Space-time surrogate models of subterranean regions

Abstract

Methods for creating and using space-time surrogate models of subsurface regions, such as subsurface regions containing at least one hydrocarbon formation. The created surrogate models are explicit models that may be created from implicit models, such as computationally intensive full-physics models. The space-time surrogate models are parametric with respect to preselected variables, such as space, state, and/or design variables, while also indicating responsiveness of the preselected variables with respect to time. In some embodiments, the space-time surrogate model may be parametric with respect to preselected variables as well as to time. Methods for updating and evolving models of subsurface regions are also disclosed.

1 . A method for using a space-time surrogate model of a subsurface region to predict subterranean conditions, the method comprising:
 selecting input values for which a predicted space-time response from a subsurface region is desired, wherein the input values include values for at least two preselected variables and a time value;   providing non-transitory computer readable instructions to the computer processor to cause the computer processor to generate a surrogate model of a full-physics model of a subsurface region for preselected variables at a first time value within a range of time values within at least a portion of the full-physics model and determining a corresponding surrogate model coefficient for the first time value;   repeating the generating n times for n additional time values that are different than the first time value, wherein n is an integer greater than 1, wherein the first time value and the n additional time values define a range of time values and creating a matrix of surrogate model coefficients over the range of time values;   creating an explicit space-time surrogate model of the at least a portion of the full physics model based on the surrogate models produced by the generating and the repeating, wherein the explicit space-time surrogate model is parametric for at least the preselected variables;   accessing a database of space-time surrogate function coefficients for a plurality of explicit space-time surrogate models of a full-physics model for at least the preselected variables and a time period in the subsurface region, wherein the space-time surrogate function coefficients correspond to parameterized solutions of the preselected variables for a range of time values within the time period;   comparing the selected input values to at least two solutions in the database of space-time coefficients to identify a closest solution in the database; and   determining a projected response for the selected input values based on the identified closest solution from the database of space-time surrogate function coefficients to predict the subterranean conditions for the selected input values.   
     
     
         2 . The method of  claim 1 , further comprising generating a time-varying function related to at least a portion of the matrix of surrogate model coefficients. 
     
     
         3 . The method of  claim 2 , further comprising creating the explicit space-time surrogate model of the at least a portion of the full physics model based on (1) the surrogate models produced by the generating and the repeating and (2) the generated time-varying function. 
     
     
         4 . The method of  claim 1 , wherein the comparing includes utilizing at least one interpolative or regressive function to determine the projected response based on the closest solutions. 
     
     
         5 . The method of  claim 1 , wherein the comparing includes determining a set of response space-time surrogate function coefficients for the selected input values. 
     
     
         6 . The method of  claim 1 , wherein the method further comprises at least one of storing the set of response space-time surrogate function coefficients in the database and displaying the set of response space-time surrogate function coefficients. 
     
     
         7 . The method of  claim 1 , wherein the method further includes creating the database of space-time surrogate function coefficients, and optionally creating the database of space-time surrogate function coefficients from an implicit model of the subsurface region. 
     
     
         8 . The method of  claim 1 , wherein the method includes displaying the projected response. 
     
     
         9 . The method of  claim 1 , wherein the method includes obtaining new information and updating the space-time surrogate model responsive to the new information. 
     
     
         10 . The method of  claim 1 , further comprising extracting hydrocarbons from the subsurface region based at least in part upon the determined projected response. 
     
     
         11 . The method of  claim 1 , further comprising utilizing the space-time surrogate model to predict a future determined response in the subsurface region at a future time value. 
     
     
         12 . The method of  claim 1 , further comprising extracting hydrocarbons from the subsurface region based at least in part upon the predicted future response.