In case of totally lost return, the annulus must be fully filled with fluid, normally water, as fast as we can. Water filled in annulus causes loss of hydrostatic pressure in the wellbore. This article demonstrates how to determine hydrostatic pressure reduction when water or other light fluid is used to fully fill the hole.

Note: This calculation is based on if the float is in the drill string. Therefore, there is no way that fluid from annulus can come into the string.

There are **two main concepts**, annular capacity and hydrostatic pressure, applied to determine loss of hydrostatic pressure.

**Please follow concepts below.**

**Oilfield Unit**

Height of feet of water in annulus

Height of water added (ft)= water added in bbl ÷ annular capacity in bbl/ft

Bottomhole (BHP) pressure reduction

BHP decrease in psi = (current mud weight in ppg – weight of water in ppg) × 0.052 × (ft of water added)

Note: In order to calculate bottom hole pressure reduction, we assume the column of water in annulus is true vertical depth (TVD). This calculation may not be accurate if the well has high angle so you need to determine the actual TVD from directional survey data. However, this method will be the worst case scenario of pressure reduction.

Equivalent Mud Weight at TD

EMW in ppg = current mud weight in ppg – (BHP decrease in psi ÷ 0.052 ÷ TVD ft of hole)

**Example:** Determine bottom hole pressure loss and equivalent mud weight at TD due to filling up water into annulus.

Mud weight = 13.0 ppg

Water added = 140 bbl required to fill annulus

Weight of water = 8.6 ppg **

Annular capacity = 0.1422 bbl/ft

Hole TVD = 6,000 ft

** If you fill lighter mud in hole instead of water, please adjust water weight to your mud weight.

**Number of feet of water in annulus**

Feet of water in annulus = 140 bbl ÷ 0.1422 bbl/ft

**
**Feet = 984.5 ft

**Bottomhole (BHP) pressure reduction**

BHP reduction = (13.0 ppg – 8.6 ppg) × 0.052 × 984.5 ft

BHP reduction = 225.3 psi

**Equivalent mud weight at TD **

EMW in ppg = 13.0 – (225.3 psi ÷ (0.052× 6,000 ft))

**
**EMW = 12.3 ppg

**Metric Unit**

Height of water in annulus

Height of water added (m) = water added in m^{3}÷ annular capacity in m^{3}/m

Bottomhole (BHP) pressure reduction

BHP decrease in psi = (current mud weight in kg/m^{3}– weight of water in kg/m^{3}) × 0.00981 × (m of water added)

Equivalent Mud Weight at TD

EMW in ppg = current mud weight in kg/m^{3}– (BHP decrease in KPa ÷ 0.00981 ÷ TVD m of hole)

**Example:** Determine bottom hole pressure loss and equivalent mud weight at TD due to filling up water into annulus.

Mud weight = 1550 kg/m^{3}

Water added = 20 m^{3}

Weight of water = 1030 kg/m^{3}

Annular capacity = 0.07417 m^{3 }/m

Hole TVD = 2000 m

**Height of water in annulus**

Height of water in annulus= 20 m^{3} ÷ 0.07417 m^{3}/m

**
**Height of water in annulus = 270 m

**Bottomhole (BHP) Pressure Reduction**

BHP reduction = (1550 kg/m^{3} – 1030 kg/m^{3}) × 0.00981 × 270 m

BHP reduction = 1,375 KPa

**Equivalent mud weight at TD**

EMW = 1550 – (1375 ÷ (0.00981× 2,000 m))

**
**EMW = 1480 kg/m

^{3}

**Please find the Excel sheet for calculating how much pressure loss due to lost return**

**Ref books: **Lapeyrouse, N.J., 2002. Formulas and calculations for drilling, production and workover, Boston: Gulf Professional publishing.

Bourgoyne, A.J.T., Chenevert , M.E. & Millheim, K.K., 1986. SPE Textbook Series, Volume 2: Applied Drilling Engineering, Society of Petroleum Engineers.

Mitchell, R.F., Miska, S. & Aadny, B.S., 2011. Fundamentals of drilling engineering, Richardson, TX: Society of Petroleum Engineers.