The purpose of this work is to evaluate the satur ation profile of Zubair format ion in East Baghdad Field, from log interpretation . The relati ve accurac y of four m'ethods of porosity e\alu ation , from three porosity logs (Neutr on, Densi ty and sonic logs), was tested against measured porosity from cores of eighty nine chosen intervals. The accuracy of each method was e�aluated statistically by calculating the ·correlation coefficient, standard deviation error, average percentage error and absolute average percentage error. The crossplot technique (using triangle method ) of Neutron and Density logs data was statistical parameters, hence, it optimum porositr values. found to give the .best was used to calculate It is concluded that the adoption of this method in porosity determination will result in more accurate water saturation determination particularly when using Archie's equation. �\.,;di 111eu w1u1 vdl 1 tSCc ACKNOWLEDGEMENTS For his patienc e and encourage ment, I am indebted to Dr. Rindh R. Al-Kattan who kindly supervised this work with vnlun ble comments and advices. For helpful technic�l advices and assistanc e, I am as ever indebted to Mr. !mad Jossif 1 head of loggin g secti on in reservoir and field development office and to my friend and colleague Adnan Sadie. Also, I feel deeply .appreci ated . to the head and members of the examfning committee. Special thanks to my brother Mr. M• Hameed. and to Dr. Hayder H. Jaafer and my niece Meha for their constant readiness of being helpful •. Thanks to my. colleagues Samira, Saad, Mohammed K., Mohammed E. and Medhat for their assistance in accomplishing this work. Finally, my·gratitud e and thankfullness are devoted to my family for their patience and encouragement throughout the stages of this work. II ,::,t;dr 11 reu wr u 1 vd111Scc NOMF.NCt.NrtmH Symbols: = Formation factor coefficient. = Compressibility of the t•ock frnme, ps 1-1 • Cr = Compressibility of the pore fluid I psi -t • Che = Compressibility of the hydrocarbon fluid, psi -1 = Compressibility of the pore volume. psi -1 • Cs = Compressibility o.f the grain mnter·ial • psi- 1 • Cw = Compressibility of F = Format ion factor. Gb = Bulk sheer modulus. m = Cementation factor. the water, psi -t • n =Archie exponent (saturation exponent). p = Shale fraction of the total formation volume. Rmf = Mud-filtrate resistivity, n-m. Rt = True formation resistivity, n-m. Rw = Formation-water resistivity, n-m. Rwa = Apparent formation-water resistivity, n-m. Rxo = Flushed-zone resistivity, 0-m. Sw = Water saturation, fraction. Sxo = Water saturation in the flushed zone, fraction. v = Formation velocity, ft/sec. Vc1 = Clay volume, fraction. Ve = Sonic velocity in the interstitial fluid1 ft/sec. -:. v�a = Sonic velocity in the rock matrix, ft/sec. Vv =Compressional velocity, ft/sec. r r r / �\.,;di 111eu w1u1 vd� 13Cc Vsh = Shnle volume, fraction. \3c al c !"meas = Shale indicator, fraction. = Acoustic traveltime in formation, µsec/ft. = Acoustic traveltime in fluid, µsec/ft, = Acoustic traveltime in rock matrix, µsec/ft. = Poisson's ratio. = Porosity,. fraction. = Average calculated porosity, fraction. = Average measured porosity, fraction. \3i calc = Calculated porosity in well for ith layer, fraction. !l'i meas = Measured porosity in well for ith layer, fraction. �sc = Corrected porosity for shale content, fraction. �o = Density-log apparent porosity, fraction. �fish = Neutron-log apparent porosity, fraction. = Neutron-log equivalent porosity of shale, fraction. ¢m = Porosity derived from matrix method, fraction. ¢F = Porosity derived from fluid method, fraction. ¢A = Porosity derived from average method, fraction. fb = Bulk formation density, gm/cc. fr = Density of fluid, gm/cc. Pma = Density of rock matrix, gm/cc. fsh = Density of shale, gm/cc. B = Cs /Ch • IV 0ca1111ea w1t11 ca1 11�c< 0 AAP APE BHC CF CNL FDC GR CGR ILD Sn = Absolute Average Percentage Error. = Average Percentage Error. = Borehole Compensated. = Correlation Coefficient. = Compensated Neutron. Log. = Formation Density Compensated. = Gamma Ray. = Corrected Gamma Ray, = Induction Log Deep. = Standard Deviation Error. v 'I l.tST Ofl ffOt JHF-:3 l( r S • Tltl Page ---- --- ---- --- -------- ---- ---- -- ----- -------- -- ----- ------- ------ ( � -1 } 2-3) ( 2-4) (3-1) (3-2) (3-3) (3-4) (4-1) (4-2) Thcor ticnl plot of porosity vs. transit tim with increasing shnlc as lndicated by Gamma Ray deflection •. •...•..• .•.•.... . · · · · 23 Porosity vs. travel time .• ...•• ....... ·· ·· · · · · The proposed sonic transit time-to- porosity iransform, showing comparison to Wyllie time-average equation (1956) and to suggested algorithm s by Ray�er et al. (1980) • ••... .••••. .•.•••••. . .. . .....•.. 24 Neutron-density crossplot scaled with interpolated f.a lines . ••• •.•••.. .••. ...•..... 24 Soxhlet extractor . •..••••• •...•..•. ... .. • ..... 27 Saturation apparatus . •••• ••...••••. .•. •.•.• • • . 27 Graphical representation of statistical param eters . . . . . • • • • • • . • • • • • . . • • . • . . • . • • . . • . . . . 29 Plot of �core vs. �sonic (using Wyllie equation ) for the wells of Zubair formation-East Baghdad field .• . � ......... , ... . Corrected gamm a ray-standard gamma ray relations hip for sand body No.1. , . . . . • . . . . • . • . 43 Corrected gamma ray-standard gamma ray relationship for sand body No. 2. . .. .. .. .. .. .. . -l3 vl,;d 111 l�U w Ill 1 \.Jd 1 11SCc VII Figt1re No. Title Page -------------- ------- --- --- ---- ----- -- ---- ---- --- ---- --- -------- - (4-3) (4-4} (4-5) (4-6} (4-7) (4-8} (4-9) (4-10) (4-11) (4-12) (4 .... 13) (4-14) Corrected gamma ray-standard gamma ray relationship for sand body No.3 . ••• • ••• . . ••.. . 44 Corrected gamma ray-sta ndard gamma ray relationship for sand body No.4 . • • ••••.... • .. . 44 Corrected gamma ray-standard gamma ray relationship for sand body No.5 ..•...• ... ···�· 45 Corrected gamma ray-stan dard gamma ·ray relationship for sand body No.6 . •.. ... .. •. • . . . 45 Corrected gamma ray-standard gamma ray relationship fo� �and body �o.7. !'''''''''•·· � 46 Corrected gamma ray�standard gamma ray· relationship for sand body No. 8. . ... .... : .•.• :.. 46 Corrected gamma ray-standard gamma ray relationship for the sand bodies of Zubair formation . ... ...•. • .•.. •..•. . • .. . . .• .. . 47 Bulk density��neutro� crossplot of well No.(EB-55) ... . .. . .. . ...... .. · . .. ... ..... ....... 48 Bulk density-�neutron crossplot.of well ·No . ( EB--56) . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . • . . . 49 Bulk density-�neutron crossp�ot of well No. (EB-79) .. .... ......... .. • . •· •.. .. • • ; .. .. .. . 50 Bulk density��neutron crossplot of well N 0 • ( EB-7 7 ) . . . . . . . . . . . . . . • . . I • • • • • • • • • • • • • • • • • • • 51 Bulk density-�neutron crossplot of well No.(EB-15). . .. . . . .. .... ... .. . ....... .... ..... .. 52 "c .. �Cal 111ea WI LI I Gal 11� ( ·ru Figure No. Title Page -------- ---- -------- ----- --- --- -- ----- --------------- -------- --- - (4-15) (4-16) (4-17) (4-18) (4-19) (4-20 ) (4- 21) (4-22) (4-23) (4- 24) (5-1) (5-2) (5-3) (5-4) (5-5) Bulk density-�neutroo crossplot of well No . ( EB-18 ) . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . . . . 5 3 Plot of �cor� vs. �neutroo for the wells of Zubair formation-East Baghdad field • ...... . 54 Plot of �core vs. ¢densi�y for the wells of Zub air formation-East Baghdad field. ······· 55 Plot of �core vs. �crossplo� for the wells of Zubair formation-East Baghdad field . ••..•.. 56 !i1core-�log comparisons for �ell No.(EB-55). 57 !i1core-f61og comparisons for ;.'ell Jfo. (EB-56). 58 !i1core-!i1log comparisons for �ell No.(EB-79). 59 !i1core -�log comparisons for 'Well No. (EB-77). ....... 60 !i1core-!i1log comparisons for well No. (EB-15) . 61 !i1core-�log comparisons for t-rell No. (EB-18). 62 The effect of m, a and n on the calculated value of ' Sv ' . . .......... .. ...• .•. .. ... ; . . . • . • 6 8 Resistivity-Porosity crossplot for well No.(EB-55) .... ......... ... ....... .... ......... 69 Resistivity-Porosity crossplot for well No. (EB-5 6) .. ......... - ... ... .......... ....... _ 70 Resistivity-Porosity crossplot for well No. (EB -79). . . . . . . . . . . . . . . . . . . . . . . . • • . . . . . . . . . . ·71 Resistivity-Porosity crossplot for well No.(EB-77). ................. ............. ..... 72 vl,;dl 111�u w1u1 val 11Scc [ .\ Title Figure No. --- ---- -- ---- -- ----- ----------- -- ---- -- ----- ------------ --- -- (5-6) (5-7) (5-8) Resistivity-Porosity crossplot for well No • ( EB-15 ) • • ••.••• , ••• , • • . , • • • • • • • • • • • • . • • • . . • 7 3 Resistivity-Porosity crossplot for well No. ( EB-18 ) . . ....... , . , .... , .... , ........... , . . 7 11 Resistivity-Porosity crosspl ot for the wells of Zubair formation-East Baghdad field .............. ........................... 75 '5ca1111ea w1u 1 ca111Sc< Table No. LIST OF TABLES Title x Page ----- --- --- --- --- --- -- ------- --- ------ ---- ------ --------- --- (3-1) (4-1) (4-2) (5-1) (A-1) Values of sonic velocity a nd transit time for common rock matrix, materials and casing ......... ........... .............. . 34 Actual density and 'FDC' derived de nsity for different materials commonly encountered in boreholes. . . . . . . • . . . . . . . . . 40 Correlation parameters for Neutron and Density logs as single indicators and in combinations. . . . . . . . . . . . . . . . . • . . . . . . . . 42 'Sw' data obtained frofu Modified Archie 's equation for some selected intervals of Zubair formation. I I I I t t I I t I I f I I I I I I I I I I t I 67 Measured-calculated porosity values and shale volume of the chosen intervals of Zubair formation. I t I I I I I t I I I f I I • t I f I I I I I I 83 sca1111ea Willi ca111Sc< 'l'ABLI<: OF CON'l'!o:N'l'S ABSTRAC'l' ••• ••••• ••.•.. • , , , , • • . • ..• , • . • • • · • • • • • • • • · · · · [ ACKNOWL EDGMENTS •••• I • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • I I NOMENCLATURE • • ••••. .•••. •.•• •.••.• ••• I • • • • • • • • • • • • • • • I I I LIST OF FIGUR ES •••.• , •••• , ...• •. , ••. • • , •• , ••.••• •.. • · VI LIST OF TABLES •. , • , , . , , , , , , • , •• •••• • , •· ••••. ••... •.• • · X CHAP TER ONE - INTRODUCTI ON ••.•• , •• • • ••. , .• ••• • • • · · · · • 1 CHAP TER T�O -LITERATURE REVIEW ••• • , •• , •• •. . • · • • • • • • • 3 2. 1. Sonic log • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 . Radioactive logs .... ............ ...... ..... 14 2.2.1. Evaluation of po!:osity ...... .... .... 15 2.2.2. Evaluation of clay volume .. . . . ... . . . 19 CHAPTER THREE -DETERMINATION OF POROSITY BY LABORATORY MEASUREMENTS AND SONIC LOG ,, .... .... , 25 3.1. Laboratory measurements .... . .. ...... ... .. . . 25 3.1.1. Preparing and cleaning the core samples •........• ; .... , . . . . . . . . . . . . . 2o 3.1.2 . Measurement of porosity , .. . . . . . . . . . . 26 3.2. Statistical analysis ... ... . . . . . .. . . . .. .. . . . 26 3.3. Determination of porosity by sonic log ..... 3.3.1. Time average equation CHAPTER FOUR -DETERMINATION OF POROSITY BY RADIOACTIVE 31 31 LOGS ' ...... . ... ' ........ ' . .• ' ... I •••• ' 3 6 4.1. Determination of shale volum e ........ ...... 36 4.2. Determination of porosity ...... . ;........ .. 38 4.2.1. Single porosity indicato r......... .. 38 4.2.2. Two-curves porosity indicator . ...... 11 sca1111ea w1u1 ca1 hSc< Pnge II:\\' Tl� FtVl' -\)l•:Tl\HMtNA'l'll' N F IYATEH S:\TUHi\TlON . . . • • 63 5.\. L\" 'l'nd.lrnt .l n f 'm' nnd 'a' •• t t 'e ••IP It t t I I 64 rrn· i nl nppli nti n of the Modified Archie ' q \' :l t. l Tl • I • • • ' • • • • • • • • • • ' • ' • I • • • • • • • • • • • • • • 6 6 HA ''R �lX -.., N LU I NS ANt RECOMMENDATIONS ••. • • • • • 76 6. l. . a tl ... l \ts ions . . . . . . . . . . . . . . . . . . . . . . . . . . · · · · · .... 6.:... R 'ommendations •......... ........ · · · · · · · · · · R F R N ""ES I I I I I I • I t t I I I I I I I I t I I I I t t I I I t I I I t I I I I I 1 1 1 e I APPENDIX :\ STATISTICAL PROGRAM . •••• •••• ••••• • • · · · • • APPENDIX B LOGGING SETS •••••••••••.. • .• ••.•• •.. . • • · 76 77 78 82 85 � �c...;a1111�u w1u1 val 11�Cc 1 CHAPTER ONE INTRODUCTION l\, - (East Baghdad Field is one of the recently discovered Iraqi oil· fields, havin g seve ral pay Zones. Zuba�r format ion is one of these zones at ·which we have executed this investigation. Li thologically, Zubair formation is composed mainly of sandston e with some intervals of sha ly sand and shale (particularly in the upper section); The porosity of eighty nine intervals in the water bearing zone of six wells (EB-55, EB-56 ,· EB-77, EB-79 ,-EB- 15, and EB-18) of this field was calculate d by using the following available logs:- 1- Sonic log, BHC. 2- Density log, FDC. 3-Neutron log, CNL. Neutron and Density logs are used either as single porosity indicator� using their basic equations, or in combinations, using a crossplot technique (triangle method). Hence, three porosity values are calculated from Neutro n and Density logs for each interval. On the othe r hand, the time-average equation was used to calculate por osit y from the transit time of sound wave throu gh t he forma tion which was taken from sonic log. Therefore , Several compariso ns can be made between porosity I vt.;01111�u w1u1 val 11�Cc 2 nun lo .1.of{ nnd t�hut; from other logs. \ n l \lt ln t.h •no compllrisons is the core • l\'hi�l l��n·o•1lty Wt\9 mocurnrod in the laboratory by me: thod wlt..h gus oil, at depths t lS l \' ,, .ity should be corrcc ted for shaliness. More h,\\n n ti\ thod i\l\ b used for shule volume determina tion, O._unmt\ Thy log, CGR. p -:N r ·plot using triangle method, After the four porosity values have been calculated a h int�rval, we have use d regr ession analysis (simple · , l."ession) nnd a statistical program to compare these YUl\l s with those obtained from cores in order to get the orrelation coefficient, average percentage error, absolute -!'... e-vf� a\· rage percentag e error and standard deviation erro;/. Then _.,,,, we used the porosity values otitained from the triangle · method to formulate a modified form of Archie equation to be used for water satura tion determination. \ _;• �· . ' " , \ ,,' \ '\ (' J , I f\ 'L f The r�ason of using triangle method was that it shows highest correlation coefficient and lowest percentage errors. ) The modified Archi e's equatio n is formulated by finding particular values for cementation factor {m) and the formation factor coefficient ·(a) for Zubair formation using Pikett method, in which, resistivity-porosity crossp lots for the same intervals have been executed. �\.,;di 111eu w1u1 val 11Scc: CHAPT ER TWO LITERATURE REVIEW One of the main objectives in formation evaluation is the determination of water saturation (Sw). Importance of this objective comes from the essential part of saturation determination in reserve estimation. Water saturation is defined as the fraction of pore space occupied -by water. To determine 'Sw', many other petrophysical parameters should be known, either from �ell logging or from other sources, such as the porosity. The most commonly used method for Sw determinat ion is the Archie's equationC1> :- n Sw = Where: FRw Rt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 -1 Rt = True formation resistivity, n-m, F =F ormation .resistivity factor, Rv ��Formation-water resistivity, 0-m, and n = Saturation exponent. This equation is directly applicable to the case of clean formation with homogeneous intergranular porosity, where it is found to give good results. It is also used for determination of 'Sw' in flushed zone, as follows, l I � vl,;dl 11 l�U WI ll I vdl I l�Cc II Fn. r ' \ , ... .....•.• ' .•••.•••...•........ 2 --2 s.,., -W, lt l' ' l.\1t'nt\ n ln th flush d �:one, H r = fud -f i 1 L t·n ?. n , n-m, ond r sistivity, n-m. 1'h1: f t·m ti.. n resistivity fnctor (F) is defineJ by F = ... . ....... ...•........ ...•. •.... . . ... 2-3 �"' Th r for" Eq. (2-1) can be written as:- n U Rw Sw = ------- ••...... •.......•. ...... .... ' . . . . . 2-4 !"• Rt Formation resistivity factor, as seen from Eq. ( 2-3) is o function of porosity, cementation factor (m) and forma tion factor coefficien t (a). The cementat ion factor (m) was found to be a. function of format ion lithol ogy, and to h vc ess • nt inl e f feet on 'Sw ' determi nation . It was also found Lhul g llE":ral values of m. = n = 2 and a = 1 can be used lo gi\' reason blc rcsul ts. accur1 t.. D L rmination of porosity is a vital step for the d c t 1:: r 111 i. n n t i 11 o f s l\ t 11 r a t ion , as . can be s c en from ,\rchi 's e lll• Lion. Thu rcsist .i vity o f format ion water (Rw) cnn l>• obl.1ii.n •cl from. cllt"-·ct. lnboratory measurement of for111uLio11 h·ater· rw111pl , or, nlton1ut;ivcly1 can be estimated �(.;"di 111eu w1u1 c;a111S cc Mnny methods were suggested for the d terminl\tio n of 'Rv '< Z>, whloh cnn servo as quick methods for Sw dctermin ntion. t\mong these nre 1-Pickett method �-Hnn�le method 3-Ro/Rt, ratio method. -Pickett MethodC3> :-In this method, formation resistivity readings are to be cross-plotted against porosity on logarithmic co-ordinates. The lowermost points in this plot represent the water line (Ro line), and the intercept of this line with the �-axis (at �=100%) can be used to ca 1cu1 ate ' Rw ' • This method can be considered as a quick graphi�al solution for the determination of water saturation. Hingle Method< 2 > : In this method, across-plot is constructed of (log 1/[Rt) against one porosity log reading. Formation density (Pb), sonic tran&it time (6t), and formation factor can be used in this semi-logarithmic cross-plot. As in picket t method, line is drawn through the lowest resistivity points, that represent the water zone, and 'Rw ' value can be calculated from the slop of this line. This plot con also be used for direct graphical determination of 'Sw'. -Ratio Methodf4) :-In this method, resistivity re adings of two zones around the well bore are taken into consideration. The first zone is the invaded zone next to t he w c l l Lo r c , 1.: h t c h i s n f f cc t e d b y mu cl f iJ t. r a t c . T h e "c' vt.;a l 111�u· w1u1 val 11� c second is the uninv dcd ::one, ""hlch corresponds lh original conditions in the formation. The ratio of the flushed �one resistivity to the unflushcd ::one resistivity can be sho�n to h�ve the following form, according to Archie's equation:- 2 Rio/Rt = -----(S-..·/Sxo} R. •• e e ••• e • • e • • • • • • • t • t e I 2 -5 When the fo�lowing enpiricnl relationship is substituted:- l / s S:r.o = S-..· e t • e • • • • • t I • • I e I I I I t • I I I • I I I I I I 2- 6 Solving the equation for 'Sw': R.i.:o/Rt S/S Sw = (--------} �f /R ... .......... ' ................... 2-i When 'Rw' is known, water saturation can be determined directly froo Eq.(2-7). Another method that can be used for 'Rw' and 's ... • <leterraination. is the apparent \>ater resistivi ty met hod's) . Thi::; method emplo:,-s the det�rr.iinatio n of minimum 'Rw.i • by using the following equation (in assuming t hat s .... =1) same Rt R··a = F ·· ········ ··· ······ ······· ·· ·· ······ �-8 �hen se\·cr al intervals of wat�r bearin� ��one hnvP the values or (Rw;a. )a1111 there is :\ fair nr.\\)\lllt of C�l'laittt.y vl,;dl If lt!U WI LI I vdll l�Cc Lhut this value corresponds to 'Rw'. Therefore, when '11w' is known from this method, t Sw' substituting Eq.(2-7) in Eq.(2-1) can be calculated Sw=� ..... ...... ..... ... ...... .... ..... . . R ... a by 2-9 All the above mentioned methods are based on Archie's equation, and arc mostly valid for clean formation. Deterrnination of porosity from log s has been discussed by ncurnerous numbers of articles. In this 5ection, an attempt �ill be made to summarise some of the essential articles dealing with sonic and radioactive log s ns porosity indicators. 2-1 Sonic log: The principle of sonic logging tool is bnsed on the propagation of elastic vibrations in the formation. Sonic logging is a recording of the transit time of sound wave as it travels through one foot in the format ion, i.e. is a measure of sonic velocity in the formation. Since the mid-1950's, the sonic lo� has become on0 0� the most cornmonl j. used methods for porosity de termination in oil and sas reservoirs< 6 >. Although the sonic log can be run in both compacted and unc 'ompacted fot·mati ons, its recort.I in the l:itcr case need� Lo be corrected. The correction procedure s u g g es L c d Ly Ti x i .-: i· c L a 1 ' 1 > • vt;a1111ea w1u1 va1 nScc - Ther ulso found thot tho son1c l''ndl11� should b corrected for shnliness nnd fluid content. Desides porosity rlctcrmlnntion1 sonic logs cnn bo used for fracture location, gcologicnl corrolntio n, and with neut ron nnd/or density logs 1 for id n Li fl.en t.lon of litholo gy. Similar to most other logging mC'nsul'cments, the sonic log readin� is not n direct porosity \'nluc, but r thcr the time required by the sound Wl\\'e t.o travel b1;;; tween two points through th� formation, i.e., sonic \'clocity in the formation. These measured (6t's) or velocities must then be transformed into porosity. The t1·nnsformntion procedure is affected by many factors, nmong which nre<11> :- -Degree of shalincss. -Effective stress. -Type and pressure of pore fluid. -Matrix materials . -Degree and nature of cementntion. -Temperature. The trnnsformation of sonic rending into porosity had been discussed by many authors, ns follows:- Wyllie et al. (1956, 1958)<9110> have doveloped nn average velocity equation ns a conclusion of substf\ntial Laboratory work to describe velocities measured on a pile of luc i te-alurn inum discs. This cqun t ion h·as used Lo calculate the porosity of flui<l filled pores:- vL;a1111�u -vv-1u1 val r rSCc 1 1 -18 :: + ----- ... ......... ..... ......... . v Vt v •• Where: V = Formation velocity, ft/sec, � = Fractionnl porosity, Vt = Sonic velocity in the interstitial .fluid, ft/sec, and Vma = Sonic velocity in the mat eri al const ituting the matrix of the rock, ft/sec. 2-10 In terms of transit time (At), and for porosity determination, the time average equation can be wri�ten as:- � = ---------- --.... ............ ...... ..... .. 2-11 Where At, Atma and Atr are the respective transit times of the sound energy expressed in �sec/f t. Wyllie et al.< 9 > comp.ar ed the velociti es from equation with actual velocities obtained from cores measurements at atmospheric pressure. They repeated the comparison in 1958 under different pressures to simulate in situ condition s< 1 o > • They rep orted that "wh ereas all the experimental data show a considerable degree of depe ndence of velocity upon porosity, there is also a considerable scatter of data which must repres ent the influence of oth er factors such as the matrix materi al, grain size, distribu tion and sha pe of ·· .. vl,;a11neu w1u1 va111 Cc -:::::;:�--- ccmentnt ion, type temperatur e''. of liqu id in pores, pressur e and It can be noticed tha t the time average equatio n is the simplest mod el , n11d the mostly used equation in deter min ation of form ation por osit y sin ce it was deve loped . by wyllie et al. (1956). Th is is because of its sim plicit y and int uitiv ely reasona ble app earance as compared wit h othe r theo retical equat ions . Mill ican< tt) (1960 ) has deve loped a method of log inte rpretat ion in the Delaware sand , in which the effec ts of shale content can be recognized and used for correction of por osit y calcula tion . He stated that "the shale content may be cons idered as an additi ve to the sand matrix , and as such may be included as part of the mat rix in any prop osed relation between sonic velocit y and poros ity" . The refore , he added the shale as a seco nd ma tri x mate rial to Wyl lie equat ion : 1 � p 1-P-� = ---- + -----+ -- -----. . . . . . . . . . . . . 2-12 . . . . . v V1 V.s h Vma Where, P is the shale fra ction of the total volume. In terms of .t.t ' s and for poros ity calc ula tion , the equat ion may be formed as: .t.t -.6t111 a A tr -fl tm a -p . . . . . . . . . . . . 2-1 J 10 vt.;d1111�u w1u1 vd111 Cc a lt . t"'rm,q obvious thlll the seconcJ l�rm of Eq. (2-lJ) l.n rr<" lion lc�m for the prese nce or ahnlc wllhin the � nd, i. ., \tr prcsen s n por sily r duction term. �llh pr scncc o ! Sonic nnd Gamma Ray logs, h� tr s nl d Eq.(2-1�) on a grnphlca.1 cha.rt to deter mine the 1or sitr f�r both clean and shaly snnd , ns sho�n in Fig.(2-1). Gccrtsma<12l (1961 ) showed that the effect of por os ity on formation velocity can be accounted for, through the compr essibi litie s:- 2 2 B 4 (1-8) 1 \.'p :: + ---Gb + ------------ -------1 Cs 3 (1-¢-8 ) Cs + � Ct Pb 2-1-1 Where, Vp is the compre ssion al velocity (ft/sec ), Pb is the bulk density (gm/cc ), Cs and Cr the com press ibil ities (psi-1) of the mat rix grain material and the pore fluid , respectively. The bulk sheer modulus (Gb) is defined as: 3(1-�C" ) Gb = - ------ ----- 2 Cb (l+o-) .., 1 -t t I I • I I I I • t I t e I I I t t I I t I I I I I I � ._. :::> Poisson's ratio of the empt)• rock ·frame is '<1 • and B is c�1c�, where 'Cb ' is the compr essibility of the rock frame, �hich is defined us: .......... ............ ...... ... �-16 I l �L;at rneuw1u1 val 11Scc wh '\''' , '(\, ' ls the compr c·�n i bil i ty of the pore volume. The l'�l'' fl\t\d omprcss.ibility is defin ed as: c = Sw Cw t ( 1-S w ) Ch c e I I I 1 I I I I I t I I t I I I I I I • I 2-1 7 ''h�re, Ch c is the compr essib ility of the hydrocarbon flu id nnJ Cw is the compre ssibility of the water. Use of Eq.(2 -14) to.predict por osity is obvio usly f�r less attr active thnn empiric al corr elatio ns due to the number of parame ters nnd the involved calcul ations . Koke sh et al.(13) (1065) have sug�csted a completely nc� logging system , �hich is the borehole com pensated sonic s�·stem, in wh ich the errors cm:scd by irregular borehole dinrnater have been overco me . Heese<l-t) (1974 ) have used a sta tistic al approach to derive relat ionships between trans it time (6t) and por osity for reservoir rock which has eithe r linear or logari thmic statistical prope rties . He stated that "If the rock propert ies are distributed (statisti cally ) in a linear fashion , the Kell- kno\;n time-average equn ti on is derived" :·- �-t = 6 tr . � + 6 t .. a ( 1-P ) .., 'n • ' t • • I I I I I I I I I I • I I o .:. I I ---L ..J And if the prop erties (particula rly trnnsi t times ) arc di:;tdb utcd statist ical ly in a logar ithmic fash ion , an �na logous .logarithmic-tim e-n vcrage equat ion is derived:- 1-� 6 t = ( 6 t .. 11 ) ··· ·· ···· ··· ····· ······ 2-19 12 vt.;a1111�u w1u1 var 11Scc He compa red the loga rithmic tim e ave rage equation and the usual ( 1 inear) tim e ave rage equati on with laborat ory data for certain carb onat es , as shown in Fig.(2-2). He conchtded that , there is a v ery good agreemen t betw een the logarit hmic equat ion and laboratory dat a . Pro ble ms risi ng when using the time ave rage equation , par tic ula rly whe n it fails to predict th� poros ities in high formation porosity ranges (over 25"), have urged Rayme r et al�<15> (1980) to propose a new empi rical model to transfor m the transit times to porosities over the entir e theore tical por osit y range , from 0.0 to 100%, a s shown in Fig.(2-3). This figure sho ws a com pari son bet ween · their prop osed trans form and time average equat ion for Vaa :::i 1800 ; ft/sec and Vaa = 19, 500 f�/sec . One dra wback of their .suggest ed transform is that they could not fin d a single .. algori thm or equation for translating the transit times to porosities over the entir � porosity ranges (0-100%). For that reason , they divided the ent ire range into seg ments , as follo ws :- a- For the range of poros ity from O� to 37% , they proposed the following equat ion :- l • 9 (1-�) v •• ......... ... .. ... ..... 2-20 where, P is the bulk density of . the mixture and Paa is the matrix den sit y. This equat ion was suggested to be used in poro sit y dete rminat ion for zones satura ted with water. 13 '5ca1 111ea w1u1 va111Scc ltOl·•ever, if the zones are saturated with other fluid, the following equation was proposed:- 2 V1 = (1-¢) Vma + ji1 Vr 6 where , ht1 = 10 /V1 ·· ······ ·········· ······ 2-21 b-For the range of porosity from 47% to 100%, the proposed equation is:- I I I I I I 1 I I I I I I 2-22 c-For 37% to 47% poros ity range � the propo sed equat ion i$:- --0.37 t I 0.47 ia At ---- ------ At1 + ia --- ------ -6tz ..... . . . . 2-23 = 0.1 or 0.47 -� At = ---- ------At1 0.1 2-2 Radioactive logs 0.1 ¢ -0.37 + ----- ----- 0.1 Atr .. . . . . .... 2-24 Neutr on , Density and Gamma Rays logs are the most widely used radioactive logs in the field of formation evaluat ion, particularly for po rosity and shale volume determination. The first logging operation using radiat ion of nuclear origin was performed in the begining of 1940's to sca1111ea w1u1 e"a1 �c< tnnrnH\ rnd in tlon lurn bo n HI\\\' \'Ht·pon i1 of \'nllhi\ U\'o lcgtJ Ln ndllltlon to \It' t. \'11'\ \ l\ l. \ I\ I th t! t c'tlon 1 lithology formotlon N utr n l l!�i11R cl vi omit· n utron thnt responds to th" hydl'o� 'l\ ontcnt in th fot·mntion, which inclu des hrdr ' n f liquid pr s •nt in para spnco1 matd� and in clny lnttic (if th� formution contnin� · cloy). Density loggin� dovicc measures the bu lk density (ma r ix nnd fluid domd tics) by cmi t ting Gn mmn Rny into the foruwtion . Tho Gnmm•\ Rny logging device m�asures the naturnl rodionctivity of the formntion . Sine tho most of rodionctiYe minerals exist in shales nnd clnys, the Gnmmn Ray log cons idercd to be the most widely used lo!! ns n shnlc or clny indicator . The n utron nud donsity lotts hnve bt'.Cl\ in use for mnny ye 1rs ns poros ity indlcnlors. They o, n be used ns single indicator� , combined to each other in crosnplot t\.lchn i qucs, or com bl nctl t.o o t:.hcr l o�s ( m1ch as son le) , for better cvnluot ion of pol' nity. , 16 · The Density log measures the bulk formation density, ther efore , porosity deriv ed from th is log will represe nt the total formation porosity<16). Neut ron log respo nds to the hydrogen content of the formation. Hyd rogen ions exist .. mainly in the pore filling fluids, but they can be also found in the 111atrix and in clays (in the cases of shaly formation ). When this is the case , the neutr on porosity needs to be corrected for hydr ogen content of matrix and sha le . The .effect ive porosity can be estimated by cross plot tec hni que of dens ity -neutron data, and it was noticed that calcula ted effecti ve poro sity by this techn ique provides the most mean ingful measuremen t of in-situ por osit y< I 7) .. Var.io"Us methods have been proposed by many authors that deal with these two rad ioact ive logs as porosity indicatin g devic es . An approach of porosity determi nation for thin bed s from Neut ron logs has been proposed by Edward s and · Simpson< 18 > ( 1955 ). Actu ally they deve loped an equation to correct the deflect ions of Neutron logs in thin bed s. They also introdu ced the scintillometer int o the field of radioactivity logging to make it possible to dete rm ine bed thickness accur ately . Wahl et a1.c19> (1964 ) propo sed a new dens ity logg ing tool in which the effects of the mud cake and hole i rr.egulari ties could be overcome. This tool was called the compensated formation density tool, FOC. ,A seal ii IEU WI ti I GCft=fl SCc Th ' �· o n " 111 d c d t h n t t h 0 to 0 l .c L v o n If o o d m c" o u r c me n t s f r m l' " c11rnt don!lltlcs withou t noodlnl-C mud cake and b l'"h l' irr gull1ritlcs c:orrcctlono, hence, more accurate porositi R will be obtu incd by npplyln� the following �q\it\tlon:- ·· ······· ··· ······ ···· ·· 2-25 Hhcre: f'b = Forraatio n bulk density, gm/cc, Pc = Fluid density, gm/cc , nnd f' 1a a = Hat. r ix dens i t y , gm I cc • Neut ron-D ens ity crosspl ot has been propo sed by Schlumberger company<20> (1968) for better porosity evaluation. The method wus called 'The Du�l Mineral Method'. It acco unts for the presence of more than one mineral in the formation matrix. Both '�N 1 and 'Pb ' are plott ed on a specially des igned chart, see Fig. (2 -4). Each line repr esents one min eral . The points so cross-p lott ed on the chart can be used for direct poros ity and lithology deter mination. Poupon et ul.(ZI) (1071) proposed a nc;.-r.icthod (com plex lithology method), which is more general than the Due l Mineral Method bccnuse it take s into ncco unt the effects of the shulincss nnd hydrocarbon on the porositr nnd lithology tlctcrmination. The method wns used in n compu ter progrnm calle d COnilli\ND, which facil itates the nurn0r011n I 7 h 11 1 II 11 I f r lP'. pl t I t I tl n I (. h 1· rr<'o l I n t chnlciu t. r·1ulr d �1' l lly wh h m1 1 :< I l h loKY · \ omp,, r' � n h '· m d h t. I.' n h on1p n [\ t cl N •u t. r n l NL I ( 1."hi v r mu I flk nnd bore !Pl" i.rr Hl rit.i.'s ff ctF) on th pi h rmnl N utron t ls y Trum n c l,(22) (1972). Th r con lud d thnt th rmin d sh le ontcnt nn p ro i. y by th CNL-I n ity -ro�splot are more accur t th n tho · pr ,·ious Neutron om utat ions . (such as S:'-JP)-Dens i.tr det rmined by cross plot by A progr am for hand-held calculators hnvo been developed by Ching and Krug(2JJ (1978) for crossplot analys is in which the FDC-C NL- GR' and deep inves tiga ti on resistivit y logs can be used. This prog ram cnn be cons idered as a quick method to · deter mine e f fee ti ve poros ity, shale content and water satur ation . Ch ing and KrudwingC 2•1 J (1980 ) have modified the proposed qu ick method of dens ity-Neu tron crossplot analysis (usin g hand-he ld calcu lator s ) by WU and KrugC 2 J > ( 1978), by means of using pol ar coordinates thnt made the program more compact, effic ient and more quicker in de ter min at ion of shale conten t1 poros ity nnd wn ter-saturation. S\•ulius<25> (19 86) sugges ted a new techn ique to transform Neutron log deflections into acc ur-nt e Neutron porosity log . In that me thod , he used computers to unnlyze ancJ rescale the Neu tron log deflections to a more accut·nt porosi tr log, Then on equa l. ion 1111s lor.ivcJ in which the vl;dllll�U Willi UJ co rresponding porosities to the neutron log deflections can be obtain ed. Many logs can be used ns shale or clay indic ators , the most common are SP , Neu tron , Density and Garama Ray logs . The clay volume can be calcu lated by sin�le le� or by a combi nation of tl-•o or more logs. Tlie following is a revie;..· of the �ost interestin g res ear che s dea ling with radioactive logs as a shale or clay indicators:- Po upon and Gaymard(26) (1970) discussed the eval uat ion of clay logs as clay indicators . They stated that "each clay indicator is calibrated in such a way that it gives eit her a good approximation of the volurae of clny when the conditions are favorable for· that particular indicator , or an upper limit of the clay volume". They used, in add ition to the res is ti vi ty, SP and sonic logs, the radioactivity logs as clay indicators that include Gamma Ray log as a single clay indicator and Neutr on log as eithe r a single clay indicat or or co1:1bined cla;- indicat0r ;dtli Density le,;. It bas been reported that 1.-hen "tht:re is i:-ture than or,c litholog:: within the forraations {such as linestonc and sar.d stone), the use of one (VCL = 0 line) in cross-plottin g of ncu tron-dcns i t:r data is not favorable. Howeve r, it's pr0 fcrablc to di \·idc the forr:ia t ion in to intervals, taking 1 '.) '5ca1111ea w1u1 Ga1 I I �Sec the lithology into nccou nt, nnd to dcflnc for cnch lnt. r:vnl the appropriate VC L = O line. Heslop< 2 7 > ( 197'1) proposed a new method to culculate the clay volume using Gonima Ray log, His met.hod included new technique to estim ate the shale and sand lines by us ing Gamma Ray-Densi t;r crossplo t and Neu tron-D ensit y c rossplo t · He had als o calc ulated the clay volume by using the X-Ray diffraction for 357 feet of examined sampl es . He found that there �as a linea r relationship bet ween the determined clay volumes by x-ray diffraction and those deter mined by Gamma Ray response for the same interval. Therefore, Heslop stated that "the Gamm a-ray response tc-clay content of elastic rocks is linear". A new logging tool has been sugges ted by Se rra et al.< 2 !l) in 1980 's (Natural Gamma ray spectrosco py , NGS) , whose reading can be analysed to determine the nature and qualities of the radioactive material s, and considered to be an improved shale indicator. This tool has responded to the existence of thorium , uranium and potassium within the formation, and by applying the following equat ions , the perce ntage volumes of these radioact ive miner als within shale can be found :- Th -Thm in (Vsh )rh = Ths Ii -Th111 in . . . . . . . . . . . . . . . . . . . . . 2-2 6 :. ( 5C81 ii IEU Will I CaTnSCc U -l'• n ······· ··••i•• ······· 2-'27 K -Kain (Vsh h :: ......... ........ .... 2-28 Ksh -Kn.in Upon the de�ermination of e, Th, and K by app lication of the 1.·cightcd .!.cast square s solut ion , the total gamma rny respons e can then be found by linenr combination:- GR = ATh t Bl1 + CT' ,\. . ' . ' ............ ....... .... . Where A,B,C are coefficients obt ained from a special tes� procedure of the log tool. and th is shale indica tor defined as follo�s:- GR -GR"1 in (Vsh)GR = ----- --------­ GRs h -GRoax ......... ............ 2-30 TheJ; slated that "the uranium is associated with radioactive mineral s other than those found in shale , so it is gener ally not a reliable shale indicat or". Dccnusc t.hil t I they h.u\·e eliminated t.hc u;:-aniun contribution from the tot3l gamma ray response:- GRs = ATh + CK It I I I I I It I It I I I I I' t I It I I I I I It I I 2-31 Where GR!! is the uranium free gamma ray resp onse , and this shale indicator is Jcfincd as follows :- seal ii 1eu WI ti I CaTTISCc z (V h ).:t GI? -GUs 111 I" : ---- ---- ----- -- - Gth G h -GR!J" ft x '7 ... 2 -::i .-; It I. I I I I I I I I I. I I I I W Thus, they concluded that ORs loe; is a better shole indicntor than GR loc. Quirein, ct al.<29> (1981) suggested a ne� approa ch in ,.;hich the ...., l.'.lj. \·olumes and ossoc iated clo y bou nd 1.;ater ,. lur.ics from lc·g data can be determined. The regression techniques for log data and core data used in thi s app roach to provide first-order estimates of how each logg ing to:Jl responds to expected clay or minerals types. �l,;dl 111�u w1u1 vd1 Sec • 60 ..:.: ._ ....... lJ 41 ..., � 50 <J 40 0 b � lOr--:----,--...,.-------------, , ........ .. v, ••• 110;)0 h,"tu; v'•••·• •JOO h/111 'UIUf, ••• 0.[llS,oll'flff D•l"•I •••• ••'l•rl4 • ,, .. 1••• 'O ZO IQ ••••14"t hf1tcl•r• I , ' .... •t ''''•" _,_,L--�J'-�--'-----1 � "r---t-- ---l __ _:_-/-__;j_��--'---.l.---l 0 a: w !!:. ).J S(C.IH. -- · Fig.( 2-1) Theore tical plot of porosity v� transit time 'l'lith increasing shale as indicated by � ARBUCKLE @ CADDO e LANSING-KC 6 �AOO X 5 10 Gamma Roy deflection 15 20 25 � (%) FIGURE(2-2 ) POROSIT Y VS TRAVEL TIME ( Pext .. 2000 psi , Pt • 0 , BRINE SATURATED) 23 �t.;al 111eu w1u1 val Cc eo - - c:: Cl) u .... \fl/yllic ot '11 Timu-1\vernna E�ul.ltion (Vm::: 1800ll ft/sec, VI 5300 lt/socl (Vm=19J0ll lt/s'c, Vl:::5300 ft/sec) �so -PROPOSED SANDSTONE c:: ·- • >- t: en 0 er: 0 a.. 40 - 20- GO TRANSFORM (liquid Saturation) �----- -:: / - - - ___ _ __,( __ _ ----- 7 --/ .,.,/·\ 1 ,,, i=±- - =- -- + , ''vi ,,, v,2 '''" v .. ; 100 120 140 160 SONIC TRANSIT TIME-in'JL sec/ft Fig.(!·3) T•.� proposed sonic lnnsit tiae·la porosltJ transCor1, shoving co1puison lo V7llie tiae- ,,erace eqvation (1956) and to sugaested ,1gorith1s b7 la71er et al. 11980). ('r • t SNP limcstono Porosity Fig. l· 4-Ncutron-dcnsily crossplot scaled with interpolated (Im.a lines. 1 . . . �'" � vl,;d1 111�u w1u1 vd111 Cc Cll,\PTER THJlEE Dl\TRRH t Nt\TJml OF PO ROS ITT UY Lt\ OOR1\ TOHY HEASUREH"ENTS Mm SON IC LOG . nrJer to have accura te correlation between the c re an�ly3is and the �ell logs interpreta tion, all poro�i�r ,·.:il ucs that can be measu red froo the cores and enable u:; c compare it with the �ell lobs ••ere measured. This pnrt inclu des the description of the apparatus used and the expe rim ental proc edure . Cal ibr atio ns fe r each appara tus , needed , �ere done before beginning of the runs. 3-1-1 Prepnr._L n.J!. and cleaning the core samples: -·� l .. Eig �ty Nine plugs were cut from the cored section of 6 wells of the Zubair format ion-East Baghdad oil field . The cut ting were both in \'ertical and horizontal direct ions , us in� one diameter of core drill ! 1 inch) nnd water a3 [4 coola nt. The core samp les that �ere used for poros ity by mercu ry injection measurements, were cleaned in soxhlet extractor, (see Fig.3-1) by refluxing them with n mixtu re of equal ,-olumc of pure bcn�cnc (Ctill6), toluene (C1Hs) and methanol (CJ130JI), until no change in the colour of the vl,;dl 111�u w1u1 vd111Scc 111i.:lllrt' 0ccur •.,,., ,\ft.er Lh' :..;.:1r.rplc� h<id been dric·t.I in the ven, they were rcudr for Lcsting. 3-1-2 Mcrurn rcmcn t o f_p_Q_r_q_;i i t.z: - The poro3 itr values, as shown in Table (A-1), of the =ix �ells had been measured by using core samples of 1 inch !lni:lctcr nncl in.::h long b�: snturntlon rr;cthod u:>in,; .;.1�; oil h·ith dcn:;it;i=0.8� ::;:n/cc n:; :i satu ration liquid. Figure 3-2 sho ws the sche mat ic diagram of saturation :lppnr atus. 2-2 Stat ist ical Analy sis A corre ction factor of a value of 0.9 5 is use d as an n�eragc correction for the whole poros ity values that ::;;casur cd exper iment ally in order to use these values as reference in evaluat ing the porosity values that calculated frora logs . We have used statistica l anal:, ·sis between the two Yariables, the measured porosity fro m core and the calcula ted po rosi ty from sonic log, in 1\hich the fo llowin6 c0���lati on parameters are calculated :- 1-Average percenta ge error, APE . 2-Absolut e average percentage error , AAPE. 3-Standard deviation err or, SD. The ave rage perce ntage error was the most investigating used parameter in com pari ng the perfor mance of various correlation combination, APE, defined as:- vl,;al 111t:u w1u1 vat 11Scc: tr Stu�/�/ 11ltt1tlor flti'mblr Clufrt"c �"''" Fie.(3-1) Soxhl et extractor 1 To.Atm. Vacuum Volve Sample _.=�Gos oil -. - ..... Saturation appara tus 2i sca1111ea WI u 1 CatiiS c< (APE)i : �i calc -�i •eas * 100 ... ' ..... .. . 3-1 �i •eas l\'here. P1calc = calcu lated porosity in well for ith san dstone �i•�•s = measur ed por osit y in well for ith sandstone layer . The definition of each of the se parame ters is as follO\.o 'S: - D {APE)i APE = I: --------••• • • e • • • • e • • • e e • t e e e • e • · e t e •a 3-2 I = 1 n n I {APE )i I AAPE = I: ------- --- ....... .. ... ............. 1 = 1 n n 2 [ (APE)i -APE ] / (n-1) ... .... ...... . 3-4 SD = 1�1 {Whe re n is the n umber of data points). These parame ter s are repr esented graph ica lly in Fig.(�-3). It shoul d be not ed that the magnitude of the average per centage err or, APE , will be appar ently small when negative error s cancel pos itive errors . The abso lute average percent age err ors ove rcome this can cel lin g eff ect by transforming all negat ive errors to equal magni tude pos itiv e error s. The refore , this parameter is always greater than 28 .- I �c...;a111 l�U WI LI I v�l I l�Cc 29 ��o :.- 1 () .• • II ... . ·- I LI I)_ ·:I � ..... ·" .. ,. . .,F. _J ,.,, . " - -10 -· • - • 1 �) -· --:>O - l'iq.( 3. 3 ) lit <J! •l1iurl l\1�p1 •:::1:1 1'1il i1111 vr :;lrrl.i:_;lic<ri jJllrl 11111:lc:1 :-.. \ �l,;CIJ IJ l�U WI u I vat I l�Cc �cr o, nnd it equnl s =cr o if -nnJ onlr if-the erro r for all cnscs in the sample is ccr oc�n> . The stnndn rd deviation is 3 meas ure of the scat teri ng of errors nbo ut the average percentage error. For comp let eness , regr ess ion analy sis (simple linear regression ) of calculated poros ity from cores was perf -0r med in order to calculate the ir corr clntio n coefficient . The corr elat ion coe ffic ient is defined as:- n r: ( � i , ca l c -0 ca 1 c ) ( � i , meas -im ens ) i = 1 CF = ---- --- ------ ------- --- -------- -- ---- - --- --- - Where: n 2 I: (�i,calc -�calc) i = 1 n I: l�i,•eas i = 1 �calc = average cal cul ated porosity n 2 -im ea s ) 3-5 = I: 9'1,calc/n i = t . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 �meas = ave rage measured poros ity n = I: �i,meas /n i = 1 t I I I I It It I I I I I I It It t I I It t It I ") - v-, The corr elati on coefficie nt measures the accuracy of the lin ear relati onship between the calculated and mcns ured porosity data. In a lin ear reg ress ion, line of a corr elat ion ' cocfficiL•nt of (+1.0) inc.licntes that all data points lie exactly on the linej converse ly a correlntlon coe ffi cient of (0.0) indicates tha t no linear relationship exists between the regressed variables< Jo> , The compu ter progra m used in these calculations is given in appe ndix 'A' . 3-3 Dete��inal!.Q..�_Qf_..lli,> rosity by sonic log The basic model was used for poro sity calcu la tio n from sonic log is the tim e average equatio n, which is the classical method . This mode l is disc ussed below. 3-3-1 Yime average egua�ion The fir st trans format ion of the measured sonic trans it time into quant itative evaluation of por osity was developed by Wyllie et al.<9> (1956). Sin ce then , this equat ion was adopted to transform aco ustic vel ocity or trans it time to por osit y particularly for compact clea n san dstone format ions< 6>. Equat ion ( 2-1 O) is the time average equat ion de tined in ter ms of velocit ies . This equat ion could be also defin ed in terms of transit times, • e e e 8 I e e I e e • I • I t • • • I I I • I 3-8 Where At, .t.tm:i and .Atf are the respec tive transit tim es of the sound ener�y expre ssed in µsec/ft. 31 vl;d1111�u vv1u1 vdri Sec > The use of equation (3-g ) r equ ires knowledge of matrix and fluid transit times. In the case of the wat er bearing zone of Zubair Sand, 6t.a=51.3 µsec/ft (compact ed sandstone) and 6tr =189 µsec/ft (water filled pores) �e re used (see Tabl e 3-l )CJ4,7 l. Thes e values we re adopted considering clean sandstone in the intervals selec ted. This equa tio n is deri ved to des cri be the transit tirnc of sound wave thr ough the matrix and pore fluids . Hence 1 in the exist ence of any shal e withi n the rock , the deriv ed porosity from the equation must be corrected for the shale content by using the fol lowin g empiric al equation de\'eloped by Texier et al .<7> (1959), which was widely accepted in sonic log inte rpre tatio n:- �s c = �1s * Where: 1 2-C( • I e • I I I I I I I I I I I I I I I I I I I I I I I I I I 3-9 �sc = Corr ected po rosi ty for shale content, Ps = Derived porosity from Wyllie equation , and C( = Shale indicato r (C( = 1-Vsh ). This correction 1.-a�· applied on all log intcr\'al s selected, after the po ros ity values of those inter val s ha\'e been calc ulate d using the time average equation. A graphical repr esent ation of these values versus those derive d from cores at cor rcspond inO{ depths is sho�n in Fig . ( J--l ) 1 in which the following correlation parameters (using the statisLic'-11 nrd regression pro�rarn ) �er e calculatct.I. 32 '5Cdl 111ea WI Cl I Cal l �Cc SD A \PE APE CF ------ -- 12.511 ll.576 -ll .555 0.922 It is obv ious from the se high percentages errors, that time average equat ion �i"ves unsat isf actory results when it is used for por osity dctcr min atio� of Z°ubair formation- East Dnchdn d oil fiel d . Comp ari son plots have been also prep ared in Figs· (:1-26c) throuch (·1-31 c), in i.·hich 1 the calc ulated por osity V.'.l.l ues using Wyl 1 ie equation and those measured from cores nrc plott ed versus depths . It is indic ated, thr ough these fig ures, that an obvious dist inction between the por osity values measured from cor e samples and those caf cula ted fro m sonic lo� (using time ave rage equat ion ) is occured . 33 Tnlllc (3-1) Values of sonic velocity nnd transit time for common rock matrix, material s and casing. ------------- ----------------------- ---- --- ----- --- ---- --- �led i um Vui ll (ft/sec) tit.a (µsec/ft) -------- - ------------ -------- - - - --- ---- ----- --- -------- --- Snn dst onc 18000-1 9500 55.5-51 .3 - - - - -- --- ---- ---- -- - --- ------- --- ---- ----- - - -- --9 --- --- --- Lir.ic�tone 21000-23000 4 7. 6-·� 3. 5 ----- -- - - ---- - ---------------- - ---- --- ------- -------- - D0lcmitc 23000 43. 5 ------- -------------------- ------ - - - -------- ----- ----- Anh�·dr i te 20000 50.0 ----------- --�-- ------- ---- - ---- -- --- -------- ----- ------- Salt 15000 66.7 ------- ------ -- ------- ---- ----- - - --- - ------- --- ------�---- Casing (iron) 17500 57.0 -- -- ------- - ------ - --- ------ -------- - -- ----- --- --- ----- --- Air (atm. pressure) 1100 909 Water 5300 189 Oil .f2QO 238 'I. I I . 0 :.: � 0 u 14 12 CF= 0.022 SD= 12.511 AAPE= J 1.G .. /G APE= -11.555 ¢ sonic ... .. If *• 14- .... �· 14- * 35 *-II * ·• If ·Ill" .. -II 14- ... w•+ " . .. LI I I I I I I I I I I I I I I I I I I I I I I I I ll I I I I I I I I I I I I I I I I I I I I I I I I I L .. LLL 10 12 14 16 18 20 22 Fif,.()-4) ]:>lot of �core vso.Ws�riic (u[iing Wyllie eq_uat�on)for the Wells of Zuba1 r formation-East Bachaad f1ela. � vl,;dl 11 l�U WI LI I vdl I �Cc CHAPTER FOUR. DET ERM INATION OF POR OSITY BY RADIO ACT IVE LOG S In thi s cha pte r, the available rad ioa cti vit y logs (Neu tron, Dens ity & Gamma Rai) will be use d for calc ulati ng pores i ty · Since shale aff ec'ts every logg ing measu reme nts , por osity values .calc ula ted from the se logs need to be corrected for shal iness . Rad ioact ive logs wil l be used , in addition to poros ity deter min ation in a given inte rval , as shal e indicators for that inter val , as describ ed below . 4-1 Determination of shale vol ume The shale volume. (Vsh .> · for · each chosen inter val was deter min ed by usin g Gamma Ray, Neutron and Density logs. Gamma Ray log was used as a sin gle shal e indica tor , by the follow ing basic relat ionship :- GR -Gnm in Vsh = • • • • I I I I I I • • I I I I I I • t t t t I 4-1 GR111 a.:.: -GR111 in Whe re: GR111 in = Rad ioa ctivity rea ding in c}ean for mat ions , GR1u ax = Rad ioa ctivi ty rea ding in shal e format ions , and GR = Rad ioa cti vity rea din g from log . 36 ..::>t;d1111eu w1u1 vdl Neu tron and Dens ity lol!s were used in combinations tl11·ou�h cross plot techn iques. In fact , two types of Gamma Ray cur ves are available, the fir st i s the standard (total) Gamma Ray curve ( SGR) , in i.·hich the read ing repr esents a linear combination of r0tassiu m, Thorium and· Uran ium amounts, a3 defined b)' the following equation< 28 > :- SGR = ATh + BU + CK et•• t' '' t. If I It I• t t It t t t If t �-2 Where A, n I c are coefficients obtained test procedure of the log tool . from special The secon d type is the corrected Gatlrna nay curve ,· CGR, in which, a Uranium free measureme nt is recorded. It is simply a linear combinat ion of Gamma Rays from thorium and potass ium only, as defined by the followin g equat ion :- CCR = ATh + CK .......... .... ' . . . . . . . . . . . . . . . . 4 -3 Because of the existence of Uranium in association i>ith rad ioa ctiv e miner als other than those found in shaL:: , sue h as organic material s, the corr cc ted Garru!\ :i. Rn:: log l. s Lcl icn:.J to be a better shale ind icatcr, dcterminlng shale \·olume for each inter val by using E ( • 1) I the 'CGR' loo" was not ava1· l .... blc i· n all ·,q .. ,- ' lOWCVe r, u the 1>ells investigated, therefore, the data of 'SGR' log L < i I; c; 11 f u t" ::> .'.1 n d bod i cs i n 1; c l l 3 1� h c re ' CG R ' 1 o g i s r o co rd e d (ED-5�, ED-56, E0-77, EB-79), at depths of those missing ' s r; r. ' l 1 ;,: i 11 v ·.:! 11 s ( E 0-1 8 , En-1 fi ) arc u::: c d i n th c rt.: g t· e �-; s lo n ., 5Cdl ii 1eu WI ti I �7 Program lo give a l' d inenr rclntionships that can be use to determine CGR values f rorn SGR log dn ta, as shown in Figs· (4-1) through (4-8), in which , a straight line equation and correlation coefficient for each sand body of missing 'CGR' log wells are deter min ed. 'CGR' and 'SGR' logs data are repl otted toge the r, as sho�n in Fig.(4-9)· to give n single general equa tion of its re pre sen tat i ve 1 ine , \.·h ich can be applied to each inten·al of Zubair formation. As it was mentioned earlier, the Neut ron and Dens ity logs arc used in combinations through the techn ique of cross plot to deter min e shale volume. In -thi s techn ique the trian gle methodC 31� was used . The use of more than one shale indic ator is recom mend ed , as the calcul ated shale volume from any one method can often be overestimated<26>. There fore, the lowest cal�ulated value of the three method s was used in· the cor rectio n of por osity derived from logs. , 4-2 Determination of porosity Neutron arid density logs were used as single indica tors and in combina tions to deter min e poros ity value for each chosen inter val, as described below:- 4-2-1 Single porosity indicator Through the recorded dens i tics, the density log i-:as used as a single porosity indicator to determine the 38 vt;d1111�u vv1u1 vdll Cc porosity for intervals with no shale conte nt using the following basic equation<J2) :- ,,.0. --'J.I ---------- • • It •• I I " • I I I • It e It It It I It I It I I It • I • I It I f'ma -f't Hhere: r� = Format ion bulk density, gm/cc, fma= Hatri:·: density, gm/cc , and Pc = Fluid densit�, gm/cc . For intervals conta ining shale, the equat ion was used< J J > : - fb = �o fr + (Vsh) f'�h + (1-�o-Vsh) f'ma Where , f'sh is density read ing in shale section, gm/cc . follo'l-1ing . . . . � . . � -5 In the use of the previous equat ion, we have to select matrix and fluid densities. According to our case (water satur ated sand stone intervals), 2.65 gm/cc can be adopted as matrix densi ty and 1.0 gm/cc as pore-filling fluid density, as shown in Table (4- 1), in wh ich , den sit ies from density log and actual dens iti es of most common materials encounter ed in formations are tabulatcd<34l. 39 I '5Ca1 111eu w1u1 val 11�Cc > Table (1-1) Actual density and 'FDC' derived porosity for d·rr . 1 ercnt matcr 1als commonly encountered in borehol es. ------- - -- -- - --- --- - --- -- - ---- - - - ------ -- - - --- - - ---- ------ Formula Actual density FDC density - - ------------ --- - ------ ----- --- ---- ------ ------- ---- - Qu.:irtz 2.654 2.648 -- - ---- -- -- -- - - --- - -- - - ---- ---- - ---- --- - - --- --- --- ---- -- -- Calcite CaCOJ 2 .710 2.710 --- - - ---- - --- -- -- - -- -- -- ---- -- - ----- ----- -- -- ---------- -- - Dolomite CaC01 HgC()J 2 .870 2.876 --- - --- -- --- - - -- - ---- -- -------- ---- - - - - - -- -- -- --- --- -- - - -- Anhydrite CaS(;-1 2.960 2.977 ------ -- ------ ---- -- - ----- - - --- ------------- - --- ---- --- --- KCl 1.934 1. 863 -- --- ---- - ----- -- ---- --- - -- ------ ---- ---- -- - -------- -- -- -- Halite NaCl 2.165 2.0 32 ------- -- ��---- ------------- --- -------------- - - ----- ---�-- Gypsum CaS012H20 2.300 2.351 Fresh water 1. 000 1.0 00 ------- ----- ----- ------- ----------- -- ---------------- --4�� Salt water 200 ,000 ppm 1.146 1.135 ---- ---- ---- -------- �----- ---------------- --- ----- --� -���� Oil n ( CH2 ) 0.850 0.8 5 -- ---- -------- ---- -------- -------- ---------- -- -- ---------- Gas C1 • I 114 • 2 1.325f>g-0.188 ------- --- ---- -- --- ----- - - --- ----- --- --- -=-�--- 9 - 0-0¢¢ � Neutron log was also used as a single shale indicator for porosit y determination. The po rosit y value of each chosen inte rval was cal cu lated f rorn neutron log by directly read ing its response . To use this value of poros ity for comparison with that calculate d from other logs, it should be corrected for ·shale con tent by using the following basic equat ion:- 9'�c = �N +· �Nsh•V9h • . . • . • • • • • • • • • • • • • • • • • • • • • • 4 -6 ·10 ,::,t;dl 11 reu wr u 1 vdl' '"Cc ·11 Whcr" : �N•h = Measured porosity from Neutron log in the shale section. and Vsh = Shale volum e. %. 4-2-2 Two-curves Porosity indicator Through this phase of work . neutrcin and dens ity data were used to determine poro� ity employing the cross plot techniq ue. In this t-echnique the triangle method was used, in "·hich. the derived porosity values (�N ) from neutron log were plotted versus the deriv ed density v"alue s at the same depths , for each well, as shown in Figs .(4-10) through (4-15). Accor ding to the two man ners of us ing the Neutron and Density logs in porosity deter minat ion , there will be three porosity values o�tained for each chosen interv al . The se three value s were plotted versus the corresponding core porosity as shown in Figs .(4-16 ) thro ugh {4-18), in which, cor relation coe ffic ient, standard deviation error, average percenta ge error and absolute average percentage error for each of them were calculate d, as shown in Table (4-2). The calculated results �f log porosities obtaine d by the three approaches are compared with the corre spond ing core porosity as shown in Figs• ( 4-19) throu gh ( 4-24}, for the six wells: vL;a1rr1t=u w1u1 val 11�Cc Figures 26n lo Jln for poros ity vnlucs derived trom Neutron log. Figures 2Gb to Jlb for poros ity value determ� ned by <'-'w-rb ) crossplot (usin� trin n�le method ) Figures 26 d lo 3ld for porosit y values deriv ed from density log. Table (4-2) Correlation parameters for Neutron and Density logs as single indicators and in combinat ions --���h�� ----- ---------- -��� ------��;� ---- ---;�--- -- ---�;--- � -=------------ -- - - ---------- ------ ----- ---- - - -----7---- Neutron log 1.699 4.870 6.8 53 0.906 ----- ----- ---- ----- ----- ------ --------- ------ -- -------��=�- Density log 1.262 5.0 48 7.4931 0.8 83 ------ -- - - -- --------- --- -- ------------- -0� -�-����< ��04----- ¢N-rb crossplot (using triangle method) 2.276 4.5 91 6.2 44 0.9 23 ---- ------ -- --- --- --------- ------- ---- --- -------- ------ ---- ¢N-fb crossplot (using published chart) 13.096 13.096 14.739 0.884 -------- --------- ------- ---------------- --- ------------ - - - Through its lowest percentage erro rs and highest correlation coe ffici ent , as seen from Table (4-2), the �N-fo crossplot (using tri ang le meth od) is the best method that can be used for more accurate determination of porosity than other methods for Zubair format ion-East Daghdnd oil field. 12 o_ .-;( CL CJ u I I ' 0l 111 111I 111111 11111111 1111111111111 11111111 111 111 11111 • , ,J I� (j 8 10 12 14 16 20 15 10 5 SGR ,API Fig.( 4 -1 ) Correcled gamma ray-Standard gamma ray relationship for sand body No. 1 . CGR= 0.611 SGR t 0.808 CF= o .. 816 * * I I I [ J ! I I I I LJ.LI I I I I I I LLJ_ll I I I I I I t I 0 LD .... LJ_l_LU .... l.LLLU 1 15 20 '.L5 .3U c 10 . � SGR ,API � .... l �d <Jornn·1c-i rcr/-�:;tondrJrd <JornrnrJ roy f·l·.�.(4 -2 ) lj_ilr_rl��_..';11i1i ror sand lwu/ No. L. I,� U !tJ1 ,_, �\.,;di 111eu w1u1 Gd111Scc ()_ -:.( ·IO r:------------------. CGI�= 0.997 SGR -5. 1g1 .30 CF= o.924 .. . '---"' 20 - er: 0 u · 10 Q_ <( ·)': Fig.( 4 - 3 ) Correcled gamma ray-Standard gamma ray relationship for sand body No. 3 . CGR= 1.263 SGR -7.487 CF=o.965 '-..../ 20 -:: er (..'.) u 10 . l_LLJ_LLl...LJ.__j_lLLLU I I I I LLLLLLLIJ_J LI I I u..LiJ_U I I I LLLL.J .. JQ .-Jr 30 o - 10· 1 s --:J r., -SGf� (API) (-:,Jrt r:L:li;d <H.11nn•'.l r<JJ'/1-si1un<rJ1ur"d A <�urnrr:o 1 uy 1--i •J. ( 4 -t,.) · · -J ·r n�luliori:::l";ip f•A '.:.Ull( JOI.'/ o. . 44 �1.,;d1111�u w1u1 vdl 1Scc ,,---.. Cl. ·.:.( -._... u: <...'.) 0 ... --. (L <( .._,., ()'.'.: G u :20 10 8 4 CCR-0.U7G SGR + J.1S7 CF=o.928 ._._...__.__.__LJ I I I I I I I I I I I I I I I I I I I I I I I I I I I I "1 I I I I I 5 10 15 20 SGR (1\PI) Fig.( 4 -5 ) Corrected gamma roy-StanJard gornma ray· _relotionsllip for sand ·body No. 5 . CGR= 0.512 SGR + 0.826 CF=o.876 �· _/ /. ..- v� /.--�/ .. � * ... • I I 25 0 otLilJJ.J_J�L 5;!:-' LI LI .LI .LI JI _ _._, _._! -'-' 11' 1 JOLLLL Ll. I I ' 1 'sl I I I I I I I I 2'cf-1-1 -'---'-L...1__._,1_,2 5 SGH (API) -. ..t ···• <Jwnrno roy-Ston<.lurJ �umrnu ruy F. ( 4 6 ) Cun el, t,u I d "I r. l<J. - 1 �·, .J11�1·iip for sand JO Y ,. o. v . re Lh 1 .., ·15 ,::,t;dr 111eu w1u1 vdl 11Scc a: (.') 10 (_) ,-..._ 0.. � er: 0 u 5 CGR= 0.674 SGR + 1.023 CF= o.95o 10 15 SGR (API) 20 25 Fig.( 4 -7) Correclecl gamma ray-Stand ard garnma ray relotionship for sand lJody No. 7 . CCR= 1.2GO SCR -4.884 CF=o.988 • .. � � II- Fic-i .(A _ 8) Cun ccled grJrnrn<J my-Sta ndarcl u <J01nrna ray :.i ., ,.c:utiurdiiµ for �and I.Judy No. u . 46 vl,;dl 111�u w1u1 vdl 11Scc • 20 C' 15 Q_ � ............ rr (_') 10 u 10 � CL <{ � � 0 u 5 CGR= 0.674 SGR + 1.023 JI CF= o.95o .. * .. M .. /� .. • �./.� ... v� 10 15 20 25 SGR (API) .. Fig.( 1 -7) Correcled gornrna ray-Stand ard garnma ray relotion�hip for sand body No. 7 . CGR= 1.2GO SGR -4.854 CF=o.988 .. ... )!- ... * I I I I I I I I I I I l I I I I I I I l l l I I I I I I I I I I I I I I I G 8 10 12 SGR (API) Fig.('1 _ l3) Currccl�d gomma my-Standard garnmo ray r.:.:lutiunsl1iµ for sand body No. S . 46 vl,;dl 111t!u w1u1 vd111Scc: 0:: (.'.) u 10 5 CGR= 0.850 SGR -1.841 CF=-=o.913 * .. ·11-. II- * * M- Ii- II ·II J. ll- II � ·• 1(-11 ***K- .. II- *** * )I; • ·• .. • II 47 . •· oo.t;--'--L...L ..LJLL_L-1-� '-1L6�'__J...J-.-1-..L-JL-.l.1_,_1�'�2���1.__..1_._1_.__._L-L_._�1�3�6�-L'-L..l..-L-L.Ll_ '. SGR (API) 40 , I Fi9.(4-9 ) Corrcde<l gc1mma rc1y-:-Slandard_ gamma my rclation3hip for the sond bot.lies or Zub(llr Form al1on. vl,;dl 111�u w1u1 vdl 1Scc � � I/) 0 .... 0 0... "' "'1· \ 0 l:-OJ () ..-- 0 0 ·-�· L 'J r·.J � . 0 N • 0 • 0 _Ll�--1��1-��Jl��l-�_L�-L- ---l'--�.l-��,�'.-:-�-'-�-'-�-' r'> LO N ,...... L{) I() I m L.J.. - 0 z Q > ;.> ..._ 0 - c C.:.. er. (/'. 0 .... u c 0 L . _, {.J c $ I > tll c c; -;:::; ..::.! ::; c::i - c rl I -.:::- '- C" L.... vl,;dl lll�U Willi \.Jdlll 'Cc ?> C/J D 5 [l.. � �. \ \ ""\ '\ • 0 o_ • 0 \ \ \ . • ri 0 0 ·I :J 1 . :!'. . iJ , .. . ' :..-· ·- ·:.. - c ,_ L l _!. _ __,_ _ __._ _ _i _ _..1 __..J _ __!_ .. - - l I J- l------. l.> ---- - ---0 ,_. I I I l 'l I .... J .'. I 1' I '· I I'. l;; i( l '; :: 'l�J i. ··'' / �.• ' • / • '' ' • I l'l I() 1·1 "' �t.;al 111eu w1u1 val 1 �Cc �· £ VI 0 l-o Cl. \• o_ N 0 r:·· (., ' , ,, •.·I • 0 J_ _ _J_ __ J ___ , _ __.J_L.---1 50 • � El ,....._ Gl r-- I c.n w ...._,, 0 z C) 3 � 0 0 0. Vl VI 0 le. u c 0 � +.J ::> <11 c '& I >... _, V1 c .Oi -0 � :l OJ ,,.-..... (\J .-i I v ·- CT• u... �Cc" �c...;a1111�u w1u1 val v * .. � (/) 0 I- 0 a... 1.I ,,. 0 I') 0 ('J \\\ �'\\ I \ \ \ \ "' I \ "' \ "" � \ "-.. ' ' \. .. \ "' >',,\ '� \ \� � \. " :.�' • 0 o_ • • ,..... l.O -·· I 1 __ J _ _j __ _ L __ 1 _ __t. __ L__.J __ 1 __ _! ___ 1__ ,_, -----_ _ _ ____ !_ ___ . (_l r• > I() l"·I 5 t .......... " " I ill l.1J ...._, 0 z <11 > .__ 0 0 a.. en (,1 0 \._ u c 0 I.. ..... ::> CV c . '$.. I � .....> <II c .(lJ � .::L. ::> CD ........ c<"\ � I "<;t' ....... Ol � �L;at u 1eu w1u1 var r Sec I I [ __ _ L 0 -. _ __i _ _ __,_ () ,-_, ('·I 1.·I 0 t•) 1() N 52 arnScc � ":'\ � t/l 0 \... 0 0... 0 ('\J o_ 0 0 •:> \'•J ('\I • 0 --- - ,. " :! "- '\. . , {I 0 � ,IC � � 0 ,�· <J 0 \ �' \ c���/1.�;!J;,.;1!:.:u.)u :1111n � ro I m Ld .._. 0 :c! (ji > ...... 0 .... 0 0.. lll lll 0 I.. u c 0 \.. - ::> U> c '!$. I >-..., 'iii c II.> \) �� :::> co ...-..,. ll• ,-; ·;:;- '-' C'\ Li.. 1n OJ 0 x Ql L 0 u 12 CF= O.DOG SD= 6.853 AAPF.= 4.070 APE= 1.0D9 • * ·• .. .. ·• • * • </J neulror1 FiB.(4-16) Plot of JJcore vs. �neutron for the Wells of zubai r formation-East Baghd.ad ·field. 28 l{) Ol 0 x Q) .... 0 0 12 I I cP= o.mm SD= 7.403 AAPE= 5.040 APE� 1.262 .. ·• •\ .. 55 ·f • • .. u111111l111111111l1111 11111l111111111l111111 8 12 . 16 20 24 . 28 </> den:;i_ty Fig.(4-17) Plof of ft/core vs • .0'density for the Welle of Zubair forma tion-EaB t Baghdad. fi"ld . vt.;01111�u w1u1 val 11�Cc 22 tC 20 in 18 (}l 0 x (!) ..... 0 0 � 16 14 12 CF= 0.023 SD= G.244 AAPE= 4 .• 591 AP.E= 2.270 r;f cro�s plot t • ·• • ** • * * ... .Fig.(4-18) Plot of .({core vs. ,0'croRsplot for the Wells of Zubair formation-East Ba�hdad field. 56 v<.;a1111�u w1u1 va111Scc " .t\ n - I .. ,, •• ..., .H.lJ Yi.n ----··-\� . .. ; . .-.. . "---· .--�··-.. ���- �c - -;/>.:· ... �·· \ .. •••• t,11"'''"" \ Purw< ily \t J2.0 1r0-.--.- r--.-, ---.-:.:'.' 1-· .. I-·· I-··- 8 JJ.O - )t ...: ., a. .. u .H.0 •••• )1.1 -.=-:- .:.· -.. . -··\ (Wytli�· (�.j1J(Jti1>11) I . .�::;.o �-------------· (Q ' ' O I .. .- \ " It ... ·-· ,., '"J :-\ . ,- ... .. ''- GJ .. .-, J.J.O .s�.o -··-- -........ - • • • •'/": (Ir.) ,...,, .. -· \ \ \ .. .. ·.· '\" . \ . J�· •. n ._ _ _ _ _ _ _ _ __ _ _ :.u.o -�·1.0 (1.o) -------,-·-· . - -'li.:.·1•� •••• �1 .. 111:;ily \ .. 57 . � ·, . '" ' -' .'1�'1.0 •--------------- Fig0(4-I9) µcore -0'1.og comparisons for Well No.(EB-55). vt.;01111�u w1u1 val 11�cc 0 0 .- >< ,-, l: ...... r· ..... n. u 0 a r.:o .- x E - :5 a.. Ill c:.i l'or<i::;ily :-t1 jo U 1 n .,,, · r--r-..----.-- r-1- · ·' .-.,--· r-··-r··- 31.0 .sz.o 33.0 31.0 .)2.0 33.0 ' ' ' ' '• ' . ', ' ' ' - ... :." .. ..,: ... · ... . -· �---- ·---- -- ----- ' ·,, '. ' ---i><:orc ..... � (a) f.'oru:;ily :.t ' ' . ' . ' ' L------ - - -·-------. -· ... 0 0 -�:-- ·�· [, (I Ill Cl 58 -�1.0 --1icorc -• • • • ix: {Ir. ) J2.0 .13.0 .__ ____ ___ ___ ___ __ . (h) f'orn::;ily � "1[ 010 _, ). ��- ..--.--� T-r··-· Jl.O I..) 0 - Y. ,·-. <.: \. '-� ..<: -� ' .. 32.0 r.J . . . . '-,�� � i1dr.n:;il y ·...:.-.. . .. ··-·.; ·---- .3.?i.O . ·----· ··--·--- -·- (u) Figo(4-2o) ftJcore -�log comparisons for Well No.(EB-56). 'c' �t,;a1111eu w1u1 va111� c I .. ' ,. �· CJ 0 � � •i c u. • u ::•_n jl.Q J'o1 o:.:i\ y • .. _ .. _ __ _ ... _ ------- ---- --i/.oeore - • • • • '/J (Wyllit, uyuuliun) . . • I I I ·. ·. -�2.0 - ----- (<.) .., .. . ,) I 'vr o: ily 14 10 .so.o ·-, . -i -r-r--r--r:..;·.::c 1 o .)U.!J v ..: .. 31 .U 31.r, 3?.<I .?ill.O 10 t: .31.0 ' ..._ .. .c: .. 0 . 'l.I· Cl 3:1..U ••••'/'-:-.(Ir,) (i.) ..... :· .. . . r--r·-- r··-1--r-r-'::l-· ·1 - ··.·:: ... • • • • j.\dcn::ity (•I) . I . 5'J .,,. /. I -·· .J Fig.(4-21) f1core -�loe comp�risons for Well No.(EB-77). �l,;d1111eu w1u1 vd11 �Cc " , .... , \I:" l y :•� ,,, ,, .11> ti --r-1 ·- r-,--.. ,-,-T-.,.--r .. � .) .IU . .... .. .. .. .. --.. · .. . ' I _.I . ' . ' . . " --·-- .... -. .. :- ' "·· .. . 1: .• , 'l • .J .l ,. ,, ,, •J n " \ .. "· •JJ u r·) r .. J� .• 1 • • • • �1u·-..1\11u1 .l:'..:l 10 . .m.13 -1-·-r-1 (u) .-. .:.'-....... ·,· c; - _ �:s:._:--��-- .. ' .31�.u -.. -- - -· .... (t.) ' ) ' I ;.; , .... � '· .. ... \J. u• 0 JO.ll 11-' -...--, :s 1.:� :� l .II J2.J J2.H �1.l\ 3l.H . ·"·.· . ... -·-.... ' . .. �· .. . '·-· ........ . '/'<:1.,1(' • ••• ,,.� (11'.) -------------�--· -··-··- ,-,-�-·-·'' "\ ', ', ',., -· · ... ',. ... ..... _, _____ _ - ... ,.... ....... -- · ..... .. · ... \ ' --�"..C.·•" \ '.\ .�··. 60 l'.j I I . .. 1 Fig.(4-22) ffcore -{Jlog comparisons for Well No.(illl-79). I I vl,;dl 111t!u w1u1 vdl �Sec: ..._., 0 0 I\ romty ·� I 11!_ -.,,. J7.,1 -, 1---.-r---r- ···' 3U.0 - 39.U 39.5 ' r·--1-·T--r-,, ., .............. > ) l ....... -... J,�1-=-..= .... -:;-·"""I . . , , . , , . . . , , , • -r/n:nrC" I 'or m�i I y I(, .37.51,....0--..---�-,- .---.r--·-, ....... ,. 1:::, , , ·-· r .. 1 -· - ' � ",, -....... ' ' -, ...... .. \._.'.j, -��-�- t JB.5 . , ......... ..:; - <t_ .... 0 . . , , , , • , , . I ' , I -Ylc:uro • •• ·Y' (Wylli» cquuli1111) '---- ·-·-- ---- ---.. -0 38.0 - ,._, ,E, ':i! .313. 5 �· l'. Ill w JU.0 61 -r/1<.orn • e • • 1/;L• lit: ) 39.5 .__ _ _ _ ____ _ ____ . (Ii) Porosity It JH.5 • • • • lt1dcn::;itr ·---·- -----·----J (d) Fig.(4-23) ecore -�log comparisons for Well No.(EB-15). �t,;dllll�U Willi I I . I: vdl I Sec ,, I 0 .. • o o o :'I, "\t\l_N\ ..... ' :-. 57. �. 1) I' •-' C..I u .. )( . !1.0 - -" -�· L------ ----- J<i.5 1::.0----.--.--�-.---.--.. -.- r --� ..... "' {W �:, "'""'" "") E J7 .. 5 '··· . ' '· .s u. .. 0 38.5 ' ' /,.../';) -- ------ --- -·--·. - (<) 62 r<iro�;il y ::J .�G.�, 1!0�--,-1--r-r--r-.,. -i··--r - --'(lct�C J7.0 -· •• • • c�,. {Ty.) "=' I l_I \ -� .... � J/.�) .. '1' .. . . ) .... , - :.; JS.O ........ S/,5 - ( '� ... u. " I.I ' ' ' ' ' ' ' . I \ ' \ '· ·, . � ... .. ··.� . :-. ) .. � .. -(l,<-rr. 2'S . i - - • • • • ��u�n�itr r ,.., ' ..,..o: .· '\ /\ ·---- ·- --- -- ·- · ... ·····-··--- · ...... 1 (d) Fig.(4-24) I:/core -Olog comparisons for Well No.(EB-!8). CHAPTER FIVE DETERMINATION OF WATER SATURAT ION In the pr evi ous chapt ers , p orosity was calcu lated by several me thods , so. as to selec t the best porosity value, to be used for satur a tion deter mination, due to its significant effect on 'Sw ' calculat ion. The methods disc uss ed are:- 1- Neut ron log as a sing le por osity indicator , 2-Density log as a single poros ity indicator , 3- Ne utr on -Dens ity crosspl ot , using triangle method , 4- Sonic log, us ing the time average equation . Core por osities we re also measur ed , and -used as reference valu es . We have no ticed through the compa risons made between the poros ities derived from those methods and cor e por osities 1 Neutron log and the crossplot technique (using triangle meth od ) yield favo rable correlation parameters , when compare d with other used methods. Thro ugh the ·appl ic�t ion of the tr long le method in porosity calculat ion 1 it was found to give the highest correlation coeffici ent and lowest percent age err ors . Therefore , triangle method �as adopted to obtain porosity to be use d in determination of water saturation by Arch ie's equation. €3 sca1111eu w1u1 ca111 c< 6 .J These cnlculated porosity values were also used in a rossplot technique (Pickett Method)<JJ, where they are plot tcd versus calcula ted res is ti vi ty n1lues at the sa me depths in order to get spe cific val ues .of the cemen tati on factor (m) and the format ion coefficie nt factor (a) of the Zubair format ion, as explained below. 5-1 D�tcrmin ation of m and a The gene ral ly accepted values of cementation factor {m) and formation coefficie nt factor (a) are 2.0 and 1.0, respect ively .. These ,-alues were used exte::nsively in