Method for scaling mixing operations
View Patent ↗A method for determining mixing time for a variety of vessels is disclosed. This method utilizes information about the configuration, such as vessel diameter, impeller diameter and speed, fluid density and viscosity, and fluid height to determine the appropriate mixing time. In another embodiment, the parameters used to create small batches of material can be used to scale up to larger vessel sizes.
1. A method of determining the salt dissolution time of a salt into a fluid in a first configuration, said configuration having a vessel of a first size, a first impeller and a first mixer operating at a first RPM, comprising:
a. calculating a first mixing parameter (MP) for said first configuration, said parameter defined as
M
P
=
(
ND
2
)
(
D
T
)
2
(
N
Q
ND
3
T
2
H
)
,
where N comprises the RPM of said mixer, D comprises the diameter of said impeller, N Q comprises the power number of said impeller, T comprises the diameter of said vessel, and H comprises the height of said fluid in said vessel;
b. creating a second configuration, using a vessel of a second size, said fluid, said salt, a second impeller and a second mixer operating at a second RPM;
c. calculating a second mixing parameter (MP) for said second configuration;
d. determining a salt dissolution time for said second configuration;
e. creating a third configuration, using a vessel of a third size, said fluid, said salt, a third impeller and a third mixer operating at a third RPM;
f. calculating a third mixing parameter for said third configuration;
g. determining a salt dissolution time for said third configuration;
h. determining two coefficients, α and β, such that said second mixing parameter and its associated salt dissolution time, and said third mixing parameter and its associated salt dissolution time, both satisfy the equation:
Dissolution Time=α×( MP ) β ; and
i. determining the salt dissolution time of said first configuration based on said first mixing parameter, α and β.
2. The method of claim 1 , wherein a diameter of said second impeller and a diameter of said third impeller are the same and a power number of said second impeller and a power number of said third impeller are the same.
3. The method of claim 1 , wherein said second mixer and said third mixer are the same.
4. The method of claim 1 , wherein said second size and said third size are the same.
5. The method of claim 1 , where said first size is greater than said second and third sizes.
6. The method of claim 1 , wherein a diameter of said second impeller and a diameter of third impeller are the same, a power number of said second impeller and a power number of said third impeller are the same, said second mixer and said third mixer are the same, said second size and said third size are the same, and said second RPM differs from said third RPM.
7. The method of claim 6 , wherein said first size is greater than said second and third sizes.
8. A method of determining the salt dissolution time of a salt into a first fluid in a first configuration, said configuration having a vessel of a first size, a first impeller and a first mixer operating at a first RPM, comprising:
a. calculating a first mixing parameter (MP) for said first configuration, said parameter defined as
M
P
=
(
ND
2
ρ
μ
)
(
D
T
)
2
(
N
Q
ND
3
T
2
H
)
,
where N comprises the RPM of said mixer, D comprises the diameter of said impeller, ρ comprises the density of said fluid, μ comprises the viscosity of said fluid, N Q comprises the power number of said impeller, T comprises the diameter of said vessel, and H comprises the height of said fluid in said vessel;
b. creating a second configuration, using a vessel of a second size, a second fluid, said salt, a second impeller and a second mixer operating at a second RPM;
c. calculating a second mixing parameter (MP) for said second configuration;
d. determining a salt dissolution time for said second configuration;
e. creating a third configuration, using a vessel of a third size, a third fluid, said salt, a third impeller and a third mixer operating at a third RPM;
f. calculating a third mixing parameter for said third configuration;
g. determining a salt dissolution time for said third configuration;
h. determining two coefficients, α and β, such that said second mixing parameter and its associated salt dissolution time, and said third mixing parameter and its associated salt dissolution time, both satisfy the equation:
Dissolution Time=α×( MP ) β ; and
i. determining the salt dissolution time of said first configuration based on said first mixing parameter, α and β.
9. The method of claim 8 , wherein a diameter of said second impeller and a diameter of said third impeller are the same, and a power number of said second impeller and a power number of said third impeller are the same.
10. The method of claim 8 , wherein said second mixer and said third mixer are the same.
11. The method of claim 8 , wherein said second size and said third size are the same.
12. The method of claim 8 , where said first size is greater than said second and third sizes.
13. The method of claim 8 , wherein said second fluid and said third fluid are the same.
14. The method of claim 8 , wherein a diameter of said second impeller and a diameter of third impeller are the same, a power number of said second impeller and a power number of said third impeller are the same, said second mixer and said third mixer are the same, said second size and said third size are the same, and said second RPM differs from said third RPM.