Drilling performance optimization with extremum seeking

Abstract

A drilling optimization method including perturbing one or more drilling control parameters with a periodic or a stochastic signal during a drilling process, estimating at least one drilling performance measure to optimize the drilling process based on the perturbed one or more drilling control parameters, perturbing the at least one drilling performance measure with a periodic or a stochastic perturbation source through demodulation, determine a next best estimate of the one or more drilling control parameters to optimize the at least one drilling performance measure, perturbing the next best estimate by a periodic or a stochastic perturbation source through modulation, and feeding the perturbation next best estimates of the one or more drilling control parameters back to the drilling process.

What is claimed is: 
     
         1 . A method comprising:
 perturbing a drilling control parameter with a periodic or a stochastic signal during a drilling process;   estimating or calculating a drilling performance measure to optimize the drilling process based on the perturbation of the drilling control parameter;   perturbing the drilling performance measure by multiplying the drilling performance measure with a periodic or a stochastic perturbation source through demodulation;   determining a next best estimate of the drilling control parameter to optimize the drilling performance measure;   perturbing the next best estimate by a periodic or a stochastic perturbation source through modulation; and   feeding the perturbed next best estimate of the drilling control parameters to the drilling process.   
     
     
         2 . The method of  claim 1 , further comprising feeding the drilling performance measure through a high-pass filter. 
     
     
         3 . The method of  claim 1 , further comprising feeding the perturbed drilling performance measure through a low-pass filter. 
     
     
         4 . The method of  claim 1 , wherein determining the next best estimate comprises integrating a gradient to calculate the next best estimate. 
     
     
         5 . The method of  claim 1 , wherein feeding next best estimate to the drilling process includes adjusting the one or more drilling control parameters thus optimizing the selected at least one drilling performance measure. 
     
     
         6 . The method of  claim 1 , drilling at least a portion of a wellbore based on the perturbed next best estimate. 
     
     
         7 . The method of  claim 1 , wherein estimating, perturbing, determining, perturbing, and feeding the perturbed next best estimate are repeated until a gradient is less than a predetermined threshold. 
     
     
         8 . The method of  claim 7 , wherein the predetermined threshold is zero. 
     
     
         9 . A drilling system comprising:
 a drilling rig operable to form a wellbore in a subterranean formation, the drilling rig having one or more processors and a memory coupled therewith, the one or more processors operable to execute instructions stored on the memory that cause the cause the drilling system to:
 perturb a drilling control parameter with a periodic or a stochastic signal during a drilling process; 
 estimate or calculating a drilling performance measure to optimize the drilling process based on the perturbation of the drilling control parameter; 
 perturb the drilling performance measure by multiplying the drilling performance measure with a periodic or a stochastic perturbation source through demodulation; 
 determine a next best estimate of the drilling control parameter to optimize the drilling performance measure; 
 perturb the next best estimate by a periodic or a stochastic perturbation source through modulation; and 
 feed the perturbed next best estimate of the drilling control parameters to the drilling process. 
   
     
     
         10 . The drilling system of  claim 9 , further comprising feed the drilling performance measure through a high-pass filter. 
     
     
         11 . The drilling system of  claim 9 , further comprising feed the perturbed drilling performance measure through a low-pass filter. 
     
     
         12 . The drilling system of  claim 9 , wherein determine the next best estimate comprises integrate a gradient to calculate the next best estimate. 
     
     
         13 . The drilling system of  claim 9 , wherein feed the next best estimate to the drilling process includes adjust the one or more drilling control parameters thus optimizing the selected at least one drilling performance measure. 
     
     
         14 . The drilling system of  claim 9 , drill at least a portion of a wellbore based on the perturbed next best estimate. 
     
     
         15 . The drilling system of  claim 9 , wherein estimate, perturb, determine, perturbing, and feed the perturbed next best estimate are repeated until a gradient is less than a predetermined threshold. 
     
     
         16 . The drilling system of  claim 15 , wherein the predetermined threshold is zero. 
     
     
         17 . A non-transitory computer-readable medium comprising executable instructions, which when executed by a processor, causes the processor to:
 perturb a drilling control parameter with a periodic or a stochastic signal during a drilling process;   estimate or calculating a drilling performance measure to optimize the drilling process based on the perturbation of the drilling control parameter;   perturb the drilling performance measure by multiplying the drilling performance measure with a periodic or a stochastic perturbation source through demodulation;   determine a next best estimate of the drilling control parameter to optimize the drilling performance measure;   perturb the next best estimate by a periodic or a stochastic perturbation source through modulation; and   feed the perturbed next best estimate of the drilling control parameters to the drilling process.   
     
     
         18 . The non-transitory computer-readable medium of  claim 17 , further comprising feed the drilling performance measure through a high-pass filter. 
     
     
         19 . The non-transitory computer-readable medium of  claim 17 , further comprising feed the perturbed drilling performance measure through a low-pass filter. 
     
     
         20 . The non-transitory computer-readable medium of  claim 17 , wherein estimate, perturb, determine, perturb, and feed the perturbed next best estimate are repeated until a gradient is less than a predetermined threshold.