Automatic Iteration of Upstroke and Downstroke Damping Factors with Iterative Bisection Method

Abstract

A method for calculating a downhole card for an oil and gas well includes setting a damping factor to an initial value, calculating a downhole card using the initial load value, and determining whether the difference between a true load value and an effective load value is within a desired error tolerance. If not, the method can also include setting a new damping factor to a value equal at a mid-point between the initial damping factor and a damping factor bound, recalculating the downhole card using the new damping factor, and determining whether the difference between a new true load value and a new effective load value is within a desired error tolerance. If not, the method can also include setting the new damping factor to a value equal at a mid-point between the previous damping factor and a damping factor bound.

What is claimed is: 
     
         1 . A method for calculating a downhole card for an oil and gas well, the method comprising:
 (a) setting a damping factor to an initial value;   (b) calculating a downhole card using the initial load value;   (c) determining whether the difference between a true load value and an effective load value is within a desired error tolerance;   (d) where the difference between the true load value and the effective load value is outside the desired error tolerance, setting a new damping factor to a value equal at a mid-point between the initial damping factor and a damping factor bound;   (e) recalculating the downhole card using the new damping factor;   (f) determining whether the difference between a new true load value and a new effective load value is within a desired error tolerance; and   (g) where the difference between the new true load value and the effective load value is outside the desired error tolerance, setting the new damping factor to a value equal at a mid-point between the previous damping factor and a damping factor bound.   
     
     
         2 . A method for calculating a downhole card for an oil and gas well, the method comprising:
 (a) setting a first damping factor;   (b) calculating a first downhole card using the first damping factor;   (c) determining whether a first difference between a first true load value and a first effective load value is within a predetermined error tolerance;   (d) in response to determining that the first difference is outside the predetermined error tolerance, setting a second damping factor at a midpoint between the first damping factor and a damping factor bound; and   (e) calculating a second downhole card using the second damping factor.   
     
     
         3 . The method of  claim 2 , further comprising determining whether a second difference between a second true load value and a second effective load value is within the predetermined error tolerance. 
     
     
         4 . The method of  claim 3 , further comprising, in response to determining that the second difference is outside the predetermined error tolerance, setting a third damping factor at a mid-point between the second damping factor and the damping factor bound. 
     
     
         5 . The method of  claim 4 , further comprising calculating a third downhole card using the third damping factor. 
     
     
         6 . The method of  claim 2 , wherein the first and second damping factors include first and second upstroke damping factors, respectively. 
     
     
         7 . The method of  claim 6 , wherein setting the first damping factor includes setting the first damping factor to 0.25. 
     
     
         8 . The method of  claim 2 , wherein the first and second damping factors include first and second downstroke damping factors, respectively. 
     
     
         9 . The method of  claim 8 , wherein setting the first damping factor includes setting the first damping factor to 0.5. 
     
     
         10 . The method of  claim 2 , further comprising performing a primary convergence test prior to determining whether the first difference is within the predetermined error tolerance. 
     
     
         11 . A method for generating a downhole card for an oil and gas well, the method comprising:
 (a) setting an upstroke damping factor;   (b) setting a downstroke damping factor;   (c) generating a downhole card using the upstroke damping factor and the downstroke damping factor;   (d) calculating a top of stroke load;   (e) calculating an average upstroke load between a standing valve opening point and a standing valve closing point;   (f) calculating a downstroke load at a traveling valve opening point;   (g) calculating an average downstroke load between the traveling valve opening point and a traveling valve closing point;   (h) performing a primary convergence test, including:
 (i) calculating a horsepower difference between a pump horsepower and a hydraulic horsepower, and 
 (ii) determining whether the horsepower difference is within a first predetermined error tolerance; 
   (i) in response to determining that the horsepower difference is outside the first predetermined error tolerance, performing a secondary convergence test, including:
 (i) calculating an upstroke load difference between the top of stroke load and the average upstroke load, 
 (ii) calculating a downstroke load difference between the downstroke load and the average downstroke load, 
 (iii) determining whether the upstroke load difference is within a second predetermined error tolerance, and 
 (iv) determining whether the downstroke load difference is within a third predetermined error tolerance; and 
   (j) in response to determining that the upstroke load difference is outside the second predetermined error tolerance and/or that the downstroke load difference is outside the third predetermined error tolerance, performing a bisection iteration, wherein the bisection iteration is repeated until (A) the horsepower difference is within the first predetermined error tolerance, (B) the upstroke load difference is within the second predetermined error tolerance, and (C) the downstroke load difference is within the third predetermined error tolerance.   
     
     
         12 . The method of  claim 11 , wherein the bisection iteration includes:
 (i) determining an upstroke direction for the upstroke damping factor,   (ii) determining a downstroke direction for the downstroke damping factor,   (iii) setting a midpoint of a range between the upstroke damping factor and an upstroke damping factor bound as a new upstroke damping factor,   (iv) setting a midpoint of a range between the downstroke damping factor and a downstroke damping factor bound as a new downstroke damping factor, and   (v) generating a new downhole card using the new upstroke damping factor and the new downstroke damping factor.   
     
     
         13 . The method of  claim 11 , further comprising calculating the pump horsepower using Riemann Sums where the pump horsepower is equal to an area of the downhole card. 
     
     
         14 . The method of  claim 11 , further comprising calculating the standing valve opening point. 
     
     
         15 . The method of  claim 11 , further comprising calculating the standing valve closing point. 
     
     
         16 . The method of  claim 11 , further comprising calculating the traveling valve opening point. 
     
     
         17 . The method of  claim 11 , further comprising calculating the traveling valve closing point. 
     
     
         18 . The method of  claim 11 , further comprising calculating a pump intake pressure. 
     
     
         19 . The method of  claim 11 , wherein setting the upstroke damping factor includes setting the upstroke damping factor to 0.25. 
     
     
         20 . The method of  claim 11 , wherein setting the downstroke damping factor includes setting the downstroke damping factor to 0.5.