Systems and methods for the quantitative estimate of production-forecast uncertainty

1. A method for updating posterior geological models, comprising:

a) computing new geological realizations for a prior geological model using a computer processor;

b) computing an exact likelihood of an objective function using the new geological realizations for the prior geological model or an acceptable number of the new geological realizations for the prior geological model;

c) defining an initial state for a sequential Monte Carlo chain based on the exact likelihood of an objective function;

d) defining a new sample based on the initial state for a sequential Monte Carlo chain and a random sample from the prior geological model;

e) computing an approximate likelihood of an objective function using the new sample;

f) repeating step d), based only on another random sample from the prior geological model, and step e) until the approximate likelihood of an objective function meets an acceptance criteria;

g) computing another exact likelihood of an objective function using the new sample if the new sample meets the acceptance criteria;

h) repeating step d), based only on another random sample from the prior geological model, and steps e) through g) until the another exact likelihood of an objective function meets another acceptance criteria;

i) repeating step d), based only on another random sample from the prior geological model, and steps e) through h) until a convergence criteria is met; and

j) storing each new sample that meets the acceptance criteria and the another acceptance criteria, each new sample representing a respective updated posterior geological model for the prior geological model.

2. The method of claim 1 , further comprising defining a number (N) of new geological realization to compute for the prior geological model.

3. The method of claim 1 , wherein the new geological realizations are computed using parameters for the prior geological model.

4. The method of claim 1 , further comprising dynamically ranking each updated posterior geological model.

5. The method of claim 4 , further comprising:

evaluating the ranked updated posterior geological models; and

executing a business decision based on the evaluation.

6. The method of claim 1 , further comprising:

dynamically ranking the new geological realizations; and

selecting the acceptable number of the new geological realizations based upon the dynamic ranking of the new geological realizations.

7. The method of claim 1 , further comprising:

dynamically ranking each updated posterior geological model;

selecting a best ranked updated posterior geological model;

replacing the prior geological model with the best ranked updated posterior geological model;

renaming the best ranked updated posterior geological model as the prior geological model;

defining a number (N) of new geological realizations to compute for the prior geological model; and

repeating the steps of claim 1 .

8. The method of claim 1 , further comprising executing a business decision based on each updated posterior geological model.

9. The method of claim 7 , wherein the best ranked updated posterior geological model represents a highest ranked updated posterior geological model.

10. The method of claim 4 , wherein each updated posterior geological model is ranked by an ultimate recovery factor corresponding to each respective updated posterior geological model.

11. A non-transitory program carrier device tangibly carrying computer executable instructions for updating posterior geological models, the instructions being executable to implement:

a) computing new geological realizations for a prior geological model;

b) computing an exact likelihood of an objective function using the new geological realizations for the prior geological model or an acceptable number of the new geological realizations for the prior geological model;

c) defining an initial state for a sequential Monte Carlo chain based on the exact likelihood of an objective function;

d) defining a new sample based on the initial state for a sequential Monte Carlo chain and a random sample from the prior geological model;

e) computing an approximate likelihood of an objective function using the new sample;

f) repeating step d), based only on another random sample from the prior geological model, and step e) until the approximate likelihood of an objective function meets an acceptance criteria;

g) computing another exact likelihood of an objective function using the new sample if the new sample meets the acceptance criteria;

h) repeating step d), based only on another random sample from the prior geological model, and steps c) through g) until the another exact likelihood of an function meets another acceptance criteria;

i) repeating step d), based only on another random sample from the prior geological model, and steps e) through h) until a convergence criteria is met; and

j) storing each new sample that meets the acceptance criteria and the another acceptance criteria, each new sample representing a respective updated posterior geological model for the prior geological model.

12. The program carrier device of claim 11 , further comprising defining a number (N) of new geological realizations to compute for the prior geological model.

13. The program carrier device of claim 11 , wherein the new geological realizations are computed using parameters for the prior geological model.

14. The program carrier device of claim 11 , further comprising dynamically ranking each updated posterior geological model.

15. The program carrier device of claim 14 , further comprising:

evaluating the ranked updated posterior geological models; and

executing a business decision based on the evaluation.

16. The program carrier device of claim 11 , further comprising:

dynamically ranking the new geological realizations; and

selecting the acceptable number of the new geological realizations based upon the dynamic ranking of the new geological realizations.

17. The program carrier device of claim 11 , further comprising:

dynamically ranking each updated posterior geological model;

selecting a best ranked updated posterior geological model;

replacing the prior geological model with the best ranked updated posterior geological model;

renaming the best ranked updated posterior geological model as the prior geological model;

defining a number (N) of new geological realizations to compute for the prior geological model; and

repeating the steps of claim 11 .

18. The program carrier device of claim 11 , further comprising executing a business decision based on each updated posterior geological model.

19. The program carrier device of claim 17 , wherein the best ranked updated posterior geological model represents a highest ranked updated posterior geological model.

20. The program carrier device of claim 14 , wherein each updated posterior geological model is ranked by an ultimate recovery factor corresponding to each respective updated posterior geological model.