Trabalho - Reservatórios

Problema Injeo de gua - 01

As curvas de Krw e Kro de um meio poroso so dadas pelas relaes:

Krw=(Sw Swc)2

Kro=(So Sor)2

Outros dados so:Swc=0,25Sor=0,25o=1,0 cpw=1,0 cp

Considerando um fluxo linear, pede-se:

1. Calcule e faa um grfico da curva fw versus Sw2. Calcule e faa um grfico da derivada de fw versus Sw 3. Calcule e faa um grfico dos perfis de saturao de gua para os seguintes valores de volumes porosos injetadosa. t = 0,25b. t = 0,75c. t = 1,25

Soluo:

1) Calcule e faa um grfico da curva fw versus Sw

1.1- Calculando krw e kro:

Como: e

Temos:

e

Usando:

SwSw (continuao)

0,250,51

0,260,52

0,270,53

0,280,54

0,290,55

0,30,56

0,310,57

0,320,58

0,330,59

0,340,6

0,350,61

0,360,62

0,370,63

0,380,64

0,390,65

0,40,66

0,410,67

0,420,68

0,430,69

0,440,7

0,450,71

0,460,72

0,470,73

0,480,74

0,490,75

0,5

Obs: Tabela ao lado a continuao da primeira.

Ento vem:

krwkro

3,08149E-330,25

0,00010,2401

0,00040,2304

0,00090,2209

0,00160,2116

0,00250,2025

0,00360,1936

0,00490,1849

0,00640,1764

0,00810,1681

0,010,16

0,01210,1521

0,01440,1444

0,01690,1369

0,01960,1296

0,02250,1225

0,02560,1156

0,02890,1089

0,03240,1024

0,03610,0961

0,040,09

0,04410,0841

0,04840,0784

0,05290,0729

0,05760,0676

0,06250,0625

0,06760,0576

0,07290,0529

0,07840,0484

0,08410,0441

0,090,04

0,09610,0361

0,10240,0324

0,10890,0289

0,11560,0256

0,12250,0225

0,12960,0196

0,13690,0169

0,14440,0144

0,15210,0121

0,160,01

0,16810,0081

0,17640,0064

0,18490,0049

0,19360,0036

0,20250,0025

0,21160,0016

0,22090,0009

0,23040,0004

0,24011E-04

0,251,97E-31

1.2- Calculando fw:

1.2.1- Para o = 1 cp.

Como :

fwfw(continuao)

1,2326E-320,539936102

0,000416320,579491256

0,0017331020,61829653

0,004057710,65600624

0,007504690,692307692

0,0121951220,726928896

0,0182555780,759643917

0,0258166490,790275762

0,0350109410,818696884

0,0459704880,844827586

0,0588235290,868632708

0,0736906210,890117035

0,0906801010,909319899

0,1098829650,926309379

0,1313672920,941176471

0,1551724140,954029512

0,1813031160,964989059

0,2097242380,974183351

0,2403560830,981744422

0,2730711040,987804878

0,3076923080,99249531

0,343993760,99594229

0,381703470,998266898

0,4205087440,99958368

0,4600638981

0,5

1.3- Calculando fw:

1.3.1- Para o = 5 cp.

Como :

fwfw(continuao)

6,16298E-320,854398382

0,0020781380,873263057

0,0086058520,890099909

0,0199645080,905079638

0,0364298720,918367347

0,0581395350,930120015

0,0850661630,940484938

0,1170009550,949598884

0,1535508640,957587806

0,1941514860,964566929

0,2380952380,970641102

0,2845719660,975905332

0,332717190,98044541

0,381662150,984338597

0,4305799650,987654321

0,4787234040,990454867

0,525451560,992796038

0,5702446720,994727781

0,6127080180,996294772

0,6525668840,997536946

0,6896551720,998489996

0,7239001970,999185815

0,7553058680,999652898

0,7839359810,999916708

0,8098987631

0,833333333

1.4- Calculando fw:

1.4.1- Para o = 10 cp.

Como :

fwfw(continuao)

1,2326E-310,921483097

0,0041476570,93234429

0,0170648460,941854877

0,0391474550,950175121

0,070298770,957446809

0,109890110,963795006

0,1567944250,969329799

0,2094912360,974147956

0,2662229620,978334462

0,3251706140,981963928

0,3846153850,985101855

0,443061150,987805758

0,4993065190,990126166

0,5524681270,992107495

0,6019656020,99378882

0,6474820140,995204547

0,6889128090,996384998

0,7263131440,997356923

0,7598499060,998143947

0,789761540,998766954

0,8163265310,999244428

0,839840030,999592742

0,860597440,999826419

0,8788835350,999958352

0,8949658171

0,909090909

Tabela com todos os dados:

Swkrwkrofw (o = 1 cp)fw(o = 5 cp)fw(o = 10 cp)

0,253,08149E-330,251,2326E-326,16298E-321,2326E-31

0,260,00010,24010,000416320,0020781380,004147657

0,270,00040,23040,0017331020,0086058520,017064846

0,280,00090,22090,004057710,0199645080,039147455

0,290,00160,21160,007504690,0364298720,07029877

0,30,00250,20250,0121951220,0581395350,10989011

0,310,00360,19360,0182555780,0850661630,156794425

0,320,00490,18490,0258166490,1170009550,209491236

0,330,00640,17640,0350109410,1535508640,266222962

0,340,00810,16810,0459704880,1941514860,325170614

0,350,010,160,0588235290,2380952380,384615385

0,360,01210,15210,0736906210,2845719660,44306115

0,370,01440,14440,0906801010,332717190,499306519

0,380,01690,13690,1098829650,381662150,552468127

0,390,01960,12960,1313672920,4305799650,601965602

0,40,02250,12250,1551724140,4787234040,647482014

0,410,02560,11560,1813031160,525451560,688912809

0,420,02890,10890,2097242380,5702446720,726313144

0,430,03240,10240,2403560830,6127080180,759849906

0,440,03610,09610,2730711040,6525668840,78976154

0,450,040,090,3076923080,6896551720,816326531

0,460,04410,08410,343993760,7239001970,83984003

0,470,04840,07840,381703470,7553058680,86059744

0,480,05290,07290,4205087440,7839359810,878883535

0,490,05760,06760,4600638980,8098987630,894965817

0,50,06250,06250,50,8333333330,909090909

0,510,06760,05760,5399361020,8543983820,921483097

0,520,07290,05290,5794912560,8732630570,93234429

0,530,07840,04840,618296530,8900999090,941854877

0,540,08410,04410,656006240,9050796380,950175121

0,550,090,040,6923076920,9183673470,957446809

0,560,09610,03610,7269288960,9301200150,963795006

0,570,10240,03240,7596439170,9404849380,969329799

0,580,10890,02890,7902757620,9495988840,974147956

0,590,11560,02560,8186968840,9575878060,978334462

0,60,12250,02250,8448275860,9645669290,981963928

0,610,12960,01960,8686327080,9706411020,985101855

0,620,13690,01690,8901170350,9759053320,987805758

0,630,14440,01440,9093198990,980445410,990126166

0,640,15210,01210,9263093790,9843385970,992107495

0,650,160,010,9411764710,9876543210,99378882

0,660,16810,00810,9540295120,9904548670,995204547

0,670,17640,00640,9649890590,9927960380,996384998

0,680,18490,00490,9741833510,9947277810,997356923

0,690,19360,00360,9817444220,9962947720,998143947

0,70,20250,00250,9878048780,9975369460,998766954

0,710,21160,00160,992495310,9984899960,999244428

0,720,22090,00090,995942290,9991858150,999592742

0,730,23040,00040,9982668980,9996528980,999826419

0,740,24011E-040,999583680,9999167080,999958352

0,750,251,97E-31111

1.5- Grficos das curvas fw x Sw:

2) Calcule e faa um grfico da derivada de fw versus Sw

2.1 - Calculando a derivada de fw versus Sw:

Atravs de: pode-se determinar o :

Como :

2.1.1- Para o=1 cp e sabendo-se que w=1 cp, e usando Sor=0,75 e Swc=0,25, temos:

Fazendo ponto a ponto para cada Sw, vem:dfw/dSw (Para o = 1 cp)dfw/dSw (Para o = 1 cp) (continuao)

4,44089E-163,980851086

0,0849278393,92401192

0,1802186053,831265114

0,2866130953,70545243

0,404802723,550295858

0,5353955983,370174471

0,6788754533,169879104

0,8355531472,954366881

1,0055111592,728534857

1,1885420682,497027348

1,3840830452,264085848

1,59114952,033444884

1,808272371,80827237

2,0334448841,5911495

2,2640858481,384083045

2,4970273481,188542068

2,7285348571,005511159

2,9543668810,835553147

3,1698791040,678875453

3,3701744710,535395598

3,5502958580,40480272

3,705452430,286613095

3,8312651140,180218605

3,924011920,084927839

3,980851086-3,55271E-15

4

2.1.2- Para o=5 cp e sabendo-se que w=1 cp, e usando Sor=0,75 e Swc=0,25, temos:

Fazendo ponto a ponto para cada Sw, vem:

dfw/dSw (Para o = 5 cp)dfw/dSw (Para o = 5 cp) (continuao)

2,22045E-151,993618376

0,4232284351,782201131

0,8887282591,588020469

1,3876543251,410681224

1,9077574391,249479384

2,4337479721,103510565

2,9481026730,971753816

3,4322834420,853134468

3,8682439280,746569841

4,2400186060,651001302

4,5351473920,565415728

4,7457054130,488858935

4,8687820530,420443156

4,9063649320,359350198

4,8646995780,304831581

4,7532820280,256206601

4,583680480,212859081

4,3683722990,174233301

4,1197378930,139829537

3,8492928020,109199447

3,5671819260,081941503

3,2819162860,057696597

3,0003070440,036143877

2,7275420080,016996888

2,4673518730

2,222222222

2.1.3- Para o=10cp e sabendo-se que w=1cp, e usando Sor=0,75 e Swc=0,25, temos:

Fazendo ponto a ponto para cada Sw, vem:

dfw/dSw (Para o = 10 cp)dfw/dSw (Para o = 10 cp) (continuao)

-1,381227211,159487162

-0,7480944491,01575548

4,44089E-150,889030313

0,8429496980,777378654

1,7472538990,67904029

2,6677256840,592431118

3,5520028660,516137838

4,3473010510,448907591

5,0079520210,389634976

5,5018158730,337348043

5,8139373920,291194258

5,9467394540,250427078

5,9171597630,214393459

5,751933970,182522465

5,4824455940,154315034

5,1402722590,129334873

4,7540280960,107200417

4,3476010560,087577771

3,9395579120,07017454

3,5433575910,054734454

3,1680212890,041032688

2,8189855660,028871801

2,4989587670,018078213

2,2086823270,008499152

1,9475566010

1,714126676

2.2 Grficos da derivada de fw versus Sw:

3) Calcule e faa um grfico dos perfis de saturao de gua para os seguintes valores de volumes porosos injetadosa. = 0,25b. = 0,75c. = 1,25

3.1- Clculando :

Sabendo-se que:

3.1.1- Para o = 1 cp, com = 0,25, = 0,75 e = 1,25, temos:

(continuao) (continuao) (continuao)

1,11022E-160,9952127713,33067E-162,9856383145,55112E-164,976063857

0,021231960,981002980,0636958792,943008940,1061597994,9050149

0,0450546510,9578162780,1351639542,8734488350,2252732564,789081392

0,0716532740,9263631080,2149598212,7790893230,3582663694,631815538

0,101200680,8875739640,303602042,6627218930,50600344,437869822

0,1338488990,8425436180,4015466982,5276308530,6692444974,212718089

0,1697188630,7924697760,509156592,3774093280,8485943163,96234888

0,2088882870,738591720,626664862,2157751611,0444414343,692958601

0,251377790,6821337140,7541333692,0464011431,2568889483,410668571

0,2971355170,6242568370,8914065511,8727705111,4856775853,121284185

0,3460207610,5660214621,0380622841,6980643861,7301038062,83010731

0,3977873750,5083612211,1933621251,5250836631,9889368752,541806105

0,4520680930,4520680931,3562042781,3562042782,2603404632,260340463

0,5083612210,3977873751,5250836631,1933621252,5418061051,988936875

0,5660214620,3460207611,6980643861,0380622842,830107311,730103806

0,6242568370,2971355171,8727705110,8914065513,1212841851,485677585

0,6821337140,251377792,0464011430,7541333693,4106685711,256888948

0,738591720,2088882872,2157751610,626664863,6929586011,044441434

0,7924697760,1697188632,3774093280,509156593,962348880,848594316

0,8425436180,1338488992,5276308530,4015466984,2127180890,669244497

0,8875739640,101200682,6627218930,303602044,4378698220,5060034

0,9263631080,0716532742,7790893230,2149598214,6318155380,358266369

0,9578162780,0450546512,8734488350,1351639544,7890813920,225273256

0,981002980,021231962,943008940,0636958794,90501490,106159799

0,995212771-8,88178E-162,985638314-2,66454E-154,976063857-4,44089E-15

135



5,55112E-160,4984045941,66533E-151,4952137822,77556E-152,492022971

0,1058071090,4455502830,3174213261,3366508490,5290355442,227751414

0,2221820650,3970051170,6665461951,1910153511,1109103241,985025586

0,3469135810,3526703061,0407407441,0580109181,7345679061,76335153

0,476939360,3123698461,430818080,9371095382,3846967991,561849229

0,6084369930,2758776411,8253109790,8276329243,0421849651,379388206

0,7370256680,2429384542,2110770040,7288153623,6851283411,21469227

0,8580708610,2132836172,5742125820,6398508514,2903543031,066418085

0,9670609820,186642462,9011829460,5599273814,835304910,933212301

1,0600046510,1627503263,1800139540,4882509775,3000232570,813751628

1,1337868480,1413539323,4013605440,4240617965,668934240,70676966

1,1864263530,1222147343,559279060,3666442025,9321317660,611073669

1,2171955130,1051107893,651586540,3153323676,0859775660,525553945

1,2265912330,089837553,6797736990,2695126496,1329561650,449187748

1,2161748940,0762078953,6485246830,2286236856,0808744720,381039476

1,1883205070,064051653,5649615210,1921549515,9416025350,320258252

1,145920120,053214773,437760360,159644315,72960060,266073851

1,0920930750,0435583253,2762792240,1306749755,4604653740,217791626

1,0299344730,0349573843,089803420,1048721535,1496723660,174786921

0,96232320,0272998622,8869696010,0818995854,8116160020,136499308

0,8917954820,0204853762,6753864450,0614561284,4589774080,102426879

0,8204790710,0144241492,4614372140,0432724484,1023953570,072120746

0,7500767610,0090359692,2502302830,0271079083,7503838060,045179847

0,6818855020,0042492222,0456565060,0127476663,409427510,02124611

0,616837968-2,22045E-161,850513905-6,66134E-163,084189842-1,11022E-15

0,5555555561,6666666672,777777778



1,11022E-150,289871793,33067E-150,8696153715,55112E-151,449358952

0,2107374240,253938870,6322122730,761816611,0536871221,26969435

0,4368134750,2222575781,3104404240,6667727352,1840673741,111287891

0,6669314210,1943446632,0007942630,583033993,3346571050,971723317

0,8880007170,1697600722,664002150,5092802174,4400035830,848800362

1,0868252630,148107783,2604757880,4443233395,4341263130,740538898

1,2519880050,129034463,7559640160,3871033796,2599400260,645172298

1,3754539680,1122268984,1263619050,3366806936,8772698420,561134488

1,4534843480,0974087444,3604530440,2922262327,267421740,48704372

1,4866848640,0843370114,4600545910,2530110327,4334243180,421685053

1,4792899410,0727985644,4378698220,2183956937,3964497040,363992822

1,4379834930,062606774,3139504780,1878203097,1899174630,313033848

1,3706113980,0535983654,1118341950,1607950946,8530569920,267991824

1,2850680650,0456306163,8552041940,1368918496,4253403240,228153081

1,1885070240,0385787593,5655210720,1157362765,9425351190,192893793

1,0869002640,0323337183,2607007920,0970011555,434501320,161668592

0,9848894780,0268001042,9546684340,0804003134,924447390,134000522

0,8858393980,0218944432,6575181930,0656833284,4291969890,109472214

0,7920053220,0175436352,3760159670,0526309053,9600266110,087718175

0,7047463920,0136836142,1142391750,0410508413,5237319580,068418068

0,6247396920,0102581721,8742190750,0307745163,1236984590,05129086

0,5521705820,007217951,6565117450,021653852,7608529080,036089751

0,486889150,0045195531,460667450,013558662,4344457510,022597766

0,4285316690,0021247881,2855950070,0063743642,1426583440,01062394

0,3766105901,12983176901,8830529480

0,3305785120,9917355371,652892562

3.2- Encontrando a saturao de gua no choque e o seu respectivo fw (pelo grfico)

Ponto de choque: Sw = 0,57



3.3-Grficos dos perfis de saturao de gua.

3.3.1- Para = 0,25, temos:

Sw Sw (continuao)Sw Sw (continuao)SwSw(continuao)

0,251,11022E-160,510,9952127710,255,55112E-160,510,4984045940,251,11022E-150,510,28987179

0,260,021231960,520,981002980,260,1058071090,520,4455502830,260,2107374240,520,25393887

0,270,0450546510,530,9578162780,270,2221820650,530,3970051170,270,4368134750,530,222257578

0,280,0716532740,540,9263631080,280,3469135810,540,3526703060,280,6669314210,540,194344663

0,290,101200680,550,8875739640,290,476939360,550,3123698460,290,8880007170,550,169760072

0,30,1338488990,560,8425436180,30,6084369930,560,2758776410,31,0868252630,560,14810778

0,310,1697188630,570,7924697760,310,7370256680,570,2429384540,311,2519880050,570,12903446

0,320,2088882870,580,738591720,320,8580708610,580,2132836170,321,3754539680,580,112226898

0,330,251377790,590,6821337140,330,9670609820,590,186642460,331,4534843480,590,097408744

0,340,2971355170,60,6242568370,341,0600046510,60,1627503260,341,4866848640,60,084337011

0,350,3460207610,610,5660214620,351,1337868480,610,1413539320,351,4792899410,610,072798564

0,360,3977873750,620,5083612210,361,1864263530,620,1222147340,361,4379834930,620,06260677

0,370,4520680930,630,4520680930,371,2171955130,630,1051107890,371,3706113980,630,053598365

0,380,5083612210,640,3977873750,381,2265912330,640,089837550,381,2850680650,640,045630616

0,390,5660214620,650,3460207610,391,2161748940,650,0762078950,391,1885070240,650,038578759

0,40,6242568370,660,2971355170,41,1883205070,660,064051650,41,0869002640,660,032333718

0,410,6821337140,670,251377790,411,145920120,670,053214770,410,9848894780,670,026800104

0,420,738591720,680,2088882870,421,0920930750,680,0435583250,420,8858393980,680,021894443

0,430,7924697760,690,1697188630,431,0299344730,690,0349573840,430,7920053220,690,017543635

0,440,8425436180,70,1338488990,440,96232320,70,0272998620,440,7047463920,70,013683614

0,450,8875739640,710,101200680,450,8917954820,710,0204853760,450,6247396920,710,010258172

0,460,9263631080,720,0716532740,460,8204790710,720,0144241490,460,5521705820,720,00721795

0,470,9578162780,730,0450546510,470,7500767610,730,0090359690,470,486889150,730,004519553

0,480,981002980,740,021231960,480,6818855020,740,0042492220,480,4285316690,740,002124788

0,490,9952127710,75-8,88178E-160,490,6168379680,75-2,22045E-160,490,376610590,750

0,510,50,5555555560,50,330578512

Usando apenas os valores em destaque (correspondem ao valor de Sw a partir do choque e com at no mximo 1), temos:

3.3.2- Para = 0,75, temos:


0,253,33067E-160,512,9856383140,251,66533E-150,511,4952137820,253,33067E-150,510,869615371

0,260,0636958790,522,943008940,260,3174213260,521,3366508490,260,6322122730,520,76181661

0,270,1351639540,532,8734488350,270,6665461950,531,1910153510,271,3104404240,530,666772735

0,280,2149598210,542,7790893230,281,0407407440,541,0580109180,282,0007942630,540,58303399

0,290,303602040,552,6627218930,291,430818080,550,9371095380,292,664002150,550,509280217

0,30,4015466980,562,5276308530,31,8253109790,560,8276329240,33,2604757880,560,444323339

0,310,509156590,572,3774093280,312,2110770040,570,7288153620,313,7559640160,570,387103379

0,320,626664860,582,2157751610,322,5742125820,580,6398508510,324,1263619050,580,336680693

0,330,7541333690,592,0464011430,332,9011829460,590,5599273810,334,3604530440,590,292226232

0,340,8914065510,61,8727705110,343,1800139540,60,4882509770,344,4600545910,60,253011032

0,351,0380622840,611,6980643860,353,4013605440,610,4240617960,354,4378698220,610,218395693

0,361,1933621250,621,5250836630,363,559279060,620,3666442020,364,3139504780,620,187820309

0,371,3562042780,631,3562042780,373,651586540,630,3153323670,374,1118341950,630,160795094

0,381,5250836630,641,1933621250,383,6797736990,640,2695126490,383,8552041940,640,136891849

0,391,6980643860,651,0380622840,393,6485246830,650,2286236850,393,5655210720,650,115736276

0,41,8727705110,660,8914065510,43,5649615210,660,1921549510,43,2607007920,660,097001155

0,412,0464011430,670,7541333690,413,437760360,670,159644310,412,9546684340,670,080400313

0,422,2157751610,680,626664860,423,2762792240,680,1306749750,422,6575181930,680,065683328

0,432,3774093280,690,509156590,433,089803420,690,1048721530,432,3760159670,690,052630905

0,442,5276308530,70,4015466980,442,8869696010,70,0818995850,442,1142391750,70,041050841

0,452,6627218930,710,303602040,452,6753864450,710,0614561280,451,8742190750,710,030774516

0,462,7790893230,720,2149598210,462,3774093280,720,0432724480,461,6565117450,720,02165385

0,472,8734488350,730,1351639540,472,2157751610,730,0271079080,471,460667450,730,01355866

0,482,943008940,740,0636958790,482,0464011430,740,0127476660,481,2855950070,740,006374364

0,492,9856383140,75-2,66454E-150,491,8727705110,75-6,66134E-160,491,1298317690,750

0,530,51,6980643860,50,991735537


3.3.3- Para = 0,75, temos:


0,255,55112E-160,514,9760638570,252,77556E-150,512,4920229710,255,55112E-150,511,449358952

0,260,1061597990,524,90501490,260,5290355440,522,2277514140,261,0536871220,521,26969435

0,270,2252732560,534,7890813920,271,1109103240,531,9850255860,272,1840673740,531,111287891

0,280,3582663690,544,6318155380,281,7345679060,541,763351530,283,3346571050,540,971723317

0,290,50600340,554,4378698220,292,3846967990,551,5618492290,294,4400035830,550,848800362

0,30,6692444970,564,2127180890,33,0421849650,561,3793882060,35,4341263130,560,740538898

0,310,8485943160,573,962348880,313,6851283410,571,214692270,316,2599400260,570,645172298

0,321,0444414340,583,6929586010,324,2903543030,581,0664180850,326,8772698420,580,561134488

0,331,2568889480,593,4106685710,334,835304910,590,9332123010,337,267421740,590,48704372

0,341,4856775850,63,1212841850,345,3000232570,60,8137516280,347,4334243180,60,421685053

0,351,7301038060,612,830107310,355,668934240,610,706769660,357,3964497040,610,363992822

0,361,9889368750,622,5418061050,365,9321317660,620,6110736690,367,1899174630,620,313033848

0,372,2603404630,632,2603404630,376,0859775660,630,5255539450,376,8530569920,630,267991824

0,382,5418061050,641,9889368750,386,1329561650,640,4491877480,386,4253403240,640,228153081

0,392,830107310,651,7301038060,396,0808744720,650,3810394760,395,9425351190,650,192893793

0,43,1212841850,661,4856775850,45,9416025350,660,3202582520,45,434501320,660,161668592

0,413,4106685710,671,2568889480,415,72960060,670,2660738510,414,924447390,670,134000522

0,423,6929586010,681,0444414340,425,4604653740,680,2177916260,424,4291969890,680,109472214

0,433,962348880,690,8485943160,435,1496723660,690,1747869210,433,9600266110,690,087718175

0,444,2127180890,70,6692444970,444,8116160020,70,1364993080,443,5237319580,70,068418068

0,454,4378698220,710,50600340,454,4589774080,710,1024268790,453,1236984590,710,05129086

0,464,6318155380,720,3582663690,464,1023953570,720,0721207460,462,7608529080,720,036089751

0,474,7890813920,730,2252732560,473,7503838060,730,0451798470,472,4344457510,730,022597766

0,484,90501490,740,1061597990,483,409427510,740,021246110,482,1426583440,740,01062394

0,494,9760638570,75-4,44089E-150,493,0841898420,75-1,11022E-150,491,8830529480,750

0,550,52,7777777780,51,652892562


Problema Injeo de gua 02

Um experimento de laboratrio foi conduzido para determinar as permeabilidades relativas de um meio poroso. As propriedades de rocha e fluidos esto abaixo:

=0,20Swc=0,20A=12,5 cm2Sor=0,20L=40,0 cmo=10,0 cpk=100 mdw=1,0 cp

Os dados de produo do experimento foram:

gua Inj./Vp

gua Prod./ VpQwleo Prod./VpQoP/PiFol

10,10,00,10000,80411

20,20,00,20000,60811

30,30,01470,28530,43610,266

40,40,08810,31190,37370,199

50,50,16820,33180,33400,158

60,60,25240,34760,30580,132

70,70,33920,36080,28470,112

80,80,42800,37200,26800,098

90,90,51820,38180,25450,087

101,00,60950,39050,24330,077

111,10,70180,39820,23380,07

121,20,79480,40520,22570,063

131,30,88850,41150,21850,058

141,40,98270,41730,21230,054

151,51,07730,42270,20670,056

1. Calcule e grafe as curvas de permeabilidade relativa ao leo e gua versus saturao de gua ( Kro, Krw vs Sw )2. Faa um grfico da razo Krw/Kro vs Sw3. Faa um grfico de fw vs Sw

3) Calcule e grafe as curvas de permeabilidade relativa ao leo e gua versus saturao de gua ( Kro, Krw vs Sw )

3.1- Calculando F0l:Como:

3.1.1 Traando a curva Qo versus , para se obter Fol (com os dados da tabela dada):

De forma que o valor de Fol pode ser obtido pela derivada de cada trecho dessa curva.Ento, fazendo-se a tangente de cada trecho (diferena do Qo posterior de um ponto subtrado pelo seu Qo dividido pela diferena do posterior de um ponto subtrado pelo seu ), temos como valores de Fol para cada ponto, menos para os pontos de = 0,1 e = 0,2, pois h um mudana de inclinao muito significativa relativa a esses pontos e os demais:

gua Inj./Vp

leo Prod./VpQoFol

10,10,1000-

20,20,2000-

30,30,28530,266

40,40,31190,199

50,50,33180,158

60,60,34760,132

70,70,36080,112

80,80,37200,098

90,90,38180,087

101,00,39050,077

111,10,39820,07

121,20,40520,063

131,30,41150,058

141,40,41730,054

151,50,42270,056

3.2- Calculando Fwl:Como:

Temos:Fwl

-

-

0,734

0,801

0,842

0,868

0,888

0,902

0,913

0,923

0,93

0,937

0,942

0,946

0,944

3.3- Calculando Swl:Como:

ou

E sabendo-se que , vem:

Temos:Swl

-

-

0,4055

0,4323

0,4528

0,4684

0,4824

0,4936

0,5035

0,5135

0,5212

0,5296

0,5361

0,5417

0,5387

Ento :

gua Inj./Vp

leo Prod./VpQoFolFwlSwl

10,10,1000---

20,20,2000---

30,30,28530,2660,7340,4055

40,40,31190,1990,8010,4323

50,50,33180,1580,8420,4528

60,60,34760,1320,8680,4684

70,70,36080,1120,8880,4824

80,80,37200,0980,9020,4936

90,90,38180,0870,9130,5035

101,00,39050,0770,9230,5135

111,10,39820,070,930,5212

121,20,40520,0630,9370,5296

131,30,41150,0580,9420,5361

141,40,41730,0540,9460,5417

151,50,42270,0560,9440,5387

3.4- Grfico de wL versus SwL ( com uma estimativa da continuao da curva).

2) Faa um grfico da razo Krw/Kro vs Sw

2.1-Calculando Krw/Kro:

J, sabendo-se o valor de Sw, calculamos agora o valor de Krw/Kro , atravs de:

Com:o=10,0 cpw=1,0 cp

SwlKrw/Kro

--

--

0,40550,27594

0,43230,402513

0,45280,532911

0,46840,657576

0,48240,792857

0,49360,920408

0,50351,049425

0,51351,198701

0,52121,328571

0,52961,487302

0,53611,624138

0,54171,751852

0,53871,685714

2.2- Grfico de Log(Krw/Kro) versus Swl:

1) Calcule e grafe as curvas de permeabilidade relativa ao leo e gua versus saturao de gua ( Kro, Krw vs Sw ).

Fazendo o grfico de G versus , pode-se traar uma reta tangente, onde sua interseo com o eixo G ser Fol/Kro.De forma que conhecemos o valor de Fol, podemos obter o valor de Kro e assim o valor de Krw pela razo Krw/Kro j conhecida

Fazendo a tangente ponto a ponto e encontrando a equao para cada curva, pode-se encontrar o valor de G para igual a zero (ponto de interseco com o eixo de G) e os demais valores desejados:

oL/KrooLKroKrw/KroKrw

-----

-----

0,70,2660,380,275940,104857

0,580,1990,3431030,4025130,138103

0,50,1580,3160,5329110,1684

0,450,1320,2933330,6575760,192889

0,420,1120,266660,7928570,1942853

0,380,0980,257890,9204080,237364

0,360,0870,2416671,0494250,253611

0,350,0770,221,1987010,263714

0,340,070,2058821,3285710,273529

0,3250,0630,1938461,4873020,288308

0,3150,0580,1841271,6241380,299048

0,30,0540,181,7518520,315333

0,310,0560,1806451,6857140,304516

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