Method and system for a multi-level nonlinear solver for reservoir simulations

A system, comprising:

• a plurality of wells in a geological region of interest, wherein the plurality of wells comprises a first well;
• a plurality of pressure sensors in a wellbore for the first well in the geological region of interest;
• at least one flow rate sensor that measures a production rate for the first well;
• and
• a reservoir simulator comprising a computer processor and coupled to the plurality of wells, wherein the reservoir simulator is configured to perform a method comprising:
• obtaining wellbore pressure data from the plurality of pressure sensors;
• obtaining flow rate data from the at least one flow rate sensor;
• obtaining grid model data for the geological region of interest;
• obtaining, from the plurality of wells, well data
• determining a simulated well network for the first well in the geological region of interest for a reservoir simulation,
• wherein the simulated well network comprises a well source node, a plurality of wellbore links, and a plurality of reservoir perforation links, and
• wherein at least one reservoir perforation link among the plurality of reservoir perforation links corresponds to a perforation operation that perforates a casing in the wellbore for the first well;
• determining, based on the grid model data, the wellbore pressure data, the flow rate data, and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method;
• determining, based on the grid model data, the well data, the wellbore pressure data, the flow rate data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method;
• performing, based on the grid model data and the second simulation solution, the reservoir simulation of the geological region of interest for a predetermined period of time using a third search method;
• and
• determining a predicted production rate for the first well based on the reservoir simulation.

A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions being configured to perform a method comprising:

• obtaining wellbore pressure data from a plurality of pressure sensors in a wellbore for a first well in a geological region of interest;
• obtaining flow rate data from at least one flow rate sensor that measures a production rate for the first well;
• obtaining grid model data for flail the geological region of interest and well data for a plurality of wells in the geological region of interest,
• wherein the first well among the plurality of wells;
• determining a simulated well network for the first well in the geological region of interest for a reservoir simulation,
• wherein the simulated well network comprises a well source node, a plurality of wellbore links, and a plurality of reservoir perforation links, and
• wherein at least one reservoir perforation link among the plurality of reservoir perforation links corresponds to a perforation operation that perforates a casing in the wellbore for the first well;
• determining, based on the grid model data, the wellbore pressure data, the flow rate data, and the well data, a first simulation solution for a first constraint rate equation decoupled from the simulated well network and using a first search method;
• determining, based on the grid model data, the well data, the wellbore pressure data, the flow rate data, and the first simulation solution, a second simulation solution for a second constraint rate equation coupled to the simulated well network and using a second search method;
• performing, based on the grid model data and the second simulation solution, the reservoir simulation of the geological region of interest for a predetermined period of time using a third search method;
• and
• determining a predicted production rate for the first well based on the reservoir simulation.