Page 91 - Handbook Of Multiphase Flow Assurance

86 4. Hydraulic and thermal analysis

3
2
L ρβ ∆ T buoyancy
Grashof Gr = g =
µ 2 viscousforce

hd convective heat transfer
Nusselt Nu = =
k conductive heat transsfer
a Sc thermal diffusion
Lewis Le = = =
D AB Pr mass diffusion
µ
ρ viscousmasstransfer
Schmidt Sc = =
D AB diffusive mass transfeer

K L convective mass transfer
Sherwood Sh = c =
D diffusive mass trannsfer
ρ vD fluid inertia
2

Weber We = droplet = = = interactionoftwo fluidsatinterface
σ interface surfacetension

advectiveheattransfer
Peclet Pe = PrRe =
HEAT
diffusive heat traansfer
advectivemasstransfer
Pe MASS = Sc Re =
diffusive mass transfer
D
Graetz Gz = Hydraulic RePr
HEAT
L
D
Gz MASS = Hydraulic Re Sc
L
The use of dimensionless numbers may be useful in understanding flow characteristics. For
example Beggs and Brill used Froude number in coordinates to present a flow regime map.
Someday multiphase software tools will be able to plot each of these dimensionless values,
which may lead to new understanding of multiphase flow phenomena and improved ma-
chine learning pattern recognition.

Software

Software can be broadly classified as capable of solving steady state and transient flow mo-
tion. Both classes include both empirical and mechanistic models, with the possibility to use
two phase flow as in vapor-liquid, three as in gas-liquid-water or four phases with addition
of a drilling mud fluid. In some instances solids transport may be added so flow of up to five
phases may be modeled.