Modeling of an industrial mixing valve and electrostatic coalescer for crude oil dehydration and desalination

ABSTRACT

This paper aims to present a new model for an industrial desalination system including a mixing valve and an electrostatic coalescer. This model uses a one-dimensional population balance equation in steady-state conditions. The effect of hydrodynamic, diffusion and electrostatic mechanisms on the collision or breaking of water droplets dispersed in crude oil was considered. Also, using the film drainage model, the droplet coalescence rate has been determined. The developed model can predict the outlet droplet size distribution as well as the desalination and dehydration efficiency. The simulation results showed good agreement with the industrial data. Finally, the effect of some important parameters on the electrostatic desalination process, such as mixing valve pressure drop, electric field intensity, crude oil viscosity, crude oil temperature, diluting water flow rate, and crude oil API on the efficiency of the process was analyzed. The results indicated that by increasing the crude oil temperature from 314 to 334 K, the efficiency of dehydration improves from 97.95% to 99.02%. Also, reducing crude oil API from 33 to 30 and crude oil viscosity from 4 to 2 mPa.s caused a decrease in water separation by 2.88% and 1.16%, respectively.

KEYWORDS:

• Mixing valve
• population balance
• electrostatic coalescer
• electric field
• droplet

Nomenclature

A	=	Hamker coefficient [J]
C	=	Adjustable parameter [-]
Ca	=	Capillary number [-]
d	=	Droplet diameter [m]
eij	=	Collision efficiency [-]
E	=	Electric field intensity [Vm−1]
f (v,w)	=	Daughter drop size distribution function [-]
g	=	acceleration Gravity [m s−2]
g (d)	=	Breakage frequency [s−1]
K	=	Adjustable parameter [-]
kB	=	Boltzmann’s constant [J K−1]
m	=	The number of droplets formed per breakage of a droplet [-]
n(v,z)	=	Continuous number density [m−3]
Ni(z)	=	Discrete number density [m−3]
P	=	Pressure [Pa]
tres	=	Resident time [s]
T	=	Temperature [K]
u	=	Velocity [ms−1]
v	=	Droplet volume [m3]
V ij	=	The relative velocity [ms−1]
w	=	Droplet volume [m3]
We	=	Weber number [-]
z	=	Length [m]
Greek symbols	=
$\beta$	=	Coalescence rate [m3 s−1]
$\gamma$	=	Shear rate [s−1]
$\delta$	=	The ratio of small drop diameter to large drop diameter [-]
$\epsilon$	=	Permittivity [F m−1]
$\theta$	=	Collision frequency [s−1]
$\lambda$	=	Kolmogorov length scale [m]
$\mu$	=	Dynamic viscosity [Pa s]
$\mu \prime$	=	Dynamic viscosity ratio of water and oil [-]
$v$	=	Kinematic viscosity [m2 s−1]
$\xi$	=	Rate of energy dissipation [m2 s−3]
$\rho$	=	Density [kg m−3]
$\sigma$	=	Interfacial tension [N m−1]
$\tau$	=	Contact time [s]
$\phi$	=	Water fraction in emulsion [-]
Superscript	=
Br	=	Brownian force
E	=	Electric force
Ds	=	Differential sedimentation
Ls	=	Laminar shear
T	=	Turbulent force
Subscripts	=
i, j, k	=	Class number index
$c$	=	Continuous phase
d	=	Dispersed phase
eq	=	Equivalent

Research highlights

• A new model for an integrated mixing valve with an electrostatic coalescer in an industrial plant is presented.

• The simultaneous effect of the mechanisms of differential sedimentation, laminar shear, Brownian motion, and electric force on the droplet coalescence rate in the electrostatic coalescer was considered.

• The high accuracy of the model has been confirmed in comparison with industrial data.

• The effect of important parameters such as the degree of API, viscosity, and temperature of crude oil on the electrostatic desalination process has been investigated.

Acknowledgments

The research of the corresponding author is supported by a grant from Ferdowsi University of Mashhad (N. 3/58374)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Statement of Novelty

• A new model for an integrated mixing valve with an electrostatic coalescer in an industrial plant is presented.

• The simultaneous effect of the mechanisms of differential sedimentation, laminar shear, Brownian motion, and electric force on the droplet coalescence rate in the electrostatic coalescer was considered.

• The high accuracy of the model has been confirmed in comparison with industrial data.

• The effect of important parameters such as the degree of API, viscosity, and temperature of crude oil on the electrostatic desalination process has been investigated.

Additional information

Funding

The authors reported there is no funding associated with the work featured in this article.