Estimating casing wear due to drill string reciprocation

A method comprising:

• simulating a drilling operation with a mathematical model of drilling a wellbore with a drill bit coupled to an end of a drill string extending into the wellbore, wherein a portion of the wellbore is lined with casing, the mathematical model being stored in a non-transitory medium readable by a processor for execution by the processor;
• reciprocating the drill string through the wellbore for a plurality of up strokes and a plurality of down strokes according to reciprocation parameters that include a reciprocation operation time, a drill string revolutions per minute (rpm), a stroke length for the plurality of up and down strokes, and a stroke rate for the plurality of up and down strokes;
• calculating an up stroke normal force and a down stroke normal force for the casing or a section thereof based on the reciprocation parameters using a soft string model, a stiff string model, a finite element model;
• calculating an up stroke casing wear based on the up stroke normal force using a reciprocation casing wear model;
• calculating a down stroke casing wear based on the down stroke normal force using the reciprocation casing wear model;
• calculating a reciprocation casing wear based on the up and down stroke casing wears;
• calculating a total casing wear for the casing or the section thereof based on the reciprocation casing wear using a total casing wear model;
• assigning a threshold value for the total casing wear for the casing or the section thereof;
• and
• changing at least one parameter of the drilling operation when the total casing wear exceeds the threshold value.

A drilling system comprising:

• a drill bit coupled to an end of a drill string extending into a wellbore, wherein a portion of the wellbore is lined with casing;
• a pump operably connected to the drill string for circulating a drilling fluid through the wellbore;
• a control system that includes a non-transitory medium readable by a processor and storing instructions for execution by the processor for performing a method comprising:
• receiving reciprocation parameters related to reciprocating the drill string within the wellbore for a plurality of up strokes and a plurality of down strokes, the reciprocation parameters including a reciprocation operation time, a drill string revolutions per minute (rpm), a stroke length for the plurality of up and down strokes, and a stroke rate for the plurality of up and down strokes;
• calculating an up stroke normal force and a down stroke normal force for the casing or a section thereof based on the reciprocation parameters using a soft string model, a stiff string model, a finite element model;
• calculating an up stroke casing wear based on the up stroke normal force using a reciprocation casing wear model;
• calculating a down stroke casing wear based on the down stroke normal force using the reciprocation casing wear model;
• calculating a total casing wear during the reciprocating based on the up and down stroke casing wears;
• and
• calculating a total casing wear for the casing or the section thereof based on the reciprocation casing wear using a total casing wear model.

A non-transitory medium readable by a processor and storing instructions for execution by the processor for performing a method comprising:

• receiving reciprocation parameters related to reciprocating a drill string through a wellbore lined with casing for a plurality of up strokes and a plurality of down strokes, the reciprocation parameters including a reciprocation operation time, a drill string revolutions per minute (rpm), a stroke length for the plurality of up and down strokes, and a stroke rate for the plurality of up and down strokes;
• calculating an up stroke normal force and a down stroke normal force for the casing or a section thereof based on the reciprocation parameters using a soft string model, a stiff string model, a finite element model;
• calculating an up stroke casing wear based on the up stroke normal force using a reciprocation casing wear model;
• calculating a down stroke casing wear based on the down stroke normal force using the reciprocation casing wear model;
• calculating a total casing wear during the reciprocating based on the up and down stroke casing wears;
• and
• calculating a total casing wear for the casing or the section thereof based on the reciprocation casing wear using a total casing wear model.