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==

==Lognormality and log probability paper==

==Lognormality and log probability paper==

[[File:Uncertainties-impacting-reserves-revenue-and-costs_fig1.png|thumbnail|'''Figure 1.''' Location of mode, median, and mean shown schematically on a lognormal frequency distribution.]]

[[File:Uncertainties-impacting-reserves-revenue-and-costs_fig1.png|300px|thumbnail|'''Figure 1.''' Location of mode, median, and mean shown schematically on a lognormal frequency distribution.]]

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:Uncertainties-impacting-reserves-revenue-and-costs_fig2.png|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]]).

==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===

[[About taxes|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]]

* [[Economics: 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]]