Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing 1

Transcription

1 PETROPHYSICS, VOL. 48, NO. 1 (FEBRUARY 2007); P ; 28 FIGURES, 2 TABLES Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing 1 Alberto Mendoza 2, Wil liam E. Preeg 3, Carlos Torres-Verdín 2, and Faruk O. Alpak 2,4 We quan tify the influ ence of mud-fil trate invastion on com pen sated neu tron and den sity mea sure ments acquired in ver ti cal and hor i zon tal wells. Our objec tive is to assess the influ ence of the spa tial dis tri bu tions of fluid sat u ra tion and salt con cen tra tion on generic com pen sated nuclear tools. The case of hor i zon tal wells is of pri mary inter est because of the com plex spa tial dis tri bu tion of flu ids around the bore hole caused by mud-fil trate inva sion com - bined with vari a tions of fluid den sity, per me abil ity ani so - tropy, fluid mobil ity, and grav ity seg re ga tion, among other fac tors. We sim u late the pro cess of inva sion for the sit u a tion wherein water-base mud fil trate invades a gas-bear ing for ma tion. The sim u la tions also con sider the mix ing of salt between mud-fil trate and con nate water. Sub se - quently, the cor re spond ing nuclear tool responses are sim - u lated with the Monte Carlo N-Par ti cle (MCNP) code using com pen sated source-sen sor con fig u ra tions sim i lar to those of com mer cially avail able wire line tools. To this end, we intro duce generic mod els of ther mal neu tron and den sity tools referred to as Long horn Nuclear Well Log - ging Tools. We per form cal i bra tion and cor re la tion of the sim u lated nuclear mea sure ments to appraise their con sis - tency and accu racy against stan dard indus try mod els. Results from this study con firm that pres ence of mud-fil trate inva sion reduces, and even elim i nates, the effect of gas on neu tron tool poros ity mea sure ments. It was also found that salt con cen tra tion of con nate water ABSTRACT causes an effect oppo site to that of gas on the sim u lated neu tron mea sure ments. More impor tantly, the effect of salin ity con trast, caused by fresh mud fil trate dis plac ing salty con nate water, empha sizes the gas effect on neu tron mea sure ments for the case of shal low inva sion. The effect of salt mix ing is less crit i cal for the case of den sity mea - sure ments. It was also found that the pres ence of non-axisymmetric dis tri bu tions of mud fil trate and salt con cen tra tion around the wellbore biases the esti mates of den sity and appar ent neu tron poros ity. For the case of hor - i zon tal wells, depend ing on the loca tion of the tool around the per im e ter of the wellbore, both neu tron and den sity mea sure ments are influ enced by non-axisymmetric spa - tial dis tri bu tions of flu ids result ing from inva sion. This effect is most notice able for tool loca tions at the top and bot tom of the wellbore. For the cases con sid ered in this paper, dif fer ences in the esti mated neu tron poros ity asso - ci ated with tool loca tion around the wellbore were as high as 3 p.u. For den sity mea sure ments, the cor re spond ing dif fer ences in poros ity were as large as 5 p.u. for poros ity val ues greater than 20 p.u. For the case of vari able per me - abil ity ani so tropy ratios, the sim u lated neu tron and den - sity poros ity val ues exhib ited dif fer ences of up to 7 p.u. depend ing on the tool loca tion around the wellbore with respect to actual val ues of for ma tion poros ity. Keywords: neu tron log, den sity log, Monte Carlo mod el ing, hor i zon tal wells, inva sion mod el ing Manu script received by the Edi tor Decem ber 14, 2005; revised manu script received Octo ber 27, Mod i fied from a pre sen ta tion at the SPWLA 46th Annual Log ging Sym po sium, New Orleans, Lou i si ana, paper PP. 2 The Uni ver sity of Texas at Aus tin, Depart ment of Petro leum and Geosystems Engi neer ing, 1 Uni ver sity Sta tion Mail Stop C0300, Aus tin, TX ; cverdin@mail.utexas.edu, albertom@mail.utexas.edu 3 Con sul tant, 2025 rue de St Tropez, Aus tin TX 78746, ; wpreeg@aus tin.rr.com 4 Cur rently with Shell Inter na tional E&P; Omer.Alpak@shell.com 2007 Soci ety of Petrophysicists and Well Log Ana lysts. All rights reserved. 28 PETROPHYSICS February 2007

2 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing INTRODUCTION There is a need in the oil indus try to sim u late the response of nuclear well log ging tools in spe cial bore hole con di tions and envi ron ments. Such mod el ing capa bil ity has not been widely avail able because spe cific details of the design of nuclear well-log ging tools are needed to prop erly sim u late their mea sure ments. Ser vice com pany tool designs are usu ally pro pri etary and there fore unavail able for accu - rate mod el ing by aca demic and oil field tech ni cal experts. In this paper, we intro duce a generic set of nuclear tools referred to as the Long horn nuclear well log ging tools. Such generic tools have been designed to emu late the response of ser vice com pany tools as described in the open tech ni cal lit er a ture. The intent is to syn the size the most impor tant prop er ties and func tions of com mer cially avail - able nuclear tools, and to draw gen eral con clu sions on the behav ior of the mea sure ments in com plex log ging con di - tions. Results from our sim u la tion work show that the Long horn tools pro vide an accept able match to the response of many of the ser vice com pa nies doc u mented bore hole envi ron men tal effects. These results do not rep re - sent an exact match to the response of any ser vice com - pany s tool. We empha size that pro pri etary designs will be needed for accu rate sim u la tion of the response of com mer - cially avail able tools. Ellis et al. (2003) described a generic design of ther mal neu tron tools to illus trate the sen si tiv ity of the mea sure - ments to for ma tion poros ity and slow ing-down length. Their study pri mar ily con sid ered the depend ence of slow - ing-down length on the near-to-far detec tor count ratio. Ther mal neu tron mea sure ments were stud ied for the case of water-sat u rated for ma tions. In a sub se quent pub li ca tion, Ellis et al. (2004) dis cussed the gen eral sen si tiv ity of ther - mal neu tron mea sure ments to lithol ogy, gas sat u ra tion, and pres ence of shale. Sherman and Locke (1975) quan ti fied poros ity and matrix lithol ogy effects on the depth of inves - ti ga tion of sev eral neu tron and den sity tools. Based on exper i men tal work, the same authors stud ied inva sion effects on a salt-water-sat u rated for ma tion by plac ing var i - ous flu ids within sev eral arbi trary shells of inva sion. Sub se - quently, Wiley and Patchett (1994) used a deter min is tic dif - fu sion code to model ther mal neu tron and poros ity mea - sure ments across numer ous lithologies to address the prob - lems of inva sion and dif fer ences in radial length of inves ti - ga tion. Tit tle (1992) used ana lyt i cal dif fu sion the ory to cal - cu late the effect of inva sion on nuclear mea sure ments at spec i fied radial lengths of inva sion. How ever, the reported sim u la tions based on dif fu sion the ory mod eled both sources and sen sors as infin i tes i mal objects. Mak ing use of the Long horn nuclear log ging tools (LNLT) intro duced in this paper, we pri mar ily focus our work on mea sure ments acquired in the pres ence of mud-fil - trate inva sion and salt mix ing in ver ti cal and hor i zon tal wells. This set of tools includes source-sen sor con fig u ra - tions for both ther mal neu tron and bulk den sity mea sure - ments. We use a Monte Carlo code to assess the sen si tiv ity of the LNLT to real is tic non-sym met ric spa tial dis tri bu tions of mud fil trate and salt con cen tra tion in the pres ence of gas-bear ing for ma tions. The main dif fer ence between this paper and pre vi ously pub lished stud ies on the numer i cal sim u la tion of nuclear tool mea sure ments is that we quan tify spe cific con di tions of mud-fil trate inva sion as opposed to arbi trary uni form inva sion pro files. We pay spe cial atten - tion to the effects of salt con cen tra tion and mud-fil trate inva sion in the detec tion of gas with neu tron and den sity logs. Scott et al. (1982) described a log a rith mic cross-plot of the near- and far-detec tor count rates referred to as spine and ribs cross-plot. In this paper, we pro vide sim i lar graph i cal rep re sen ta tions for the LNLT and com pare them to pre vi ously pub lished spine and ribs cross-plots. Pre vi ous work on the numer i cal sim u la tion of neu tron logs in hor i zon tal wells includes the assess ment of measurements in the pres ence of beds below and adja cent to the wellbore, as well as tear-drop inva sion for a log - ging-while-drill ing (LWD) com pen sated neu tron tool. In that study, Ellis and Chiaramonte (2000) ana lyzed the inter play between radial length of inves ti ga tion and radial length of inva sion. They mod eled non-axisymmetric tear-drop inva - sion in a 25-p.u. sand. In the pres ent paper, we ana lyze the response of the LNLT for spe cific spa tial dis tri bu tions of flu - ids and salt con cen tra tion sim u lated for a gas-bear ing for ma - tion invaded with water-base mud fil trate. DESCRIPTION OF LONGHORN NUCLEAR TOOLS The ther mal neu tron poros ity tool and the den sity tool assumed in this paper were mod eled with the Monte Carlo N-Par ti cle (MCNP) trans port code main tained by Los Alamos National Lab o ra tory. A detailed descrip tion of the MCNP trans port code is given by the X-5 Monte Carlo Team (2003) in their offi cial man ual A Gen eral Monte Carlo N-Par ti cle Trans port Code, Ver sion 5. This sec tion of the paper describes the tool mod els and com pares their cor re - sponding calibrations to published data for commercial tools. Ther mal Neu tron Poros ity Tool Fig ure 1 shows the geo met ri cal con fig u ra tion of the Long horn ther mal neu tron poros ity tool. It con sists of two helium ther mal neu tron detec tors and a 16-curie AmBe neu tron source. Table A.1 describes the geo met ri cal dimen - sions and source-sen sor con fig u ra tion assumed for the February 2007 PETROPHYSICS 29

3 Mendoza et al. Long horn ther mal neu tron poros ity tool. The energy of the AmBe neu tron source is sam pled as shown in Fig ure 2 (Soran et al., 1990). Fig ures 3 and 4 com pare the near- and far-detec tor count rates sim u lated for the Long horn tool to those of Schlumberger s CNT 1 thermal tool described by Scott et al. (1982). The count rates for the Long horn tool are sim i lar to those of the Schlumberger s CNT at low val ues of poros ity and some what larger at high poros ity val ues. Fig ures 5 and 6 indi cate that the cor re spond ing envi ron men tal cor rec tions for tool stand off and bore hole size are very sim i lar for both the Long horn and Schlumberger s CNT ther mal tool. Each MCNP sim u la tion per formed to sim u late Long horn neu tron tool mea sure ments required approx i mately 38 min utes of com puter time on a 2.8 GHz Pentium 4 com puter. This pro - vided results with sta tis ti cal pre ci sion of ±2 % for the near detec tor, and ±0.6% for the far detec tor after run ning 2 mil - lion par ti cle his to ries using an opti mum weight-win dow vari ance reduc tion tech nique. Den sity Tool Fig ure 7 describes the com po nents and dimen sions of the Long horn den sity tool. It con sists of two sodium-iodide detec tors and a 1.5-curie 662 kev Cs 137 gamma ray source. Table A.2 in Appen dix A pro vides a com plete descrip tion of the geo met ri cal dimen sions and source-sen sor con fig u - ra tion assumed for the Long horn den sity poros ity tool. Fig ure 8 com pares the near- and far-detec tor count rates FIG. 1 Descrip tion of the Long horn ther mal neu tron poros ity tool. The tool con sists of an AmBe neu tron source as well as long- and short-spaced detec tors. In this par tic u lar exam ple, the diam e ter of the bore hole is equal to 8 in. Sim u la tions of tool mea sure ments con sider the pres ence of both bore hole and for - mation properties. 1 Mark of Schlumberger FIG. 2 Energy spec trum of the AmBe neu tron source. FIG. 3 Cross-plots of near- and far-detec tor count rates as a func tion of water-filled lime stone poros ity. Solid and dashed spines describe the behav ior of the Long horn and CNT-G (Scott et al., 1982) ther mal neu tron tools, respec tively. 30 PETROPHYSICS February 2007

4 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing asso ci ated with both the Long horn den sity tool and the BHI (Baker Atlas) den sity tool described by Bigelow (1995). The com par i son is per formed using a tra di tional spine and rib pre sen ta tion. When com par ing tool responses, we pay care ful atten tion to the dynamic range (count rate vari a tion for the cal i bra tion blocks) for each detec tor as well as to the slope of the spine and ribs. We found that the count rates of both near and far detec tors for the alu mi num and mag ne - sium cal i bra tion blocks were sim i lar for the Long horn and BHI den sity tools. Sim u lated ribs for low- and high-den sity mudcake are sim i lar for the two tool designs. Due to the pho to elec tric effect, low-energy pho tons (energy lower than 200 kev) have a higher prob a bil ity of being absorbed com pletely on impact with an atom, result - ing in kinetic energy being trans ferred to the atom and a low-energy pho ton being ejected from it. Pho to elec tric effects on the LNLT sim u la tions dis cussed in a sub se quent sec tion did not con trib ute to the responses because pho tons with ener gies below 200 kev were dis crim i nated in the count rates of the two detec tors. Trans port of the emit ted gamma rays through the for ma - tion takes place by way of inter ac tions with elec trons. Atten u a tion is caused by Compton scat ter ing for ener gies above 125 kev (Schultz et al., 1985). There fore, the den sity tool response ( a ) is related to elec tron den sity ( e ). The FIG. 5 Neutron environmental correction for tool standoff in an 8-in bore hole. The solid and dashed curves com pare the Long - horn (LNLT) and Dual-Spac ing Neu tron Log (CNL 1 ) water-filled lime stone poros ity read ings, respec tively, for the case of a 15 p.u. water-filled lime stone. FIG. 4 Comparison of the Thermal Neutron Porosity Tool near-to-far count ratio against that of pub lished tool mod els. The curves show the rela tion ship between detec tor-count ratio and poros ity for the case of water-filled lime stone with an 8-in bore - hole. The Long horn tool model (LNLT) matches the generic (Ellis et al., 2003) and CNT-G (Scott et al., 1982) responses at low val ues of poros ity and fol lows a sim i lar trend at high val ues of poros ity. FIG. 6 Neutron environmental correction for borehole size. The solid and dashed curves com pare the Long horn (LNLT) and Dual-Spac ing Neu tron Log (CNL 1 ) water-filled lime stone poros ity read ings, respec tively, for the case of a 15 p.u. lime - stone. 1 Mark of Schlumberger February 2007 PETROPHYSICS 31

5 Mendoza et al. rela tion ship between elec tron den sity and bulk den sity ( b ) is given by e Z 2 b A, (1) Z where ( A ) is the aver age ratio of atomic num ber to atomic weight of the for ma tion. A rela tion ship between elec tron den sity from the tool response and bulk den sity, assum ing a water-filled lime stone, is com monly used to cal cu late val - ues of bulk den sity. This well-estab lished rela tion ship is writ ten as (Bigelow, 1995), (3) b LS where LS is the den sity esti mated from the far-detec tor response and is the den sity cor rec tion obtained from the spine-and-ribs chart shown in Fig ure 8. Each MCNP sim u la tion with the Long horn den sity tool required approx i mately 106 min utes of com puter time on a 2.8 GHz Pentium 4 com puter that included the sim u la tion of 30 mil lion par ti cle his to ries using an opti mum weight-win dow vari ance reduc tion tech nique. This pro - vided results with a sta tis ti cal pre ci sion of ±2% for the near detec tor, and ±1% for the far detec tor. b (2) The above equa tion also remains a good approx i ma tion for the cases of fluid-sat u rated sand stone and dolo mite if b a (Schultz et al., 1985). Fur ther more, start ing from the rela tion ship described by equa tion (2) to cal cu late sin - gle-detec tor den sity response, the for ma tion bulk den sity (com pen sated den sity), b, is given by e FIG. 7 Descrip tion of the Long horn den sity poros ity tool. The dia gram shows the rel a tive loca tions of the Cs 137 source of medium-energy gamma rays, and of the long and short-spaced NaI crys tals with photomultiplier tubes used as detec tors. The tool includes an iron cas ing (blue), and a tung sten pad hous ing (orange). In this par tic u lar case, the diam e ter of the bore hole is equal to 8 in. For ma tions are indi cated in yel low and the small dots dis play cal cu lated pho tons. Each point rep re sents a col li - sion of a pho ton that even tu ally reaches one of the detec tors. FIG. 8 Spine and rib cross-plot plot describ ing the rela tion - ship between gamma-ray counts at the short- and long-spaced detec tors for den sity poros ity tools. The spine from the Long - horn Nuclear Log ging Tool (LNLT) is dis played in solid lines with ribs for light and heavy mudcake, and the com mer cially avail - able tool (Bigelow, 1995) is plot ted in dashed lines along with its rib calibration. The magnesium calibration block is identified with dia monds, whereas the alu mi num cal i bra tion block is iden - ti fied with squares. 32 PETROPHYSICS February 2007

6 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing SIMULATION OF MUD-FILTRATE INVASION For the pur pose of sim u lat ing the response of the den sity and ther mal neu tron poros ity tools in the pres ence of inva - sion, we sim u lated the pro cess of mud-fil trate inva sion for a gas-bear ing for ma tion drilled with a water-base mud. Spa - tial dis tri bu tions of water sat u ra tion, salt con cen tra tion, and gas sat u ra tion result ing from the pro cess of mud-fil trate inva sion were stud ied for both ver ti cal and hor i zon tal wells. The ver ti cal well pen e trates a sand-shale sequence con - sist ing of a top sand of 25 p.u., fol lowed in depth by a shale bed, and a bot tom sand of 15 p.u. The same rock-fluid prop - er ties of the top sand were assumed for the case of a hor i - zon tal well. Addi tion ally, the pro cess of mud-fil trate inva - sion was sim u lated for sands with poros i ties equal to 10 p.u., 15 p.u., and 20 p.u. for hor i zon tal wells. With the excep tion of poros ity, the remain ing wellbore and for ma - tion petrophysical param e ters were the same as for the top sand described in Table B. Fig ure 9 describes the petrophysical and geo met ri cal prop er ties of the for ma tion used in the ver ti cal-well sim u la tions includ ing spe cific prop er ties for each of the two sands. To account for per me abil ity ani so tropy, we con sid ered ratios of 1, 3, 5, and 10 for the case of the 25 p.u. sand. This decreased the ver ti cal per me abil ity from 300 md to 100, 60, and 30 md. Fig ure 10 includes sec tion views of the spa tial FIG. 9 Graph i cal descrip tion of the for ma tion prop er ties included in the ver ti cal bore hole model used for the sim u la tion of mud-filtrate invasion. FIG. 10 Sec tion views of gas sat u ra tion, salt con cen tra tion, and bulk den sity. The sec tion views are taken on a plane per pen dic u lar to the axis of a hor i zon tal well and the time of inva sion is three days. Pan els on the left col umn describe the cell discretization scheme used in the sim u la tion of nuclear logs with MCNP. Col ored cells illus trate the non-axisymmetric spa tial dis tri bu tion of sat u rat ing flu ids for the case of a 25 p.u. sand for per me abil ity ani so tropy val ues of 10 and 1, and a 10 p.u. iso tro pic sand. February 2007 PETROPHYSICS 33

7 Mendoza et al. distributions of fluid saturation and salt concentration resulting from the sim u la tion of mud-fil trate inva sion in sands of 25 p.u. and 10 p.u. together with the numer i cal grid used to sim u late the cor re spond ing nuclear logs with MCNP. As described by Alpak et al. (2003), the numer i cal sim u - la tion of the inva sion pro cess explic itly con sid ers the influ - ences of per me abil ity, fluid vis cos ity, rel a tive per me abil ity, cap il lary pres sure, fluid den sity, and grav ity seg re ga tion. Ini tially, the for ma tion is 70% sat u rated with gas and 30% sat u rated with water of NaCl con cen tra tion equal to 150,000 ppm. These ini tial fluid sat u ra tions were dis placed by mud-fil trate inva sion con sist ing of water of salt con cen - tra tion equal to 5,000 ppm. The mud-fil trate inva sion pro - cess was numer i cally sim u lated with the ECLIPSE 1 com - mer cial black-oil multiphase fluid-flow sim u la tor. We enforced a value of cm/s for the speed of radial mud-fil trate inva sion along the bore hole wall. This value is 1 Mark of Schlumberger con sis tent with the inva sion speeds reported by Dussan et al. (1994). Inva sion in the ver ti cal well model was numer i cally simulated with 14,580 grid blocks, whereas the sim u la tion of inva sion in the hor i zon tal well model required 29,584 grid blocks for a res er voir of 291 ft of radial extent. Fig ures 11 and 12 are sec tion views of gas sat u ra tion and salt con cen tra - tion, respec tively, result ing from the sim u la tion of the pro - cess of mud-fil trate inva sion for the case of a ver ti cal well. In both sec tion views, the time of inva sion is three days. Fig ures 13 and 14 are sec tion views of gas sat u ra tion and salt con cen tra tion, respec tively, result ing from the sim u la - tion of the mud-fil trate inva sion pro cess for a hor i zon tal well. The sec tion views are taken on a plane per pen dic u lar to the bore hole axis and the time of inva sion is three days. As in the case of the ver ti cal well, Fig ure 13 indi cates that the spa tial dis tri bu tion of water sat u ra tion is non-uni form after inva sion; it remains nota bly affected by grav ity seg re - ga tion. On the other hand, the spa tial dis tri bu tion of salt con cen tra tion is not as dif fused as the spa tial dis tri bu tion of water sat u ra tion. FIG. 11 Sec tion view of gas sat u ra tion for the case of a ver ti cal well sub jected to axisymmetric mud-fil trate inva sion after three days of inva sion. Refer to Fig ure 9 and Table B for a descrip tion of the asso ci ated fluid and for ma tion prop er ties. The fig ure dis - plays deeper inva sion and higher water con cen tra tion near the wellbore for the lower sand (15 p.u.) than for the upper sand (25 p.u.). In addi tion, mud-fil trate inva sion causes a ver ti cal gra di ent of water saturation. FIG. 12 Sec tion view of salt con cen tra tion for the case of a ver - ti cal well sub jected to axiymmetric mud-fil trate inva sion after three days of inva sion. Refer to Fig ure 9 and Table B1 for a descrip tion of fluid and for ma tion prop er ties. As opposed to the spa tial dis tri bu tion of water sat u ra tion shown in Fig ure 11, the spatial distribution of salt concentration is almost identical in both sands. 34 PETROPHYSICS February 2007

8 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing NUMERICAL SIMULATION OF NUCLEAR TOOL MEASUREMENTS Simulation of thermal neutron porosity measurements Sim u la tion of ther mal neu tron mea sure ments was per - formed with MCNP. We assumed the Long horn ther mal neu tron poros ity tool con fig u ra tion described ear lier to sim u late the mea sure ments. Sim u la tions con sid ered the cases of ver ti cal and hor i zon tal wells described in the pre vi - ous sec tion both with and with out the pres ence of mud-fil - trate inva sion. Sim u la tion of neu tron poros ity logs was per formed at a sam pling rate of 0.5 ft in depth start ing from the bot tom of the for ma tion model. Every cal cu lated point is dis played at the depth of the mid point between the source and the long-spaced detec tor. The sta tis ti cal pre ci sion of the mea - sure ments is approx i mately ± 0.3 p.u. for the top sand, and ±0.4 p.u. for the bot tom sand. MCNP sim u la tions gen er ally require more com puter time at the same sta tis ti cal pre ci sion for the case of higher den sity mate ri als. For hor i zon tal wells, the accu racy of the mea sure ments is approx i mately ±0.5 p.u. for sim u la tions per formed in the pres ence of inva sion. Neu trons inter act pri mar ily with hydro gen nuclei in the for ma tion, whereby the spa tial dis tri bu tion of hydro gen index in the for ma tion is crit i cal to accu rately sim u late ther - mal neu tron mea sure ments. Fig ure 15 is a sec tion view of hydro gen con cen tra tion in atomic weight frac tion for the case of a ver ti cal well. Fig ure 16 is a sec tion view of hydro - FIG. 14 Sec tion view of salt con cen tra tion for the case of a hor - i zon tal well sub jected to mud-fil trate inva sion. The sec tion view is taken along a plane per pen dic u lar to the bore hole axis and the time of inva sion is three days. FIG. 13 Sec tion view of gas sat u ra tion for the case of a hor i - zon tal well sub jected to mud-fil trate inva sion. The sec tion view is taken along a plane per pen dic u lar to the bore hole axis and the time of inva sion is three days. FIG. 15 Sec tion view of hydro gen con cen tra tion (atomic weight frac tion) for the case of a ver ti cal well and axisymmetric mud-fil trate inva sion after three days of inva sion. February 2007 PETROPHYSICS 35

9 Mendoza et al. gen con cen tra tion in atomic weight frac tion for the case of a hor i zon tal well after three days of inva sion. These sec tion views were plot ted directly from the sim u lated spa tial dis - tri bu tions of water sat u ra tion. In addi tion, the cal cu la tion included the chem i cal com po si tion of the var i ous rock types assumed in the model. FIG. 16 Sec tion view of hydro gen con cen tra tion (atomic weight frac tion) for the case of a hor i zon tal well sub jected to mud-fil trate inva sion. The sec tion view is taken along a plane per pen dic u lar to the bore hole axis and the time of inva sion is three days. Simulation of density tool measurements We used the Long horn den sity tool model intro duced ear lier to per form sim u la tions of den sity mea sure ments with MCNP. The sim u la tions include the same ver ti cal and horizontal for ma tion mod els with and with out the pres ence of mud-fil trate inva sion and salt mix ing. Vari a tions of fluid sat u ra tion and salt con cen tra tion due to inva sion altered the original bulk density of the formation. Consequently, the poros ity esti mated from the tool response was biased because we assumed a con stant fluid den sity in the cal cu la - tion. Fig ures 17 and 18 are sec tion views of for ma tion bulk den sity for the cases of invaded ver ti cal and hor i zon tal wells, respectively. The average statistical precision of the simulated bulk den sity mea sure ments was approx i mately ±1 p.u. INTERPRETATION OF SIMULATION RESULTS We sim u lated neu tron and den sity poros ity logs for the case of a ver ti cal well. For hor i zon tal wells, neu tron and den sity poros ity mea sure ments were sim u lated at spe cific tool loca tions around the per im e ter of the bore hole wall. FIG. 17 Sec tion view of bulk den sity for the case of a ver ti cal well and axisymmetric mud-fil trate inva sion after three days of invasion. FIG. 18 Sec tion view of bulk den sity for the case of a hor i zon tal well sub jected to mud-fil trate inva sion. The sec tion view is taken along a plane per pen dic u lar to the bore hole axis and the time of inva sion is three days. 36 PETROPHYSICS February 2007

10 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing Fig ure 19 shows sim u lated logs of neu tron poros ity for the ver ti cal well model before and after inva sion. Before inva sion, the appar ent neu tron poros ity is approx i mately 6 p.u. across the 15 p.u. lower sand. This dif - fer ence of poros ity is due to pres ence of gas in the for ma - tion. How ever, the under es ti ma tion of neu tron poros ity due to this gas effect is rel a tively low because of the high salt con cen tra tion of con nate water. Salt con cen tra tion has the oppo site effect to that of gas on the neu tron log. On the other hand, after inva sion, the sim u lated neu tron poros ity is approx i mately 15 p.u. There is no appre cia ble gas effect on the sim u lated neu tron poros ity mea sure ment after inva sion because of the rel a tively deep radial length of inva sion. These results remain con sis tent with those reported by Wiley et al. (1994). More over, salty for ma tion water is dis - placed away from the bore hole wall by fresh mud-fil trate, thereby reduc ing the effect of salt con cen tra tion on the sim - u lated neu tron log. For the top sand (25 p.u.), the radial length of inva sion is shal low enough for the tool to remain sen si tive to pres ence of gas. In both cases, before and after inva sion, the poros ity is under es ti mated due to pres ence of gas. How ever, because of shal low inva sion, sat u ra tion of water is high near the wellbore and this reduces the effect of gas. Before the onset of inva sion, the result ing appar ent neu tron poros ity is approx i mately 10 p.u., com pared to 15 p.u after inva sion. In this case, com par i son of the neu tron logs sim u lated before and after inva sion indi cates that the effect of gas decreases pri mar ily because of the increase of water sat u ra tion near the bore hole. More over, the dis place ment of salt water in the for ma tion by fresh mud fil trate fur ther reduces the effect of salt con cen tra tion. Fig ure 20 shows the den sity log numer i cally sim u lated with MCNP before and after inva sion for the case of a ver ti - cal well. Mak ing use of the spine-and-rib cal i bra tion dia - gram shown in Fig ure 8 and described by equa tion (3), we cal cu lated the appar ent bulk den sity from the sim u lated tool response. The den sity from the near detec tor was com pared to that of the far detec tor ( cal cu la tion) to assess inva sion effects based on the dif fer ence in radial length of inves ti ga - tion inher ent to each detec tor. The sim u lated log den si ties con sis tently increase after inva sion because of the dis place - ment of gas by mud fil trate near the bore hole wall. As expected, radial length of inva sion is less crit i cal to den sity than to neu tron mea sure ments. Fig ures 21 and 22 show the sim u lated appar ent neu tron poros ity (NPHI) and den sity poros ity (DPHI) logs for the case of a ver ti cal well before and after inva sion, respec - tively. The appar ent den sity poros ity was cal cu lated from the appar ent bulk den sity log assum ing a quartz matrix of den sity equal to 2.65 g/cm 3 and a sin gle fluid of den sity equal to 1.1 g/cm 3 for salty for ma tion water, and 1.0 g/cm 3 for mud fil trate. The equa tion for this cal cu la tion is FIG. 19 Numer i cally sim u lated neu tron poros ity logs (water-filled sand stone poros ity units) for the ver ti cal well model. Sim u lated neu tron poros ity logs are shown for the cases of vir gin and invaded for ma tions. Refer to Fig ure 9 and Table B for a descrip tion of the asso ci ated fluid and for ma tion prop er ties. FIG. 20 Numer i cally sim u lated bulk den sity logs for the ver ti cal well model. Sim u lated bulk den sity logs are shown for the cases of vir gin and invaded for ma tions. The dark solid curve shows the dif fer ence between the far- and near-detec tor den sity val ues. Refer to Fig ure 9 and Table B for a descrip tion of the asso ci ated fluid and formation properties. February 2007 PETROPHYSICS 37

11 Mendoza et al. D b f m m, (4) where m, and f are the matrix and fluid den si ties, respec - tively, in g/cm 3, and b is the bulk den sity in g/cm 3. The sim u lated appar ent neu tron and den sity poros ity logs across the top sand (25 p.u.) exhibit the low neu - tron-high den sity cross over that is char ac ter is tic of gas-sat - u rated for ma tions. Con versely, the two sim u lated logs over - lap across the lower sand (15 p.u.) because in this case both mea sure ments are pri mar ily sen si tive to mud fil trate (deep inva sion, Fig ure 21). The cross over between the two logs, how ever, remains vis i ble when the log sim u la tions are per - formed prior to the onset of inva sion (Fig ure 22). Bulk den sity and appar ent poros ity mea sure ments for the hor i zon tal model were sim u lated at sev eral tool loca tions around the per im e ter of the bore hole wall, includ ing top, right, bot tom, and left. Fig ure 23 describes the sim u lated val - ues of appar ent neu tron poros ity (water-filled sand stone poros ity) both before and after the onset of inva sion in the 25 p.u. top sand. Table 1 sum ma rizes these sim u la tion results in terms of their per cent change with respect to the response at the bot tom loca tion after inva sion. In addi tion, Fig ure 24 describes the sim u lated val ues of den sity poros ity (water-filled sand stone poros ity) for var i ous tool loca tions around the per im e ter of the bore hole. Table 2 sum ma rizes the den sity sim u la tions in terms of their per cent change with respect to the case of the bot tom loca tion after inva sion. TABLE 1 Sum mary of appar ent neu tron poros ity val ues (water-filled sand stone poros ity units) numer i cally sim u lated for a hor i zon tal well with and with out pres ence of mud-fil trate inva sion in the 25 p.u. top sand. The per cent poros ity change was cal cu lated with respect to the read ing sim u lated at the bot tom-hole location after three days of inva sion. NPHI NPHI no inva sion three days of Tool loca tion (p.u.) invasion (p.u.) % of change Top % Right % Bot tom Left % We observe that the sim u lated neu tron and den sity mea - sure ments are sen si tive to pres ence of gas regard less of tool loca tion around the per im e ter of the bore hole. For 25 p.u., the max i mum poros ity dif fer ence before and after inva sion was only approx i mately 4 p.u. Such a small dif fer ence can be explained by anal ogy to the case of a ver ti cal well: as mud fil trate dis places gas near the wellbore, it decreases both gas sat u ra tion and salt con cen tra tion. Con se quently, the sen si tiv ity of the mea sure ments to gas sat u ra tion is dimin ished by the rel a tive increase of water sat u ra tion near the bore hole. The max i mum change of sim u lated neu tron mea sure ments occurs between the top and bot tom loca tions FIG. 21 Numerically simulated bulk density and neutron poros - ity logs (both expressed in water-filled sand stone poros ity units) for the case of a ver ti cal well model sub jected to mud-fil trate inva sion. The time of inva sion is three days. Den sity poros ity was cal cu lated for a sand stone matrix assum ing a sin gle fluid of den sity equal to 1.0 g/cm 3. FIG. 22 Neu tron poros ity and den sity poros ity sim u lated before the onset of inva sion. Den sity poros ity was cal cu lated assum ing a sand stone matrix of den sity equal to 2.65 g/cm 3, and a sin gle fluid of den sity equal to 1.1g/cm PETROPHYSICS February 2007

12 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing TABLE 2 Sum mary of bulk den sity and den sity poros ity (water-filled sand stone poros ity units) val ues sim u lated for a hor i zon tal well with pres ence of mud-fil trate inva sion in the 25 p.u. top sand. The per cent poros ity change was cal cu - lated with respect to the read ing sim u lated at the bot - tom-hole loca tion after three days of inva sion. Bulk Den sity DPHI Tool loca tion (g/cm 3 ) (p.u.) % of change Top % Right % Bot tom Left % of the tool along the per im e ter of the bore hole wall. The sim - u lated tool mea sure ment is 2 p.u. lower at the top loca tion com pared to the sim u la tion at the bot tom loca tion. This result can be explained as due to the rel a tive dif fer ences in the spatial distributions of fluid saturation and salt concentration. The sim u lated value of appar ent neu tron poros ity after the onset of inva sion is 2 p.u. higher than the value obtained for the case of no inva sion at the top tool loca tion, and 4 p.u. higher at the bot tom tool loca tion. In both cases, the appar ent neu tron poros ity is still lower than the true poros ity (25 p.u.) because of the gas effect. The larger change at the bot tom loca tion is due to grav ity seg re ga tion of mud fil trate result ing in deeper radial inva sion at the bot tom of the well. When the tool is located at the top of the bore hole, the sim u lated value of bulk den sity is closer to the one sim u - lated prior to the onset of inva sion (2.082 g/cm 3 ). Slightly higher den sity val ues were obtained for the sim u la tion at the bot tom tool loca tion because at this loca tion the mea - sure ment is only mar gin ally influ enced by pres ence of gas. The sim u lated bulk den sity was g/cm 3, i.e. 1.3% higher than the den sity mea sured at the top loca tion (2.083 g/cm 3 ). Such a dif fer ence causes a 4.8% decrease in the cal - cu lated poros ity assum ing quartz matrix and mud-fil trate as the sin gle fluid type (Fig ure 24). Neu tron mea sure ments are influ enced not only by spa tial vari a tions of fluid sat u ra tion but also by the spa tial dis tri bu tion of salt con cen tra tion. Larger radial length of inves ti ga tion of the neu tron tool com pared to den sity mea sure ments explains the larger neu - tron sen si tiv ity to tool posi tion in a hor i zon tal well. We observe marked dif fer ences in the esti mated neu tron and den sity poros ity val ues due to the posi tion ing of the tool around the per im e ter of the wellbore. Dif fer ences in esti mated poros ity due to tool loca tion dra mat i cally increase for cases above 20 p.u. because of the shal lower radial length of inva sion. Spe cif i cally, dif fer ences in the esti mated neu tron poros ity due to tool loca tion are as high FIG. 23 Numerically simulated values of apparent neutron poros ity (water-filled sand stone poros ity units) for the case of a hor i zon tal well model. The plots describe poros ity val ues sim u - lated at dif fer ent tool loca tions around the per im e ter of the bore - hole wall, both with and with out pres ence of mud-fil trate inva - sion. FIG. 24 Numer i cally sim u lated val ues of den sity poros ity (water-filled sand stone poros ity units) for the case of a hor i zon - tal well model. The curves describe poros ity val ues sim u lated at dif fer ent tool loca tions around the per im e ter of the bore hole wall, both with and with out pres ence of mud-fil trate inva sion. The time of inva sion is three days and the den sity of mud fil trate is 1.0 g/cm 3. February 2007 PETROPHYSICS 39

13 Mendoza et al. as 3 p.u. For the case of den sity mea sure ments, dif fer ences in poros ity due to tool loca tion are as high as 5 p.u. for high val ues of poros ity. The gas effect remains on both neu tron and den sity mea sure ments for all poros ity val ues regard less of tool loca tion. We observe that the vari abil ity of sim u lated neu tron and den sity poros ity val ues around the per im e ter of the wellbore is pri mar ily due to rel a tive dif fer ences in the radial length of inves ti ga tion between the two tools. Fig ure 25 com pares the sim u lated appar ent neu tron and den sity poros ity val ues (water-filled sand stone poros ity units) to the actual poros ity of the sand at sev eral tool loca - tions around the per im e ter of the bore hole wall. Fig ure 26 shows the esti mated bulk den sity val ues and the cor re - spond ing den sity cor rec tion,, for sand poros ity val ues of 10 p.u., 15 p.u., 20 p.u., and 25 p.u. as a func tion of tool loca tion around the per im e ter of the wellbore. No bore hole envi ron men tal effects were included in the sim u la tion; the result ing is due only to inva sion effects on bulk den sity near the wellbore. Neg a tive val ues of den sity cor rec tion as large as g/cm 3 were obtained for the case of 10 p.u. sand. A sig nif i cant den sity cor rec tion was obtained for the cases of 20 p.u., and 25 p.u., espe cially when the tool was posi tioned at the top of the bore hole. We quan ti fied the effect of per me abil ity ani so tropy on the response of neu tron and den sity mea sure ments. Results are shown in Fig ure 27. It can be observed that the neu tron tool is sig nif i cantly more sen si tive than the den sity tool to vari a tions in the spa tial dis tri bu tion of fluid sat u ra tion and salt con cen tra tion due to anisotropic per me abil ity. For the case of neu tron mea sure ments, sim u lated poros ity val ues can be biased by as much as 7 p.u. due to tool loca tion for the case of high val ues of per me abil ity ani so tropy ratio (10). For the same tool loca tion, the sim u lated val ues of neu tron poros ity can depart by as much as 8 p.u. for val ues of per me abil ity ani so tropy ratio between 1 and 10. For the case of den sity mea sure ments, dif fer ences in sim u lated val - ues of poros ity due to tool loca tion were as high as 7 p.u. for the case of a per me abil ity ani so tropy ratio of 10. More over, we observe that for per me abil ity ani so tropy ratios between 1 and 10, the sim u lated den sity poros ity val ues can be biased by as much as 6 p.u. for the same tool loca tion. The sim u lated neu tron poros ity val ues exhibit a clear gas effect for all cases before and after inva sion. Sim i larly, sim u lated val ues of den sity poros ity remain sen si tive to pres ence of gas before the onset of inva sion and after three days of inva - sion regard less of tool loca tion. For val ues of per me abil ity ani so tropy ratio equal to 3, 5, and 10, the sen si tiv ity of den - sity mea sure ments to gas decreases when the den sity tool is located on the right or left sides of the wellbore. Per me abil - ity ani so tropy effects on the sim u lated den sity and neu tron mea sure ments are rel a tively small (less than 3 p.u.) when the tool is posi tioned at the top of the bore hole, for all the exam ined val ues of per me abil ity ani so tropy ratios. To appraise the reli abil ity of stan dard meth ods used to FIG. 25 Numerically simulated values of apparent neutron and den sity poros ity for the case of a hor i zon tal well pen e trat ing a sand unit with poros ity val ues equal to 10 p.u., 15 p.u., 20 p.u., and 25 p.u. The plots describe poros ity val ues sim u lated at dif - fer ent tool loca tions around the per im e ter of the bore hole wall at a time of inva sion of three days. FIG. 26 Esti mated val ues of for ma tion bulk den sity for the case of a hor i zon tal well pen e trat ing a sand unit with poros ity val ues equal to 10 p.u., 15 p.u., 20 p.u., and 25 p.u. The top panel describes bulk den sity val ues sim u lated at dif fer ent tool loca - tions around the per im e ter of the wellbore. The bot tom panel shows the corresponding values of as a func tion of poros ity and tool loca tion. 40 PETROPHYSICS February 2007

14 Monte Carlo Modeling of Nuclear Measurements in Vertical and Horizontal Wells in the Presence of Mud-Filtrate Invasion and Salt Mixing cal cu late poros ity, we cal cu lated an effec tive poros ity from the sim u lated appar ent neu tron and den sity poros ity. Effec - tive poros ity was cal cu lated using the cus tom ary arith me tic and qua dratic means of the sim u lated neu tron and den sity poros i ties, namely, and 1 e N D 2 [ ], (5) e N D, (6) respec tively, where e is effec tive poros ity, N is appar ent neu tron poros ity, and D is appar ent den sity poros ity. Fig ure 28 shows the cal cu lated effec tive poros ity val ues and the cor re spond ing error in per cent poros ity. The max i mum error in the cal cu lated effec tive poros ity is approx i mately 3 p.u. for the case of a 10 p.u. sand, and the min i mum is 0 p.u. for the case of a 15 p.u. sand. These errors remain con sis tent with the cal cu lated val ues of den sity cor rec tion,. SUMMARY AND CONCLUSIONS We intro duced generic com pen sated ther mal neu tron and bulk den sity tools referred to as Long horn nuclear well log - ging tools, or LNLT. These source-sen sor con fig u ra tions pro - vide an open tool tem plate to quan tify the sen si tiv ity of nuclear mea sure ments to a wide array of petrophysical con di - tions. LNLT mea sure ments were tested and com pared against results from com mer cially avail able tools pub lished in the open tech ni cal lit er a ture. Such an exer cise indi cated that the LNLT included the most impor tant ele ments and response fac - tors of com mer cially avail able bore hole nuclear tools. Results from our study indi cate that pres ence of inva sion due to fresh water-base mud on a gas-sat u rated for ma tion and salty con nate water can sig nif i cantly influ ence bore - hole nuclear mea sure ments. For the case of ther mal neu tron tools, spe cif i cally at low val ues of for ma tion poros ity, radial dis place ment of gas by mud fil trate away from the bore hole wall causes the mea sure ment to lose sen si tiv ity to in-situ gas. On the other hand, for the case of high val ues of for ma tion poros ity, hence shal low inva sion, the effect of gas was vis i ble but some what dimin ished by the high val ues of salt con cen tra tion. There fore, it can be con cluded that radial length of inva sion as well as salt con cen tra tion con - struc tively com bine to reduce the sen si tiv ity of bore hole nuclear mea sure ments to pres ence of gas. For the same ver - ti cal well model, it was found that mea sure ments of bulk den sity were less sen si tive to the radial length of inva sion than neu tron mea sure ments because of the tool s rel a tively shal low radial length of inves ti ga tion. The char ac ter is tic FIG. 27 Numerically simulated values of apparent neutron and den sity poros ity (water-filled sand stone poros ity units) for the case of a hor i zon tal well pen e trat ing a gas-sat u rated sand unit of poros ity equal to 25 p.u., and per me abil ity ani so tropy val ues equal to 1, 3, 5, and 10. The plots describe poros ity val ues sim u - lated at dif fer ent tool loca tions around the per im e ter of the wellbore. FIG. 28 Effec tive poros i ties esti mated from the sim u lated appar ent neu tron and den sity poros ity val ues reported in Fig ure 28. Val ues of effec tive poros ity are shown for the cases of arith - me tic and qua dratic means of the appar ent neu tron and den sity poros i ties together with the true poros ity of the sand stone unit pen e trated by a hor i zon tal well. The lower pan els describe the corresponding errors in the calculation of porosity. February 2007 PETROPHYSICS 41

15 Mendoza et al. cross-over between neu tron and den sity poros ity logs across gas-sat u rated sands could only be repro duced for the case of high-poros ity sands. For the case of hor i zon tal wells, our sim u la tion results con firmed that non-axisymmetric spa tial dis tri bu tions of mud-fil trate and salt con cen tra tion can bias the response of bore hole nuclear tools. The max i mum change of neu tron poros ity was observed between the top and bot tom loca - tions of the tool around the per im e ter of the wellbore. Salt con cen tra tion had a sig nif i cant influ ence on the detec tion of gas. Before the onset of inva sion, the neu tron mea sure ment was approx i mately 15 p.u. lower than the 25 p.u. true poros - ity. After inva sion, for the case of the tool at the bot tom loca tion (where the inva sion effect is most evi dent) the neu - tron mea sure ment was 10 p.u. lower than the true poros ity. The sim u lated appar ent neu tron poros ity was lower than the true poros ity for all poros ity cases, thereby con firm ing the sen si tiv ity of the mea sure ments to gas pres ent in the for ma - tion. Larger dif fer ences of neu tron poros ity val ues were observed at higher val ues of for ma tion poros ity (20 p.u. and 25 p.u.). The max i mum dif fer ence in the sim u lated val ues of neu tron poros ity due to tool loca tion, (2.5 p.u.) was observed for the case of 25 p.u., and the min i mum (1 p.u.) was observed for the case of 10 p.u. Sim i larly, vari a tions of 2.9 p.u. and 0 p.u. of bulk den sity poros ity were cal cu lated for the cases of 20 p.u., and 10 p.u., respec tively. Over all, the sim u lated vari a tions of neu tron and den sity mea sure - ments around the per im e ter of the wellbore were rel a tively small for the case of low-poros ity for ma tions. Den sity cor rec tions,, were cal cu lated together with the sim u la tion of den sity mea sure ments. In so doing, we did not include either bore hole envi ron men tal effects or mudcake, and hence den sity cor rec tions were solely due to inva sion. For the case of hor i zon tal wells, the high est den - sity poros ity cor rec tion ( g/cm 3 ) was observed for the case of 10 p.u. The most sig nif i cant change in den sity cor rec tion due to tool posi tion was observed for the case of 20 p.u. sand between the bot tom and top loca tions of the tool. Small pos i tive den sity cor rec tions (less than 0.02 g/cm 3 ) were observed in the 15 p.u. and 20 p.u. sands. We con clude that such small pos i tive cor rec tion is well within the accu racy of the Monte Carlo cal cu la tions. Finally, we quan ti fied the effect of per me abil ity ani so - tropy on the spa tial dis tri bu tions of fluid sat u ra tion and salt con cen tra tion in hor i zon tal wells. Sim u lated neu tron mea - sure ments exhib ited higher sen si tiv ity to inva sion and hence to dif fer ent val ues of per me abil ity ani so tropy ratio than sim u lated den sity mea sure ments. The max i mum dif - fer ence of sim u lated neu tron and den sity poros ity val ues due to tool loca tion around the wellbore was 7 p.u. for the same for ma tion. Vari a tions of 8 p.u. and 6 p.u. were observed for sim u lated neu tron and den sity poros ity val ues, respec tively, for the same tool loca tion and for vari a tions of per me abil ity ani so tropy ratio between 1 and 10. ACKNOWL EDGE MENTS We express our deep est grat i tude to Harry Smith, Dar win Ellis, Joe Chiaramonte, G. Pingjun, Hugh Scott, and D. K. Steinman for their con struc tive edi to rial and tech ni cal com - ments. Fund ing for the work reported in this paper was pro - vided by UT Aus tin s Research Con sor tium on For ma tion Eval u a tion, jointly spon sored by Aramco, Baker Atlas, BP, Brit ish Gas, ConocoPhillips, Chev ron, ENI E&P, ExxonMobil, Halliburton Energy Ser vices, Mar a thon, Mex i can Insti tute for Petro leum, Norsk-Hydro, Occi den tal Petro leum Cor po ra tion, Petrobras, Schlumberger, Shell Inter na tional E&P, Statoil, Total, and Weatherford. REFERENCES Alpak, O. F., Dussan V. E. B., Habashy, T. M., and Torres-Verdín, C., 2003, Numer i cal sim u la tion of mud fil trate inva sion in hor i - zon tal wells and sen si tiv ity anal y sis of array induc tion tools: Petrophysics, vol. 44, no. 6, p Bigelow, E., 1995, Intro duc tion to wire line log anal y sis: West ern Atlas Inter na tional, Inc., Hous ton, Texas. Dussan V. E. B., Ander son, B. 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