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Comments Concerning Limited

Equation 1:  

P_{surface}  =  BHTP + ΔP_{friction} + ΔP_{perf} + ΔP_{net} − ΔP_{hydrostatic} 
Where:  
BHTP  =  Bottomhole Treating Pressure (Frac Gradient x Depth), psi 
ΔP_{friction}  =  Treating pipe friction pressure (psi) @ injection rate, psi 
ΔP_{perf}  =  Friction pressure through perforations, psi 
ΔP_{hydrostatic}  =  Hydrostatic pressure, psi 
The BHTP can usually be determined from the minifrac or can be approximated from an early time ISIP_{o} using the relationship BHTP = ISIP_{o} + P_{hydrostatic}. We are dependent upon the service company to provide accurate values for ΔP_{friction}. Early in the treatment, ΔP_{net} will be negligible as the distribution is being made across the perforated intervals as the individual fractures begin their early growth. The initial ΔP_{hydrostatic} will be calculated using density of the base fracturing fluid.
The orifice flow equation given below can be used to calculate ΔP_{perf} :
Equation 2:  

ΔP_{perf}  =^{ }  0.237 ρ Q^{2} 
D^{4} C^{2} 
Where:  
ΔP_{perf}  =  Total perforation friction, psi 
Q  =  Flow rate through each perforation, BPM/perf 
D  =  Diameter of perforation, in. 
C  =  Perforation coefficient (0.95. for round perforation) 
ρ  =  Fluid density, lbs/gal 
The procedure for setting up a Limited Entry treatment involves the following steps:
Equation 3:  

Q  =^{ }  D^{2} C √ΔP/ρ 
0.487 
If we use 280 psi, and the following data concerning the perforations:  
D  =  0.42 in. (Average diameter of perforations) 
C  =  0.95 (Coefficient of roundness of jet perforation, 1.0 is round) 
ΔP_{perf}  =  250 psi 
ρ  =  8.33 lb/gal 
Then Q  =  2.0 BPM/perf 
Table 1: Number of Perforations vs. Injection Rate (BPM) 


Rate (BPM)  No. of Perfs 
20  10 
30  15* 
40  20 
50  25* 
60  30 
70  35* 
80  40 
* It is recommended that these be rounded up to the next even number. 
Injection Rate: 40 BPM
Total Number of Perforations: 20
Perforation Friction Pressure: 280 psi
Perforation Diameter: 0.42 inches
Perforation Phasing: 180° (Wireline Conveyed)
Figure 1 — Example of Limited Entry for Hydraulic Fracturing
Limited Entry fracturing is based on the premise that every perforation will be in communication with a hydraulic fracture and will be contributing fluid during the treatment at the predetermined rate. Therefore, if any perforation does not participate, then the incremental rate/perf of every other perforation is increased, resulting in higher perforation friction. Therefore, it is important that the perforations be placed to facilitate the Limited Entry fracturing process as much as possible.
It has been shown in field operations that the most feasible perforation placement for Limited Entry is 180° phasing perforations, even when the Limited Entry perforating is conducted with a wireline conveyed perforating gun. The following reasons are given for using 180° phasing for Limited Entry:
Figure 2 — Propagation of Limited Entry Fractures with 180° Perforation Phasing
Figure 3 — Propagation of Limited Entry Fractures with
60°, 90°, and 120° Perforation Phasing
When Limited Entry is used in hydraulic fracturing, it is always worthwhile to drop perforation ball sealers during the first part of the minifrac to help break down the perforations and to help ensure that all perforations are open and ready to participate in the fracturing treatment. Biodegradable ball sealers are excellent for this purpose in that the proper range of degradability can be selected so that excellent ball performance can be achieved while the balls are seating and then are dissolved quickly at ambient reservoir conditions. (It is recommended that 50% excess soluble ball sealers be dropped to ensure significant ball action). Following the perforation breakdown and shutdown period (approximately 20 minutes) to allow the ball sealers to completely dissolve, the remainder of the minifrac can then be conducted.
At the end of the minifrac, a stepdown test should be conducted to provide an indication of nearwellbore friction. Typically the stepdown test will reflect the usual perforation friction expected for limited entry applications. It is important that one of the data points during the stepdown test provides the ΔP_{perf} at the planned injection rate. When this is done, Equation 2 can be used to determine the approximate rate/perforation which provides the ΔP_{perf} measured for the planned fracturing designed rate. The injection rate/perforation (BPM/perf) can then be divided by the injection rate (BPM) to determine the number of perforations open.
Example Calculation of Perforations Open — A minifrac is performed on a well with the zones and perforated intervals as shown in Figure 1. From the stepdown test a measurement of ΔP_{perf} is 320 psi. Using Equation 3,
Q  =^{ }  D^{2} C √ΔP/ρ  =^{ }(0.42)^{2} (0.95) (320/8.33)^{1/2} (2.053)  =^{ }  2.13 BPM/Perf^{ } 
0.487 
Therefore, with the 40 BPM injection rate achieved during the minifrac, dividing the rate/perf by the rate means that 18+ perforations are open out of the planned 20 perforations. Therefore the treatment can proceed with a relatively high degree of confidence that the designed Limited Entry treatment distribution can be achieved.
Note: If the calculations described about had shown that fewer than desired perforations were open, the ballout treatment should be repeated using higher range (less soluble) Bioballs.
Alfred R. Jennings, Jr., PE
Enhanced Well Stimulation, Inc.
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