Method and system to accelerate the nonlinear solution in numerical reservoir simulation

Abstract

Systems and methods are disclosed. The method includes obtaining a reservoir model and a production scenario. The method also includes determining a first set of parameters for a first time from the reservoir model and the production scenario, predicting, using the first set of parameters, a second set of parameters at a second, later, time, including primary variables used to determine values for a mass, a flux and a well term. Predicting includes, iteratively until a stopping criterion is satisfied, for each computational cells in the reservoir model, using the first set of parameters to determine a primary variable update and a residual, determining an updated flux and well term, predicting the second set of parameters from the updated flux and well term, assigning the second set of parameters to the first set of parameters, and determining a predicted location of unproduced hydrocarbons from the second set of parameters.

What is claimed: 
     
         1 . A method, comprising:
 obtaining a reservoir model of a subterranean region of interest, wherein the reservoir model comprises a plurality of computational cells;   obtaining a production scenario; and   using a reservoir simulator:
 determining a first set of parameters for a first time from the reservoir model and the production scenario; 
 predicting, using the first set of parameters, a second set of parameters at a second time, wherein the first and second sets of parameters comprise primary variables, wherein the primary variables are used to determine values for a mass, a flux and a well term, wherein the second time is after the first time, and wherein the predicting comprises, iteratively, or recursively, until a stopping criterion is satisfied:
 for each of the plurality of computational cells:
 using the first set of parameters to determine a primary variable update and a residual, 
 determining an updated flux and an updated well term using, at least in part, the primary variable update, 
 predicting the second set of parameters based, at least in part, on the updated flux and the updated well term, and 
 assigning the second set of parameters to the first set of parameters; and 
 
 
   determining, using an interpretation workstation, a predicted location of unproduced hydrocarbons based, at least in part, on the second set of parameters.   
     
     
         2 . The method of  claim 1 , further comprising:
 planning, using a wellbore planning system, a planned wellbore trajectory to intersect the predicted location; and   drilling, using a drilling system, a wellbore guided by the planned wellbore trajectory.   
     
     
         3 . The method of  claim 1 , wherein an updated mass is determined in part by the updated flux and the updated well term. 
     
     
         4 . The method of  claim 1 , wherein the stopping criterion is based, at least in part, upon a root mean square (RMS) of a residual vector of at least one of the primary variables and an input residual preset tolerance. 
     
     
         5 . The method of  claim 1 , wherein the stopping criterion is based, at least in part, upon a total mass balance error of each primary variable over the plurality of computational cells. 
     
     
         6 . The method of  claim 1 , wherein the stopping criterion is based, at least in part, upon a total accumulated mass balance error of each primary variable over the plurality of computational cells over all time steps. 
     
     
         7 . The method of  claim 1 , wherein the stopping criterion comprises a sum of total saturations equalling  1  within a specified tolerance. 
     
     
         8 . The method of  claim 1 , wherein an accepted saturation change is limited to a maximum of 0.2 times the updated mass, within a preset tolerance. 
     
     
         9 . The method of  claim 1 , wherein the primary variable update is determined at least in part by a Jacobian, wherein the Jacobian comprises the residual differentiated with respect to the primary variables. 
     
     
         10 . The method of  claim 1 , wherein the primary variables comprise a phase mole fraction and a saturation of at least one of oil, gas and water. 
     
     
         11 . A system, comprising:
 a reservoir simulator, configured to:
 receive a reservoir model of a subterranean region of interest, wherein the reservoir model comprises a plurality of computational cells, 
 receive a production scenario, 
 determine a first set of parameters for a first time from the reservoir model and the production scenario, and 
 predict, using the first set of parameters, a second set of parameters at a second time, wherein the first and second sets of parameters comprise primary variables, wherein the primary variables are used to determine values for a mass, a flux and a well term, wherein the second time is after the first time, and wherein the predicting comprises, iteratively, or recursively, until a stopping criterion is satisfied:
 for each of the plurality of computational cells:
 use the first set of parameters to determine a primary variable update and a residual, 
 determine an updated flux and an updated well term using, at least in part, the primary variable update, 
 predict the second set of parameters based, at least in part, on the updated flux and the updated well term, and 
 assign the second set of parameters to the first set of parameters; and 
 
 
   an interpretation workstation, configured to determine a predicted location of unproduced hydrocarbons based, at least in part, on the second set of parameters.   
     
     
         12 . The system of  claim 11 , further comprising:
 a wellbore planning system, configured to plan a planned wellbore trajectory to intersect the predicted location; and   a drilling system, configured to drill a wellbore guided by the planned wellbore trajectory.   
     
     
         13 . The system of  claim 11 , wherein an updated mass is determined in part by the updated flux and the updated well term. 
     
     
         14 . The system of  claim 11 , wherein the stopping criterion is based, at least in part, upon a root mean square (RMS) of an error vector of at least one of the primary variables. 
     
     
         15 . The system of  claim 11 , wherein the stopping criterion is based, at least in part, upon a total mass balance error of each primary variable over the plurality of computational cells. 
     
     
         16 . The system of  claim 11 , wherein the stopping criterion is based, at least in part, upon a total accumulated mass balance error of each primary variable over the plurality of computational cells over all time steps. 
     
     
         17 . The system of  claim 11 , wherein the stopping criterion comprises a sum of total saturations equalling  1  within a specified tolerance. 
     
     
         18 . The system of  claim 11 , wherein an accepted saturation change is limited to a maximum of 0.2 times the updated mass, within a preset tolerance. 
     
     
         19 . The system of  claim 11 , wherein the primary variable update is determined at least in part by a Jacobian, wherein the Jacobian comprises the residual differentiated with respect to the primary variables. 
     
     
         20 . The system of  claim 11 , wherein the primary variables comprise a phase mole fraction and a saturation of at least one of oil, gas and water.