Optimization of oil well production with deference to reservoir and financial uncertainty

• US 20020100584A1
• Filed: 08/16/2001
• Published: 08/01/2002
• Est. Priority Date: 09/01/2000
• Status: Active Grant

• Current Assignee: Schlumberger Technology Corporation (SLB)
• Original Assignee: Schlumberger Technology Corporation (SLB)
• Inventors: Wilkinson, David, Couet, Benoit, Burridge, Robert
• Granted Patent: US 6,775,578 B2
• Time in Patent Office: Days
• US Class Current: 166/250.15
• CPC Class Codes: E21B 43/00 Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells applicable only to water E03B

Abstract

Methods for optimization of oil well production with deference to reservoir and financial uncertainty include the application of portfolio management theory to associate levels of risk with Net Present Values (NPV) of the amount of oil expected to be extracted from the reservoir. Using the methods of the invention, production parameters such as pumping rates can be chosen to maximize NPV without exceeding a given level of risk, or, for a given level of risk, the minimum guaranteed NPV can be predicted to a 90% probability. An iterative process of generating efficient frontiers for objective functions such as NPV is provided.

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

$J_{\mathrm{pr}}\equiv <br><br>\underset{0}{\overset{t_f}{\int <br><br>}}<br><br>e^{-\mathrm{bt}}<br><br>r_1<br><br>\left(t\right)<br><br>q_1<br><br>\left(t\right)<br><br><br><br>t$

where J_pr is net present value of the oil produced, t is time, t_f 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

$J\equiv <br><br>J_{\mathrm{pr}}-J_{\mathrm{inj}}=\underset{k=1}{\overset{N}{\sum <br><br>}}<br><br>\underset{0}{\overset{t_f}{\int <br><br>}}<br><br>e^{-\mathrm{bt}}<br><br>r_k<br><br>\left(t\right)<br><br>q_k<br><br>\left(t\right)<br><br><br><br>t$

where J is the total payoff, N is the number of injector wells, t is time, b is the discount rate, r_k(t) is the expected cost to inject water into well k at time t, and q_k(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:

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.

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.

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.