By understanding and applying these three key principles – Boyle’s Law, hydrostatic pressure, and the volume-height relationship – the Volumetric Well Control Method can be effectively employed to manage gas kicks and maintain well control. The details are shown below.

**1. Boyle’s Law:**

This law states that for a gas at constant temperature, pressure and volume are inversely proportional. Simply put, compressing a gas increases its pressure, while allowing it to expand lowers the pressure.

Expressed mathematically:

**Boyle’s Law: P****₁****V****₁**** = P****₂****V****₂**

where:

- P₁ = Pressure of gas at condition 1
- V₁ = Volume of gas at condition 1
- P₂ = Pressure of gas at gas at condition 2
- V₂ = Volume of gas at condition 2

Although this equation simplifies the real gas law equation, PV=ZnRT, by neglecting temperature effects and gas compressibility, this equation provides a good foundation for understanding volumetric control

In well control, as a gas influx migrates up the wellbore without expanding, its pressure remains constant. Conversely, if it expands as it rises, the pressure decreases.

Preventing gas expansion during migration can be catastrophic. Since the gas enters with formation pressure, it would exert the same pressure at the surface, essentially bringing high pressure from below to the wellhead. This could rupture casing or cause a blowout.

Volumetric control addresses this by allowing gas expansion. We measure this expansion by monitoring the amount of drilling mud bled off through a choke line.

**2. Hydrostatic Pressure:**

The pressure exerted by a static fluid column equals the fluid’s hydrostatic pressure plus any pressure applied at the top.

**Pressure at Mud Column Bottom = Hydrostatic Pressure + Surface Pressure**

Similarly, the pressure exerted by a migrating gas bubble acts on the mud column below, increasing the pressure at the bottom (bottomhole pressure).

We can express this as:

**Bottomhole Pressure = Hydrostatic Pressure (below bubble) + Gas Bubble Pressure**

As the bubble moves up one foot, there’s one additional foot of mud below it, increasing the hydrostatic pressure at the bottom. If the bubble pressure stays constant while moving, the bottomhole pressure will also increase by the hydrostatic pressure of this “new” mud.

By bleeding mud from the annulus to create space for gas expansion, we reduce the mud volume and consequently, the hydrostatic pressure. This bleeding needs to be done while maintaining constant casing pressure. As per the equation above, this reduces bottomhole pressure.

In volumetric control, we can influence bottomhole pressure in two ways:

**Do nothing:**The gas bubble rises, and both bottomhole and surface pressures increase.**Bleed mud:**Assuming surface pressure stays constant, bottomhole pressure decreases by the amount of hydrostatic pressure lost due to mud removal.

Careful control of mud bleed is crucial. If surface pressure drops or hydrostatic pressure is lowered too much, an underbalanced situation can occur, allowing more gas influx. The goal is to bleed off just enough mud to maintain constant surface pressure until the lost wellbore pressure equals the pressure increase allowed before bleeding. To achieve this, we equate the desired hydrostatic pressure loss with the volume of mud bled off. The casing pressure can then be allowed to increase by this lost pressure to maintain bottomhole pressure. This is why the amount of bled mud is measured and equated to a reduction in hydrostatic pressure.

**3. Volume and Height:**

These factors are essential for calculating the reduction in hydrostatic pressure each time mud is bled from the annulus. We need to know the pressure drop resulting from each bled mud volume.

The formula for calculating annulus capacity factors

Annulus Capacity Factor (ACF) = (OD² -ID² ) ÷ 1029.4

Where:

ACF = Annulus Capacity Factor (bbl/ft)

OD = Outside Diameter of Annular Space(in)

ID = Inside Diameter of Annular Space (in)

**References**

Cormack, D. (2007). An introduction to well control calculations for drilling operations. 1st ed. Texas: Springer.

Crumpton, H. (2010). Well Control for Completions and Interventions. 1st ed. Texas: Gulf Publishing.

Grace, R. (2003). Blowout and well control handbook [recurso electrónico]. 1st ed. Paises Bajos: Gulf Professional Pub.