Abstract:
A method includes arranging shaped charges in a perforating gun to produce perforation holes in a helical pattern that is defined in part by a phase angle; and choosing four adjacent perforation holes to be created that are adjacent nearest neighbors. The distances are determined between three of the four adjacent perforation holes to be created. A standard deviation is minimized between the three adjacent perforation holes. The phase angle is set based on the minimization.

Description:
This application claims the benefit, pursuant to 35 U.S.C. § 119, to U.S. Provisional Application Ser. No. 60/132,441, entitled, “OPTIMIZING CHARGE PHASING OF A PERFORATING GUN,” filed on May 4, 1999, and U.S. Provisional Application Ser. No. 60/132,619, entitled, “OPTIMIZING CHARGE PHASING OF A PERFORATING GUN,” filed on May 5, 1999. 
    
    
     BACKGROUND 
     The invention generally relates to optimizing charge phasing of a perforating gun. 
     For purposes of enhancing production from a subterranean formation, a perforating gun typically is lowered down into a wellbore (that extends through the formation), and radially oriented shaped charges (of the perforating gun) are detonated to form perforations in the formation. Typically, specified parameters called a shot density and a phasing (described below) control the number of shaped charges of the gun and the distances between the shaped charges. If the spacing between two adjacent perforations near the sandface is too small, then a portion of the formation (called a bridge) that is located between the adjacent perforations may fail and permit communication between the perforations. This bridge failure may cause disaggregated sand to be produced through the perforations. 
     As an example, referring to FIG. 1, a perforating gun  20  includes shaped charges  10  (shaped charges  10   a ,  10   b  and  10   c , as examples) that extend around a central axis of the gun  20  in a helical, or spiral, pattern. Each shaped charge 10 points radially outwardly toward a well casing  12 , and adjacent shaped charges  10  in the spiral pattern are radially separated by a phase angle of 135° (as an example), i.e., the phasing of the shaped charges  10  is 135°. 
     SUMMARY 
     In one embodiment, a method includes arranging shaped charges in a perforating gun to produce perforation holes in a helical pattern that is defined in part by a phase angle; and choosing four adjacent perforation holes to be created that are adjacent nearest neighbors. The distances are determined between three of the four adjacent perforation holes to be created. A standard deviation is minimized between the three adjacent perforation holes. The phase angle is set based on the minimization. 
    
    
     Other embodiments and features will become apparent from the following description, from the drawings, and from the claims. 
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 is a cross-sectional view of a perforating gun. 
     FIG. 2 is a schematic side view of a perforating gun of the prior art. 
     FIGS. 3 and 4 are schematic diagrams illustrating a pattern of perforation holes in the sandface according to an embodiment of the invention. 
     FIGS. 5,  10 ,  11  and  12  are schematic diagrams illustrating patterns of perforation holes according to different embodiments of the invention. 
     FIGS. 6 and 7 are cross-sectional views of a well illustrating the design of different perforating guns according to different embodiments of the invention. 
     FIGS. 8 and 9 are cross-sectional views of wells illustrating different perforating radii for different types of wells. 
     FIG. 13 is a plot of an optimum phase angle and a minimum perforation hole-to-perforation hole distance versus the product of shot density and distance. 
     FIGS. 14,  15  and  16  depict different completion types illustrating different definitions for the distance shown in FIG.  13 . 
    
    
     DETAILED DESCRIPTION 
     Referring to FIGS. 3 and 4, an embodiment of a perforating gun in accordance with the invention has shaped charges that are arranged in a helical, or spiral, pattern to produce perforations in a sandface  40 . In particular, in some embodiments, the shaped charges are arranged to produce a corresponding spiral pattern of perforation holes  50  (perforation holes  50   a ,  50   b ,  50   c  and  50   d , as examples) in the sandface  40 . In this manner, the spiral pattern may include wrap around the sandface  40  several times, i.e., include several windings. For the exemplary pattern depicted in FIG. 3, the pattern wraps around the sandface  40  three times. It has been discovered, for the case where the spiral pattern includes approximately three or more windings around the sandface  40 , four distances L 1 , L 2 , L 3  and L 4  between adjacent shaped charges (as indicated by the corresponding perforation holes  50 ) need to be considered to maximize the distances between adjacent perforations in a formation. More particularly, the phasing of the corresponding shaped charges may be optimized by phasing the shaped charges at an optimal phase angle that causes two of the L 1 , L 2 , L 3  and L 4  distances to be approximately equal to each other. 
     For example, a perforation hole  50   b  of a first winding may be selected. For this selection, the following distances are used to determine the optimal phase angle: the distance L, between the perforation hole  50   b  and another perforation hole  50   a  of the first winding; the distance L 2  between the perforation hole  50   b  and another perforation hole  50   c  of the second winding; the distance L 3  between the perforation holes  50   a  and  50   c ; and the distance L 4  between the perforation hole  50   b  and a perforation hole  50   d  of the third winding. In particular the L 1 , L 2 , L 3  and L 4  distances may be described by the following equations: 
     
       
           L   1 ={square root over (( r +L φ) 2   +h   1   2 +L )} 
       
     
     
       
           L   2 ={square root over (( r +L φ 2 +L ) 2   +h   2   2 +L )} 
       
     
     
       
           L   3 ={square root over (( r +L φ 3 +L ) 2   +h   3   2 +L )} 
       
     
     
       
           L   4 ={square root over (( r +L φ 4 +L ) 2   +h   4   2 +L )} 
       
     
     where “r” represents the distance to the sandface  40  (for a sand prevention completion) as measured from the center of the perforating gun; “φ 1 ” represents the radial angle (about the axis of the sandface  40 ) between the perforation holes  50   a  and  50   b ; “φ 2 ” represents the radial angle between the perforation holes  50   b  and  50   c ; “φ 3 ” represents the radial angle between the perforation holes  50   a  and  50   c ; “φ 4 ” represents the radial angle between the perforation holes  50   b  and  50   d ; “h 1 ” represents a distance by which the perforation holes  50   a  and  50   b  are separated along the well axis; “h 2 ” represents a distance by which the perforation holes  50   b  and  50   c  are separated along the well axis; “h 3 ” (the sum of h, and h 2 ) represents a distance by which the perforation holes  50   a  and  50   c  are separated along the well axis; and “h 4 ” represents an axial distance between perforation holes  50   b  and  50   d.    
     From these equations, different values for φ 1  may be substituted until an optimal phase angle is found, a condition that is indicated by two of the L 1 , L 2 , L 3  and L 4  distances being equal. The distance L 4  is only significant when the product of the shot density and the distance r exceeds a predetermined threshold. In some embodiments, when the shot density is expressed in shots/foot and the distance r is expressed in inches, the predetermined threshold may be approximately  42 . 
     In other embodiments, the value chosen for distance r in the equations above may be based on the type of completion. For example, referring to FIG. 8, for a natural completion in a strong sandstone or carbonate formation (as examples) failure of the bridges between the perforations may be highly unlikely, and as a result, efficiently draining the reservoir may be a greater concern. For this case, the distance r may be chosen to maximize production from the formation. More particularly, in some embodiments, the distance r may extend from the center of a perforating gun  170  to a point of a particular perforation  182  near where the highest flow rates of production occur. In this manner, the flow rate of production fluid into the perforation  182  typically is the largest near the far end of the perforation  182 , an end that is located a distance D from the center of the perforating gun  170 . The flow rates substantially decrease closer to a sandface  180 , at a distance of approximately {fraction ( 1 / 2 )}-D to {fraction ( 3 / 4 )}-D from the center of the perforating gun  170 . Therefore, in some embodiments, to maximum the production, the distance r may extend beyond the sandface  180 . In this manner, the distance r may be assigned a value in approximately in the range of {fraction ( 1 / 2 )}-D to {fraction ( 3 / 4 )}-D. The optimal phase angle may then be computed as described above using this radius. 
     Referring to FIG. 9, as another example, the formation being perforated may be a carbonate formation, a formation into which acids may be introduced via perforations  184  (only one such perforation  184  being depicted in FIG.  9 ). In this manner, the acid may form tunnels  192 , beginning near the end of the perforation  184 . For this type of production environment, the largest flow rates occur near the tunnels  192 . Therefore, to maximize production, instead of choosing the distance r to extend to a sandface  200 , the distance r is alternatively chosen to extend to the end of the perforation  184  and have a value approximately equal to the distance D from the center of the perforating gun  190  to the end of the perforation  184 . The optimal phase angle may then be computed as described above using this radius. 
     Other values for the distance r that cause the distance r to extend beyond the sandface may be chosen based on the type of completion and/or formation. The perforating gun  170 ,  190  in the cross-sections depicted in FIGS. 8 and 9 is concentric with respect to the sandface. However the distance r may be adjusted for the eccentric arrangements, as described above. 
     The distance r is chosen to optimize some characteristic of the well. For example, FIG. 14 depicts a distance r chosen in a well  300  to establish optimum phasing at a sand interface  301 . FIG. 15 depicts a distance r chosen in a well  322  to establish optimum phasing to maximize production at a predefined distance into the formation. FIG. 16 depicts a distance r chosen in a well  334  to optimize phasing where acidization occurs. 
     FIG. 13 depicts an optimum perforation phasing for maximum perforation hole-to-perforation hole spacing. As shown, as the product of the perforation distance and the shot density increases, the optimum phase angle approaches an angle near approximately 140°. 
     Optimal phase solutions may also be found for a perforating gun that has shaped charges that are arranged in planes. In this manner, referring to FIG. 5, this type of perforating gun includes shaped charges that are arranged to produce perforation holes  102  (perforation holes  102   a ,  102   b  and  102   c , as examples) in a sandface  100 . The perforation holes  102  (and the corresponding shaped charges) are arranged in alternating planes, and the normal of each plane is parallel to the well axis. The perforation holes  102  (and corresponding shaped charges) of each plane are located between the perforation holes (and corresponding shaped charges) of an adjacent plane. In some embodiments, each perforation hole  102  (the perforation hole  102   c , for example) is located a distance L 2  from the two closest perforation holes (perforation holes  102   a  and  102   b , as examples) and located a distance (called L 1 ) from the adjacent perforation holes  120  (perforation hole  102   b , for example) of the same plane. 
     The equations to determine L 1 , L 2  and L 3  are described below: 
       L   1 =2 πr/i   
     
       
           L   2 =1/2 {square root over ( L   1   2   +L   3   2 +L )} 
       
     
     
       
           L   3 =2(12) i/N,   
       
     
     where “N” represents the number of shots per foot and “i” represents the number of shots per plane. 
     Referring to FIG. 6, in some embodiments, a perforating gun  140  may include shaped charges that are arranged to produce perforations in the sandface  150  with a specified orientation. In this manner, the shaped charges may be arranged to perforate a top portion of the sandface  150  over an angle φ 1  and arranged to perforate a bottom portion of the well casing  150  over an angle φ 2  As depicted in FIG. 6, in some embodiments, the φ 1  and φ 2  angles are approximately equal to each other, and the perforating gun  140  is concentric with the sandface  150  (i.e., a center  142  of the sandface  150  is aligned with a center  144  of the perforating gun  140 ). However, in other embodiments, the perforating gun  140  may be eccentric to the sandface  150  (a scenario described below) and/or the φ 1  and φ 2  angles may be different. 
     To determine the shot density for the lateral well, the perforation-to-perforation spacing needs to be taken into account for purposes of preventing perforation failures. Thus, this design consideration tends to decrease the shot density. However, another design consideration is the optimization of the production flow, a consideration that tends to increase the shot density. Referring to FIG. 10 that depicts a perforation pattern  194 , to take into account these considerations, the following equation describes the maximum shot density for a perforating gun in which the shaped charges are arranged in a spiral pattern:              (     24   spf     )     2     =       L   2     -       [     ϕ                 r     ]     2         ,                          
     where “spf” is the shot density, “L” is the minimum spacing between perforations  196 , “φ” is the angle of perforation, “r” is the radius of the wellbore for a centralized gun or the distance from the center of the gun to the sandface for a gun whose longitudinal axis is eccentric with respect to the axis of the wellbore and where L&gt;φr. As an example for equal to 4.25 inches (in.), φ equal to 45 degrees and L equal to 4 inches, the maximum shot density is approximately equal to 10.89. This shot density is to be contrasted to a perforating gun that has shaped charges located at zero and one hundred eighty degrees, an arrangement that produces a maximum shot density of 6. 
     As another example, FIG. 11 depicts a pattern  210  of perforation holes  208  for a perforating gun that is used in larger wellbores and has shaped charges that are arranged in a planar fashion with two charges per plane. For this case, the axial distance (L) between adjacent aligned perforation holes  208  is less than or equal to φr. For this arrangement, the maximum shot density may be described by the following equation:          spf   =     48   L       ,                          
     where “L/2” is the distance between adjacent shaped charge planes. 
     Referring to FIG. 12 that depicts a spiral perforation pattern  230 , the axial distance (called L below) between adjacent aligned perforation holes  220  in different planes may also have to be considered in the spiral phasing pattern  230  if L≦φr, a case that is depicted in FIG.  12 . In this case, “L/4” is the distance between each plane of perforation holes  220 . 
     The perforating gun may be eccentric with respect to the sandface. For example, referring to FIG. 7, a perforating gun  146  may be positioned in a casing  160  so that the perforating gun  146  rests on the bottom portion of the casing  160  and is eccentric with respect to the sandface  150 . Furthermore, it may be desired that the perforating gun  140  perforates a top portion  156  of the sandface  150 . Conventional perforating guns may assume that the perforating gun is concentric with the sandface  150 . However, this assumption may produce a perforation distribution that is larger than expected. 
     In contrast to conventional designs, the perforating gun  146  accounts for the eccentricity of the perforating gun  146  with respect to the sandface  150 . In this manner, the shaped charges of the perforating gun  146  are arranged to produce a top perforation distribution angle (called θ 1  and measured from the center  144  of the perforating gun  146  to the top portion  156 ) that is smaller than the φ 1  angle in order to perforate just the desired top portion  156 . Similarly, other shaped charges of the perforating gun  146  may be arranged to perforate a bottom portion  158  of the sandface  150 . In particular, the perforating gun  146  is closer to the bottom portion  158  than if the perforating gun  146  were at the center  142  of the well casing  150 . As a result, a bottom perforation distribution angle (called θ 2  and measured from the center  140  of the perforating gun  140  to the bottom portion  156 ) is larger than a φ 2  angle that is formed between the well center  142  and the bottom portion  156 . 
     Other embodiments are possible. For example, as depicted in FIG. 7, the φ 2  angle is less than the φ 1  angle. However, in other embodiments, the φ 2  angle may be greater than the φ 1  angle. In some embodiments, the φ 2  and φ 1  angles may be different, and the perforating gun  146  may be concentric with respect to the sandface  150 . 
     While the invention has been disclosed with respect to a limited number of embodiments, those skilled in the art, having the benefit of this disclosure, will appreciate numerous modifications and variations therefrom.