Changes

The problem is how to express our technical uncertainties realistically and in a form by which they can be utilized in economic equations and formulae. The most common convention in use today involves the formulation of a range of anticipated values for a given parameter, with probabilities—ordinarily 10%, 50%, and 90%—assigned to the values that comprise the range. For example, the geologist may think there is only a 10% chance that the anticipated pay zone will be less than 8 ft thick, 50% sure that it will be less than 12 ft thick, and 90% sure that it will be less than 18 ft thick. The same procedure can be applied to any parameter, including drainage area, production rate, decline rate, and wellhead prices.

The problem is how to express our technical uncertainties realistically and in a form by which they can be utilized in economic equations and formulae. The most common convention in use today involves the formulation of a range of anticipated values for a given parameter, with probabilities—ordinarily 10%, 50%, and 90%—assigned to the values that comprise the range. For example, the geologist may think there is only a 10% chance that the anticipated pay zone will be less than 8 ft thick, 50% sure that it will be less than 12 ft thick, and 90% sure that it will be less than 18 ft thick. The same procedure can be applied to any parameter, including drainage area, production rate, decline rate, and wellhead prices.

However, such estimates cannot be "pulled out of the air"! They must rely on objective considerations of all relevant data, especially maps, cross-sections, geophysical data, borehole log interpretations, analogous producing patterns, and other factors. Moreover, the geotechnical professional must arrive at a final distribution by "shaping it," that is, making trial estimates, examining the implications of various values in the distribution, comparing it with analog data, and adjusting it repeatedly until finally becoming comfortable with the estimates.

However, such estimates cannot be "pulled out of the air"! They must rely on objective considerations of all relevant data, especially maps, [[cross section]]s, geophysical data, borehole log interpretations, analogous producing patterns, and other factors. Moreover, the geotechnical professional must arrive at a final distribution by "shaping it," that is, making trial estimates, examining the implications of various values in the distribution, comparing it with analog data, and adjusting it repeatedly until finally becoming comfortable with the estimates.

==Biases in estimating==

==Biases in estimating==

[[File:Table rose time-value-of-money 1.jpg|thumbnail|'''Table 1.''' Biases affecting judgments under uncertainty.]]

Unfortunately, a number of psychological biases exist, many of which are described by Tversky and Kahneman,<ref name=Tversky_etal_1981>Tversky, A., and D. Kahneman, 1981, The framing of decisions and the psychology of choice: Science, v. 211, p. 453-458.</ref> that tend to produce inconsistencies whenever we estimate under uncertainty (Table 1).  

Unfortunately, a number of psychological biases exist, many of which are described by Tversky and Kahneman,<ref name=Tversky_etal_1981>Tversky, A., and D. Kahneman, 1981, The framing of decisions and the psychology of choice: Science, v. 211, p. 453-458.</ref> that tend to produce inconsistencies whenever we estimate under uncertainty ([[:Image:Table_rose_time-value-of-money_1.jpg|Table 1]]). For the development geologist, three such biases are especially dangerous:

! Type of bias || Common example

| Overconfidence || Estimators are much less accurate than they think they are.

| Availability || Recent or spectacular examples are more prone to be cited, regardless of their real frequency in nature.

| Anchoring || In estimating, a low starting point leads to a lower final estimate, and a high starting point leads to a higher final estimate.

|-

| Unrecognized limits || Geologists forecasting future discoveries may disregard nongeological factors.  

|-

| Motivation || Prospectors exaggerate the magnitude of reserves in order to sell the deal.

|-

| Conservatism || The feeling that overestimating a project is worse than underestimating it.

|}

 

For the development geologist, three such biases are especially dangerous:

# ''Overconfidence,'' which leads to excessively narrow ranges. People naturally tend to set predictive ranges that typically correspond to a confidence significantly lower than the ranges they think they are setting.<ref name=Capen_1976>Capen, E. C., 1976, The difficulty of assessing uncertainty: Journal of Petroleum Technology, v. 28, p. 843-850.</ref>

# ''Overconfidence,'' which leads to excessively narrow ranges. People naturally tend to set predictive ranges that typically correspond to a confidence significantly lower than the ranges they think they are setting.<ref name=Capen_1976>Capen, E. C., 1976, The difficulty of assessing uncertainty: Journal of Petroleum Technology, v. 28, p. 843-850.</ref>

# ''Conservatism,'' which leads to underestimates because professionals, fearing criticism, may feel it is worse to overestimate a project than to underestimate it.<ref name=Rose_1987>Rose, P. R., 1987, Dealing with risk and uncertainty in exploration--how can we improve?: AAPG Bulletin, v. 71, n. 1, p. 1-16.</ref>

# ''Conservatism,'' which leads to underestimates because professionals, fearing criticism, may feel it is worse to overestimate a project than to underestimate it.<ref name=Rose_1987>Rose, P. R., 1987, [http://archives.datapages.com/data/bulletns/1986-87/data/pg/0071/0001/0000/0001.htm Dealing with risk and uncertainty in exploration--how can we improve?]: AAPG Bulletin, v. 71, n. 1, p. 1-16.</ref>

# ''Motivation,'' which leads to overestimates because of career or economic self-interest on the part of the professional in "selling the deal."<ref name=Rose_1987 />

# ''Motivation,'' which leads to overestimates because of career or economic self-interest on the part of the professional in "selling the deal."<ref name=Rose_1987 />

==Lognormality and log probability paper==

==Lognormality and log probability paper==

Most geological and production parameters are not distributed according to a symmetrical or ''normal'' distribution, that is, they do not form a ''bell-shaped'' frequency curve. Instead, they tend to produce a frequency distribution skewed to the right, so that there are many small values and only a few large ones. Such patterns approximate a ''lognormal distribution,'' and they arise from multiplication of several factors to produce one geological parameter.<ref name=Kaufman_1963>Kaufman, G., 1963, Statistical decision and related techniques in oil and gas exploration: Englewood Cliffs, NJ, Prentice-Hall, 307 p.</ref> <ref name=Capen_1984>Capen, E. C., 1984, Why lognormal? in E. C.Capen, R. E. Megill, and P. R. Rose, ed., Prospect Evaluation: AAPG Course Notes: Tulsa, OK, AAPG, 8 p.</ref> <ref name=Megill_1984>Megill, R. E., 1984, An introduction to risk analysis, 2nd ed.: Tulsa, OK, PennWell Books, 274 p.</ref> Good examples include field sizes, production rates of wells in a field, [[porosity]]-feet (&phi;h) of reservoirs, and effective well drainage area.

Most geological and production parameters are not distributed according to a symmetrical or ''normal'' distribution, that is, they do not form a ''bell-shaped'' frequency curve. Instead, they tend to produce a frequency distribution skewed to the right, so that there are many small values and only a few large ones. Such patterns approximate a ''lognormal distribution,'' and they arise from multiplication of several factors to produce one geological parameter.<ref name=Kaufman_1963>Kaufman, G., 1963, Statistical decision and related techniques in oil and gas exploration: Englewood Cliffs, NJ, Prentice-Hall, 307 p.</ref> <ref name=Capen_1984>Capen, E. C., 1984, Why lognormal? in E. C.Capen, R. E. Megill, and P. R. Rose, ed., Prospect Evaluation: AAPG Course Notes: Tulsa, OK, AAPG, 8 p.</ref> <ref name=Megill_1984>Megill, R. E., 1984, An introduction to risk analysis, 2nd ed.: Tulsa, OK, PennWell Books, 274 p.</ref> Good examples include field sizes, production rates of wells in a field, [[porosity]]-feet (&phi;h) of reservoirs, and effective well drainage area.

Here it is important to remind the reader that in a lognormal frequency distribution, the ''mode'' (or most likely point) is positioned to the left, at the peak of the curve. The ''median'' (or 50% point) lies in the middle, separating the area under the curve into two equal parts, whereas the ''mean'' (or average) lies to the right of the median ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]). We shall be concerned mostly with the median and the mean in our estimates and calculations, generally discouraging use of the mode, as will be explained later.

Here it is important to remind the reader that in a lognormal frequency distribution, the ''mode'' (or most likely point) is positioned to the left, at the peak of the curve. The ''median'' (or 50% point) lies in the middle, separating the area under the curve into two equal parts, whereas the ''mean'' (or average) lies to the right of the median ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_1.jpg|Figure 1]]). We shall be concerned mostly with the median and the mean in our estimates and calculations, generally discouraging use of the mode, as will be explained later.

[[File:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 2.jpg|thumbnail|'''Figure 2.''' Worksheet showing graphical method of combining distributions to derive the mean reserves on three-cycle log probability paper.]]

[[File:Uncertainties-impacting-reserves-revenue-and-costs_fig2.png|300px|thumbnail|'''Figure 2.''' Worksheet showing graphical method of combining distributions to derive the mean reserves on three-cycle log probability paper.]]

In combination with the cumulative probability curve, lognormality provides us with a very useful and powerful predictive tool. Accordingly, it is important to utilize (and understand) log probability paper. Although several forms are commercially available, the three-cycle type in which the probabilities extend from 0.01% to 99.99% is recommended ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|Figure 2]]).

In combination with the cumulative probability curve, lognormality provides us with a very useful and powerful predictive tool. Accordingly, it is important to utilize (and understand) log probability paper. Although several forms are commercially available, the three-cycle type in which the probabilities extend from 0.01% to 99.99% is recommended ([[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider_capillary-pressure_2.jpg|Figure 2]]).

However, a graphical shortcut is readily available for combining any three lognormally distributed factors. This procedure is quick and can be performed manually. The example shown in Table 2 uses area of drainage, average net pay, and hydrocarbon recovery factor. Other variables important in development evaluations include initial flow rate (IP), decline rate, wellhead prices, and costs.

However, a graphical shortcut is readily available for combining any three lognormally distributed factors. This procedure is quick and can be performed manually. The example shown in Table 2 uses area of drainage, average net pay, and hydrocarbon recovery factor. Other variables important in development evaluations include initial flow rate (IP), decline rate, wellhead prices, and costs.

[[File:Rose_time-value-of-money_1.jpg|thumb|'''Table 2.''' Calculation of means (see [[:Image:Charles-l-vavra-john-g-kaldi-robert-m-sneider capillary-pressure 2.jpg|Figure 2]])]]

|-

|+'''Table 2.''' Calculation of means (see [[:File:Uncertainties-impacting-reserves-revenue-and-costs_fig2.png|Figure 2]])

|-

| P_10% value || 20 ac || x 7 ft || x 100 bbl/ac-ft || = 14,000 bbl = P_1.3% || P_10% = 28,000 || rowspan = 4 | Mz^a = 91,584 bbl

|-

| P_50% value || 32 ac || x 12 ft || x 190 bbl/ac-ft || = 72,960 bbl = P_50% || P_50% = 72,960

|-

| P_90% value || 50 ac || x 20 ft || x 350 bbl/ac-ft || = 350,000 bbl = P_98.7% || P_90% = 180,000

| Mean^a (Mz) || 33.8 ac || x 12.9 ft || x x 211 bbl/ac-ft || = 92,000 bbl ||

 

Note that multiplying the three ''P''_90% values for area, net pay, and hydrocarbon recovery does not yield a ''P''_90% value for reserves; in fact, it gives a product corresponding to 98.7%! Similarly, multiplying the three ''P''_10% values gives a reserves product that corresponds to ''P''_1.3%, not ''P''_10%.

Note that multiplying the three ''P''_90% values for area, net pay, and hydrocarbon recovery does not yield a ''P''_90% value for reserves; in fact, it gives a product corresponding to 98.7%! Similarly, multiplying the three ''P''_10% values gives a reserves product that corresponds to ''P''_1.3%, not ''P''_10%.

==Accuracy levels in geotechnical predictions==

==Accuracy levels in geotechnical predictions==

Geologists, geophysicists, and engineers think they are much more accurate than they really are. In exploration forecasting, a goal of 0.5&times; to 2&times; for area of accumulation, net pay, and hydrocarbon recovery factor is about as accurate as nature will allow us to estimate. In other words, 80% of our predictions should be within an envelope of one-half to twice that of reality. Reserves predictions may vary more because of the multiplicity effect; perhaps 0.2&times; to 5&times; is a more reasonable range to expect here. Such variances can be portrayed on log probability paper.

Geologists, geophysicists, and engineers think they are much more accurate than they really are. In exploration forecasting, a goal of 0.5&times; to 2&times; for area of [[accumulation]], net pay, and hydrocarbon recovery factor is about as accurate as nature will allow us to estimate. In other words, 80% of our predictions should be within an envelope of one-half to twice that of reality. Reserves predictions may vary more because of the multiplicity effect; perhaps 0.2&times; to 5&times; is a more reasonable range to expect here. Such variances can be portrayed on log probability paper.

Geologists working on development projects should do somewhat better than this, however, and perhaps a general range of 0.8&times; to 1.25&times; of actuality is expectable for predictions based on geological parameters and reservoir performance. Correspondingly, reserves predictions should fall within the 0.67&times; to 1.5&times; envelope for development wells, at the 80% confidence level.

Geologists working on development projects should do somewhat better than this, however, and perhaps a general range of 0.8&times; to 1.25&times; of actuality is expectable for predictions based on geological parameters and reservoir performance. Correspondingly, reserves predictions should fall within the 0.67&times; to 1.5&times; envelope for development wells, at the 80% confidence level.

===Taxes and regulatory costs===

===Taxes and regulatory costs===

[[Taxes|About taxes]] and regulatory costs, which show substantial variation, can also be expressed as ranges. Commonly, however, the effect of such governmental regulatory activity is to delay project performance, thus reducing profitability because of [[the time value of money]]. There is a clear tendency for operators to underestimate both the number and duration of such delays.<ref name=Capen_1976 /> It is also possible that future investments and operating costs will increase as a result of future regulatory activity.

[[Taxes]] and regulatory costs, which show substantial variation, can also be expressed as ranges. Commonly, however, the effect of such governmental regulatory activity is to delay project performance, thus reducing profitability because of the [[Economics: time value of money|time value of money]]. There is a clear tendency for operators to underestimate both the number and duration of such delays.<ref name=Capen_1976 /> It is also possible that future investments and operating costs will increase as a result of future regulatory activity.

==See also==

==See also==

* [[Introduction to economics and risk assessment]]

* [[Introduction to economics and risk assessment]]

* [[Expected value and chance of success]]

* [[Risk: expected value and chance of success]]

* [[The time value of money]]

* [[Economics: time value of money]]

* [[Dealing with risk aversion]]

* [[Risk: dealing with risk aversion]]

* [[Fundamental economic equations for oil and gas property evaluation]]

* [[Economics: fundamental equations for oil and gas property evaluation]]

* [[Key economic parameters]]

* [[Economics: key parameters]]

* [[Economics of property acquisitions]]

* [[Economics of property acquisitions]]

* [[Building a cash flow model]]

* [[Cash flow model]]

==References==

==References==

[[Category:Economics and risk assessment]] [[Category:Pages with unformatted equations]]

[[Category:Economics and risk assessment]] [[Category:Pages with unformatted equations]]