Methods, Program Code, Computer Readable Media, and Apparatus For Predicting Matrix Permeability By Optimization and Variance Correction of K-Nearest Neighbors

A computer-assisted method for estimating permeability at unsampled but logged interval locations in a reservoir, the method comprising the steps of:

• providing a database comprising one or more databases or lookup tables containing one or more data sets of measured well log values of a plurality of reservoir properties and a corresponding one or more data sets of measured core values of the plurality of reservoir properties for a plurality of core samples extracted from a plurality of core sample locations in a reservoir, the plurality of reservoir properties including porosity;
• filtering the database based on a level of a statistical match between measured core porosity and computed log porosity to remove unphysical extreme data to thereby form a reference database, the step of filtering including:
• removing collocated log and core data having large porosity discrepancies exceeding a certain level of difference between log and core porosity so that the two respective data types are coherent with each other, and
• performing a graphical comparison of a permeability histogram for a raw unfiltered form of the reference database with permeability histogram for the filtered form of the reference database to thereby quantify the amount of data removed during the filtering as a quality control measure to ensure that the filtering did not excessively impact the overall permeability distribution;
• normalizing each of the plurality of properties at each of the plurality of core sample locations in the filtered database using an initial value of a normalization parameter;
• selecting initial values of weights for each of a plurality of reservoir properties, an initial value of a distance power parameter, and the initial value of a normalization parameter when respective default values are not assigned or to be utilized;
• performing an optimization procedure by a computer, the optimization procedure comprising:
• performing a blind test procedure on the reference database, to include the steps of:
• removing one of the plurality of core samples from the filtered database to thereby create a new database which does not include the removed core sample,
• estimating permeability for the removed core sample according to the deterministic permeability prediction workflow, calculating an absolute value of the difference between the estimated permeability and known permeability of the removed core sample,
• repeating the steps of removing of one of the core samples, estimating permeability, and calculating an absolute value for each other of the plurality of core samples from the filtered database, and
• determining an absolute average residual value of a difference between the estimated permeability and known permeability for the plurality of core samples,
• changing the values of one or more of the weights of the plurality of reservoir properties, the value of the distance power parameter, and the value of the normalization parameter, and
• repeating the step of performing the blind test procedure utilizing the changed values and changing the values of one or more or all of the weights of the plurality of reservoir properties, the value of the distance power parameter, and value of the normalization parameter until local minimum of an absolute average residual value is reached to thereby determine optimized values of the weights for the plurality of reservoir properties, an optimized value of the distance power parameter, and an optimized value of the normalization parameter;
• and
• performing a deterministic permeability prediction workflow utilizing the optimized values of the weights for the plurality of reservoir properties, the optimized value of the distance power parameter, and the optimized value of the normalization parameter to calculate permeability at a query point or an unsampled but logged interval location encompassing the query point.

A non-transitory computer readable medium having processor readable code embodied on the computer readable medium, the processor readable code for programming one or more processors to perform the operations of estimating permeability at unsampled but logged interval locations in a reservoir, the operations comprising:

• performing an optimization procedure, the optimization procedure comprising the operations of:
• selecting initial values of weights for each of a plurality of reservoir properties and an initial value of a distance power parameter when respective default values are not assigned or to be utilized,
• performing a blind test procedure on a reference database comprising one or more databases or lookup tables containing one or more data sets of measured well log values of the plurality of reservoir properties and a corresponding one or more data sets of measured core values of the plurality of reservoir properties for a plurality of core samples extracted from a plurality of core sample locations in a reservoir,
• changing the values of one or more of the weights of the plurality of reservoir properties and the value of the distance power parameter,
• repeating the operation of performing the blind test procedure utilizing the changed values and changing the values of one or more of the weights of the plurality of reservoir properties and the value of the distance power parameter, until local minimum of an absolute average residual value is reached to thereby determine optimized values of the weights for the plurality of reservoir properties and an optimized value of the distance power parameter;
• and
• performing a deterministic permeability prediction workflow utilizing the optimized values of the weights for the plurality of reservoir properties and the optimized value of the distance power parameter to calculate permeability at query point or an unsampled but logged interval location encompassing the query point.

A non-transitory computer readable medium having processor readable code embodied on the computer readable medium, the processor readable code for programming one or more processors to perform the operations of estimating permeability at unsampled but logged interval locations in a reservoir, the operations comprising:

• accessing a database comprising one or more databases or lookup tables containing one or more data sets of measured well log values of a plurality of reservoir properties and a corresponding one or more data sets of measured core values of the plurality of reservoir properties for a plurality of core samples extracted from a plurality of core sample locations in a reservoir, the plurality of reservoir properties including porosity;
• filtering the database based on a level of a statistical match between measured core porosity and computed log porosity to remove unphysical extreme data to thereby form a reference database, the operation of filtering including:
• removing collocated log and core data having large porosity discrepancies exceeding a certain level of difference between log and core porosity so that the two respective data types are coherent with each other, and
• providing for display of a graphical comparison of a permeability histogram for a raw unfiltered form of the reference database with permeability histogram for the filtered form of the reference database to thereby quantify the amount of data removed during the filtering as a quality control measure to ensure that the filtering did not excessively impact the overall permeability distribution;
• normalizing each of the plurality of properties at each of the plurality of core sample locations in the filtered database using an initial value of a normalization parameter;
• receiving user selected initial values of weights for each of a plurality of reservoir properties, an initial value of a distance power parameter, and the initial value of a normalization parameter when respective default values are not assigned or to be utilized;
• performing an optimization procedure, the optimization procedure comprising:
• performing a blind test procedure on the reference database, to include the operations of:
• removing one of the plurality of core samples from the filtered database to thereby create a new database which does not include the removed core sample,
• estimating permeability for the removed core sample according to the deterministic permeability prediction workflow, calculating an absolute value of the difference between the estimated permeability and known permeability of the removed core sample,
• repeating the operations of removing of one of the core samples, estimating permeability, and calculating an absolute value for each other of the plurality of core samples from the filtered database, and
• determining an absolute average residual value of a difference between the estimated permeability and known permeability for the plurality of core samples,
• changing the values of one or more of the weights of the plurality of reservoir properties, the value of the distance power parameter, and the value of the normalization parameter, and
• repeating the operation of performing the blind test procedure utilizing the changed values and changing the values of one or more or all of the weights of the plurality of reservoir properties, the value of the distance power parameter, and value of the normalization parameter until local minimum of an absolute average residual value is reached to thereby determine optimized values of the weights for the plurality of reservoir properties, an optimized value of the distance power parameter, and an optimized value of the normalization parameter;
• and
• performing a deterministic permeability prediction workflow utilizing the optimized values of the weights for the plurality of reservoir properties, the optimized value of the distance power parameter, and the optimized value of the normalization parameter to calculate permeability at a query point or an unsampled but logged interval location encompassing the query point.

An apparatus for estimating permeability at unsampled but logged interval locations in a reservoir, the apparatus comprising:

• a permeability analyzing computer including a processor and memory coupled to the processor;
• and
• permeability analyzing program code adapted to cause the permeability analyzing computer to estimating permeability at unsampled but logged interval locations in a reservoir, the program code stored in the memory of the permeability analyzing computer and including instructions that when executed by the permeability analyzing computer, cause the computer to perform the operations of:
• performing an optimization procedure, the optimization procedure comprising the operations of:
• selecting initial values of weights for each of a plurality of reservoir properties and an initial value of a distance power parameter when respective default values are not assigned or to be utilized,
• performing a blind test procedure on a reference database comprising one or more databases or lookup tables containing one or more data sets of measured well log values of the plurality of reservoir properties and a corresponding one or more data sets of measured core values of the plurality of reservoir properties for a plurality of core samples extracted from a plurality of core sample locations in a reservoir,
• changing the values of one or more of the weights of the plurality of reservoir properties and the value of the distance power parameter,
• repeating the operation of performing the blind test procedure utilizing the changed values and changing the values of one or more of the weights of the plurality of reservoir properties and the value of the distance power parameter, until local minimum of an absolute average residual value is reached to thereby determine optimized values of the weights for the plurality of reservoir properties and an optimized value of the distance power parameter;
• and
• performing a deterministic permeability prediction workflow utilizing the optimized values of the weights for the plurality of reservoir properties and the optimized value of the distance power parameter to calculate permeability at query point or an unsampled but logged interval location encompassing the query point.

An apparatus for estimating permeability at unsampled but logged interval locations in a reservoir, the apparatus comprising:

• a permeability analyzing computer including a processor and memory coupled to the processor;
• and
• permeability analyzing program code adapted to cause the permeability analyzing computer to estimating permeability at unsampled but logged interval locations in a reservoir, the program code stored in the memory of the permeability analyzing computer and including instructions that when executed by the permeability analyzing computer, cause the computer to perform the operations of:
• accessing a database comprising one or more databases or lookup tables containing one or more data sets of measured well log values of a plurality of reservoir properties and a corresponding one or more data sets of measured core values of the plurality of reservoir properties for a plurality of core samples extracted from a plurality of core sample locations in a reservoir, the plurality of reservoir properties including porosity;
• filtering the database based on a level of a statistical match between measured core porosity and computed log porosity to remove unphysical extreme data to thereby form a reference database, the operation of filtering including:
• removing collocated log and core data having large porosity discrepancies exceeding a certain level of difference between log and core porosity so that the two respective data types are coherent with each other, and
• providing for display of a graphical comparison of a permeability histogram for a raw unfiltered form of the reference database with permeability histogram for the filtered form of the reference database to thereby quantify the amount of data removed during the filtering as a quality control measure to ensure that the filtering did not excessively impact the overall permeability distribution;
• normalizing each of the plurality of properties at each of the plurality of core sample locations in the filtered database using an initial value of a normalization parameter;
• receiving user selected initial values of weights for each of a plurality of reservoir properties, an initial value of a distance power parameter, and the initial value of a normalization parameter when respective default values are not assigned or to be utilized;
• performing an optimization procedure, the optimization procedure comprising:
• performing a blind test procedure on the reference database, to include the operations of:
• removing one of the plurality of core samples from the filtered database to thereby create a new database which does not include the removed core sample,
• estimating permeability for the removed core sample according to the deterministic permeability prediction workflow, calculating an absolute value of the difference between the estimated permeability and known permeability of the removed core sample,
• repeating the operations of removing of one of the core samples, estimating permeability, and calculating an absolute value for each other of the plurality of core samples from the filtered database, and
• determining an absolute average residual value of a difference between the estimated permeability and known permeability for the plurality of core samples,
• changing the values of one or more of the weights of the plurality of reservoir properties, the value of the distance power parameter, and the value of the normalization parameter, and
• repeating the operation of performing the blind test procedure utilizing the changed values and changing the values of one or more or all of the weights of the plurality of reservoir properties, the value of the distance power parameter, and value of the normalization parameter until local minimum of an absolute average residual value is reached to thereby determine optimized values of the weights for the plurality of reservoir properties, an optimized value of the distance power parameter, and an optimized value of the normalization parameter;
• and
• performing a deterministic permeability prediction workflow utilizing the optimized values of the weights for the plurality of reservoir properties, the optimized value of the distance power parameter, and the optimized value of the normalization parameter to calculate permeability at a query point or an unsampled but logged interval location encompassing the query point.