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Probabilistic methods in petroleum resource assessment, with some examples using data from the Arabian region

Rao S. Divi

Department of Earth and Environmental Sciences, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Abstract

High risks are inherently entrenched in any petroleum assessment and exploration because of the uncertainties in geological and economic factors related to the hidden resources. These risks can never be eliminated, but can be reduced by using probability methods at different stages of assessment and exploration activities. Probabilistic modeling of the historical discovery trends (discovery process) and of the spatial – temporal relationships between deposit characteristics (size, number) and geology (play analysis) has been accepted as effective methods for evaluating future discoveries, because of their capability of incorporating specific quantitative geological, technological and economic attributes related to exploration. The two major geological uncertainties that play a key role are related to the nature of parent statistical distributions of number and sizes of the fields in a given region of assessment. Statistical distributions of geological parameters can be estimated using Monte Carlo methods, taking care of the correlations, to produce field size distribution in the play or basin. Similarly, distribution of possible number of fields can be estimated incorporating also the drilling parameters. The methodologies are illustrated with examples from different parts of the world, including the Arabian Region.

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Keywords:Petroleum; Assessment; Uncertainty; Probability; Arabian gulf

1. Introduction

Assessment of hidden resources such as oil, gas, minerals, etc., is a daunting task, as it has to primarily deal with the inherent uncertainties related to these resources. Although the uncertainties arise from innu- merable sources, the most obvious ones include (1) imprecisely understood geological processes that gen- erate, transport and trap the resources; (2) insufficient geological (in the broadest sense, including geochem- ical, geophysical and other) data for the region under assessment; and (3) unavailable or incomplete existing data on the resources because of proprietary

reasons. Added to these are the uncertainties caused by the changing economic and technological issues related to the exploration, exploitation and marketing of the resources. Regardless, assessments have been needed and conducted by a variety of organizations (global, national, provincial, industrial) and for wide ranging purposes (strategic, optimal usage, conserva- tion, planning, exploration). As a result of the resource assessment endeavor since the 1950s, the technical issues related to the assessment process are better identified and understood, and the methodologies have been continuously refined and improved (Arps and Roberts, 1958; Kaufman, 1965; Roy, 1975;

Lee and Wang, 1982; Schuenemeyer and Drew, 1983, 1999; Masters, 1984; Attanasi and Drew, 1985; Davis

0920-4105/$ - see front matterD2004 Published by Elsevier B.V.

doi:10.1016/j.petrol.2003.12.003

E-mail address:[email protected] (R.S. Divi).

www.elsevier.com/locate/petrol

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and Chang, 1989; Drew, 1990, 1997; Schuenemeyer, 2002). It must be pointed out at this juncture that there is no single (or best) method that exists (or will exist ever) to meet all the situations arising from various combinations of the issues pointed out above. Essen- tially, all assessment methodologies fall within the spectrum of procedures, that at one end are mostly subjective and at the other end mostly objective; the justification or need for this subjectivity or objectivity is dictated by, among others, data availability situation in that particular case of assessment.

The objective of this paper is to present the most common methodologies that are being used at present, and give some examples of their usage with the data from the Arabian Gulf. The common methodologies may be grouped under the following five categories:

(1) Direct Assessment methods, (2) Volumetric Yield methods, (3) Play Analysis methods, and (4) Discov- ery Process methods.

2. Direct assessment methods

Essential to these methods is a well defined and comprehensive geological model that relates the presence of the required geological features in an area to the potential of resource existence in that area. As such, experts familiar with the model and the geology of the area play a fundamental role in the assessment.

The assessed resource may be in the form of a point (single number) estimate, or appropriately in view of the fundamental uncertainties inherent, in the form of a range of values, each with a differing degree of certainty (subjective probability). Among the earliest attempts using such methods, assessments for the Canadian lands(EMR, 1973)and for the USA(Miller et al., 1975) are noteworthy. More recent and improved methodology used by the U.S. Geological Survey is given byGautier et al. (1995), and a further revised version (termed ‘Seventh Approximation’) by Schmoker and Klett (2000). The methodology defines and utilizes the concept of total petroleum system in the region under consideration; a total petroleum system consists of all genetically related petroleum generated by a pod or closely related pods of mature source rocks, with similarities of the fluids of the accumulations. A petroleum system may be treated as a single assessment unit or subdivided into a number

of assessment units each with homogenous geological characters. Probabilities for at least one undiscovered field of minimum size or greater are assigned to the assessment unit.

The Arabian Gulf region contains approximately two-thirds of the world’s ultimately recoverable oil (Al Sharhan and Nairn, 1997). Jurassic carbonates produce most of the oil, although giant fields occur in the petroleum systems of Cretaceous, Paleozoic and Infra-Cambrian ages. The richness in petroleum is attributed to extensive depositional platform and sub- sequent development of intra-platform basins, extensive source-rock deposition, within these basins, multiple tectonic episodes producing large gentle structural closures coincident with peak oil generation and migration, and efficient and regionally extensive evaporate seals. Major total petroleum systems and numerous assessment units can be delineated in the region.

Two of the major petroleum provinces in the region are the Rub Al-Khali Basin and the Zagros Fold Belt.

Figs. 1 and 2, constructed using the data and results

Fig. 1. Cumulative probability distribution of undiscovered volume of oil (BBO, billions of barrels of oil) for Rub Al-Khali basin (A) and for Zagros Fold Belt (B) areas.

R.S. Divi / Journal of Petroleum Science and Engineering 42 (2004) 95–106 96

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fromUSGS (2000)study, indicates cumulative probability distributions of undiscovered oil resources, composed of at least one field equal to or greater than the minimum field size (MFS). Comparison of the distributions inFig. 1A and Bsuggests higher probabilities (especially in the modal regions) for the Zagros resources. For example, the probability for resources being at least as large as 40 BBO for the Zagros is nearly twice (0.6) that (0.3) for the Rub Al- Khali Basin. InFig. 2, the undiscovered resources are aggregated for each country (Kuwait, Iran, Saudi Arabia and Iraq), and letters L, O and T indicate onshore, offshore and total resources, respectively. In the case of Saudi Arabia and Iran, onshore resources form a large proportion of the total potential resources (Fig. 2).

3. Volumetric yield methods

In frontier areas, assessments can be made uti- lizing hydrocarbon occurrence patterns and yields in

analog areas with similar overall geologic character, tectonic framework, etc. The amounts of discovered hydrocarbons per unit volume of rock in well explored areas are applied to volumes of rocks in less explored areas with similar geological setting, at a basin or other scales of similarity (Miller, 1976). The assessment requires an understanding of the most likely field-size distribution for a basin type, and a systematic variation between the distribution and basin type (according to its morphology and tectonic genesis) is demonstrated for the basins in US (Nehring, 1981). On a global scale also, Klemme (1975, 1984) outlined the differences in 65 of the world’s basins and pointed out to a fundamental relation between the percent-rank of the five largest fields (accounting for 40 – 50% of the world’s reserves) to the basin’s morphology, size and its sedimentary fill. The 65 basins are tecton- ically classified into four main types: (I) Craton Interior Basins, (II) Continental Multi-cycle Basins, (III) Continental Rifted Basins and (IV) Delta Basins; basins II and III are further subdivided into

Fig. 2. Cumulative probability distribution of undiscovered volume of oil (BBO, billions of barrels of oil) for Kuwait (A), Iran (B), Saudi Arabia (C) and Iraq (D).

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the subtypes A, B and C. The hydrocarbon habitat in these basins vary between ‘concentrated’ (type III B) and ‘dispersed’ (type IV). For example, Mature Rifted Convergent Margin Basins (type III B) contain an average of 75% of the basin’s total reserves in their five largest fields, whereas, mod- erately mature Delta Basins (type IV) with sedimentary traps contain only 10% (Fig. 3). The average ultimate resources found in the average size of each of the five largest fields in the basin types are shown inFig. 4. For the Middle East, the field sizes in the five largest fields are shown in Fig. 5.

This advantage of this method is that it is based on direct analogy with known basin which provides a yield factor to be applied to the target basin. However, the range of variation of yield factors is large (0.01 – 2.0 MMBO per cubic mile), and as such, the selection of appropriate factor is very critical in the assessment process.

4. Play analysis methods

Play analysis methods(Houghton et al., 1993)are used in assessing semi-mature areas where some hydrocarbons have already been discovered and a reasonably good geological data base exists. An

exploration play is an area consisting of a group of prospects and/or discovered pools having common geological characteristics such as source rocks, trap- ping mechanisms, structural history, etc., that may be considered to contain undiscovered hydrocarbons.

The U.S. Geological Survey uses five play attributes—source rock, timing, migration, reservoir and trap—that are believed to control the occurrence of oil and gas in a play. Assessment of an individual play is composed of three main tasks—determination of the conditional pool size distribution for the play, estimation of the possible number of pools in the play, and quantification of the exploration risk associated with the play.

4.1. Pool size distribution

The distribution of possible sizes of pools that exist in the exploration play is conditional (conditional probability) upon the existence (marginal probability) of the hydrocarbons in the play. There are several ways of constructing the conditional pool size distribution. One common way, when the play under consideration has limited (or no) data on the sizes of discovered pools, is by using a deterministic equation that relates the expected size to relevant aspect of the geological parameters that are believed to control the size. For example,Davis (1992)applied the following

Fig. 3. Relation between basin size and percent of oil in the basin for the five largest fields. (A) Craton/Accreted Margin, (B) Rifted Convergent Margin, (C) Deltas (structured), (D) Deltas (sedimentary) (modified afterKlemme, 1984).

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equation to estimate the size for a prospect in Lansing- Kansas City field model:

BBL¼ ðAÞ ðTÞ ðUÞ ðSOÞ ðRFÞ ð7758:4Þ where, BBL is size in barrels, (A) is field area, (T) is thickness in the saturated interval in feet, (U) is porosity in percent, (SO) is oil saturation in percent, (RF) is recovery factor, and the constant 0.7758.4 is used for calibration. Using different distribution models (normal, truncated normal, lognormal) for the above geological variables, ultimate production volumes are estimated by Monte Carlo simulations.

These volumes closely compare with those estimated from the existing fields in the Lansing-Kansas City prospect(Davis, 1992).

However, the best way of defining the field size distribution is by modeling the frequency distribution of the sizes of the existing pools in the play. This is feasible only when the sample size of pool sizes is sufficient enough, so that the shape of the frequency distribution can be taken to ‘mimic’ at least ‘some part’ of the shape of the parent population. Drew (1997)extensively discusses the critical issues related to the empirical frequency distributions and problems faced in defining the shape of the parent populations.

In particular, left truncation in the empirical distribution related to the economics of oil exploration (Fig.

6), left shifting of the mode of the distribution due to discovery process (Fig. 7) and shifts in field size classes due to field growth (Table 1,Fig. 8).

The Middle East contains a disproportionately high percentage of giant and super-giant classes of field sizes. A plot of the logarithmically transformed sizes (MM bbl) of the 98 such fields in the Middle East (Fig. 9A) still displays positive skewness (departure from lognormal), and among others, one reason for this may be due to the arbitrary definition of size classes into tiny, very small, small, medium, large, major, giant super giant and mega giant(Ivanhoe and Leckie, 1993). When these 98 field are disaggregated

Fig. 5. Sizes of the five largest fields in the Middle East-Ghwar, Burgan, Safaniya-Khafji, N.W. Dome and Rumaila. The fields straddle the ‘‘normal’’ trend line, except for the Burgan field which is above the line and in the ‘‘enriched’’ part of the figure (see text for explanation).

Fig. 4. Percentage of average ultimate resources (BOE) found in average size of each of the five largest fields for different basin types. (A) Complex Carton Margin, (B) Rifted Convergent Margin, (C) Cratonic Interior, (D) Sedimentary Deltas (modified after Klemme, 1984).

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and plotted separately for the two major petroleum provinces in the Middle East, the Arabian Petroleum Province(Fig. 9B)and the Zagros Petroleum Province

(Fig. 9C), the skewness is reduced and the shapes become a bit closer that of lognormal. On the other hand, when all the 400 fields in the Arabian Gulf

Fig. 6. Left shifting of field size distributionf(S0) tof(S1) and of cost truncation pointS0toS1on the parent population, due to price rise.(Drew, 1997).

Fig. 7. Left shifting of field size distribution for Frio Strandplain play from 1959 to 1985.(Schuenemeyer and Drew, 1991).

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Basin are taken together, their distribution is nearly lognormal (Christian, 1997;Fig. 10).

4.2. Estimation of number of pools

In the play analysis, the number of fields that are yet to be discovered is estimated by extrapolating the cumulative curve for the number of fields that have already been discovered through different time peri- ods in the past. Underlying in this model is the assumption that the ‘conditions’ (economic, technological, social, etc.) under which the discoveries are made are temporally stable (constant), an assumption

that is not realistic. More appropriately, instead of using time units, the number is related to either to the area explored (Drew et al., 1980; Fig. 11A), or number of wild-cat holes drilled (Schuenemeyer and Drew, 1984; Fig. 11B), or to the total drill-hole footage. Regardless, the resulting curve cannot be taken to strictly represent the parent population at any one point in time, as it biased because of strong size-related influence; larger fields are discovered earlier than the smaller ones (Schuenemeyer and Drew, 1999;Fig. 11C).

4.3. Exploration risk

Although many aspects (economic, necessary minimum size of field, etc.) are of concern in the exploration program, the most important has to be the risk of ‘‘dry-hole’’ or in other words, not hitting (discovering) any oil pool in the exploration. One way to assess this dry-hole risk is to use past success-ratio in a reasonably well explored play, or use an analogy from other similar area. Another common way is to subjectively attach a weight (or probability) value, by the expert geologists familiar with the play, to each of the critical geological parameters that should neces- sarily be present for oil occurrence; the values reflect

Table 1

Disposition of the 146 fields that resided in Size Class 11 at least for 1 year during the period 1975 – 1988(Drew, 1997)

Disposition No. of Fields

Migrated

Growing 49

Shrinking 7

Static 50

Oscillating 18

Mortality

In Field Size 11 10

Not in Field Size 11 6

In Field Size 11 in 1988 84

Fig. 8. Actual and predicted discovery rate profiles for fields in size-class 14 in Gulf of Mexico area. (A, B) 1980 (solid line is for data; dashed line is for forecast; (A) without growth; (B) with growth); (C) 1988 data (simplified fromSchuenemeyer and Drew, 1991).

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the degree of belief in their presence in the play. Often these probability values are ‘combined’ (multiplied) to determine the joint probability for the presence of all the variables, although this multiplication assumes the unrealistic assumption of statistical independency between the geological parameters.

Two of the most objective ways of determining the dry-hole probabilities are by applying multivariate (discriminant) and Bayesian statistical methods relat- ing the spatial distributions (from maps) of the oil fields to those of the geological variables in the play.

Fig. 10. Size distribution (wiggly line) of 400 oil fields in the Middle East on logarithmic probability paper. Fitted lognormal distributions (straight lines) for the Middle East (A), North Africa (B) and U.S.A. (C) are also shown.(Christian, 1997).

Fig. 9. Frequency distributions of sizes of giant and super giant fields in the Middle East. (A) Middle East; (B) Arabian Province;

(C) Zagros Province.

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Fig. 11. (A) Cumulative number of discoveries in the Denver Basin versus area exhausted for fields of size-class 7(Drew et al., 1980); (B) Cumulative number of discoveries in the Permian Basin versus number of exploratory wells for size-class 6(Root and Drew, 1984); (C) Discovery profiles for field size-class 7, 11 and 14 in 0 – 5000 ft-depth interval of Permian Basin (Schuenemeyer and Drew, 1999).

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Harbaugh and Wendebourg (1993) illustrate how the discriminant scores can be converted into outcome probabilities for ‘successful’ drill hole (oil-bearing) as follows:

p(PjS) =p(S,P)/p(S), where,

p(PjS) = conditional probability of producer P, given knowledge of scoreS,

p(S,P) = joint probability (or frequency) of a producerPand scoreS, and

p(S) = marginal probability (or frequency) of score S.

5. Discovery process methods

Discovery Process Methods are commonly used in well explored areas where data for past exploration performance in terms of sequence of discovered fields, their characteristics (number of pools, sizes, production, reserves, etc.), and other related geologi-

cal information (number of holes and total footage drilled, areas covered, etc.) are available for sufficient time period in the past. Defining and modeling trends in these historical data and extrapolating these trends into the future to estimate some aspect of the remain- ing resources form the core in these methods. Simple decline rate models (e.g. exponential, hyperbolic) are sometimes used to describe exploration success and total resources(Dolton et al., 1981).Arps and Roberts (1958) and Drew et al. (1982) used more refined methods to estimate the number of fields and quanti- ties of resources to be discovered in the Denver Basin and the Permian Basin. Since these early studies, discovery process model has been extensively used, and an excellent review can be found inDrew (1997).

It is now well established that field size, merger and growth have significant influence on the discovery process (Drew, 1997; Fig. 12). The effect of field merger is that the discovery rate decreases for smaller fields and increases for larger fields with time. On the other hand, the effect of field size is such that larger

Fig. 12. Schematic illustration of the relation between discovery rates and field size, merging and growth rate; middle graphs are for merging and bottom graphs are for growth(Drew, 1997).

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fields are discovered earlier and the smaller ones later, and this increases the discovery rate for the smaller fields and decreases for the larger fields.

One advantage of the discovery process approach is that it allows estimates to be generated for various stages of exploration process, and the possibility of dynamic refinement of the earlier defined model.

However, identification and definition of the underlying quantitative model (curve) reflecting the discovery process are extremely difficult, because of the dynamic changes in the discovery process due to economics, technology, politics, etc. Estimated resources are extremely sensitive to the nature of the curve used (e.g.

logistic, Gompertz, exponential, hyperbolic, Pareto, log-geometric, etc.) used, and as such, there exist large differences between the resources estimated by different models. Attanasi and Carpentier (2002) demonstrate how significant is the difference in the estimated resources using variants of Pareto and lognormal models.

6. Concluding remarks

Petroleum resource assessment is a multi-faceted endeavor, and at every stage of the assessment, choices have to be made to achieve coherency in the whole process of assessment. The Inherent underlying uncertainty in the process and product of the assessment needs to be studied, modeled and estimated.

Probability (objective, subjective) methods are pref- erable to handle this uncertainty. The assessment methodologies range from one that is based entirely on geological reasoning (with few or no statistical procedures) to the other that is strictly statistical (with little or no consideration/input of geological relationships), or some form of a combination of these two end member approaches. The choice depends on the objectives (particularly, the purpose and usage) of the assessment, timeframe and data availability.

TheUSGS (2000) world petroleum assessment is one coherent methodology with explicit objectives, and tractable procedures of operation at every stage of the assessment towards achieving those objectives.

Since this assessment is at a global scale, and as such needs a generalized approach, it is fundamentally a geology-based assessment, although the final product derived utilizes some degree of probability (subjec-

tive) modeling. At a smaller scale (play analysis), more critical issues of parent population distributions of field sizes and numbers, and the dynamic changes of their sample frequency distributions due to changing economic, technological and other (field growth), can be evaluated and modeled following the methods of Schuenemeyer and Drew (1999), Attanasi and Carpentier (2002), and others. On the other hand, in frontier areas where existing resource data is sparse or none, expert judgment method following the framework ofSchuenemeyer (2002)is appropriate.

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