The length of the annulus or the length of the low-density fluid and mud density of the lost circulation can be calculated based on the annulus capacity behind the drill collar. Suppose the lost circulation volume is smaller than the annulus volume against the drill pipe. In that case, the length of the annulus (i.e., mud loss height) can be expressed in terms of the volume of the low-density fluid pumped to balance the formation pressure and annulus capacity. Here, we will discuss how to calculate the formation pressure of the lost zone while drilling.

Mathematically, If V_{l} < V_{an_dp}, the length of the low-density fluid required to balance the formation pressure is given by:

Where:

- C
_{an_dc}= annulus capacity behind the drill collar, bbl/ft - L
_{l}= length of the annulus (mud loss height) or the length of the low-density fluid, bbl - V
_{l}= volume of the low-density fluid pumped to balance the formation pressure, bbl - V
_{an_dp}= the annulus volume against drill pipe, bbl

If V_{l} > V_{an_dp}, the length of the length of the low-density fluid required to balance the formation pressure is given by:

Where:

- C
_{an_dc}= annulus capacity behind the drill pipe, bbl/ft - L
_{dc}= length of drill collar, ft - V
_{an_dc}= the annulus volume against the drill collar, bbl

## Formation Pressure Calculation For The Lost Circulation Zone

Formation pressure is given by

Where:

- D
_{v}= vertical depth of the well where the loss occurred, ft - D
_{w}= vertical depth of water, ft - P
_{ff}= formation pressure, psi **ρ**_{m}= mud density, ppg**ρ**_{w}= seawater density, ppg

In addition, improper annular hole cleaning, excessive mud weight, or shutting in a well in high-pressure shallow gas can induce fractures, which can cause lost circulation. Equations (1) and (2) show the conditions that must be maintained to avoid fracturing the formation during drilling and tripping pipe. However, Eq. (4) must also be satisfied to avoid the fracture.

Where:

**ρ**_{eq}= equivalent circulating density of mud, ppg**ρ**_{mh}= static mud weight, ppg**ρ**_{frac}= formation pressure fracture gradient in equivalent mud weight, ppg**ρ**_{s}= additional mud caused by surge pressure, ppg