# US 11,994,019 B2 · Perforation cluster design method and system based on a hybrid model to predict proppant distribution

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- Number: US 11,994,019 B2
- Document ID: US11994019B2
- Status: Granted
- Kind: B2
- Application number: 17/500,121
- Filed: 2021-10-13
- Published: 2022-04-14
- Granted: 2024-05-28
- Earliest claimed: 2020-10-14
- Assignees: Geodynamics, Inc.
- Applicants: Geodynamics, Inc.
- Inventors: Jack J. Kolle; Alan C. Mueller
- Web page: https://patentgrep.com/patent/US11994019B2

## CPC

- E21B 47/10: Locating fluid leaks, intrusions or movements
- E21B 43/267: reinforcing fractures by propping
- E21B 43/29: Obtaining a slurry of minerals, e.g. by using nozzles
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G06F 30/28: using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
- E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits
- G06F 2113/08: Fluids
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method for determining the distribution of a proppant and associated slurry exiting perforations made in a casing, which is placed in a well, includes receiving settling data describing the proppant settling in the casing; receiving a slip parameter describing a casing velocity of the proppant relative to a perforation velocity of the proppant; calculating with a computing device, based on a constant proppant concentration model, (1) initial flow rates Q′(i) of the proppant through the perforations and (2) initial flow rates Q′case(i) of the proppant through the casing, wherein i is the number of perforations; and calculating with the computing device, based on (1) a variable proppant concentration model, (2) the settling data, (3) the slip parameter, (4) the initial flow rates Q′(i) of the proppant through the perforations, and (5) the initial flow rates Q′case(i) of the proppant through the casing, normalized flow rates Q′s(i) of the proppant through the perforations.

## Claims

### Claim 1

A method for forming perforations in a casing which is placed in a well, the method comprising:
determining the distribution of a proppant and associated slurry exiting perforations to be made in the casing, the determining step comprising:
receiving settling data describing the proppant settling in the casing;
receiving a slip parameter describing a casing velocity of the proppant relative to a perforation velocity of the proppant;
calculating with a computing device, based on a constant proppant concentration model, (1) initial flow rates Q′(i) of the proppant through the perforations and (2) initial flow rates Q′case(i) of the proppant through the casing, wherein i is the number of perforations; and
calculating with the computing device, based on (1) a variable proppant concentration model, (2) the settling data, (3) the slip parameter, (4) the initial flow rates Q′(i) of the proppant through the perforations, and (5) the initial flow rates Q′case(i) of the proppant through the casing, normalized flow rates Q′s(i) of the proppant through the perforations;
placing the casing in a well adjacent to a formation;
based on the normalized flow rates Q′s(i), forming perforations in the casing with a size, orientation, and location to provide a substantially uniform placement of proppant and fluid in the formation; and
pumping slurry comprising proppant and fluid into the casing, through the perforations, and into the formation.

### Claim 2 (depends on 1)

The method of claim 1, wherein the settling data and the slip parameter are calculated with a supercomputer, while the computing device is an engineer workstation, which is slower than the supercomputer.

### Claim 3 (depends on 1)

The method of claim 1, the determining step further comprising:
calculating an ingestion area for each perforation, wherein the ingestion area is determined by a ratio of (1) the static perforation flow rate Q′(i) to (2) the static casing flow rate Q′case(i).

### Claim 4 (depends on 3)

The method of claim 3, the determining step further comprising:
calculating an ingestion area proppant concentration Xingest(i) based on the ingestion area and the settling data.

### Claim 5 (depends on 4)

The method of claim 4, the determining step further comprising:
calculating a perforation proppant concentration Xs′(i) based on the ingestion area proppant concentration Xingest(i) and the slip parameter.

### Claim 6 (depends on 5)

The method of claim 5, the determining step further comprising:
calculating dynamic proppant perforation flow rates Qs(i), based on the variable proppant concentration model, as a function of (1) the perforation proppant concentration Xs′(2) corresponding areas of the perforations, and (3) corresponding perforation exit velocities.

### Claim 7 (depends on 6)

The method of claim 6, the determining step further comprising:
performing a mass balance to obtain the normalized flow rates Q′s(i) of the proppant through the perforations, based on the dynamic proppant perforation flow rates Qs(i).