A method for determining and regulating the settling rate of a proppant in a hydraulic fracturing operation, characterized in that, the method comprises:
- (1) acquiring the mesh size of the proppant as a predetermined mesh size;
- (2) obtaining the bulk density of the proppant with the predetermined mesh size, the density of a carrier fluid, and the viscosity of the carrier fluid under reservoir temperature;
- (3) obtaining a preset sand ratio for pumping the proppant with the predetermined mesh size;
- (4) calculating the viscosity of the carrier fluid under reservoir temperature according to
- μ
- =
- μ
- 0
- ·
- e
- (
- T
- -
- T
- 0
- )
- /
- T
- 0
- wherein, μ denotes the viscosity of the carrier fluid under reservoir temperature, μ0 denotes the viscosity of the carrier fluid under surface temperature, T denotes the temperature of the target formation, T0 denotes the surface temperature;
- (5) retrieving a pre-established settling rate calculation model corresponding to the predetermined mesh size of the proppant, wherein:
- i) when the mesh size is 30/50, the settling rate is calculated according to
- v
- p
-
- 30
- /
- 50
- =
- 1
-
- 1
-
- 7
- .
- 8
-
- 3
-
- lg
-
- (
- α
- 3
-
- 0
- /
- 50
- m
- 3
-
- 0
- /
- 5
-
- 0
-
- ρ
- s
-
- 30
- /
- 50
- ρ
- l
-
- 30
- /
- 50
- )
-
- e
- -
- n
- 30
- /
- 50
-
- μ
- 3
-
- 0
- /
- 5
-
- 0
- wherein, vp30/50 denotes the settling rate of the proppant with a mesh size of 30/50, α30/50 denotes the sand ratio of the proppant with a mesh size of 30/50 during pumping, m30/50 denotes the sand ratio factor of the proppant with a mesh size of 30/50, ρs30/50 denotes the bulk density of the proppant with a mesh size of 30/50, ρl30/50 denotes the density of the carrier fluid for the proppant with a mesh size of 30/50, μ30/50 denotes the viscosity factor of the proppant with a mesh size of 30/50;
- ρ30/50 denotes the viscosity of the carrier fluid under reservoir temperature for the proppant with a mesh size of 30/50;
- ii) when the mesh size is 40/70, the settling rate is calculated according to
- v
- p
-
- 40
- /
- 70
- =
- 7
-
- 3
- .
- 8
-
- 4
-
- lg
-
- (
- α
- 4
-
- 0
- /
- 70
- m
- 4
-
- 0
- /
- 7
-
- 0
-
- ρ
- s
-
- 40
- /
- 70
- ρ
- l
-
- 40
- /
- 70
- )
-
- e
- -
- n
- 40
- /
- 70
-
- μ
- 4
-
- 0
- /
- 7
-
- 0
- wherein, vp40/70 denotes the settling rate of the proppant with a mesh size of 40/70, α40/70 denotes the sand ratio of the proppant with a mesh size of 40/70 during pumping, m40/70 denotes the sand ratio factor of the proppant with a mesh size of 40/70, ρs40/70 denotes the bulk density of the proppant with a mesh size of 40/70, ρl40/70 denotes the density of the carrier fluid for the proppant with a mesh size of 40/70, μ40/70 denotes the viscosity factor of the proppant with a mesh size of 40/70, ρ40/70 denotes the viscosity of the carrier fluid under reservoir temperature for the proppant with a mesh size of 40/70;
- iii) when the mesh size is 70/140, the settling rate is calculated according to
- v
- p
-
- 70
- /
- 140
- =
- 2
-
- 8
- .
- 3
-
- 4
-
- lg
-
- (
- α
- 7
-
- 0
- /
- 1
-
- 4
-
- 0
- m
- 7
-
- 0
- /
- 1
-
- 4
-
- 0
-
- ρ
- s
-
- 70
- /
- 140
- ρ
- l
-
- 70
- /
- 140
- )
-
- e
- -
- n
- 7
-
- 0
- /
- 1
-
- 4
-
- 0
-
- μ
- 7
-
- 0
- /
- 1
-
- 4
-
- 0
- wherein, vp70/140 denotes the settling rate of the proppant with a mesh size of 70/140, α70/140 denotes the sand ratio of the proppant with a mesh size of 70/140 during pumping, m70/140 denotes the sand ratio factor of the proppant with a mesh size of 70/140, ρs70/140 denotes the bulk density of the proppant with a mesh size of 70/140, ρl70/140 denotes the density of the carrier fluid for the proppant with a mesh size of 70/140, μ70/140 denotes the viscosity factor of the proppant with a mesh size of 70/140, ρ70/140 denotes the viscosity of the carrier fluid under reservoir temperature for the proppant with a mesh size of 70/140;
- iv) when the mesh size is 100/200, the settling rate is calculated according to
- v
- p
-
- 100
- /
- 200
- =
- 6
-
- 8
- .
- 5
-
- 1
-
- lg
-
- (
- α
- 100
- /
- 200
- m
- 1
-
- 0
-
- 0
- /
- 2
-
- 0
-
- 0
-
- ρ
- s
-
- 10
-
- 0
- /
- 2
-
- 0
-
- 0
- ρ
- l
-
- 10
-
- 0
- /
- 2
-
- 0
-
- 0
- )
-
- e
- -
- n
- 100
- /
- 200
-
- μ
- 1
-
- 0
-
- 0
- /
- 2
-
- 0
-
- 0
- wherein, vp100/200 denotes the settling rate of the proppant with a mesh size of 100/200, α100/200 denotes the sand ratio of the proppant with a mesh size of 100/200 during pumping, m100/200 denotes the sand ratio factor of the proppant with a mesh size of 100/200, ρs100/200 denotes the bulk density of the proppant with a mesh size of 100/200, ρl100/200 denotes the density of the carrier fluid for the proppant with a mesh size of 100/200, μ100/200 denotes the viscosity factor of the proppant with a mesh size of 100/200, μ100/200 denotes the viscosity of the carrier fluid under reservoir temperature for the proppant with a mesh size of 100/200;
- Each of said formulas defines the settling rate as a function of the proppant bulk density, the carrier fluid density, the sand ratio, the sand ratio factor, the viscosity of the carrier fluid at reservoir temperature, and the viscosity factor;
- (6) calculating the settling rate of the proppant using the retrieved model by inputting the bulk density of the proppant, the density of the carrier fluid, the sand ratio, and the viscosity of the carrier fluid under reservoir temperature;
- (7) determining whether the calculated settling rate meets a preset settling rate requirement;
- (8) if the calculated settling rate fails to meet the preset requirement, reselecting the mesh size of the proppant, or adjusting at least one of the following:
- the bulk density of the proppant, the density of the carrier fluid, and the viscosity of the carrier fluid under reservoir temperature;
- (9) recalculating the settling rate using the updated parameter(s) until the settling rate meets the preset requirement.