Capillary Number

What is capillary number ?

It is ratio of two forces. One is viscous force and another one is interfacial or surface tension force.

So, it is ratio of viscous to interfacial tension force.

(The viscous force can be calculated by multiplying the shear stress acting on the surface by the fluid and the area. The shear stress caused due to the viscosity of the fluid is directy proportional to the coefficient of viscosity of the fluid and the velocity gradient.)

So,

Capillary number NC = (µ)*(v)/(σ)

Where, µ is dynamic viscosity of injecting fluid.

v is superficial velocity of injecting fluid.

σ is interfacial tension between injecting and displacing fluid. (N/m).

Before explanation, things we all will be agree are.

i) As we have thick injection fluid, it can sweep our oil easily from oil reservoir in enhanced oil recovery/flooding processes.

ii) More the miscibility between injecting and production fluids, higher the recovery will be.

iii) As we lower the interfacial tension, it will lead to more miscibility. (Pure miscibility at IFT = zero).

So, For better sweep efficiency, we require more the viscosity of injection fluids and less inter facial tension between both fluids.

So, in short we require more Nc to recover more oil from reservoir.

As capillary number increase, residual oil saturation will be reduced.(more recovery.)

How to increase Nc ?

1) We can increase injecting fluid viscosity by adding chemicals like polymers (if injection fluid is water.)

That's Polymer flooding.

2) We can decrease the interracial tension force between both fluids with help of Surfactants.

That's Surfactant flooding.

We can also produce in situ surfactants with help of adding alkali to the insitu acidic crude oil. So that it will produce natural surfactant in situ.

Typical values of Nc:

In typical reservoir conditions, capillary number varies from 10−8 to 10−2

In flow of oil through an oil well drill pipe has a capillary number on the order of 1.

To visualise in video, click here.

For Concept of mobility of fluids,click here.