# US 2020/0401739 A1 · Modeling Fracture Closure Processes In Hydraulic Fracturing Simulators

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- Number: US 2020/0401739 A1
- Document ID: US20200401739A1
- Status: Published application
- Kind: A1
- Application number: 16/901,464
- Filed: 2018-01-16
- Published: 2020-12-24
- Earliest claimed: 2018-01-16
- Assignees: Halliburton Energy Services, Inc.
- Applicants: Halliburton Energy Services, Inc.
- Inventors: Jie Bai; Dinesh Ananda Shetty; Baidurja Ray; Jianfu Ma
- Web page: https://patentgrep.com/patent/US20200401739A1

## CPC

- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- E21B 43/267: reinforcing fractures by propping
- E21B 43/26: by forming crevices or fractures
- E21B 2200/20: Computer models or simulations, e.g. for reservoirs under production, drill bits
- G06F 2111/04: Constraint-based CAD
- G06F 2113/08: Fluids
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS

## Abstract

A method and system for modeling a fracture in a hydraulic fracturing simulator. The method may comprise simulating a well system with an information handling system, defining a closure criteria for a hydraulic fracturing operation, assembling at least one variable in a linear system, assembling at least one variable of a contact force in the linear system, solving for the contact force, and determining at least one opening or at least one closing of the fracture with the contact force. The system may comprise a processor and a memory coupled to the processor. The memory may store a program configured to simulate a well system with an information handling system, define a closure criteria for a hydraulic fracturing operation, assemble at least one variable in a linear system, and determine at least one opening or at least one closing of the fracture with the contact force.

## Claims

### Claim 1

A method for modeling a fracture in a hydraulic fracturing simulator, comprising:
simulating a well system with an information handling system;
defining a closure criteria for a hydraulic fracturing operation;
assembling at least one variable in a linear system;
assembling at least one variable of a contact force in the linear system;
solving for the contact force; and
determining at least one opening or at least one closing of the fracture with the contact force.

### Claim 2 (depends on 1)

The method of claim 1, wherein the assembling at least one variable of the contact force comprises a constraint Δ and a penalty parameter μ.

### Claim 3 (depends on 2)

The method of claim 2, wherein an equation λ−μ>0 is used to determine if the contact force is updated in an iteration.

### Claim 4 (depends on 3)

The method of claim 3, wherein the contact force is updated if an inequality is satisfied.

### Claim 5 (depends on 4)

The method of claim 4, wherein the contact force is updated using a second equation λ=λ−μΔ.

### Claim 6 (depends on 1)

The method of claim 1, wherein the closure criteria is unpropped, wherein unpropped is fracture closure when the fracture closure width reaches residual width.

### Claim 7 (depends on 1)

The method of claim 1, wherein the closure criteria is Propped Mode I, wherein Propped Mode I is the fracture closure when fracture closure width is equal to effective propped width.

### Claim 8 (depends on 1)

The method of claim 1, wherein the closure criteria is Propped Mode II, wherein Propped Mode II is the fracture closure when a fracture proppant concentration reaches critical concentration.

### Claim 9 (depends on 1)

The method of claim 1, further comprising determining if an assembled linear system converges.

### Claim 10 (depends on 9)

The method of claim 9, further comprising updating the closure criteria if the assembled linear system does not converge and updating the assembled linear system.

### Claim 11 (depends on 1)

The method of claim 1, further comprising identify an opening of the fracture or a closing of the fracture during the simulation.

### Claim 12 (depends on 1)

The method of claim 1, further comprising choosing a proppant and adjusting a hydraulic fracturing operation based on the contact force.

### Claim 13 (depends on 1)

The method of claim 1, wherein the solving for the contact force further comprises solving for at least one unknown variable, wherein the at least one unknown variable is commonly rock displacement, stresses, pore pressure, fracture height, fluid pressure, or proppant concentration.

### Claim 14

A system for modeling a fracture in a hydraulic fracturing simulator, comprising:
a processor; and
a memory coupled to the processor, wherein the memory stores a program configured to:
simulate a well system with an information handling system;
define a closure criteria for a hydraulic fracturing operation;
assemble at least one variable in a linear system;
assemble at least one variable of a contact force in a the linear system;
solve for the contact force; and
determine at least one opening or at least one closing of the fracture with the contact force.

### Claim 15 (depends on 14)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 14, wherein assemble the at least one variable of the contact force comprises a constraint Δ and a penalty parameter μ.

### Claim 16 (depends on 15)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 15, wherein an equation λ−μΔ>0 is used to determine if the contact force is updated in an iteration.

### Claim 17 (depends on 16)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 16, wherein the contact force is updated if an inequality is satisfied.

### Claim 18 (depends on 17)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 17, wherein the contact force is updated using a second equation λ=λ−μΔ.

### Claim 19 (depends on 14)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 14, wherein the closure criteria is unpropped, wherein unpropped is the fracture closure when fracture closure width reaches residual width.

### Claim 20 (depends on 14)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 14, wherein the closure criteria is propped mode I, wherein propped mode I is the fracture closure when fracture closure width is equal to effective propped width.

### Claim 21 (depends on 14)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 14, wherein the closure criteria is propped mode II, wherein propped mode II is the fracture closure when a fracture proppant concentration reaches critical concentration.

### Claim 22 (depends on 14)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 14, wherein the program is further configured to determine if an assembled linear system converges.

### Claim 23 (depends on 22)

The system for modeling a fracture in a hydraulic fracturing simulator of claim 22, wherein the program is further configured to update the closure criteria if the assembled linear system does not converge and updating the assembled linear system.