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Comments Concerning Limited
Entry Treatment Applications

By Alfred R. Jennings, Jr., PE — Enhanced Well Stimulation, Inc.

Limited Entry provides an excellent means of diverting fracturing treatments over several zones of interest at a given injection rate. Effectiveness of the process depends directly upon “back pressure” or perforation friction generated in the wellbore throughout the treatment due to a pre-determined rate/perforation relationship. In this fracturing process, perforation friction is desirable during the entire treatment.

Guidelines for Limited Entry Treatments

A good place to begin a Limited Entry fracture design is to consider the components of the surface pressure during a hydraulic fracturing treatment:

Equation 1:
Psurface = BHTP + ΔPfriction + ΔPperf + ΔPnet − ΔPhydrostatic
Where:
BHTP = Bottomhole Treating Pressure (Frac Gradient x Depth), psi
ΔPfriction = Treating pipe friction pressure (psi) @ injection rate, psi
ΔPperf = Friction pressure through perforations, psi
ΔPhydrostatic = Hydrostatic pressure, psi

The BHTP can usually be determined from the minifrac or can be approximated from an early time ISIPo using the relationship BHTP = ISIPo + Phydrostatic. We are dependent upon the service company to provide accurate values for ΔPfriction. Early in the treatment, ΔPnet will be negligible as the distribution is being made across the perforated intervals as the individual fractures begin their early growth. The initial ΔPhydrostatic will be calculated using density of the base fracturing fluid.

The orifice flow equation given below can be used to calculate ΔPperf :

Equation 2:
ΔPperf =  0.237 ρ Q2
D4 C2
Where:
ΔPperf = 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:

  1. Decide the value of ΔPperf to be allocated for the Limited Entry back pressure. A value of at least 200–300 psi is recommended since a value of this magnitude should be observable in the total Psurface. For example, let’s select 280 psi as the designated value for ΔPperf .
  2. With the established value for ΔPperf , use the following re-arrangement of Equation 2 to determine the rate/perf (Q). This calculation provides the rate/perforation that will be required to develop the ΔPperf to provide the 280 psi for this application of Limited Entry:
    Equation 3:
    Q =  D2 C √ΔP
    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)
    ΔPperf = 250 psi
    ρ = 8.33 lb/gal
    Then Q = 2.0 BPM/perf
  3. Based on the calculated rate/perforation, Q, the injection rate for the Limited Entry fracturing treatment will then need to be determined, based on the maximum allowable surface treating pressure (Psurf) based on Equation 1. Table 1 shows the number of perforations for several possible injection rates and the number of perforations possible for the various rates.
    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.
  4. Based on the pay zones and desirable distribution of the fracturing treatment, the perforations (see Table 1) can be specified for the Limited Entry treatment. It is suggested that the perforation “batches” be selected in even number increments to facilitate perforation placement and phasing (as described in Step 5). An example of possible distribution of perforations is given in Figure 1 below which represents multiple pay intervals to be treated using Limited Entry based on data from Table 1:

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
Figure 1 — Example of Limited Entry for Hydraulic Fracturing

Comments on Perforation Phasing and Limited Entry

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 pre-determined 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:

  1. Even numbered grouping of perforations (e.g. 6, 8, 10, etc. perforations), with 180° perforating, will force the fracturing fluid to exit on opposite sides of the pipe. Field experience (based on RA Tracer surveys) has shown that this is a satisfactory technique for Limited Entry Applications.

    Figure 2
    Figure 2 — Propagation of Limited Entry Fractures with 180° Perforation Phasing

  2. By design, each perforation in Limited Entry is expected to be involved in the treatment. If all perforations are not involved in the treatment, then the allotted ΔPperf becomes excessive because the rate/perf increases leading to a substantial increase in ΔPperf. If all perforations are involved, and the perforations are shot with 60°, 90°, or 120° phasing, multiple fracture planes may be created, leading to substantial near wellbore friction and difficulty in placing the planned fracturing treatment.

    Figure 3
    Figure 3 — Propagation of Limited Entry Fractures with
    60°, 90°, and 120° Perforation Phasing

Breaking Down Perforations and Determination of Number of Perforations Open

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 shut-down 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 near-wellbore 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 ΔPperf at the planned injection rate. When this is done, Equation 2 can be used to determine the approximate rate/perforation which provides the ΔPperf 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 ΔPperf is 320 psi. Using Equation 3,

Q =  D2 C √ΔP  = (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 ball-out treatment should be repeated using higher range (less soluble) Bioballs.

Alfred R. Jennings, Jr., PE
Enhanced Well Stimulation, Inc.

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