Probabilistic model better defines development well risks

Marc R. Connolly
Conoco Inc.
Houston

• Nomenclature Table [7311 bytes]

As opposed to traditional deterministic methods, probabilistic analysis gives decision-makers ranges of outcomes with associated probabilities of occurrence.

When building a diversified investment portfolio, this additional insight to uncertainty can provide a better comparison and ranking of projects competing for limited capital funds.

Analysis

This article analyzes the drilling of a hypothetical development well with actual field data (such as stabilized initial rates, production declines, and gas/oil ratios) to calculate probabilistic reserves, and production flow streams.

The analysis is independent of distribution type. The data were not forced into presupposed distributions, such as normal or lognormal, ignoring variability of individual reservoirs, but allowed to arrange themselves according to their natural distributions.

It is important to accurately represent production data by their natural distributions because these data often have the greatest impact on a drilling project's net present value and cash flow.

Analog operating data were included to build distributions for capital and operating costs. Economics from the Monte Carlo simulation include probabilistic production flow streams and cost distributions.

Results include single parameter distributions (reserves, net present value, and profitability index) and time function distributions (annual production and net cash flow).

Development well

The hypothetical development well is proposed for a Permian basin oil field. The operator has a 100% working interest and 87.5% net revenue interest in the well. First oil and associated gas production is expected in May of next year. The well will be drilled to a depth of 5,000 ft.

The reservoir is composed of mixed carbonates (limestone and dolomite) having variable porosity and permeability. The field is currently developed on 40-acre spacing with 57 wells. The gross pay interval is easily correlated across the field, but net pay development is sporadic and cannot be correlated between wells.

The trapping mechanism is stratigraphic with no apparent structural component. Solution gas is the predominant drive mechanism, but water influx controlled by a complex fracture system can be locally significant.

The proposed well extends into an area surrounded by producing wells. Reservoir and geologic data indicate this location will access new reserves. Although the planned well is expected to be productive, rates and volumes of oil and gas production are uncertain.

A probabilistic model for the proposed well was built by linking both production decline and economic spreadsheets to commercially available Monte Carlo simulation software. Historical production and cost data were loaded into the spreadsheets.

Input distributions for initial producing rates, decline rates, gas/oil ratios, capital expenditures, and operating costs were generated from the analog data by the Monte Carlo simulator. The simulator then randomly selected values from the input distributions taking variable dependencies into account, sequentially recalculated all spreadsheets using the random selections, compiled results, and built output distributions for reserves, production and cash flow streams, and other economic indicators in both graphical and tabular formats.

Flow performance

Initial producing and decline rate data crudely approximate normal and lognormal distributions, respectively, but gas/oil ratio data appear uniform to random (Fig. 1 [49401 bytes]).

A lack of well-defined distributions was not a factor in this analysis because the production model was calculated independently of distribution type. Data were allowed to assume their naturally occurring distributions. This resulted in a production forecast that best represented the actual well data.

Regression analysis indicated a positive dependency between the stabilized initial producing and decline rates (Fig. 2 [10848 bytes]). A correlation coefficient of +0.89 was calculated from the data.

This dependency was built into the model by using the correlation coefficient and special sampling functions available in the Monte Carlo simulation software. Further regression analysis indicated no other significant input variable dependencies.

Capital expenditures

The proposed well is expected to encounter a shallow salt section followed by an interval of sloughing shales. Three drilling scenarios are typical for wells in this field:

1. High cost-Some wells had hole problems through both the salt and shale sections. These required an additional liner hung across the shale section .

2. Most likely cost-Most wells in the field were completed with one casing string set through the salt section and a production string run to total depth.

3. Low cost-A few wells were drilled open hole to total depth with no problems. These required only one casing string.

Uncertainty in capital expenditures (Capex) is directly related to potential drilling problems. Although statistical methods similar to the reserves and flow stream calculations could have been employed, a Capex triangular distribution was used assuming a 40/60 split between tangible and intangible drilling costs, respectively.

This simplification was done because sensitivity analysis indicated Capex has a minor impact on the project's net present value. The Capex distribution defined by P10, mode, and P90 values was based on the three possible drilling scenarios and assumed 40% tangible and 60% intangible Capex, as follows:

• High cost (P10) = $950,000

• Most likely cost (mode) = $630,000

• Low cost (P90) = $500,000

Operating costs

Lifting and water disposal costs are major components of operating costs (Opex). The 57 wells in the field range from water-free completions to wells producing over 100 bw/d. Cumulative production-vs.-water/oil ratio data indicated no correlation from one well to another.

Water production is sporadic across the field and cannot be predicted with confidence for the proposed location.

As with Capex, Opex also has a minor impact on the project's net present value. Therefore, Opex was defined with a triangular distribution with P10, mode, and P90 annual cost per well based on historical data from offset wells as follows:

• High water production (P10) = $20,000

• Most likely water production (mode) = $16,000

• Low water production (P90) = $12,000.

Range of outcomes

The Monte Carlo simulator iterated the probabilistic production and economic model 1,000 times using the above input distributions along with the following assumptions:

• Production decline for the proposed well is expected to be exponential based on data from offset wells.

• Oil flow streams were projected to an economic limit of 5 bo/d as determined by cost analysis.

• Associated gas reserves and flow streams were calculated from the gas/oil ratio distribution.

• Oil and gas prices were held fixed at $17.50/bbl and $1.80/Mcf for 3 years, then escalated at an annual rate of 3%. This assumes projects being ranked for limited capital resources are evaluated and compared with the same price forecasts.

• Opex was escalated annually by 3% after the first year of production.

• Production tax is 7.68% of oil and gas revenues; the corporate tax rate is 37%.

• End of year discounting was used with a discount rate of 8%.

• The effective month for the analysis is May of next year (anticipated first production).

Resulting output distributions (Figs. 3 [32069 bytes], 4 [20027 bytes], 5 [27441 bytes], 6 [15202 bytes]) display ranges of outcomes for net reserves and annual production, net present value, profitability index, and annual after tax net cash flow.

No specific distribution types were assumed for the results. Instead, data were arranged according to their naturally occurring distributions, thereby providing ranges of outcomes with associated probabilities that best represent the output data.

Results

Table 1 summarizes the results of the hypothetical Permian basin development well using single probability values obtained from the Monte Carlo production and economic simulation.

The results suggest that this project will yield a P50 (median) net present value of $485,000 with a 1.7 profitability index.

Cumulative probability distributions quantify the chance of possible outcomes. For instance, there is a 10% chance that the actual net present value will equal or exceed $810,000, while there is a 90% chance that it will equal or exceed $50,000.

Also, although the P50 profitability index is less than 2, the P90 value is still greater than 1. This indicates a low-risk project.

In building a diversified investment portfolio, decision-makers can use this additional insight to compare and rank projects competing for limited capital funds.

Acknowledgments

I would like to thank Conoco for its permission to publish this article. The following Conoco staff members provided a critical review: Dominique Berta, Mike Decker, Frank Koskimaki, Paul McNutt, Hal Roegner, and Mike Zotzky.

Bibliography

1. Beliveau, D., "Heterogeneity, Geostatistics, Horizontal Wells, and Blackjack Poker," JPT, December 1995, p. 1068.

2. Gutleber, D.S., Heiberger, E.M., and Morris, T.D., "Simulation Analysis for Integrated Evaluation of Technical and Commercial Risk," JPT, December 1995, p. 1062.

3. Laherrere, J.H., "Discussion of An Integrated Deterministic/Probabilistic Approach to Reserve Estimations," JPT, December 1995, p. 1082.

4. McNutt, P.B., Pittaway, K.R., Rosato, R.J., and Beamer, R.E., "A Probabilistic Forecasting Method for the Huntley CO2 Projects," Paper No. SPE/DOE 27762, SPE/DOE Ninth Symposium on Improved Oil Recovery, Tulsa, Apr. 17-20, 1994.

5. Murtha, J.A., Decisions Involving Uncertainty, An @RISK Tutorial for the Petroleum Industry, Houston, 1993.

6. Patricelli, J.A., and McMichael, C.L., "Authors' Reply to Discussion of An Integrated Deterministic/Probabilistic Approach to Reserve Estimations," JPT, December 1995, p. 1084.

The Author