An object-based model for predicting the locations of undiscovered oil and gas resources, western Sverdrup Basin, Canada

Marine and Petroleum Geology 21 (2004) 767–777 www.elsevier.com/locate/marpetgeo

An object-based model for predicting the locations of undiscovered oil and gas resources, western Sverdrup Basin, Canada Zhuoheng Chena,*, Kirk G. Osadetza, Haiyu Gaob, Peter K. Hannigana b

a Geological Survey of Canada, Natural Resources Canada, 3303 33rd Street, NW, Calgary, Alta., Canada T2L 2A7 GeoQuest Merak Software, Schlumberger Calgary Technology Center, 600 322-11 Avenue SW, Calgary, Alta., Canada T2R 0C5

Received 6 December 2002; received in revised form 6 June 2003; accepted 16 June 2003

Abstract A petroleum pool, that has a common petroleum/water contact and a distinctive pressure regime, is a fundamental unit of petroleum accumulation, and can be treated as a natural object. The prediction of the undiscovered petroleum pool locations can be performed employing a method similar to that used to predict sand channels in a clastic reservoir formation. This paper presents an example for the prediction of possible locations of undiscovered petroleum pools in the western Sverdrup Basin, Arctic Canada using an object-based model. This model simultaneously considers the information from the basic geological conditions for the formation of petroleum pools and the spatial correlation among the pools. The simulated results indicate that the object-based model improves predictions of petroleum occurrences by incorporating spatial correlation information into the model and by checking the consistency of the model with geological constraints. Crown Copyright q 2004 Published by Elsevier Ltd. All rights reserved. Keywords: Petroleum resource assessment; Spatial distribution; Undiscovered resources; Stochastic simulation

1. Introduction Management of petroleum resources is important to the internal and external policies of both national governments and multinational petroleum corporations. Petroleum resource assessments play an essential role in the formulation of such policies. Estimates of undiscovered pool sizes, along with their locations, and associated uncertainties are key objectives of petroleum resource assessments. Fulfillment of these objectives provides a geo-scientific framework for economic analysis of supply as a function of price, land-use planning, and environmental impact assessment, as well as providing a framework for exploration portfolio management. Undiscovered pool size estimation has been studied extensively for over three decades (Arps & Robert, 1968; Baker, Gehman, James, & White, 1986; Chen, 1993; Chen & Sinding-Larsen, 1999; Fuller & Wang, 1993; Kaufman, 1986; Kaufman, Balcer, & Kruyt, 1975; Lee & Wang, 1983, 1985; Schuenemeyer & Drew, 1983). In contrast, the prediction of locations of the undiscovered * Corresponding author. Tel.: þ 1-403-292-7115; fax: þ1-403-292-7159. E-mail address: [email protected] (Z. Chen).

accumulations has received less attention (Chen, Osadetz, Gao, Hannigan, & Watson, 2000a). Recent demands for better resource management and improved exploration efficiency have sparked new interest in the methods for the prediction of undiscovered petroleum accumulation locations (Chen et al., 2000a; Chen, Osadetz, & Hannigan, 2001, 2002a; Gao, Chen, Osadetz, Hannigan, & Watson, 2000a; Pan, 1997). Gao et al. (2000a) recently proposed an object-based stochastic model that simulates the likely locations of undiscovered petroleum accumulations by simultaneously considering geoscience information related to pool formation and the spatial correlation among petroleum accumulations. In this model, the stochastic modeling of undiscovered petroleum pool locations is similar to the prediction of sandstone bodies within clastic formations (Berkhout, Chessa, & Martinius, 1996; Clemetsen, Hurst, Knarud, & Omre, 1989; Gao & Galli, 1998; Georgsen, Egeland, Knarud, & Omre, 1994; Georgsen & Omre, 1993; Hegstad, Omre, Tjelmeland, & Tyler, 1994; Holden, Hauge, Skare, & Skorstad, 1998; Tyler, Herriquez, & Svanes, 1994). In this paper, we apply this object-based model to the Sverdrup Basin of Arctic Canada to highlight the regions with

0264-8172/$ - see front matter Crown Copyright q 2004 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.marpetgeo.2003.06.001

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large potential for reserve growth due to future exploration. There are several reasons for choosing the Sverdrup Basin as the application case study for the object-based model. First, the Sverdrup Basin is a Canadian ‘frontier’ basin. Although there is great potential for additional petroleum reserves, unfavorable economic conditions due to remote location, harsh environment, and a lack of infrastructure prohibit exploration and development activities at the present time. However, the growing demand for petroleum, particularly for natural gas, will make Sverdrup Basin one of the frontier basins for future reserve additions in North America. Second, a similar study predicting the locations of undiscovered petroleum resources was conducted by our research group using different techniques (Chen, Osadetz, Embry, Gao, & Hannigan, 2000b). This forms an ideal basis for the comparison of methods, as well as, providing a focus for the discussion of the advantages and drawbacks of each of these methods.

2. The object-based model The object-based petroleum resource model has been discussed in detail by Gao et al. (2000a). A pool, with a common petroleum/water contact and a distinct pressure regime, is the fundamental unit of accumulation that can be regarded as a natural object. In the object-based model, pool accumulation objects are described by their central location, volumetric properties and other geological characteristics. All the properties associated with the object are parameterized as a vector (a marked-point) that describes the pool characteristics. Generally, two types of pools may exist in an exploration play: discovered pools and pools yet to be discovered, which form a pool combination. Suppose that there are N pools in a play, among which n are discovered. Let ui be a markedpoint vector associated with the ith pool ði ¼ 1; 2; …; NÞ: Accordingly, all N pools, or a pool combination, in the play can be parameterized with a matrix variable, u ¼ ðu1 ; u2 ; …; uN Þ: There are infinite pool combinations, u; because of the uncertainties in the N 2 n undiscovered pools. Intuitively, the prediction of undiscovered pools (locations and characteristics) is to find an appropriate pool combination that is consistent with all of the available information; whereas statistically, one seeks to construct a stochastic model that generates undiscovered pools so that the corresponding pool combination is consistent with available observations and interpretations. We know that a pool exists only if all the prerequisite geological conditions for the formation of a petroleum accumulation are present at a specific location. This general knowledge can, in principle, eliminate all locations where the necessary conditions are not met. Unfortunately, available information is often insufficient and it only allows the construction of perception maps, such as geological favorability maps that reflect the interpretation of available data (Chen, Osadetz, Embry, & Hannigan, 2002b; Chen et al., 2000a, 2001). This type of map is only indicative and

its quality relies on the quality and quantity of information available as well as the method by which the map was constructed. Past experience indicates that the aggregate properties of petroleum accumulations, such as the pool size, pool area, average net pay, and porosity may follow a lognormal distribution. The lognormal model has been used widely in conventional resource assessment (Arps & Robert; 1968; Baker et al., 1986; Chen, Sinding-Larsen, & Sammatray, 1994; Davis & Chang, 1989; Kaufman et al., 1975; Lee & Wang, 1985). In addition, studies show that petroleum accumulations may not occur in a random fashion, but in some spatial clustering pattern (Harbaugh, Doveton, & Davis, 1987). For example, a field could be a natural aggregate of several pools with separate water/oil contacts and different pressure regimes, occurring in a geographic area with restricted areal extent. There may be several trends (plays) in a basin and several petroleum-bearing basins in a continent. Petroleum accumulations are individual objects with well-defined boundaries that often exhibit some spatial correlation features in an area (Barton, Scholz, Schutter, & Thomas, 1991; Chen et al., 2001, 2002a; La Pointe, 1995). The distance between any two petroleum accumulations may vary considerably, but still exhibit some spatial characteristics. Individual objects of petroleum accumulation may display a preferable orientation or geometric features controlled by tectonic and depositional processes. These are the spatial features that can be quantified using spatial statistics. There are other geoscience information and data, such as the location of dry wells, and estimates of individual pool sizes from other studies, which can be used to constrain the prediction of undiscovered pool locations. To formulate a stochastic model that incorporates these observations and interpretations, the following generalizations are made: Hypothesis A. The locations of undiscovered petroleum pools are subject to the petroleum-bearing favorability map, fBL ð·Þ: This means that the likely locations of undiscovered oil and gas accumulations must meet all the necessary geological conditions. The estimation of map fBL ð·Þ should consider all the geological, geophysical and exploratory history information in a manner that mimics the decisionmaking process of the deterministic petroleum explorer’s process of prospect identification. In this study, a standardized geological favorability map with values varying from 0 to 1 was used to represent the location distribution function fBL ð·Þ: Hypothesis B. Pool properties are subject to a specific statistical model, fBP ð·Þ: This statistical model can be inferred from either the characteristics of discovered pools/fields or from compiled information from play analogues. Hypothesis C. Within a petroleum field, pools may show clustering characteristics, while paired pools from different fields are assumed to be independent of each other.

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Hypothesis D. The property of anisotropy of clustered pool groups can be described by an average azimuth angle and an average anisotropy ratio. The simulated pool combinations must be consistent with available data. The following constraints are introduced into the model: Constraint A. Predicted geological properties at simulated pool locations should be consistent with mapped geological characteristics at those locations. Constraint B. A simulated pool can be generated only outside the exclusion domain that is determined by dry wells and discovered pools. This means that an undiscovered pool should not coincide with a discovered pool, while a dry well excludes any other result at the same location (which is a conservative approach). Constraint C. Pool distributions in a play occur following some basic constraints, such as the minimum and maximum distances between two pools, and within the range of the minimum and maximum values of pool properties. Constraint D. All the simulated pools are located in the most favorable regions of the play not yet occupied by discovered pools. Constraint E. All the pool sizes are assumed to follow a specific probability distribution within a play. A stochastic model considering all the hypotheses and constraints can be written as a probability density function (Gao et al., 2000a):

pðuÞ / Ig ðulcÞIe ðulcÞIm ðulcÞfB ðuÞfI ðuÞ

ð1Þ

where fB ðuÞ ¼

N Y

fBL ðu1i ÞfBP ðu2i Þ;

i¼1

fI ðuÞ ¼

Y

fIP ðlu1i 2 u1j lÞ;

1#i,j#N

and (as illustrated in Fig. 4) 8 b1 > > > > > > > a1 þ a2 d > > > > > > > 1 > > > < fIP ðdÞ ¼ a3 2 a4 d > > > > > > b2 > > > > > > a 2 a6 d > > > 5 > > : 1

d # b1 b1 , d # b2 b2 , d # b3 b3 , d # b4

ð2Þ

b4 , d # b5 b6 , d # b6 d . b6

The functions Ig ðulcÞ; Ie ðulcÞ and Im ðulcÞ are indicators, corresponding to constraints A, B and C, respectively. Hypotheses A and B are described by function fB ðuÞ: Function fI ðuÞ corresponds to hypotheses C and D. In Eq. (2),

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d is the distance between two objects, b1 and b2 are values between 0 and 1, a1 ¼ ðb2 b1 2 b1 Þ=ðb2 2 b1 Þ; a2 ¼ ð1 2 b1 Þ=ðb2 2 b1 Þ; a3 ¼ ðb4 2 b3 b2 Þ=ðb4 2 b3 Þ; and a4 ; a5 and a6 can be derived the same way. If fIP is constant, the objects tend to exhibit a random distribution. The independence chain of the Hastings algorithm is used to generate an appropriate structure for pool combinations in a play. An objective function, that measures the distance between characteristics of realization and desired constraints, is constructed from both the pool size distribution and an entropy maximum criterion. By maximizing entropy, all simulated undiscovered pools are placed in their most favorable locations. For the mathematical details of the model and the proposed algorithms, the reader is referred to Gao et al. (2000a) and Gao, Osadetz, Chen, Hannigan, and Watson (2000b). A Cþþ program has been developed recently by the Geological Survey of Canada (GSC) for the purpose of predicting undiscovered pool locations. The executable code of the model is publicly available as a GSC Open File (Osadetz, Gao, & Chen, 2003). In some occasions, pools and fields are difficult to distinguish because of insufficient information. In our application, the term accumulation is used where pool and field are difficult to distinguish.

3. Geological framework of the Sverdrup Basin The Sverdrup Basin is a major extensional basin underlying the Queen Elizabeth Islands of the Canadian Arctic Archipelago. The stratigraphic succession, up to about 13,000 m thick, comprises Carboniferous to early Tertiary marine and non-marine strata. Petroleum exploration occurred in the Sverdrup Basin between 1969 and 1986. Over this time period, 119 wells were drilled and 19 petroleum fields, consisting of 8 oil and 25 gas pools, were discovered. Estimated total in place reserves are 294.1 £ 106 m3 oil and 500.3 £ 109 m3 gas (Chen et al., 2000b). The discovered petroleum fields all occur within a broad fairway extending from western Ellef Ringnes Island southwestward to northeastern Melville Island (Fig. 1) and are accumulated in structural traps. Oil and gas accumulations found to date are present mainly in the uppermost Triassic – lower Jurassic porous sandstones of the Heiberg Group beneath thick argillaceous strata of the Jameson Bay Formation (Fig. 2). The regional petroleum geology has been summarized by Embry (1991) and Waylett and Embry (1993). The stratigraphy and structural geology of the area are described by Balkwill (1983), Balkwill, Hopkins, and Wall (1982), Balkwill and Roy (1977), Embry (1991), and Harrison (1995). Internally, the basin is deformed both by diapiric structures developed accompanying the episodic flow of Carboniferous evaporites (Balkwill, 1978) and by Barremian to Cenomanian basaltic volcanism and diabase intrusions (Embry & Osadetz, 1988). In the Eocene, and subsequently,

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Fig. 1. Location of the study area and exploration results in the western Sverdrup Basin, Canadian Arctic Islands. Locations are described using latitude and longitude. Subsequent maps (Figs. 7–9) display the same region using Lambert project (CM: 111.58, base lat.: 498, Lambert lower std. lat.: 498, Lambert higher std. lat.: 778) for computational convenience. Black, discoveries; dark gray, untested structures; hatched, salt diapirs; light gray, drilled structures.

Sverdrup Basin was deformed during the Eurekan orogenies, the structures of which include high amplitude folds and thrust faults (Harrison et al., 1999). The effects of Eurekan orogenesis are intense in northeast Sverdrup Basin and subdued in the southwest (Harrison et al., 1999). The combination of reservoir diagenesis, influenced by magmatism during the early Cretaceous to earliest late Cretaceous rifting phase, and the differences in structural history and style partition the Sverdrup Basin. A region of reduced petroleum potential occurs in eastern Sverdrup Basin, specifically Axel Heiberg and Ellesmere islands, where

the effects of Mesozoic magmatism and Tertiary deformation are the strongest. In eastern Sverdrup Basin, a generally deeper erosional level has removed or breached the most prospective reservoir strata in many structures. A region of higher petroleum prospectivity occurs in western Sverdrup Basin, west of Hassel Sound, where the volume of Cretaceous magmatism and its impact on reservoir diagenesis is reduced. The generally higher erosional level in western Sverdrup Basin preserves Triassic to Lower Cretaceous reservoir formations in a region where structure is dominated by lower amplitude folds. These structures,

Fig. 2. Stratigraphic distribution of discovered oil and gas reserves (right, oil £ 106 m3, unshaded, gas £ 106 m3, o.e., shaded), and generalized stratigraphic chart (left), the western Sverdrup Basin, Canadian Arctic Islands (unshaded: Shale dominated, shaded sand dominated).

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though diverse in their characteristics comprise a single anticlinal petroleum play that was prospected effectively using combinations of surface mapping, and onshore and offshore reflection seismic surveys, the latter being acquired and interpreted under difficult conditions. The Hecla field adjacent to Sabine Peninsula, Melville Island has the strongest stratigraphic entrapment component. Seismically mapped structural closures, and diapiric structures in western Sverdrup Basin are illustrated on Fig. 1. The amplitude and closure area decreases south-westward due to waning Eurekan diastrophism and thinning of the Carboniferous evaporites. A variety of salt structures, some of which rise to, or near the sea floor, occur throughout the study area. These vary from circular diapiric domes to long salt walls (Balkwill, 1978, 1983; Balkwill & Fox, 1982). Salt pillows core many of the anticlinal structures that host petroleum fields. Such structures have protracted and complicated growth histories. Growth may have started as early as latest Paleozoic – earliest Triassic time with episodes of accelerated diapirism in response to both rapid sedimentation and early Tertiary orogeny (Balkwill, 1978, 1983; Balkwill & Fox, 1982). As a result the anticlines on the Ringnes islands are high in amplitude, while those adjacent to Sabine Peninsula are broad with very shallowly dipping limbs. Normal faults cutting many of the fields act alternatively as either seals or migration conduits (Waylett & Embry, 1993). The primary effective source rocks in the Sverdrup Basin are bituminous marine shales in the Middle to Upper Triassic Schei Point and Blaa Mountain groups (Brooks, Embry, Goodarzi, & Stewart, 1992; Powell, 1978). The western Sverdrup Basin encompasses a wide range of source rock maturity from immature on the basin edges to over-mature in the basin center. The main stage of petroleum generation occurred generally between late early Cretaceous and latest Cretaceous time (Brooks et al., 1992; Goodarzi, Brooks, & Embry, 1989; Goodarzi et al., 1993) and most of the strata reached or passed through the maturity window (Brooks et al., 1992; Goodarzi et al., 1993). Secondary migration in this basin is complicated, perhaps involving re-migration of some of the previously trapped petroleum (Waylett & Embry, 1993). Vertical migration pathways and seepage are indicated by stacked pools in a number of structures, while oil staining is common in water-bearing structural closures as well as in gas fields (Gentzis & Goodarzi, 1993). The lack of complete spatial correspondence between the maturity of oils and source rocks indicates that basin uplift, re-migration of pretrapped petroleum, and localized source rock maturity variation due to igneous intrusions and salt structure emplacement are factors responsible for maturity discrepancies between source rocks and oils (Curiale, 1992). This explanation is supported by the fact that measured oil maturity shows a strong correlation with present-day reservoir temperature.

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Heiberg sandstones, a major fluvial-deltaic deposit with thickness varying between over one thousand meters in the basin center and a featheredge on the basin flanks, are the primary reservoirs (Embry, 1983). The reservoir porosity appears to be good along the southern flank of the basin as well as in the Maclean Strait area. The porosity becomes unfavorable in the northeast due to deep burial and diagenesis, and in the northwest due to unfavorable depositional facies. Chen et al. (2002b) studied the spatial characteristics of geological favorability using available geological data. The result of the study, a geological favorability map, was used as a basis for our current geological understanding for petroleum accumulation in this area for the simulation presented here.

4. Simulation There are two sets of parameters that need to be prepared for the simulation: individual pool characteristics and interobjects relationships among the pools. A multivariate lognormal distribution model is used for describing the individual pool properties. In the present version, only pool area and net pay are considered. The inter-object relationships are features characterizing the spatial relationship among the petroleum accumulations and the parameters are determined by using either statistical or geostatistical methods. In additional to these two sets of parameters, field class sizes and number of fields in each class are used as constraints in the simulation. 4.1. Parameters for individual pool characteristics The characteristics of individual pools are primarily controlled by basinal tectonics and diastrophism, depositional process and the availability of petroleum for filling potential accumulations. Structural traps are broader in the southwest where the basin was affected less extensively by the tectonics. Net pay appears to be primarily controlled by depositional environment. Both, pool area and average net pay can be fitted well by a lognormal distribution (Fig. 3a and b). Due to sampling bias in exploration (selective drilling) (Drew, Attanasi, & Schuemeneyer, 1988; Kaufman et al., 1975; Lee & Wang, 1985; Schuenemeyer & Drew, 1983), direct calculation of the lognormal distribution parameters may lead to biased distribution model. Chen et al. (2000b) studied the impacts of exploration sampling on the estimation of lognormal parameters in this basin. The results show that selective exploration drilling had significant impact on the parameter estimation for gas and oil fields. In order to derive unbiased distribution parameters, the multivariate discovery process model (Lee, Osadetz, & Hannigan, 1999) was used. The estimated lognormal parameters for pool area are m ¼ 7:3345 and s ¼ 1:4697; and m ¼ 2:5705 and s ¼ 0:6962 for net pay.

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Fig. 5. Empirical variagram estimated from exploratory drilling results.

Fig. 3. Observed and fitted distribution of closure areas (a) and net pay (b) of the discoveries.

4.2. Inter-object relationships

at location r: If the well at location r is productive, IðrÞ ¼ 1; otherwise, IðrÞ ¼ 0: The indicator, IðrÞ; is used to study the spatial correlation of the exploration drilling outcomes. Fig. 5 is a variogram of the indicator, from which we can make inference on parameters b1 and b2 : It appears that a correlation exists between discovered fields when the distances are less than 30 km. At distance over 30 km, the occurrence of petroleum accumulations appears to be random. It is reasonable to set the distance for the limit of inter-fields correlation at b2 ¼ 30 km: Fig. 6 is a histogram of the distances of paired discoveries. The bi-mode distribution of the inter-field distances may indicate a clustering feature of the petroleum accumulations. In fact, the petroleum accumulations in the eastern portion of the western Sverdrup Basin are trapped in high amplitude anticlines with predominant elongation to the northwest. In contrast, the accumulations in the southwest are trapped in anticlines of lesser amplitude, some with a significant stratigraphic entrapment component

Gao et al. (2000a) proposed a stepwise function (Eq. (2)) to characterize the inter-object relationship (Fig. 4). The determination of the parameters in Eq. (2) is discussed below. Suppose that a play was penetrated by n exploratory wells that represent a statistical sample drawn from that play. In the sample, each well represents a tested object. Let IðrÞ be an indicator denoting the outcome result of an exploratory well

Fig. 4. Object interaction stepwise function.

Fig. 6. Histogram of the distances among the discovered fields.

Z. Chen et al. / Marine and Petroleum Geology 21 (2004) 767–777 Table 1 Field size distribution input as the constraint for simulation Class size

Number of fields

9.4–18.8 18.8– 37.5 37.5– 75.0 75.0– 150.0 150.0– 300.0 300.0– 600.0

29 36 20 10 3 2

Field size class unit is 106 m3 oil equivalent in place.

(i.e. the Hecla Field) without particularly preferable orientation. Based on the statistics (Figs. 5 and 6), 180 km is chosen for the end of random field distance ðb3 Þ: The maximum distance of the fields, b4 ; is set at 190 km representing the greatest possible distance between two fields within a field cluster. The average distance between field clusters b5 is set at 200 km representing the distance between the centers of the clusters. The independent distance between clusters ðb6 Þ is set to be 250 km. The repulsive factor, b1 ; describes the inter-dependencies among fields in each field cluster. The larger the b1 ; the lesser the restriction would be on accepting a minimum distance of fields less than the defined distance b1 : When b1 is 0, there is no accepted combination with two fields having a distance greater than b1 : If b1 is set at 1, it means that the predefined b1 will have no impact on the simulation. The attraction factor, b2 ; is a parameter for interdependencies among field clusters. Setting b2 to 0 means no field combination with a maximum field distance greater than b4 is accepted. In contrast, if b2 is set to 1, b4 ; b5 and b6

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will not be effective. From the statistical/geostatistical study of the data, we found that both the inter-dependencies among the fields and the field clusters are weak. Therefore, b1 and b2 are set at 0.80 and 0.90, respectively. 4.3. Field size constraint Chen et al. (2000b) assessed the petroleum potential of the western Sverdrup Basin. In their assessment, around 100 oil and gas fields in the size range from 8.1 to 115 £ 106 m3 oil equivalent, corresponding to pool area sizes from 919 to 50,018 ha were predicted to exist. The predicted field size distribution from the multivariate lognormal model and 100 fields in the above specified rang were used as constraints in this simulation. The field size class and number of fields in each class for the simulation is listed in Table 1. 4.4. Geological favorability map The geological favorability map (Fig. 7) that was derived from a previous study of the characterization of spatial distribution of undiscovered petroleum resources in the Sverdrup Basin (Chen et al., 2002b) was adopted for this simulation. The details with respect to the method and data used for the construction of the geological favorability map appear in Chen et al. (2002b). 4.5. Simulation Using the parameters and constraints discussed in this section, 200,000 field combinations were simulated

Fig. 7. Overall geological favorability map derived by integrating reservoir quality, source rock quality, preservation condition and structural characteristics. The gray bar at right indicates the overall geological favorability score contour values. Pink, oil/gas field; cyan, tested prospect; green, untested prospect.

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Fig. 8. Simulated probability map using the object-based model. The gray bar at right indicates the posterior probability contour values. Pink, oil/gas field; cyan, tested prospect; green, untested prospect.

and about 1/10 of the simulated combinations were accepted. Each of the accepted combinations of petroleum occurrence represents one of the equal-probable realizations of petroleum accumulations consistent with our data and current understanding of the petroleum geology in this region. The simulation combinations were then converted to a probability map of petroleum occurrence (Fig. 8) to represent the general pattern of possible petroleum occurrences.

5. Discussion and conclusions The object-based model simulates the locations of undiscovered petroleum accumulation using information from geological knowledge as well as the spatial correlation of the pool/field and other geological constraints. The likelihood of petroleum accumulation occurring at a specific location is expressed as occurrence probability, which is derived from hundreds of thousands of equally probable combinations of petroleum accumulations and reflects the uncertainty inherited from the data as well as our understanding of the spatial characteristics of petroleum accumulations. The results of the simulation represents a refinement of our general understanding with respect to the possible locations of undiscovered petroleum accumulations indicated by the geological favorability map. Compared with the geological favorability map (Fig. 7), the size of the most favorable areas (probability value from 0.8 to 1.0) shrinks from 27 to 10% of the simulated probability map (Fig. 8).

The best 10% area (probability ranging from 0.8 to 1.0) on the simulated probability map contains 7 discoveries; whereas on the favorability map, the same areal extent (favorability ranging from 0.89 to 1.0) contains only 4 discoveries. After simulation, the model downgrades the areas where were previously thought most favorable, which are less consistent with other available information, and put these in less favorable categories. Simulated results show that some discoveries in the southeast are not always located in the areas of highest predicted probability. From an information consistency point of view, areas of high probability indicate better consistency with available information as compared to the low probability areas. Therefore, exploration drilling success rate should be greater in higher probability areas, but not necessarily greater with respect to commercial success. Target selection is usually based on a combined consideration of exploration risk and potential rewards. The fact that many small prospects remain untested in the areas with high probability suggests that previous exploration was mainly focused on prospects with moderate risk, but high economic rewards. It is interesting to compare the predicted probability map (Fig. 8) with a posterior probability map (Fig. 9) that is produced by updating a prior probability derived from probability kriging of the exploratory drilling outcomes (discoveries and dry wells), with the geological favorability map using Bayesian conditional probability (Chen et al., 2002b). The two maps used the same information: the geological favorability and the spatial correlation of petroleum occurrences. In constructing the posterior

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Fig. 9. A posterior probability map of petroleum occurrence for the Heiberg Group, western Sverdrup Basin, produced by updating a prior probability derived from exploration drilling results with the geological favorability map in Fig. 7. The gray bar at right indicates the posterior probability contour values. Pink, oil/gas field; cyan, tested prospect; green, untested prospect.

probability map, the spatial correlation information is imbedded in the prior probability map and the geological favorability was subsequently incorporated through Bayesian updating. As thus, the posterior probability map has a dominant influence from past exploratory results. The highest probability was assigned to the area of highest exploratory success and favorable geological condition. If exploratory drilling results represent an unbiased sample and the spatial resolution is sufficient, the posterior probability map would be an unbiased representation of spatial occurrences of petroleum accumulation. However, the data analysis (Chen et al., 2000b) shows that exploratory drilling in this basin was selective and that discovery results represent a statistically biased sample. The prior probability map directly derived from a biased and non-exhaustive drilling data set, ignores small features or areas between tested dry holes where many sizable oil and gas accumulations may exist. As a consequence, the size of areas of high to moderate probability values is smaller on the posterior probability map. The posterior probability maps may under-state the possibility of petroleum occurrence and represent a pessimistic view of petroleum potential. Chen et al. (2002a) proposed methods that calibrate the sampling bias for stochastic modeling. In contrast, the object-based model predicts the spatial occurrence of petroleum accumulations based on the spatial distribution function (the geological favorability map) constrained by the spatial correlation conditions as defined in Eq. (2) as well as the other properties of petroleum accumulations. The predicted petroleum occurrences are

subject to the spatial distribution function. The simulated probability map is, therefore, similar to the geological favorability map. The improvement results from adjusting the spatial occurrences on the favorability map by downgrading the areas of poor consistency with data. Thus, the predictions are more consistent with all the information available. As the determination of parameters for the spatial correlation is separated from the simulation, the bias in the available data can be corrected using different methods. However, the determination of the parameters involves, to some degree, a component of subjectivity. The model, on one hand, has the flexibility to integrate experience gained from past exploration and hard data. On the other hand, the subjectivity may be difficult to express. Compared with pure statistical models (Kaufman & Lee, 1992; Pan, 1997), this object-based model is better constrained by our general understanding of the petroleum geology. The simulated spatial pattern of petroleum occurrences is, in general, consistent with the geological favorability map. The dependency to the geological favorability map indicates that the reliability of the output is sensitive to the quality of the input favorability map. This could be a drawback if the quality of geological favorability is not reliable. From the petroleum occurrence probability map (Fig. 8), it is clear that there are several potential areas for future exploration in the Heiberg Group. Most explicitly, many medium to small-untested prospects remain in the southeast of the basin around Lougheed Island and southern Maclean Strait, where geological conditions are favorable

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and the probability for petroleum occurrence is high. For the western part of the basin, there are also number of untested prospects. The major risks in that area appear to be source rock maturity and reservoir quality (Chen et al., 2002b). Structural traps were the major targets of previous exploration in this region. Study has shown that stratigraphic components play a role in some of the gas fields (e.g. Hecla field). With a renewed exploration effort, we predict that explorers will find petroleum accumulations in stratigraphic traps, particularly along the southeastern frank of the basin, where the geological favorability for petroleum accumulation is high. Another area for future reserve growth is predicted to come from a number of the tested prospects. The exploration maturity is considered very low. The western Sverdrup Basin, about 150,000 km2, has been tested with only 119 wells, many of which are concentrated around existing discoveries. The average seismic grid is about 10 km £ 5 km (Chen et al., 2000a,b). With such a low seismic grid density, the reflection seismic captures only large features of the structures and the higher frequency structural details remain undetected. A study of seismic time and depth conversion indicates that seismic velocity varies considerable in this basin. It is expected that real structure of the basin is much more complicated than the one revealed by the current, now 20-year-old seismic surveys and wells. Considering the fact that many trap fill fractions are generally about 10% of the closure area (Waylett & Embry, 1993), it is possible that with detailed seismic or well control, many of the current single closed structures would reveal multiple closures and additional prospects. Petroleum could be found in those prospects on previously tested regional culminations, even where the existing tests are dry. The object-based stochastic model produces a map indicating the likely locations of petroleum accumulations, which reflects our understanding of the spatial occurrences of petroleum accumulation and is consistent with available information. It provides useful information for strategic decision-making or exploration drilling planning, and sets a consistent basis for prospect ranking in any region of interest.

Acknowledgements This work was supported by Geological Survey of Canada Project #950003 and the Panel for Energy Research and Development, Natural Resources Canada. We thank Dr Dale Issler, Geological Survey of Canada for carefully reading through the manuscript and giving useful suggestion and comments. This paper is benefited from reviews by R. Ehrlich and R. Meneley. Geological Survey of Canada contribution #2003044.

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