# US 9,752,388 B2 ยท Estimating casing wear due to drill string reciprocation > Agents: this data is available as JSON from the patentgrep API and MCP server โ€” see https://patentgrep.com/llms.txt - Number: US 9,752,388 B2 - Document ID: US9752388B2 - Status: Granted - Kind: B2 - Application number: 14/917,398 - Filed: 2015-06-12 - Published: 2017-06-08 - Granted: 2017-09-05 - Earliest claimed: 2015-06-12 - Assignees: Landmark Graphics Corporation - Applicants: Landmark Graphics Corporation - Inventors: Aniket; Adolfo Gonzales; Robello Samuel - Web page: https://patentgrep.com/patent/US9752388B2 ## CPC - E21B 12/02: Wear indicators - E21B 47/00: Survey of boreholes or wells (monitoring pressure or flow of drilling fluid E21B21/08) - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - E21B 41/00: Equipment or details not covered by groups E21B15/00 - E21B40/00 - G06F 2111/10: Numerical modelling - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) ## Abstract Estimating casing wear during a reciprocation portion of a drilling operation may take into account the forces that cause casing wear during the up and down strokes independently. For example, during a drilling operation, a method may include reciprocating the drill string through the wellbore for a plurality of up strokes and a plurality of down strokes according to reciprocation parameters; calculating an up stroke normal force and a down stroke normal force for the casing or a section thereof; calculating up and down stroke casing wears based on the up and down stroke normal forces, respectively, using a reciprocation casing wear model; calculating a reciprocation casing wear 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. ## Claims ### Claim 1 A method comprising: drilling a wellbore penetrating a subterranean formation 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; reciprocating the drill string within 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; 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. ### Claim 2 (depends on 1) The method of claim 1, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of the drill string. ### Claim 3 (depends on 1) The method of claim 1, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of the casing or the section thereof. ### Claim 4 (depends on 1) The method of claim 1, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of a drilling fluid contained in the wellbore. ### Claim 5 (depends on 1) The method of claim 1, wherein the up and down stroke casing wears are further based on a contact distance per stroke according to Equation 1, where AD is the stroke length and RD is a rotational distance of the drill string contact distance per stroke=โˆš{square root over (AD2+RD2)} Equation 1, ### Claim 6 (depends on 1) The method of claim 1, wherein calculating the total casing wear is further based on a drilling casing wear caused by the drill string during drilling. ### Claim 7 (depends on 1) The method of claim 1 further comprising: tripping the drill string through the wellbore, wherein calculating the total casing wear is further based on a tripping casing wear caused by the drill string during a tripping operation. ### Claim 8 (depends on 1) The method of claim 1 further comprising: rotating the drill string without axially moving the drill string along the wellbore, wherein calculating the total casing wear is further based on a rotating off bottom casing wear caused by the drill string rotating the drill string without axially moving. ### Claim 9 (depends on 1) The method of claim 1 further comprising: assigning a threshold value for the total casing wear for the casing or the section thereof; and performing a remedial operation on the casing or the section thereof when the total casing wear exceeds the threshold value. ### Claim 10 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. ### Claim 11 (depends on 10) The method of claim 10, wherein the at least one parameter of the drilling operation is a composition of the casing or the section thereof. ### Claim 12 (depends on 10) The method of claim 10, wherein the at least one parameter of the drilling operation is a composition of the drill string or a section thereof. ### Claim 13 (depends on 10) The method of claim 10, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of the drill string. ### Claim 14 (depends on 10) The method of claim 10, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of the casing or the section thereof. ### Claim 15 (depends on 10) The method of claim 10, wherein the up and down stroke casing wears are further based on a wear factor based on physical and material properties of a drilling fluid contained in the wellbore. ### Claim 16 (depends on 10) The method of claim 10, wherein the up and down stroke casing wears are further based on a contact distance per stroke according to Equation 1, where AD is the stroke length and RD is the rotational distance of the drill string contact distance per stroke=โˆš{square root over (AD2+RD2)} Equation 1. ### Claim 17 (depends on 10) The method of claim 10, wherein calculating the total casing wear is further based on a drilling casing wear caused by the drill string during drilling. ### Claim 18 (depends on 10) The method of claim 10 further comprising: rotating the drill string without axially moving the drill string along the wellbore, wherein calculating the total casing wear is further based on a rotating off bottom casing wear caused by the drill string rotating the drill string without axially moving. ### Claim 19 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. ### Claim 20 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.