2- The F-PHI-m Cross-plot-A New Approach for Detecting Natural Fractures in Complex Reservoir Rokcs by Well Log Analysis

7/29/2019 2- The F-PHI-m Cross-plot-A New Approach for Detecting Natural Fractures in Complex Reservoir Rokcs by Well Lo

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SPWLA NINETEENTH ANNUAL LOGGING SYMPOSIUM, JUNE 1516.1

THE F-p-m CROSS PLOT - A NEW APPROACIH FOR DETECTINGNATURAL FRACTURES IN COMPLEX RESERVOIR ROCKS BY WELLLOG ANALYSZS

Orlando G6mez-River0Petroleos Mexicanos, Mexico City, Mexico

I. ABSTRACTA computer oriented method is presented for detecting the pres--ence of natural fractures in complex reservoir rocks with very low matrixporosity using only conventional well logs. Vugs, complicate still more

the problem of fractured reservoir rocks . The method also allows for -the determination of probable existence of vugs. This novel approach ischaracterized mainly by a new practical use of the formation resistivityfactor, F , together with porosity and all other parameters normally -employed in well log analysis. I t is necessary the use of nuclear poros-ity logs, such as neutron and density gamma -gamma, but it can be ap- -plied even in cases with limited logging program. Minimum well loggingprogram, however, normally requires deep and shallow suitable resist--ivity logs and at least one nuclear porosity log; a gamma-ray curve isdesirable. As a matter of fact, the method is a general approach; therefore, it can be applied also, with advantage, to non fractured, non corn--plex reservoirs, for computing connate water saturation and a permeabil-ity indicator.

The application of this method may permit a better selection of -intervals for testing wells in reservoir rocks with complex porosity sys-tem, which can save considerable rig time during completion operations.The method is illustrated with example wells which include fractured reservoirs from the recently discovered fields of Southeast Mexico.II. INTRODUCTION

Naturally fractured reservoirs have always been a very difficult -task for their study and operation. A recent publication1 shows the importance of the problem, as testified by the 214 references it contains -on literature about this special subject. This world-wide problem has beenapproached in different ways, which vary from core analysis through res-ervoir performance studies; well logging tchniques and well log analysishave been one of the most important ways for a more comprehensive un--derstanding of this problem. Vugs, frequently present together with frac-tures, and lithology changes, complicates more the problem.

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Fracturing may occur in any kind of reservoir rock, but more typ-ically they are present in carbonate rocks. Their characteristics may -range from massive, vuggy and fractured reservoirs to the highly strati--fied reservoirs, depending upon the position of the reservoir rock with re-spect to the original depositional environment and the influence of furtherdiagenetic processes modifying their original textures. Even though the -amount of primary porosity in initial carbonate sediments is higher thanin initial sandstone sediments, the final porosity in carbonate rocks issmaller than in sandstone rocks. In carbonate rocks, primary inter - -granular porosity is more variable than in sands, because of its wide va_riety in grain size and shape; besides, these carbonate rock original poresystems can be modified because of the post-ilepositional diagenetic effects.

There are five main natural processes of porosity and permeabilityalteration that commonly occur in carbonate rocksa. Some of them can -increase these reservoir parameters, some can decrease them and someothers can produce either of these effects. Such processes are: leaching,dolomitization, fracturing, recristalization and cementation.

Leaching, generally improve porosity and enhance permeability. -Dolomitization, on the other hand, may increase the pore size or may -destroy permeability. But, main effect of dolomitization seems to be per-meability increase, as observed in practice 2, by better development of -solution vugs in dolomites; as a consequence of dolomitization, natural fracturing may be produced more easily because of the brittle nature of dolom-ites.Fracturing may become productive very low porosity rocks, whichotherwise would be non productive. Generally, fractures increase porosi -ty very little but notably increases permeability. They are more commonin tectonically active areas, such as the area where the recently discov-ered fields in SE Mexico3 are located.Recristalization, can produce higher porosities in carbonate rocksbut the associated permeability is very low and difficult to determine. Certain cements can destroy porosity even in small amounts.The method here presented is intended to identify complex porous

fractured rocks, such as those briefly outlined above, by using only welllogs. It makes use of a computer program that may throw numericallisted results of SW, (2) m, a and F which can also be displayed ascomputed curves. Nevertheless,-one of the most efficient presentations ofdata for getting the most out of the method is as F-p-m cross-plots, -The different presentation of data serves different purposes. Listed numerical values are used for selecting the intervals for testing the well and --evaluating the importance of the well oil and gas reserve. The F -Q) -m -cross-plot gives an overall view of the well as a prospect for obtaining -

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production from naturally fractured zones, from non fractured zones or ifan artificial fracturing will be necessary for making the well productive ormore

II I. 1

productive.II I. BASIS OF THE METHOD

Theoretical and Practical BackgroundMain theoretical and practical basis of this new approach are con--tained in two previous publications 435, and will be briefly reviewed hereupon. The more general F-9 relationship is considered to be:

F=a/pm . . . (1)On the other hand, the following relationship has been found to exist -between parameters a and m of the above equation4 :

m = A - B log a . . . (2)Various practical applications have been derived from the basic re-lation ( 2 ). The scope of this study is the development of a method fordetecting natural fractures by an approach which basically involves the -use of Eq. ( 2 ). New abundant additional data of a and m, for sandsand carbonate rocks, have verified this relationship and supports its va-lidity; the statistical correlationis combined with Eq. ( 1 ), thelog a= Al?@+ log F

+ B log @

coefficient is above 0.9. When Eq. ( 2 )following expression is obtained 4:. . . (3)

Equations ( 2 ) and ( 3 ) show that a_ and m can be computed by onlyusing well logs; i. e, no assumptions are necessary for these parameters.A method have been established for computing a and m with reasonable -accuracy, even in hydrocarbon bearing formations. 42 5 For making moreeasy in some cases the computation of m, charts of Figs. 1, 2, and 3 weredeveloped, which are solutions of Eqs. ( 2 ) and ( 3 ). These charts are -widely used in this method and have the following characteristics.-Numerical values of constans A and B are as listed below.

Table I . Numerical Values ofConstants A and B* Rock Constant /Woe A BSand 1.8 1.291 Carbonate1 2.03 1 0. 9

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Fig. 1. - Chart for


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As A and B are statistical constants, their value may vary -according to the amount and nature of a and m data available. Never-theless, it has been found in practicethat this variation is just small and

unimportantposes.Fig. 3. - Chart for determing a or m.4-

for practical quantitative and qualitative interpretation pur-

- Porosity (ZJ , s total shale or clay free porosity; therefore, itincludes intergranular primary porosity and any other kind of porositysuch as fractures and vugs, effective or not effective.- Formation factor, F , is effective formation factor; according-ly, isolated, non interconnected porosity will behave, electrically, asnon porous permeable matrix rock.As can be observed in Figs. 1 and 2, every m curve crosses each

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other at a common point. This is a very important and basic information.The relative position of this point in the charts depends upon the valuesof constants A and B. Unique values of F and @ characterizes this -point for each of both charts. The coordinates, F and Q> of these - -crossing points can be obtained through Eqs. ( 2 ) and ( 1 ). By makingm = 0 in Eq. ( 2 ) the value of a at the intersecting point with thea axis in Fig. 3 is obtained; Eq_ ( 1 ) shows that this value also e-quals the formation resistivjty factor, F, at the crossing point of all mcurves of Figs. 1 and 2. The corresponding porosity can be obtained -from Eq. ( 1 ). The numerical values of F and 0 obtained for the -crossing points are as follows:

Table 2. - Common crossing pointsof the m curves.RockType I F Idi ISands I 24.8 1 16.8 1Carbonates I 180 1 7.7 1

For a better understanding of the method, a brief description ofsome complex typical porous systems is necessary; this will be accom-plished in the next section.I I I . 2 Characteristics of Basic Porous Systems.

Figures 4 ( a ), ( b ) and ( c ) are schematic representations of -three carbonate rock basic porous systems. Fig. 4 ( a ) represents a rockwith only primary intergranular very low porosity, saturated with only brine.The normal electrical behaviour of rocks in this porosity range would fol--low the il lustrated trend in the companion figure at the right.Now, let us assume that the same porous system as above exists,but with effective fractures (Fig. 4 b). Even when fractures, generally,do not increase porosity very much, it do increase permeability; of -

course, cases are where fractures constitutes almost the total porosity,* Fractures, are also very efficient channels for electricity flow; accord-ingly, formation resistivity factor for this second porous system wouldbe lower than in case ( a ) and the position of the F, $21 point wouldbe very different; the more intensive and effective the fracturing, thelower the resistivity factor.Finally, a third typical case may exist, as shown in Fig. 4 ( c).The same rock as in the first case but with solution channels and inter-

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connected vugs. Even though leaching does not increases porosity verymuch, permeability is notably increased; as conductivity is also increasedvery much, resistivity factor decreases. Total porosity is higher than -in the two preceding cases and frequently is in the medium to low range;then the positionin the companion

of-the F, p,diagram.

point would be quite different, as indicated

Fig. 4. - Basic porous systems andtheir electrical behaviour.plot The relative position of the F, (B point in the F, (D m cross-is one of the basic interpretation points of departure of the methodhere presented for detecting fractures. There are well logging techni--ques from which reasonable accurate porosity values can be obtained, -but resistivity factor determination still can rely on computations - -through equations. The approach here presented is characterized main-ly by the computation of formation resistivity factors by only well logs;but in practice this has to be performed principally in hydrocarbon bearing intervals, and the more accurate this determination the more dependable the method. The .mechanism to arrive at computed F values wilr

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be described in what follows immediately.IV. DESCRIPTION OF THE METHOD

The method here presented for detecting fractures, essentially -consists in determining the total porosity and the formation resistivity -factor in each analyzed level. Porosity must be obtained from nuclearlogs. Equations for obtaining porosity using neutron-density logs combi--nations are given in the literature, which allow for lithology, shale orclay content and hydrocarbon corrections. 6y 7, 8 For determining the formation resistivity factor, it is necessary to use a porosity independent 1equation. As the method, more frequently, has to be applied to h dro-carbon bearing formations, the following general equation is used: !YRxoF=---- (Rcl )x0Rmf z. . . . (4)(RclJ xo - Rx0 Vcl ,Sxo

in terms of clay parameters; hydrocarbon correction Sxo, is accomplishedby the following set of equations:5&o=-fhr(l-

As may be realized, the computation of the formation resistivity fattor , implies a trial and error procedure in using equations ( 4 ) through (6-j;and the computation of connate water saturation is involved.

a and With the final computed data of F and (D , a value for parametersm is also computed, using Eqs. ( 2 ) and ( 3 ).

plotted Each point, defined by the F, p, computed data as above, is -on charts of figures 1 and 2. The relative position of any pointwith respect to F, $2) and m in the cross-plot will help to determine - -whether or not the analyzed level is within a fractured zone, has predominantely vugular porosity or is a normal reservoir rock with almost --only primary intergranular porosity.

In applying Eqs. ( 4 ) through ( 6 ) in fractured rocks, severalassumptions have to be made.- Oil may be accumulated in primaryvugs. Microfractures, provide the necessarycarbons from the low porosity small blocks

porosity, fractures and -means for draining hydro-to the main fracture system.

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- Mud filtrate flushing occurs in the low primary porosity system -as well as in fractures and effective vugs.- The electrical deep and shallow devices measure, respectively, -average values of R, and Rx0 of the composite porous system of primary -

porosity, vugs and fractures.- Computed water saturations are average values of the total ef-fective porous system.V. INTERPRETATION PRINCIPLES OF THE METHOD

v. 1 Detection of FracturesWyllie and Gregory 9, conducted laboratory experiments in orderto ascertain the effect of increasing the amount of cement on the forma-

tion resistivity factor of initially unconsolidated porous medium. The -result was a rapid increase in resistivity factor, ensuing as porosityis decreased by the presence of cement material. This was true for allthe different artificial porous systems used by the authors, every one ofwhich had its own F-p relationship, i. e. , its particular parameters aand m. A similar cementation process like this is supposed to have =taken place in natural original sediments. As was mentioned in other -section, original porosity of sediments is high and, during the geologictime, several factors can modify it, one of which is the cementation - -process. But these excellent experiments of Wyllie and Gregory do notreveal what will happen when porosity reduction is carried out to the -lowest range of porosity found in practice. This is what will be triedon below.

Figure 5, is a crossplotting of laboratory F, Q , data reportedKeller lo, of modern reef sediments (dots). byFoPE omparison,tory data of basalt rock reported by Keller et F, @ labora -al are also crossplotted inthe same figure (squares). They include unhthified and partially lithified -sediments, leached and recristalized lirnestone and dolomite. In general,the higher porosities and their corresponding lower formation resistivity -factors of the carbonate group belonging to the unlithified and partially lith-ified sediments, are what more resemble the initial F - p characteristics -of primary sediments before any diagenetic and diastrophic process may - -have ocurred. The rest of the sediments have suffered some alteration ei -b-ther by diagenesis and/or moderate diastrophism.

I t can be observed that the carbonate sediment plotted points fol-low the general m curves trend; most of them are located in the crossplot NW region and only just a few in the SW. It ,can also be realized-that the m values for each plotted point are consistently high. All thissediments petrophysical behaviour recall the results of the Wyllie and -Gardner experiments cited at the begining of this section; i. e. , the - -

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more the reduction of initial porosity, the higher the resistivity factor.But all these observable facts deserve some further analysis and will bereviewed with more detail below.Figure 6 is designed to represent the general petrophysical behav-

iour of initially unconsolidated sediments, when subject to increased ce-mentation. Let us assume we have a very high porosity, very high permeability porous carbonate sediment, with an initial resistivity factor and prilrmary porosity of about 2 and 4Ox,respectively. As soon as the ce--menting natural process starts, porosity reduction begins to occur: con-sequently , resistivity factor increases. I f no other geological modifyingfactor is present, this cementation process would continue to the lowestporosity ranges in the highest resistivity factor region, following the --same m curves trend. But this rarely happens in nature as an isolatedprocess, during the geologic time. Compaction, a process necessarily -present, also reduces porosity. Diastrophism, may be present in a -variable degree and is one of the processes which most favorably modifythe characteristics of some rocks. A high porosity, moderatly cementedrock can support more efficiently all kind of deformations without frac-turing, but a very low porosity, very cemented rock is more susceptibleto fracturing. I t seems to exist a porosity critical point for a rock, be-low which chances for fracturing increase. I t is postulated that this -porosity is given by the common intersecting point of all the m curvesin Figs. 1 and 2, as appears in Table 2. Suppose a rock continuouslybeing cemented has reached a low primary porosity value of about 5% -with a resistivity factor around 700, as schematically indicated in Fig. 6.Let us postulate also that this same rock is fractured and porosity re-mains about the same order of magnitud; resistivity factor, however, willdecrease considerably, as shown also in same figure at left, and the -point may change its relative position from SE to SW; the more intensivethe fracturing the more the shifting of the point to the left.

During the cementation process, pore interconnection may be de-stroyed and constitute isolated important porous volume. No matter thenature of their fluid content, these voids will behave, electrically, as -they were non porous material; this means high resistivity factors forthe total pore system; nevertheless, nuclear logs will give total porosity.The combination of highly non interconnected or poorly interconnected -porosities, above the crossing point of the m curves, and high resistivityfactors will locate the F, 9, points in the NE cross-plot area.v* 2 Detection of Probable vugs.

Return now to the cross-plots NW region of Figs. 5 and 6. Whenleaching creates effective vuggy porous systems, permeability is very -high. High permeability often is also a characteristic of reefal systems.Nevertheless, porosity is not necessarily high for these porous models,

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and frequently is in the medium to low range, as mentioned before. -These conditions all together may produce another porous system modelof economic importance of low to very low formation resistivity factor.Representative F, Q, , points of effective vugular conditions will fall inthe cross-plots NW area with high m computed values.v .3 Primary Porosity.

I f only primary porosity exists, the plotted points will fall in theNW and SE areas with moderate to low m values.of m, the higher the permeability. 5 The higher the valueSome points may fall also in the -NE region, when not interconnected primary porosity exists.v .4 Ambiguous Cross -Plot Regions.

As it normally happens in statistical studies, almost always therewill be doubtful F, $?I , points which may belong to one of two cross-plotregions. For example, in the case of fractured systems, some plottedpoints will fall in the limit area of SW and SE regions. Criteria mustbe exerted in these cases in order to interpret the results of computa-tions. Some points in the SE region may be considered as fractured -rock conditions, favorable for production; probably, limiting values arein the range of m = 0.5.

Other important ambiguous cross-plot regions are located in thelimit between the NW and SW areas. The F,p , plotted points, close tothe limiting line, may belong to rocks with petrophysical characteristicsof both contiguous areas; i. e. , vugs and fractures. But this case is nota critical one, because these two conditions are favorable for production.

By following a similar reasoning as above, alike conclusions canbe derived for the NW-NE and NE-SE areas. But these are the less fa-vorable limits between areas, for production.VI . FIELD EXAMPLES

Well 1This case is presented for comparison and reference conditions.Fig. 7 is the F-p -m computer cross-plot of a well drilled in a J urassicGlitic limestone. As can be realized, most of the F,@ plotted pointsfall within the NW area, and the computed m values are within the rangefound in the laboratory for this particular field. Few points are scat --tered in all the remaining areas. Computed values of F are consideredto be moderate. Initial production of this well was about 700 Bls/day.The interpretation of this cross-plot indicates the well production

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is from primary porosity and permeability because the values of the -computed parameters mostly belongs to these particular conditions.Well 2

Fig. 8 is the F-p -m cross -plot of the producing interval of a wellof the new Southeast Mexico Cretaceous area. The reservoir rock is -known to be a low porosity fractured complex carbonate. Unlike the pre-ceding example, almost all the plotted points fall within the SW area, -which confirms the well is producing from a fractured rock. Initial production of this well was 3,500 Bls/day of oil .VII . CONCLUSIONS

A method has been presented for detecting natural fractures incomplex reservoir rocks by well log analysis. First results show that -the method can be applied principally for differentiating potentially pro-ductive from non productive low porosity reservoir rocks. I t can alsobe applied for detecting probable vuggy porosity when this is a predom-inant characteristic.

The application of the method requires the use of porosity nuclear logs and suitable electrical resistivity logs.Numerical values of F, p, SW , a and m, are obtained through acomputer program, which can also be displayed as computed logs. Bya special crossplotting of the F, 8 , computed data, the main probable

characteristics of the porous systems can be predicted; i. e. , whether -fractured, vuggy or with only primary porosity.First results of the application of the method indicate that highly pro-ductive low porosity fractured reservoir rocks are characterized mainlyby relatively low computed formation resistivity factors and negative com-puted values of m. Very low resistivity factors, medium to high porosities,and high positive m computed values, characterize probable vuggy zones.Equations for computing F and Sw, are general expressiones, -used whatsoever the porosity system be; therefore, the validity of com-

putations remains for any case. I f the rock has only primary porosity,the computed values of a and m can be used as permeability indicators.ACKNOWLEDGEMENT

The author would like to express his appreciation to the Pemexs management for permission to present and publish this paper. Appreciation is-also indebted to Mr. Roberto Torres Navarro from the Mexican PetroleumInstitute who directed the necessary computations for the example wells.

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F :(D :SW :sxo :Rt :Rxo :Rw :Rmf :Rcl :Vcl :m :

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List of SymbolsFormation resistivity factorPorosityConnate water saturationMud filtrate water saturationFormation true resistivityFormation true resistivity in the flushed zoneFormation water resistivityMud filtrate resistivityClay resistivityClay fraction in the rockCementation exponentCoefficient of F-p relationStatistical constants of the a-m relationResidual hydrocarbon correction factor

REFERENCES1. - Aguilera, R. ; Van Poolen, H. K. :

ly Fractured Reservoirs.Current Status on the Study of natural

The Log Analyst May-June, 1977.2. - Jordine, D. ; Andrews, D. F. ; Wishart, J. W. ; Young, J. W. :Distributionand Continuity of Carbonate Reservoirs. Jour. Pet. Tech. July, 1977.3. - France, Alvaro:Giant New Trend Balloons SE Mexicos Oil Potential .The Oil & Gas Jour. Sept. 19,1977.

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4. - Gbmez-Rivero, 0. : A Practical Method for Determining Cementation -Exponents and Some Other Parameters as an Aid in Well Log Analy-sis. The Log Analyst, Sept. -Oct. , 1976.5. - Gomez-Rivero, 0.: Some Considerations About the Possible Use ofthe Parameters a and m as a Formation Evaluation Tool Through -Well Logs. SPWLA 18th Annual Logging Symposium, J une 5-8,1977Houston, Texas.6. - Burke, J . A. ; Campbell, R. L. J r. ; Schmidt, A. W. : The L itho-PorosityCrossplot I , The Log Analyst (SPWLA), Nov. -Dec. 1969.7. - Poupon,A. ;Clavier, C. ; Dumanoir, J .; Gaymard, R. ; Misk, A. : LogAnalysis of Sand-Shale Sequences -A Systematic Approach , --J our. Pet. Tech, J uly 1970.8. - Poupon, A. ; Hoyle, W. R. ; Schmidt, A. W. : Log Analysis in For- -mations with Complex Lithologies SPE Paper 2925, 45th SPE AINEFall Meeting, 1970.9. - Wyllie, M. R. J . ; Gregory, A. R. : Formation Factors of UnconsolidatedPorous Media: Influence of Particle Shape and Effect of Cementation.Pet. Trans. AI ME, 1953.10. - Keller, George V. : Electrical Resistivity of Modern Reef Sedimentsfrom Midway Atoll, Hawaii. SPWLA 10th Annual Logging Symposium,May 25-28,1969. Houston, Texas.11. -Keller, G. V. ; Murray, J . C. ; Towle, G. H. : Geophysical Well Logsfrom the Kilauea Geothermal Research Drill Hole. SPWLA Trans. -1974.

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A130UT THE AUTHORORLANDO GOMEZ RIVERO, is presently -at the head of the Reserves General De-partment of Petroleos Mexicanos(PEMEX)at Mexico City, which has the responsi -bility for reserves estimates and well loganalysis. After graduating from the Insti -tuto Politecnico National, Mexico City, witha petroleum engineering degree in 1953, -he has been always working for Pemex; -first in Coatzacoalcos, Veracruz, where hewas in charge of the SOUIh Zone ReservoirEngineering Department from 1957 to 1966.After this latter date he was promoted toMexico City Reservoir Engineering Gener -al Offices. He has taught well logs at theInstituto Polit6cnico National and is the

author of the book: REGISTROS DE POZOS - PARTE I - TEORIA E INTERPRETACION (1975). Also he has authored and coauthored sixteen arti - -cles. He received the 1967 JUAN HEFFERAN medal prize of the Asociacion de Ingenieros Petroleros de Mexico (AIPM) for best article pub-=lished. He is a member of SPE of AIME, SPWLA, AIPM, Colegio de Ingenieros Petroleros de M@xico and Asociaci6n Mexicana de Geologos Petro=leros. His name is listed in Whos Who in the South and Southwest ofU. S. A.

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2- The F-PHI-m Cross-plot-A New Approach for Detecting Natural Fractures in Complex Reservoir Rokcs by Well Log Analysis