Claims
- 1. A method for optimizing oil well production, comprising:
a) optimizing an objective function of oil well production for a risk aversion constant; b) generating an efficient frontier of the optimized objective function over a range of risk aversion constant values; and c) setting a parameter of oil well production based on the efficient frontier.
- 2. A method according to claim 1, wherein:
said step of optimizing includes calculating the objective function for at least one deterministic variable and at least one stochastic variable.
- 3. A method according to claim 2, wherein:
said step of optimizing includes calculating the objective function for a plurality of stochastic-variable values for each set of deterministic-variable values.
- 4. A method according to claim 3, wherein:
said step of optimizing includes calculating said objective function for a plurality of deterministic-variable values for each risk aversion constant value.
- 5. A method according to claim 1, wherein:
said objective function is selected from the group consisting of Net Present Value of the oil well, quantity of oil produced, and percentage yield.
- 6. A method according to claim 2, wherein:
said deterministic variable includes the flow rate of an injection well.
- 7. A method according to claim 6, wherein:
said deterministic variable includes the flow rates of a plurality of injection wells.
- 8. A method according to claim 2, wherein:
said stochastic variable is selected from the group consisting of oil patch radius, market price for oil, and interest rate.
- 9. A method according to claim 1, wherein:
said step of optimizing includes calculating the mean and variance of the objective function for a set of deterministic variable values.
- 10. A method according to claim 9, wherein:
said step of optimizing includes calculating the mean and variance of the objective function for a set of stochastic variable values for each deterministic variable value.
- 11. A method for optimizing production in an oil field having at least one production well and at least one injection well where production is subject to a plurality of uncertainty parameters and a plurality of risk aversion constants, said method comprising:
a) choosing a risk aversion constant K; b) choosing a set of flow rates for the production well(s) and injection well(s); c) for each uncertainty parameter value, calculating and storing an objective production function; d) calculating the mean and variance of the objective function set obtained in step (c) to obtain an objective function F(K) of the risk aversion constant chosen in step (a); e) repeating steps (b) through (d) until an optimal F(K) is found for the risk aversion constant K chosen in step (a); f) storing the means and variances calculated in step (d), when the optimal F(K) is found for the risk aversion constant K chosen in step (a); g) repeating steps (a) through (f) for each risk aversion constant; h) generating an efficient frontier based on the set of means and variances stored in step (f); and i) optimizing production by setting the flow rate for the production well(s) and the injection well(s) based on the efficient frontier.
- 12. A method according to claim 11, wherein:
the objective production function calculated in step (c) is chosen from the group consisting of net present value of the oil field, quantity of oil produced, and percentage yield.
- 13. A method according to claim 11, wherein:
the objective function calculated in step (c) is 12Jpr≡∫0tfe-btr1(t)q1(t)ⅆtwhere Jpr is net present value of the oil produced, t is time, tf is the time production ceases, b is the discount rate, r1(t) is the expected price of oil per barrel at time t, and q1(t) is the rate of production at time t.
- 14. A method according to claim 11, wherein:
the objective function calculated in step (c) is 13J≡Jpr-Jinj=∑k=1N∫0tfe-btrk(t)qk(t)ⅆtwhere J is the total payoff, N is the number of injector wells, t is time, b is the discount rate, rk(t) is the expected cost to inject water into well k at time t, and qk(t) is the rate of production at time t.
- 15. A method according to claim 11, wherein:
F(K)=(1−K)η−Kσ, where η is the mean and σ is the standard deviation.
- 16. A method according to claim 11, wherein:
the variances calculated in step (d) are based on (σ−)2=E{[min(F−η,0)]2}, where σ− is the semi-deviation, E{ } represents the expected value of the expression in the braces, and η is the mean.
- 17. A method according to claim 11, wherein:
- 18. A method according to claim 11, wherein:
- 19. A method for optimizing oil well production, comprising:
a) optimizing an objective function of oil well production for a risk aversion constant; b) generating an efficient frontier of the optimized objective function over a range of risk aversion constant values; and c) plotting the efficient frontier as a two-dimensional graph.
- 20. A method according to claim 19, wherein:
one axis of the two-dimensional graph is standard deviation of the objective function of oil well production.
- 21. A method according to claim 19, wherein:
one axis of the two-dimensional graph is semi-deviation of the objective function of oil well production.
- 22. A method for optimizing a stochastic process, comprising:
a) defining an objective function related to the process; b) for a plurality of risk aversion constants, optimizing a linear combination of the mean and standard deviation or semi-deviation of the function; and c) defining an efficient frontier based on the optimized linear combination for each risk aversion constant.
Parent Case Info
[0001] This application claims the benefit of provisional application serial number 60/229,680 filed Sep. 1, 2000, the complete disclosure of which is hereby incorporated by reference herein.
Provisional Applications (1)
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Number |
Date |
Country |
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60229680 |
Sep 2000 |
US |