Procedure for the Parabolic Projection of Geological Assessments of Conventional Oil and Gas Resources with Examples

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1 John H. Walsh Energy Advisor Abstract There is now major concern about the extent of the world s endowment of conventional oil resources and the North American supply of natural gas. This paper presents the details of the parabolic projection technique for the interpretation of geological assessments of undiscovered resources of conventional oil and gas in terms of production-time curves. The object is to present the methodology that was devised over the last decade in sufficient detail to allow this type of projection to be used and interpreted readily by others. Specific examples of its application are taken from some recent papers. The examples include a projection of the Mean Value for the world s conventional oil resources published by the U.S. Geological Survey in 000, the techniques devised for dealing with the Reserves Addition and the problem posed by the existence of idle capacity in the global oil system, and the plateau peak now likely in Canadian natural gas production. The procedure used to calculate these special cases is presented along with the results in raphical form. Introduction T Page 1

2 Figure 1: Illustration of Terms Used in Parabolic Projection Technique Production = p Gigabarrels/Year (0il) OR TCF/Year (Gas) 10 Plot of Production versus Time q 1 Cumulative Production to t 1 +Q s -q 1 =Q u t=0 t=t 1 Peak p = P YMost Recent Historical Year XX = Staging Point at t = t 1 Total Area of Staged Parabola = Q s Area of Overlap Section = q 1 Time = t in Years Zone of Interest t=t Methodology of the Parabolic Projection Technique The Basic Parabolic Relationships p=at +bt Whenp=0,t=Tandsoa=-b/T: b may then be expressed in terms of Q, the total area of the parabola, by integration from 0 to T: Q=p dt = -b/3 T + b/ T ;thusb=q/t q/q = 1.5 r r 3... Equation 3 Q = /3 PT... Equation Assessing the Value of Q u Page

3 Selection of the Staging Point Method of Iterative Solution Testing the Iteration Page 3

4 World Production in GB/Year Figure : U.S. Geological Survey World Mean Case Reserves Addition after Peak Production Year Mean Value - Reserves Addition after peak Mean Value - No Reserves Addition Parabolic Boundary of Overlap Section Vertical Boundary of Overlap Section Historical World Oil Production Staging Year 19 Peak Production of 9.3 Gb/Year in Page

5 Population (Billions) OR Barrels per Capita Figure 3: World Population and Conventional Oil Production per Capita World Population Scenario:.5.5 Max of Billion in World Population Actual World Population Extrapolated Case 1: Per Capita Oil Production Case : Per Capita Oil Production Case 3: Per Capita Oil Production Case : Per Capita Oil Production Historical Per Capita Oil Consumption Case 1 Peak: Case Peak: 0.9 Case 3 Peak: 01.1 Case Peak: 0.1 The Reserves Addition Special Cases Page 5

6 Oil Production in GB/Year Figure : Effect of Idle Capacity on Parabolic Projection of World Conventional Oil Production + 10 million barrels/day + 5 milllion barrels/day + 3 million barrels/day + 1 million barrels/day Underlying Case Historical World Oil Production Year The Problem of Idle Capacity Page

7 World Idle Production Capacity Million Barrels per Day Figure 5: Relation Between Idle Capacity and Date of Peak Production on World Conventional Production Year World Peak Production GB/Year Page 7

8 Production in GB/Year Figure : Alternative Treatment of Idle Capacity in World Conventional Oil Production Peak: 90.5 million Barrels/day Peak: 5.5 million Barrels/day Peak: 0.5 million Barrels/day Reserve Addition of 7 GB effective after coincident peak in all cases + 10 mmbbl/day in GB/yr + 5 mmbbl/day in GB/yr Underlying Parabola GB/yr Possible Track in Production GB/yr Historical Production GB/yr Year Page

9 Figure 7: Parabolic Projection of National Energy Board `Supply Push' Case Assessment of Natural Gas Resources Natural Gas Production in TCF Peak of. TCF in 01 Parabolic Projection of Gas Resources Plateau Peak at 7 TCF/Year Plateau Peak at TCF/Year Parabolic Boundary of Overlap Section Vertical Boundary of Overlap Section Historical Gas Production in TCF Staging Point in 199 Nominal Peak Cumulative Production Equivalent Year Extension 1.5 years Extension 5. years Plateau Peak Cases Page 9

10 Conclusion T References 1. Charkes Hall, Predeep Tharakan, John Halleck, Cutler Cleveland, and Michael Jefferson, Hydrocarbons and the Evolution of Human Culture, Nature, Vol., pp November 003. (Web: J.H. Walsh, Parabolic Projection of World Conventional Oil Production Based on Year 000 Resource Assessment of the U.S. Geological Survey, Proceedings of the Canadian Association for the Club of Rome, Series, No. 3 Spring/Summer 00. (Web: pages.ca.inter.net/~jhwalsh/wusgs.html) 3. J.H. Walsh, World Oil Production and Per Capita Oil Consumption, Updated Yearly. (Web: pages.ca.inter.net/~jhwalsh/oilcap.html). J.H. Walsh, Parabolic Adjustment for Idle Capacity in the World Conventional Oil Production System, (Web: pages.ca.inter.net/~jhwalsh/wusgsi) 5. National Energy Board, Canada s Energy Future: Scenarios for Supply and Demand to 050, Calgary, Alberta, July, 003. (Web: J.H. Walsh, Parabolic Projection of Four Assessments of Canada s Conventional Natural Gas Resources, August 003. (Web: pages.ca.inter.net/~jhwalsh/wngcanada.html) 7. J.H. Walsh, Conventional Natural Gas Production Decline Patterns, September 003. (Web: pages.ca.inter.net/~jhwalsh/wnatgas.html) December 003; Revised January Lambton Avenue, Ottawa, Ontario, K1M 0Z Tel: (13) jhwalsh@ca.inter.net Web Site: pages.ca.inter.net/~jhwalsh/index.html Page 10