System and method for monitoring and controlling underground drilling

A method of monitoring the operation of a drill string drilling into an earthen formation so as to form a bore hole using a drill bit, comprising the steps of:

• a) operating said drill string at a first set of operating parameters, said first set of operating parameters comprising the speed at which said drill bit rotates, said drill string experiencing vibration at first and second locations along said drill string when operating at said first set of operating parameters, said vibration at said first and second locations being characterized by amplitudes, the amplitudes of said vibration at said first and second locations being related by a relationship;
• b) determining the values of said parameters in said first set of operating parameters;
• c) inputting said determined values of said parameters in said first set of operating parameters into a finite element model of said drill string;
• d) using said finite element model of said drill string with said inputted values of said parameters to determine at least a portion of the vibratory mode shape of said drill string when operating at said first set of operating parameters;
• e) using said portion of said vibratory mode shape to determine said relationship between the amplitude of vibration at said first location to the amplitude of vibration at said second location when operating at said first set of operating parameters;
• f) measuring the amplitude of vibration of said drill string at said second location when operating at said first set of operating parameters;
• g) determining the amplitude of vibration of said drill string at said first location by applying to said measured vibration at said second location said relationship between the amplitude of vibration at said first location to said amplitude of vibration at said second location determined from said portion of said vibratory mode shape.

A non-transitory computer-readable storage medium having stored thereon computer-executable instructions for a method of monitoring the operation of a drill string drilling into an earthen formation so as to form a bore hole using a drill bit, the method comprising the steps of:

• a) determining the values of the parameters in a first set of operating parameters at which said drill string is operating, said drill string experiencing vibration at first and second locations along said drill string when operating at said first set of operating parameters, said vibration at said first and second locations being characterized by amplitudes, the amplitudes of said vibration at said first and second locations being related by a relationship;
• b) inputting said determined values of said parameters in said first set of operating parameters into a finite element model of said drill string;
• c) using said finite element model of said drill string with said inputted values of said parameters to determine at least a portion of the vibratory mode shape of said drill string when operating at said first set of operating parameters;
• d) using said portion of said vibratory mode shape to determine said relationship between the amplitude of vibration at said first location to the amplitude of vibration at said second location when operating at said first set of operating parameters;
• e) measuring the amplitude of vibration of said drill string at said second location when operating at said first set of operating parameters;
• f) determining the amplitude of vibration of said drill string at said first location by applying to said measured vibration at said second location said relationship between the amplitude of vibration at said first location to said amplitude of vibration at said second location determined from said portion of said vibratory mode shape.

A method of monitoring the operation of a drill string drilling into an earthen formation so as to form a bore hole using a drill bit, comprising the steps of:

• a) applying a torque to said drill string at a location proximate the surface of the earth so as to rotate said drill string, said application of torque at said location proximate the surface resulting in torque being experienced at first and second locations along said drill string between said drill bit and said location at which said torque is applied proximate the surface, said torque at said first and second locations being related by a relationship, said drill string undergoing angular deflections at said first and second locations;
• b) determining the values of parameters in a first set of operating parameters associated with said rotation of said drill string;
• c) inputting said determined values of said parameters in said first set of operating parameters into a finite element model of said drill string;
• d) using said finite element model of said drill string with said inputted values of said parameters to determine said angular deflections in said drill string at at least said first and second locations along the length of said drill string when operating at said first set of operating parameters;
• e) using said angular deflections at said first and second locations along said drill string to determine said relationship between said torque on said drill string at said first and second locations;
• f) measuring said torque on said drill string at said second location when operating at said first set of operating parameters;
• g) determining said torque on said drill string at said first location by applying to said measured torque at said second location said relationship between said torque on said drill string at said first location to said torque on said drill string at said second location.

A method of monitoring the operation of a drill string having a drill bit drilling into an earthen formation, comprising the steps of:

• a) determining a set of operating parameters for said drill string that will result in the maximum rate of penetration of said drill bit into said earthen formation;
• b) inputting said set of operating parameters into a finite element model of said drill string;
• and
• c) using said finite element model with said inputted set of operating parameters to predict the vibration in said drill string that will result from operation of said drill string according to said set of operating parameters;
• wherein the step of using said finite element model to predict vibration in said drill string comprises performing a forced response analysis by applying an oscillating weight on said drill bit.

A method of monitoring the operation of a drill string having a drill bit drilling into an earthen formation, comprising the steps of:

• a) obtaining a data base relating sets of operating parameters for said drill string to rates of penetration of said drill bit into said earthen formation when operating at said sets of operating parameters;
• b) using a finite element model of said drill string to predict vibration in said drill string when operating at said sets of operating parameters;
• and
• c) using said data base relating sets of operating parameters to rates of penetration and using said predictions of vibration to predict the maximum rate of penetration of said drill string into said earthen formation that will not result in the vibration in said drill string violating a predetermined criteria;
• wherein the step of using said finite element model to predict vibration in said drill string comprises performing a forced response analysis by applying an oscillating weight on said drill bit.