Method and system for controlling a washout area

Abstract

A method for evaluating and controlling a washout region of a wellbore placed in a formation includes: obtaining information about the wellbore and the formation; establishing a washout indicator function as a function of time and location; computationally determining whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and upon finding presence of the washout region in the specific depth range, quantifying the washout region. The washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary.

What is claimed is: 
     
         1 . A method for evaluating and controlling a washout region of a wellbore placed in a formation, comprising:
 obtaining information about the wellbore and the formation;   establishing a washout indicator function as a function of time and location;   computationally determining whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and   upon finding presence of the washout region in the specific depth range, quantifying the washout region,   wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.   
     
     
         2 . The method of  claim 1 , wherein the quantifying the washout region comprises:
 identifying a cross-sectional area demarcated by the boundary between the washout region and the formation and an original circumference of the wellbore at each depth in the specific depth range;   dividing the cross-sectional area into sections and computing each area of the sections;   obtaining a summation of the sections at each depth in the specific depth range; and   determining a volume of the washout region, by totaling for all depths in the specific depth range, the summation of the sections at each depth.   
     
     
         3 . The method of  claim 2 , wherein the information about the wellbore and the formation comprises:
 in-situ stress measurement;   weight of mud within the specific depth range; and   strength properties of rocks in the formation.   
     
     
         4 . The method of  claim 3 , wherein the information about the wellbore and the formation further comprises:
 for each depth in the specific depth range, a wellbore diameter, an inclination angle of the wellbore, and an azimuth of the wellbore.   
     
     
         5 . The method of  claim 3 , wherein the information about the wellbore further comprises:
 a pore pressure of rocks in the formation.   
     
     
         6 . The method of  claim 1 , wherein the washout indicator function is based on a wellbore stress model and a rock breakout failure criterion. 
     
     
         7 . The method of  claim 3 , wherein the washout indicator function identifies the washout region using Mohr-Coulomb failure criterion. 
     
     
         8 . The method of  claim 2 , further comprising:
 setting a target of mud weight to be used in the wellbore.   
     
     
         9 . The method of  claim 2 , further comprising:
 altering a drilling rate for digging the wellbore.   
     
     
         10 . The method of  claim 2 , further comprising:
 transmitting an alert of at least one of the following: the washout region of a predetermined size range; and the washout region expanding at a predetermined rate range.   
     
     
         11 . A system for evaluating and controlling a washout region of a wellbore placed in a formation, comprising:
 a hardware processor, operatively connected to an interface and a memory that:
 obtains information about the wellbore and the formation; 
 establishes a washout indicator function as a function of time and location in the formation; 
 determines whether the washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation at each depth in a specific depth range; and 
 upon finding presence of the washout region, quantifies the washout region in the specific depth range; 
   the interface for inputting and outputting a signal that the hardware processor processes; and   the memory that stores the information about the wellbore and the formation,   wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.   
     
     
         12 . The system of  claim 11 , wherein the hardware processor quantifies the washout region by:
 identifying a cross-sectional area demarcated by the boundary between the washout region and the formation and an original circumference of the wellbore at each depth in the specific depth range;   dividing the cross-sectional area into sections and computing each area of the sections;   obtaining a summation of the sections at each depth in the specific depth range; and   determining a volume of the washout region, by totaling for all depths in the specific depth range, the summation of the sections at each depth.   
     
     
         13 . The system of  claim 12 , wherein the information about the wellbore and the formation comprises:
 in-situ stress measurement;   weight of mud within the specific depth range; and   strength properties of rocks in the formation.   
     
     
         14 . The system of  claim 13 , wherein the information about the wellbore and the formation further comprises:
 for each depth in the specific depth range, a wellbore diameter, an inclination angle of the wellbore, and an azimuth of the wellbore.   
     
     
         15 . The system of  claim 13 , wherein the information about the wellbore and the formation further comprises:
 a pore pressure of rocks in the formation.   
     
     
         16 . The system of  claim 11 , wherein the washout indicator function is based on a wellbore stress model and a rock breakout failure criterion. 
     
     
         17 . The system of  claim 15 , wherein the washout indicator function identifies the washout region using Mohr-Coulomb failure criterion. 
     
     
         18 . The system of  claim 12 , wherein the hardware processor further:
 sets a target of mud weight to be used in the wellbore.   
     
     
         19 . The system of  claim 12 , wherein the hardware processor further:
 alters a drilling rate in digging the wellbore.   
     
     
         20 . A non-transitory computer readable medium storing instructions executable by a hardware processor of a computer, the instructions comprising:
 obtaining information about a wellbore and a formation;   establishing a washout indicator function as a function of time and location in the formation;   computationally determining whether a washout region exists by calculating the washout indicator function on a cross section of the wellbore and the formation, at each depth in a specific depth range; and   upon finding presence of the washout region, quantifying the washout region in the specific depth range,   wherein the washout indicator function returns: a negative value for a point within the formation; a positive value for a point within the washout region; and zero for a point on a boundary between the washout region and the formation.