System and method for performing oilfield simulation operations

1. A method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein, the method comprising:

determining a time-step for simulating the reservoir using a reservoir model, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations;

calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions of the reservoir model corresponding to the time-step, the plurality of CFL conditions being calculated for each of the plurality of gridded cells and comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, the composition CFL condition and the saturation CFL condition being calculated based on an isothermal simulator, the temperature CFL condition being calculated based on a thermal simulator;

simulating a first cell of the plurality of gridded cells using the thermal simulator with an Implicit Pressure, Explicit Saturations (IMPES) system to obtain a first simulation result, the first cell having no CFL condition of the plurality of CFL conditions with a value greater than one;

simulating a second cell of the plurality of gridded cells using the thermal simulator with a Fully Implicit Method (FIM) system to obtain a second simulation result, the second cell having at least one CFL condition of the plurality of CFL conditions with a value greater than one; and

performing the oilfield operation based on the first and second simulation results.

2. The method of claim 1 , wherein calculating the plurality of CFL conditions comprises:

decoupling the plurality of partial differential equations by separating a temperature effect, a composition effect, and a saturation effect in the reservoir model to generate a plurality of decoupled equations; and

calculating the temperature CFL condition, the composition CFL condition, and the saturation CFL condition using the plurality of decoupled equations.

3. The method of claim 1 , wherein the multi-phase system has a plurality of phases and the reservoir model has no mass transfer among the plurality of phases, and wherein calculating the plurality of CFL conditions comprises:

deriving a general temperature CFL expression to calculate the temperature CFL condition, the general temperature CFL expression being independent of a number of phases of the multi-phase system.

4. The method of claim 1 , wherein performing the oilfield operation comprises:

preparing a forecast of the oilfield operation based on the first and second simulation results; and

improving production from the reservoir based on the forecast.

5. The method of claim 1 , wherein performing the oilfield operation comprises:

preparing a development plan of the oilfield operation based on the first and second simulation results.

6. The method of claim 1 , wherein the time-step comprises at least one selected from a group consisting of a second, a minute, an hour, a day, a week, a month, and a year.

7. A method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein, the method comprising:

determining a time-step for simulating the reservoir, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations, the multi-phase system having a plurality of phases;

calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions of a first reservoir model corresponding to the time-step, the first reservoir model having no mass transfer among the plurality of phases, the plurality of CFL conditions being calculated for each of the plurality of gridded cells and comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, the composition CFL condition and the saturation CFL condition being calculated based on an isothermal simulator, the temperature CFL condition being calculated based on a thermal simulator;

simulating a first cell of the plurality of gridded cells using the thermal simulator with an Implicit Pressure, Explicit Saturations (IMPES) system to obtain a first simulation result, the thermal simulator having mass transfer among the plurality of phases, the first cell having no CFL condition of the plurality of CFL conditions with a value greater than one;

simulating a second cell of the plurality of gridded cells using the thermal simulator with a Fully Implicit Method (FIM) system to obtain a second simulation result, the second cell having at least one CFL condition of the plurality of CFL conditions with a value greater than one; and

performing the oilfield operation based on the first and second simulation results.

8. The method of claim 7 , wherein calculating the plurality of CFL conditions comprises:

decoupling the plurality of partial differential equations by separating a temperature effect, a composition effect, and a saturation effect in the first reservoir model to generate a plurality of decoupled equations; and

calculating the temperature CFL condition, the composition CFL condition, and the saturation CFL condition using the plurality of decoupled equations.

9. The method of claim 7 , wherein calculating the plurality of CFL conditions comprises:

deriving a general temperature CFL expression to calculate the temperature CFL condition, the general temperature CFL expression being independent of a number of phases of the multi-phase system.

10. The method of claim 7 , wherein performing the oilfield operation comprises:

preparing a forecast of the oilfield operation based on the first and second simulation results; and

improving production from the reservoir based on the forecast.

11. The method of claim 7 , wherein performing the oilfield operation comprises:

preparing a development plan of the oilfield operation based on the first and second simulation results.

12. The method of claim 7 , wherein the time-step comprises at least one selected from a group consisting of a second, a minute, an hour, a day, a week, a month, and a year.

13. A method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein, the method comprising:

determining a time-step for simulating the reservoir, the reservoir being represented as a plurality of gridded cells and being modeled as a multi-phase system using a plurality of partial differential equations, the multi-phase system having a plurality of phases with no mass transfer among the plurality of phases;

calculating a plurality of Courant-Friedrichs-Lewy (CFL) conditions corresponding to the time-step, the plurality of CFL conditions being calculated for each of the plurality of gridded cells and comprising a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, the composition CFL condition and the saturation CFL condition being calculated based on an isothermal simulator, the temperature CFL condition being calculated based on a thermal simulator;

simulating a first cell of the plurality of gridded cells using the thermal simulator with an Implicit Pressure, Explicit Saturations (IMPES) system to obtain a first simulation result, the first cell having no CFL condition of the plurality of CFL conditions with a value greater than one;

simulating a second cell of the plurality of gridded cells using the thermal simulator with a Fully Implicit Method (FIM) system to obtain a second simulation result, the second cell having at least one CFL condition of the plurality of CFL conditions with a value greater than one; and

performing the oilfield operation based on the first and second simulation results.

14. The method of claim 13 , wherein calculating the plurality of CFL conditions comprises:

decoupling the plurality of partial differential equations by separating a temperature effect from a composition effect and a saturation effect in the thermal simulator to generate a plurality of decoupled equations; and

calculating the temperature CFL condition using the plurality of decoupled equations.

15. The method of claim 13 , wherein calculating the plurality of CFL conditions comprises:

deriving a general temperature CFL expression to calculate the temperature CFL condition, the general temperature CFL expression being independent of a number of phases of the multi-phase system.

16. The method of claim 13 , wherein performing the oilfield operation comprises:

preparing a forecast of the oilfield operation based on the first and second simulation results; and

improving production from the reservoir based on the forecast.

17. The method of claim 13 , wherein performing the oilfield operation comprises:

preparing a development plan of the oilfield operation based on the first and second simulation results.

18. The method of claim 13 , wherein the time-step comprises at least one selected from a group consisting of a second, a minute, an hour, a day, a week, a month, and a year.

19. A method of optimizing computer usage when performing simulations for a reservoir using a reservoir model wherein the reservoir model is gridded into cells, the method comprising:

a. determining a preferred percentage of cells to be simulated using an Implicit Pressure, Explicit Saturations (IMPES) system for optimizing computer usage;

b. determining a time-step for simulating the reservoir;

c. calculating Courant-Friedrichs-Lewy (CFL) conditions according to the time-step for each cell of the reservoir model including calculating a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, the composition CFL condition and the saturation CFL condition being calculated based on an isothermal simulator, the temperature CFL condition being calculated based on a thermal simulator;

d. calculating a percentage of cells having no CFL condition with a value greater than one;

e. determining whether the percentage calculated from step d is equal to or greater than the preferred percentage and if not, reducing the time-step and returning to step c;

f. simulating, by the thermal simulator, all cells having no CFL value greater than one using the IMPES system; and

g. simulating, by the thermal simulator, all cells having CFL values greater than one using a Fully Implicit Method (FIM) system.

20. The method of claim 19 , wherein step c comprises:

providing a plurality of partial differential equations to model the reservoir in the reservoir model, wherein the plurality of partial differential equations model a temperature effect, a composition effect, and a saturation effect;

separating the temperature effect, the composition effect, and the saturation effect to generate a plurality of decoupled equations; and

computing the temperature CFL condition, the composition CFL condition, and the saturation CFL condition using the plurality of decoupled equations.

21. The method of claim 19 , the reservoir being modeled as a multi-phase system using a plurality of partial differential equations, wherein step c comprises:

deriving a general temperature CFL expression to calculate the temperature CFL condition, the general temperature CFL expression being independent of a number of phases of the multi-phase system.

22. The method of claim 19 , wherein the time-step comprises at least one selected from a group consisting of a second, a minute, an hour, a day, a week, a month, and a year.

23. A computer system with optimized computer usage when performing simulations for an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein, the computer system comprising:

a processor;

memory;

and software instructions stored in memory to execute on the processor to:

a. determine a preferred percentage of cells to be simulated using an Implicit Pressure, Explicit Saturations (IMPES) system for optimizing computer usage;

b. determine a time-step for simulating the reservoir;

c. calculate Courant-Friedrichs-Lewy (CFL) conditions according to the time-step for each cell of the reservoir model including calculating a temperature CFL condition, a composition CFL condition, and a saturation CFL condition, the composition CFL condition and the saturation CFL condition being calculated by an isothermal simulator, the temperature CFL condition being calculated by a thermal simulator;

d. calculate a percentage of cells having no CFL condition with a value greater than one;

e. determine whether the percentage calculated from step d is equal to or greater than the preferred percentage and if not reduce the time-step and return to step c;

f. simulate, by the thermal simulator, all cells having no CFL value greater than one using the IMPES system; and

g. simulate, by the thermal simulator, all cells having CFL values greater than one using a Fully Implicit Method (FIM) system.

24. The computer system of claim 23 , wherein step c comprises:

providing a plurality of partial differential equations to model the reservoir in the reservoir model, wherein the plurality of partial differential equations model a temperature effect, a composition effect, and a saturation effect;

separating the temperature effect, the composition effect, and the saturation effect to generate a plurality of decoupled equations; and

computing the temperature CFL condition, the composition CFL condition, and the saturation CFL condition using the plurality of decoupled equations.

25. The computer system of claim 23 , wherein the time-step comprises at least one selected from a group consisting of a second, a minute, an hour, a day, a week, a month, and a year.