Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not .... conductivity logs, it does not change thickness, the sands are thinner and with peaks .... ESCALA : gráfica. Km.20. RESTINGA ALI.
SPE 69541 A Fractal Model for the Vertical Distribution of Sands in the Perales Oil Fields in the Basin of Golfo San Jorge (Argentina) Julio.C.Hlebszevitsch and Eduardo.Breda Repsol-YPF
Copyright 2001, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Buenos Aires, Argentina, 25–28 March 2001. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract The irregularity and discontinuity that the sands present in the vertical sections of the Bajo Barreal Formation lead us to the concept that these sands present a difficult and chaotic distribution. The tuning effects and lack of resolution of the seismic information leads us on a search for new models and methodologies to find a model for the distribution of these sands. The objective of this work is to demonstrate the fractal behavior of the sets of sands, and the need to keep this property in mind for any type of geostatistical analysis, since these types of analysis generally assume a normal distribution of the data population in opposition of the fractal concept. The term fractal was first defined in 1975 by Benoit Mandelbrot to describe the geometry of those objects which have an extremely irregular shape, interrupted and fragmented, and continue being so at any scale chosen for study. The fractal dimension (D) allows us to quantify the degree of irregularity of a geometrical set or of a natural object. An important consequence of this scale exponent is that a population of objects that respond to a fractal distribution will not have average values of its properties, being able to speak only of the distribution of sizes, of which a specific object or phenomenon occurs within a specific interval of time or space. An important concept is that the fractal behavior only occurs within a range of scales in nature, and no natural object is indefinitely fractal. The punctuated behavior of the sedimentation brings, as a consequence, the distribution of the sands presented in a discontinuous form, and for that reason describable from a fractal viewpoint. Based on these observations, there is a need
to characterize the population of sands in the Bajo Barreal Formation as a fractal set. Likewise, these results of the subsurface have been verified with data from outcroppings, having obtained similar results. The fractal vision has contributed to the discrimination of parasequences, the recognition of a distribution model of the sands, and the conclusion that the most important problems in these oil fields are the pathways of migration and trapping of hydrocarbons and not the presence of sands as was previously assumed.
Geological setting The San Jorge basin is located between the Andean range and the Atlantic passive margin. It’s an intracratonic basin with an extensive dominant tectonics, limited with structural basement highs (Fig.1). The west edge of this basin (which is discussed in this paper) is characterized with a compressional system with a general north-south direction. This system comprehends asymmetric anticlines whose vergece changes along the strike (1). The area of study corresponds to Perales oil field. These oil fields are limited with WNW-ESE normal faults. All of these oil fields form part of a great structure associated to a master fault. This master fault generated rollovers, and crestal collapse grabens where the oil fields are (2). Figure(2). The classic statigraphic section is showed in the figure 2 (after Bellosi, 1998 ). But some modifications were done in this scheme for Bajo Barreal Fm as a consequence of the analysis done during this study. The Seccion Tobacea was separated from the Bajo Barreal Fm. And the rest of the formation was divided in three units, which can be recognized with electric logs and seismic sections. The lower unit can be assimilated to Bajo Barreal inferior described in outcrops of the San Bernardo range, while the second and third units (or the last only), could correspond to Laguna Palacios member. The separation of these sedimentary units arise from the following evidences:
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J. HLEBSZEVITSCH AND E. BREDA
1- The filtered conductivity logs have three distinctive zones, where the base line shows abrupt changes. 2- The concentration of sand levels is different in the three units. 3- There are changes in the sonic and density logs jumps in the base line. 4- In the seismic sections we can see that the limits of the units correspond to reactivations of extensive faults. 5- In general, the fluids are different in the units. 6- In the front limb of the Perales anticline there are dykes, which are limited to the top of the first section, then show a change in the reologic behavior of the rocks in the Bajo Barreal Fm. (3) 7- The widespread distribution of these limits. In the figure4 we can see the well YPF.SC.PP.x-4 with the electric logs and the seismic line. From these evidences we define three members within Bajo Barreal Fm in the Perales subsurface. Anticlinal Perales member: corresponds to the lower unit of Bajo Barreal Fm. (we don’t take in account the Seccion Tobacea unit). This member has relatively low values of conductivity logs, it does not change thickness, the sands are thinner and with peaks very shaped in S.P. logs. It has light oils. The seismic reflectors within of this unit are defined but discontinuous. Puesto Perales member: corresponds to the second unit and has intermediate values in the base line in the conductivity logs; it has changes of thickness near the faults. There are more number of sand levels and these have a flattened expression in the S.P. log. In general this member presents viscose oils, and in La Cueva area it has gas or water. The seismic reflectors are poorly defined and discontinuous. La Cueva member: presents the highest values of conductivity. The number of sands levels decreases in relation with Puesto Perales member, and the thickness of this unit changes near the faults. The sand levels have water. The reflectors are well defined and continuous.
Work's hypothesis
SPE 69541
registered, and the same could be associated with seasonal changes, exceptional rains, tectonic or climatic changes, etc. Under normal conditions, the sedimentary processes (erosiondeposition) are in equilibrium and they have low importance or, at least, will be masked with episodes of greatest magnitude. There are examples of both models, a reef is an example of gradualism and a turbidite is an example of punctuated model. In this paper we assume that geological record under study has a punctuated behavior .
Fractals To understand the fractal concept, first we need to remember the typological dimension concept. The typological dimension of a point is 0, of a straight line is 1, and of a plane are 2. In other words this is an Euclidian dimension of the objects. But, these objects may be very irregular; a curve can cover more closely a surface than another curve or a straight line. Thus, the curves have different shapes but maintain the typological dimension 1. The fractal dimension quantify the shape of the curve and in the last example, the curves that cover more closely a surface have a fractal dimension of nearly 2., though the typological dimension is 1. Different distributions and density of cover of objects will have different fractal dimension. In the figure 4 we show a Cantor set, example of fractal distribution (5).
Simple fluvial model which responds to a fractal model In this paper, we suppose that distributions of sand levels in a vertical section are like segments, which represent episodic sedimentation (7). Then, if a well crosses a sand body, this recorded a superposition of depositional events, which laterally will be represented with sand levels more thinly separated with shale lithologies. The different locations will present sands (and equivalents lithologies), in vertical sections, like evidences of different sedimentary events. The thickness and number of sands beds can change but not the spatial relation among these like a Cantor set
Gradualism vs. Punctuated equilibrium
Methodology
One of the greatest debates in the natural science is to consider the geological record gradual or punctuated. The gradual model assumes than the geological processes are continuous while they act. In contrast, the punctuated model assumes that the geological record is discontinuous and responds to process and events that acted and overcame the natural media (4). In this way, we could assume for a fluvial system (for example), that flows greatest to normal (media natural values) could remain
We selected the wells that crossed the Bajo Barreal Fm. totally. For the study of Bajo Barreal Fm. the sand lithologies and equivalents was determined with cutting record, and then codified to discriminated lithologies. To determine the fractal dimension we use the “ box counting method”. For the study of Anticlinal Perales member, it was necessary to use electric logs. In this case the conductivity logs were
SPE 69541
A FRACTAL MODEL FOR THE VERTICAL DISTRIBUTION OF SANDS IN THE PERALES OIL FIELDS IN THE BASIN OF GOLFO SAN JORGE (ARGENTINA)
edited with a “squaring method” using a window of 500 ohm.m. (5) But the variability of these logs made in different years made necessary an alternative method. The same consist in establishing cutoff values defined in relation to the Seccion Tobacea. Thus, the value which discriminated the Seccion Tobacea would be used to discriminate the Bajo Barreal’s members. Defined the Anticlinal Perales member, the sand levels were codified using the S.P. logs and cutting record, and codified, and corroborated the results with Sonics, density and resistivity logs. Finally the box counting method was used to determinate the fractal dimension (8 and 9). In both cases the results are presented in a log –log graphic. The figures 5 to 10 show the results. Nine wells were selected ( YPF.SC.PP.x-2, x-3, x-4, x-5, x-6; YPF.SC.PPN.x-1, YPF.SC.n-35 e YPF.SC.Lcu.e-2 y 4). Additionally, outcrops descriptions of Bajo Barreal Fm. realized in Cañadon Grande, San Bernardo range, were took in account (11). The fractal dimension for the lower member was 0.7145. This value is coherent with the values of Anticlinal Perales in subsurface.
Results The fractal behavior occurs in nature within a range of scales, for the sands of Bajo Barreal Fm. and Anticlinal Perales member this range is up to 30 to 40 meters of thickness. Since McNamara et al. (11), “ the ranges of fractality can be used to decipher characteristic scales and thresholds at which physical processes operate”. This point is very interesting because a sedimentary intervals (parasequences?) of same thickness were defined in others oil fields in the same area (Sanagua and Merletti, verbal communication). The fractal dimension for Bajo Barreal Fm. is between 0.7 and .75; while for Anticlinal Perales member is between 0.6 and 0.7.
Conclusions 1- Three rock-stratigraphic units are differenced in the subsurface of Perales oil fields. These units are natural units, because are easily distinguished, and have seismic and electric characteristics. 2- The Bajo Barreal Fm. has a fractal behavior, and the same for the Anticlinal Perales member 3- The fractal range is between 1 and 40 meters, and these reflect the minimum genetic sedimentary unit. 4- The fractal dimension for Anticlinal Perales is 0,60 to 0,7 for different oil fields in Perales, and between 0.7 and 0.8 for Bajo Barreal Fm.
3
5- A fractal behavior signifies that we cannot use a geostatiscal analysis, which assumes a regular distribution to the sand bodies. 6- A fractal distribution suggests that presence of sands is not a limitation to these oil fields. 7- The presence of sands with oil in low and high structures means that the control is over sands bodies, and not over the formation. 8- The quality of the wells depends of the areal distribution of the sand bodies, and the structural position of the well respect a each sand body, and the relation of these sands to the normal fault which was a migration pathway. 9- Then, the principal control of these reservoirs are the normal faults, which determine in first place the areal development of the sands and then the oil migration.
Acknowledgments The contents of this paper were benefited significantly through careful reviews and comments by J.Homovc, C.Torres Verdin, E. Strelkov and J. Sanagua.
References (1) Figari, E. et al. (1999). Los sistemas petroleros de la cuenca del Golfo San Jorge: síntesis estructural, estratigráfica y geoquímica. IV Congreso de exploración y desarrollo de hidrocarburos. (2) Homovc, J. y Hlebszevitsch, J. ( 1999). Estructuras de colapso extensional en el Cretácico superior de la cuenca del Golfo San Jorge, Yacimiento Los Perales, Provincia de Santa Cruz. XIV Congreso Geológico Argentino. (3) Homovc, J.; Chiaramonti, L. ; Hlebszevitsch, J. y Koremblit M. ( in press) Characterization and formation of fracture arrays in the Chubut Group, San Jorge basin, Argentina. (4) Gould.S.(1994). El pulgar del panda. Reflexiones sobre historia natural y evolución. Crítica. Grupo GrijalboMondadori. Barcelona. (5) Mandelbrot, B. (1987). Los objetos fractals. Tusquets Editores. (6) Doveton,J. (1994). Geologic log analysis using computer methods. AAPG. (7) Malinverno, A. (1997). On the power law size distribution of turbidite beds. Basin Research. Blackwell Science Ltd.
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(8) Middleton,G., Plotnick,R. and Rubin,D. (1995): Nonlinear dynamics and fractals. New techniques for sedimentary data. SEPM Short Courses No.36. (9) Turcotte, D. (1992). Fractals and chaos in geology and geophysics. Cambridge University Press. (10) Sciutto, J. (1978) Perfil complementario Cañadon Grande. Sierra de San Bernardo. Provincia de Chubut. Informe Y.P.F. Inédito. (11) McNamara et al.(1999), An analysis of an artic channel network using a digital elevation model. Geomorphology, 29 (339-353)
SPE 69541
A FRACTAL MODEL FOR THE VERTICAL DISTRIBUTION OF SANDS IN THE PERALES OIL FIELDS IN THE BASIN OF GOLFO SAN JORGE (ARGENTINA)
SPE 69541
5
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Figure 1: Geologic setting of Perales oil fields (after Figari et al.,1999).
Bloque colgante de las fallas distensivas
SSW
625
750
Bloque cabalgante de las fallas inversas
Figure 3.The classic statigraphic section (after Bellosi, 1998).
1125 875
Ubicación de la sección sísmica Intervalo entre dos isocronas 25 msec
1250
1000
N
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YPF.SC.PP.N.x-1
YPF.SC.PP.x-4
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1000
2000
3000 4000
2490000
Figure 2. Time Structure map to the top of Seccion Tobacea, with the location of the wells and the seismic line showed in the figure 3.
Figure 4. Well with the electric logs over a seismic line showing the three units of Bajo Barreal Fm.
NNE
6
J. HLEBSZEVITSCH AND E. BREDA
SPE 69541
ypf.sc.ppn.x-1D= -0,6016
ypf.sc.n-35 D= -0,6582
2.5
2
2
R = 0,9812
R = 0,9973
2 N=1,R=1
1.5 N=2,R=1/3
1 ypf.sc.pp.x-1 D = -0,6461
N=4,R=1/9
0.5
2
R = 0,992 N=8,R=1/27
0 -3
D=logN/logR=log2/log1/3=log4/log1/9=log8/log1/27=0.6039
-2.5
-2
-1.5
-1
-0.5
Figure 8. Logarithmic scale of measuring unit vs. Logarithm of number of units with sands in Anticlinal Perales member in the wells YPF.SC.PP.x-1, YPF.SC.PPN.x-1 e YPF.SC.n-35.
Figure 5. Cantor set, example of fractal model.
pp.x4 D= -0,7816 2
R = 0,9958 ypf.sc.lcu.e-2 D=0,6864 2
1.5
2
pp.x-3 D= -0,7294 1
2
R = 0,9987
1.5
ypf.sc.pp.x-3 D=0,6091
pp.x-2 D= -0,722 0.5
2
2
R = 0,9972
1 ypf.sc.pp.x-5 D= 0,6784
0
0.5
2
R = 0,9904
2.5 2
2.5
R = 0,9975
R = 0,9892
0
-2.5
-2
-1.5
-1
-0.5
0
0 -3
-2.5
-2
-1.5
-1
-0.5
0
Figure 6. Logarithmic scale of measuring unit vs. Logarithm of number of units with sands in Anticlinal Perales member in the wells YPF.SC.LCu.e-2, YPF.SC.PP.x-3 y 5.
Figure 9. Logarithmic scale of measuring unit vs. Logarithm of number of units with sands in Bajo Barreal Fm in the wells YPF.SC.PP.x-4, 2 y 3.
2
ypf.sc.pp.x-6 D= -0,6687 2 ypf.sc.pp.x-4 D= -0,6854 R = 0,9991 2
R = 0,9946
1.5
2.5 2
1
y = -0.7145x + 0.2693 2
R = 0.9956
1.5
0.5
1
ypf.sc.lcu.e-4 D= -0,6468 2
R = 0,9995
0 -2.5
0.5
-2
-1.5
-1
-0.5
0
0 -3
-2.5
-2
-1.5
-1
-0.5
0
Figure 7. Logarithmic scale of measuring unit vs. logarithm of number of units with sands in Anticlinal Perales member in the wells YPF.SC.Lcu.e-4, YPF.SC.PP.x-4 y 6.
Figure 10: Logarithmic scale of measuring unit vs. Logarithm of number of units with sands in the lower member of Bajo Barreal Fm in the outcrops of Cañadón Grande, Sierra de San Bernardo.
