’NDATTCNS It is
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EEfiDN2WON
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T TemDerature T = Average temperatu
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= :ieat eddy dfusivity = Xoent eddy
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in Exchar.ge: Tubes”, Chem. Engr.
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Oil Gas J., 58 (38), 87—91 (Sept.
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U U F--I C) (f
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The o1ubi1ity of 5i/54°Cparafin wa
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— — .‘.ti+ c:Lic gravity The
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In section Al .4 the auount of pcra
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0 •) X S (N U ‘0 -° CD c-) ( -
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I-] H — C C) p 0’ H 0’ H CD C
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fully refined paraffin wax in keros
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— A12 — The cloud point decrens
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— A3 — Tnble A2.1 Ca1culccd c i
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calibration constants are given in
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— Al? — Table A3.3.1 Calibratio
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— A19 — APPENDIX 4 THE PRDGR’
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C NC = C C REiCS EACH SET OF RE[iJC
Page 182 and 183: 13.42 7.40 7.SC 33.90 33.10 13.8 0.
Page 184 and 185: TIME TI TO TKI TKC DPK EPW DPT V CF
Page 186 and 187: 81.15 7.45 7.7C 33.40 32.70 30.0 0.
Page 188 and 189: RUN A1C—4 TIME 1WI TWO TKI TKC DP
Page 190 and 191: RUN 82—6 TIME TiI TC TKI TKC OPK
Page 192 and 193: TIME TWI TWO TKI TKC OPK CPW OPT V
Page 194 and 195: RUN B7—1C TIME TWI TWC TKI TKO DP
Page 196 and 197: RUN B9—12 T V’E ThI TWC TKI TKC
Page 198 and 199: RUN C1—1t T1’E IWI TWO TKI TKC
Page 200 and 201: PUN C2—15 TIME T’iI T0 TK1 TKC
Page 202 and 203: }U•” C-16 TIME TWI TWO TKI TKC
Page 204 and 205: TIME flit TC TKI TKO DPK DPW OPT V
Page 206 and 207: UN C5-18 TIME TWI TfD TKI TKO DPK C
Page 208 and 209: 14.25 7.IC 10.2C 39.10 38.00 8.8 0.
Page 210 and 211: RUNJ C8-2C T[’E TWE T0 TKI (Hg) (
Page 212 and 213: TIVE M)*2 C) TWI TWO TKI TKC DPK op
Page 214 and 215: Tt’iE TWI TC TKI TKO OPK CPW DPT
Page 216 and 217: — A23 — APPENDIX 5 OALT2RATTUNS
Page 218 and 219: T—- TEI\iFERATUFE (°C) —I’ U
Page 220 and 221: d Average C Table A5.2 0.0452 0.025
Page 222 and 223: 11.1 6.517 10.5 6.418 10.1 6.346 9.
Page 224 and 225: — A27 — Tib1e A6.2 Pun Dl .irn
Page 226 and 227: -A29- Table A6.4 Pun 1)3 ‘ Time (
Page 228 and 229: Time — A51 — Table A6.5 Run D5
Page 230 and 231: — A33 — APPENDIX 7 EOUNDARY LAY
Page 234 and 235: — = u — u = in — + ± + + or
Page 236 and 237: I A8.21 Data 2 Subroutines usng ite
Page 238 and 239: — ALf1 — Equations L.7.4.3 and
Page 240 and 241: — A1i•3 — Lt Prorran Use The
Page 242 and 243: DIM /\3.2./>. THE iJNI/E?j\I. \ELC)
Page 244 and 245: C DF1ENSIOH VIS(2.) REAL NUWSI INTE
Page 246 and 247: C C SUt3ROUTINE DATA INTEGER SR C C
Page 248 and 249: LI) I Li . 0 0 X .. (1•) U.. UI
Page 250 and 251: C C WRt 1E(6,’O) 60 FQR’AT(1HLf
Page 252 and 253: te 4Z’Xt’9’911’XZ’ 3DNVIS
Page 254 and 255: C C C C C )fl:O .0 DO ‘O 1=3,9,2
Page 256 and 257: C, .4:’. 0 0 —; —s iZ fl r;
Page 258 and 259: KINEMATIC VISCOSITY AT WALL 0.07407
Page 260 and 261: YP UP TP Y U T VIS TC CR PR 39.00 1
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paraffin wax deposition and fouling

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