Method for exploiting a geological reservoir from a reservoir model matched by the computation of an analytical law of conditional distribution of uncertain parameters of the model

Abstract

The invention is a method for exploiting a geological reservoir to exploit hydrocarbons or provide gas storage. The exploitation is defined on the basis of a reservoir model calibrated relative to dynamic data. The calibration is carried out by computing an objective function for a set of reservoir models. The objective function makes it possible to determine an analytical law of conditional distribution of the uncertain parameters of the model to generate new reservoir models added to the set of reservoir models.

1 - 11 . (canceled) 
     
     
         12 . A method for exploiting a geological reservoir according to an exploitation scheme defined on a basis of a reservoir model, comprising a grid associated with parameters θ of the reservoir, comprising:
 a) providing a reservoir model matched to data measured within the reservoir constructed by:
 i) generating an initial set of reservoir models stochastically from laws of probability p(θ) of the parameters θ; 
 ii) determining an objective function F(θ) that measures a deviation between dynamic data y 1 , . . . , yn acquired during exploitation, dynamic data simulated by a flow simulator and the reservoir models belonging to the set; 
 iii) determining from the objective function F(θ) an analytical law p(θ|y 1 , . . . , yn) of conditional probability of the parameters θ from knowledge of the measured dynamic data y 1 , . . . , yn; 
 iv) generating at least one new reservoir model with the analytical law p(θ|y 1 , . . . , yn) and adding the at least one new model to the set of reservoir models; 
 v) reiterating steps ii) to iv) and determining a reservoir model which minimizes the objective function; 
 
 b) determining an optimum exploitation scheme for the reservoir by simulating the exploitation of the reservoir with the matched reservoir model and the flow simulator; and 
 c) exploiting the reservoir by implementing the optimum exploitation scheme. 
 
     
     
         13 . The method according to  claim 12 , comprising determining the conditional analytical law p(θ|y 1 , . . . , yn) by determining an approximation of a function G(θ) such that G(θ)=exp(−F(θ)) and then computing the analytical law from
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         14 . The method according to  claim 13 , comprising determining the approximation of the function G(θ) by computing G(θi)=exp(−F(θj)) for models i belonging to the set and then interpolating the values of G(θi). 
     
     
         15 . The method according to  claim 14 , comprising interpolating the values of G(θi) by kriging. 
     
     
         16 . The method according to  claim 12 , wherein during step iv) at each iteration new reservoir models are generated from which M1 models are chosen and added to the set and the set of reservoir models is made during construction of the initial set of M 0  of models. 
     
     
         17 . The method according to  claim 13 , wherein during step iv) at each iteration new reservoir models are generated from which M1 models are chosen and added to the set and the set of reservoir models is made during construction of the initial set of M 0  of models. 
     
     
         18 . The method according to  claim 14 , wherein during step iv) at each iteration new reservoir models are generated from which M1 models are chosen and added to the set and the set of reservoir models is made during construction of the initial set of M 0  of models. 
     
     
         19 . The method according to  claim 15 , wherein during step iv) at each iteration new reservoir models are generated from which M1 models are chosen and added to the set and the set of reservoir models is made during construction of the initial set of M 0  of models. 
     
     
         20 . The method according to  claim 16 , comprising sampling the M 0  models of the initial set using a latin hypercube. 
     
     
         21 . The method according to  claim 16 , wherein M 1  models are added to the approximation of the function G(θ). 
     
     
         22 . The method according to  claim 20 , wherein M 1  models are added to the approximation of the function G(θ). 
     
     
         23 . The method according to  claim 21 , wherein at least some of the M 1  models are models for which approximation of the function G(θ) provides maximum values. 
     
     
         24 . The method according to  claim 22 , wherein at least some of the M 1  models are models for which approximation of the function G(θ) provides maximum values. 
     
     
         25 . The method according to  claim 21 , wherein at least some of the M 1  models are models for which a quality of the approximation of the function G(θ) has kriging variances which are highest for the new models. 
     
     
         26 . The method according to  claim 24 , wherein at least some of the M 1  models are models for which a quality of the approximation of the function G(θ) has kriging variances which are highest for the new models. 
     
     
         27 . The method according to  claim 12 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         28 . The method according to  claim 13 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         29 . The method according to  claim 14 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         30 . The method according to  claim 15 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         31 . The method according to  claim 16 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         32 . The method according to  claim 20 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         33 . The method according to  claim 23 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         34 . The method according to  claim 25 , comprising carrying out a sensitivity study by computing objective functions such that each objective function is computed for parameters or for a limited time interval relative to available information. 
     
     
         35 . A computer program product that is downloadable from a communication network, and/or stored on a medium that can be read by computer, and/or executed by a processor, comprising program code instructions for executing the method on a computer comprising:
 a) providing a reservoir model matched to data measured within the reservoir constructed by:
 i) generating an initial set of reservoir models stochastically from laws of probability p(θ) of the parameters 
 ii) determining an objective function F(θ) that measures a deviation between dynamic data y 1 , . . . , yn acquired during exploitation, dynamic data simulated by a flow simulator and the reservoir models belonging to the set; 
 iii) determining from the objective function F(θ) an analytical law p(θ|y 1 , . . . , yn) of conditional probability of the parameters θ from knowledge of the measured dynamic data y 1 , . . . , yn; 
 iv) generating at least one new reservoir model with the analytical law p(θ|y 1 , . . . , yn) and adding the at least one new model to the set of reservoir models; 
 v) reiterating steps ii) to iv) and determining a reservoir model which minimizes the objective function; 
   b) determining an optimum exploitation scheme for the reservoir by simulating the exploitation of the reservoir with the matched reservoir model and the flow simulator; and   c) exploiting the reservoir by implementing the optimum exploitation scheme.