## April 2019

## Process Engineering

# Solve gravity separation challenges

Separation of oil, water, gas and solids (sand) droplets/particles is one of the most common requirements in most oil and gas facilities.

Separation of oil, water, gas and solids (sand) droplets/particles is one of the most common requirements in most oil and gas facilities. While separation helps in attaining product specifications, not all separation facilities operate as desired. Although the calculation basis is simple, not all operating scenarios are foreseen during initial sizing, which is usually carried out at a single conservative operating point. Calculations are based on terminal velocities, which are dependent on relative densities. The bigger the difference, the easier the separation. Evaluating the sizing on the full operating range of temperature, pressure and properties may identify the relative difference, which varies with operating conditions, and problems originating due to “crossing of fluid densities” highlight the inefficient separation zones. Evaluating the separation efficiencies at the entire operating range to identify any potential inefficient zones is discussed here.

Separation theory. Liquid droplets drop out of a gas phase when the force of gravity on the droplet is more than the drag force of the gas moving around the droplet. The mathematical description of these forces is given in Eq. 1:

V_{t} = (2 × g × M_{p} × (ρ_{l} – ρ_{g})/(ρ_{l} × ρ_{g} × A_{p}C’))^{0.5 }= (4 × g × D_{p} × (ρ_{l} – ρ_{g})/(3 × ρ_{g} × A_{p}C’))^{0.5} (1)

The drag coefficient is a function of the Reynolds number and the particle shape of the flowing gas. In this case, the shape of the particle is assumed as a solid rigid shape. Therefore, the Reynolds number is given as Eq. 2:

Re = 1488 × Dp × Vt × ρ_{g}/μ (2)

A trial and error solution is needed for this form, because both the terminal velocity and particle size are involved (Eq. 3):

C’ × (Re)^{2} = 0.95.10^{8} × ρ_{l} × Dp^{3} × (ρ_{l} – ρ_{g})/μ^{2} (3)

In Stoke’s Law, for Reynolds numbers less than 2, there exists a linear relationship between the Reynolds number and the drag coefficient (laminar flow). Since Stoke’s law is valid, Eq. 3 is defined in Eq. 4:

V_{t} = 1488 × g × Dp^{2} × (ρ_{l} – ρ_{g})/18 × μ (4)

The droplet diameter for a Reynolds number of 2 can be calculated by using 0.025 for *K _{CR}* in Eq. 5:

D_{p} = K_{CR} × ((μ^{2}/(g × mg × (ρ_{l} – ρ_{g})))^{0.33 }(5)

Intermediate law applies for Reynolds numbers between 2 and 500, so the terminal settling law can be defined by Eq. 6:

V_{t} = 3.49 × g^{0.71} × Dp^{1.14} × (ρ_{l} – ρ_{g})^{0.71}/(ρ_{g}^{0.29} × μ^{0.43}) (6)

The droplet diameter at a Reynolds number of 500 is found by using 0.334 for *K _{CR}* in Eq. 5. This law is valid for several of the liquid-liquid and gas-liquid droplet settling phenomena in gas processes.

Newton’s Law is valid for a Reynolds number from 500 to 200,000 and is applied widely in the separation of large particles/droplets from a gas phase. The drag coefficient is approximately 0.44 for Reynolds numbers above 500. Putting the value of *C’*=0.44 into equation Eq. 7 redefines Newton’s Law as:

V_{t} = 1.74 × (g × D_{p} × (ρ_{l} – ρ_{g})/ρ_{g})^{0.5} (7)

The Reynolds number upper limit is 200,000, and *K _{CR}* is 18.13 within the Newton’s Law region.

For a simple gravity separation tank, where a residence time is allowed for an acceptable level of separation between base salts and water (BS&W) and a heavy oil like that found in the oil sands of Alberta, Canada or similar scenarios. A case in point requires separation between 2% BS&W and 18% bitumen + 18% diluents (dilbit). The property and sizing profiles over the entire operating range are graphically represented in** FIGS. 1** and **2, **which show that higher temperatures usually favor separation. Based on these property profiles and terminal velocities, the separation tank holdup times and sizes are calculated in **FIGS. 3** and **4.**

Operating parameters can change due to varying process conditions, including change of wells or ambient temperatures, BS&W and dilbit concentrations, temperature and pressure or specific gravities. Considering the new set of operating conditions as BS&W=0.14% and an operating temperature of 20°C (68°F), the resulting changes in the fluid properties and calculated sizing profiles are represented in **FIGS. 5 **and **6.**

The densities of 0.14% BS&W and 18% dilbit are crossing at approximately 20°C (68°F). The calculated terminal velocity of bitumen in BS&W becomes zero, which does not support efficient separation. In** FIGS. 7 **and **8,** the resultant tank holdup times and sizing profiles are shown.

The results show that the separation efficiency, for this case, will begin to decrease at approximately 10°C (50°F), peaking at 20°C (68°F) and becoming normal at approximately 30°C (86°F). Usually these operating condition variations occur relatively slowly in operating facilities. If monitoring these conditions is not possible, inefficient separation can result.

To mitigate this problem, simulations should be based on operating conditions and properties of fluids obtained through laboratory assessment. This information can be used to optimize the operating conditions and allow the maximum separation efficiency. In some cases, where oil-water emulsions are present, the need to add demulsifiers together with temperature optimization can be identified. The key is to be able to analyze the varying properties of the fluids that require separation at the entire operating range, visually in graphical form.

A spreadsheet-based simulation of the entire spectrum of operating conditions and fluid properties can allow quick evaluations. These fluid properties, in terms of equations, can be built into the spreadsheet to allow seamless simulations to be conducted. A typical spreadsheet input and output profile is shown in** FIG. 9.**

The procedure can be used for multiple types of separators, from two-phase to three-phase, vertical or horizontal, to barrel tanks and even emulsion treaters. It can be used to analyze existing separation problems or to evaluate a separate problem for servicing. **HP**

**Nomenclature**

*V*Terminal gas velocity, m/sec_{t}*g*Gravitational acceleration, m/sec^{2}*M*Mass of the droplet, kg_{p}*ρ*Liquid phase density, kg/m_{l}^{3}*μ*Viscosity of gas, Pa.s*ρ*Gas phase density, kg/m_{g}^{3}- A
_{p}Droplet cross sectional area, m^{2} *C’*Drag coefficient of the particle*D*Droplet diameter, micron_{p}*K*Factor for terminal velocity_{CR}

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