Proppant transport model for well system fluid flow simulations

Patent metadata

Field	Value
Publication number	US-9367653-B2
Application number	US-201314144084-A
Country	US
Kind code	B2
Filing date	Dec 30, 2013
Priority date	Aug 27, 2013
Publication date	Jun 14, 2016
Grant date	Jun 14, 2016

Abstract

In some aspects, a one-dimensional proppant transport flow model represents flow of a proppant-fluid mixture in a subterranean region. The one-dimensional proppant transport flow model includes a proppant momentum conservation model that balances axial proppant momentum in an axial flow direction of the proppant-fluid mixture against dynamic changes in transverse proppant momentum. In some instances, the proppant momentum conservation model can vary the axial proppant momentum, for example, to account for interphase momentum transfer between the proppant and the fluid.

First claim

The invention claimed is:

1. A proppant transport flow modeling method comprising:
generating a one-dimensional proppant transport flow model representing flow of a proppant-fluid mixture in a subterranean region, the one-dimensional proppant transport flow model comprising a proppant momentum conservation model that balances axial proppant momentum in an axial flow direction of the proppant-fluid mixture against dynamic changes in transverse proppant momentum, the proppant momentum conservation model including a variable representing changes of a momentum of a proppant when the proppant settles into a bed of settled proppant and when the proppant becomes re-suspended from the bed of settled proppant into the proppant-fluid mixture;
simulating, by operation of a data processing apparatus, proppant transport in a well system fluid in a well system based on the one-dimensional proppant transport flow model including the proppant momentum conservation model; and
controlling an injection treatment in the well system by controlling a fluid parameter or a fracture treatment plan based on the simulating the one-dimensional proppant transport flow model.

2. The method of claim 1 , wherein the proppant momentum conservation model varies the axial proppant momentum to account for interphase momentum transfer between a proppant and a fluid of the proppant-fluid mixture during suspension and re-suspension of the proppant.

3. The method of claim 1 , wherein the proppant momentum conservation model varies the axial proppant momentum in the axial flow direction to account for proppant settling in another direction different from the axial flow direction.

4. The method of claim 1 , wherein the momentum conservation model varies the axial proppant momentum to account for temperature evolution of the proppant-fluid mixture.

5. The method of claim 1 , wherein the one-dimensional proppant transport flow model comprises a mass flux conservation model that accounts for a bed height and settling velocity of the proppant in the proppant-fluid mixture.

6. The method of claim 1 , wherein the one-dimensional proppant transport flow model represents flow of the proppant-fluid mixture in at least one of a wellbore or a fracture in a subterranean rock formation.

7. The method of claim 1 , wherein the one-dimensional proppant transport flow model includes a finite difference model and a plurality of discretized governing flow equations, and operating the one-dimensional proppant transport flow model comprises solving the discretized governing flow equations.

8. A non-transitory computer-readable medium storing instructions that, when executed by a data processing apparatus, perform operations comprising:
generating a one-dimensional proppant transport flow model representing flow of a proppant-fluid mixture in a subterranean region, the one-dimensional proppant transport flow model comprising a proppant momentum conservation model that balances axial proppant momentum in an axial flow direction of the proppant-fluid mixture against dynamic changes in transverse proppant momentum, the proppant momentum conservation model including a variable representing changes of a momentum of a proppant when the proppant settles into a bed of settled proppant and when the proppant becomes re-suspended from the bed of settled proppant into the proppant-fluid mixture;
simulating, by operation of a data processing apparatus, proppant transport in a well system fluid in a well system based on the one-dimensional proppant transport flow model including the proppant momentum conservation model; and
controlling an injection treatment in the well system by controlling a fluid parameter or a fracture treatment plan based on the simulating the one-dimensional proppant transport flow model.

9. The computer-readable medium of claim 8 , wherein the proppant momentum conservation model balances the axial proppant momentum and the transverse proppant momentum based on the equation:

∂

(

A
0

⁢

ρ
p

⁢

ϕ
p

⁢

v
p

)

∂
t

+

∂

(

A
0

⁢

ρ
p

⁢

ϕ
p

⁢

v
p
2

)

∂
η

+

∂

(

A
0

⁢

P
p

⁢

ϕ
p

)

∂
η

-

A
0

⁢

ρ
p

⁢

ϕ
p

⁢
g
⁢

⁢
cos
⁢

⁢
θ

=

-

ρ
p

⁢

Assignees

• Halliburton Energy Services Inc

Inventors

• Madasu Srinath
• Lin Avi

Classifications

• G06F30/23 Primary

  using finite element methods [FEM] or finite difference methods [FDM] · CPC title

• E21B43/267 Primary

  reinforcing fractures by propping · CPC title

• G06F2111/10

  Numerical modelling · CPC title

• G06F2217/16

  Physics · mapped topic

• E21B21/08

  Controlling or monitoring pressure or flow of drilling fluid, e.g. automatic filling of boreholes, automatic control of bottom pressure (valve arrangements therefor E21B21/10) · CPC title