## Understand Hydrostatic Pressure

In a well, any pressure created by a static column of fluid is called ‘Hydrostatic Pressure’ (HP); at any given True Vertical Depth (TVD). With ‘hydro’ representing water, which exerts pressure, ‘static’ means it has no movement. Any pressure developed by a column of fluid that isn’t moving, therefore, can be considered hydrostatic pressure; fluid in this sense can be either liquid or gas.

The relationship of hydrostatic pressure is shown in the equation below.

HP (Hydrostatic Pressure) = density x g (gravity acceleration) x h (True Vertical Depth, TVD)

In oilfield term, the formula above is modified so that people can use it easily. The formulas are as follows:

HP (Hydrostatic Pressure) = Constant x MW (Mud Weight or Mud Density)  x TVD (True Vertical Depth)

HP (psi)  = 0.052 x MW (ppg) x TVD (ft) ** Most frequent used in the oilfield **

HP (psi) = 0.007 x MW (pcf) x TVD (ft)

HP (kPa) = 0.00981 x MW (kg/m3) x TVD (m)

Depending on which unit is used for calculation, there are several conversion factors such as 0.052, 0.007, 0.00981 for instant as you can see from the equations above.

According to the equations above, Hydrostatic Pressure is not a function of hole geometry. Only mud weight and True Vertical Depth (TVD) affect on Hydrostatic Pressure. For example (a picture below); well A and well B have the same vertical depth. With the same mud density in hole, the bottom hole pressure due to hydrostatic pressure is the same. The only different between Well A and Well B is mud volume.

This concept is basic and very important for many aspects such as well control, balance cementing, u-tube, etc.

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.

## Corrected D exponent

The original “d” exponent is good for constant mud weight but in reality several drilling operations drill with various mud weights in hole due to weight up. In order to account for mud weight variation, so modification of d exponent, called “corrected d exponent”, has been made to correct for mud weight changes.

The corrected d-exponent is listed below.

dc = log (R ÷ 60N) ÷ log (12W ÷ 1000D) x (MW1 ÷ MW2)

Where;

dc = corrected “d” exponent

R = penetration rate in feet per hour

d = exponent in drilling equation, dimensionless

N = rotary speed in rpm

W = weight on bit in kilo pound

D = bit size in inch

MW1 = initial mud weight in ppg

MW2 = actual mud weight in ppg

Example: Determine the corrected d-exponent from following information.

Rate of penetration (R) = 90 ft/hr

Rotary drilling speed (N) = 110 rpm

Weight on bit (W) = 20 klb

Bit Diameter (D) = 8.5 in

MW1 = 9.0 ppg

MW2 = 12.0 ppg

Solution: dc = log [90÷ (60 x 110)] ÷ log [(12 x 20) ÷ (1000 x 8.5)] x (9.0 ÷ 12.0)

dc = 1.20 x 0.75

dc = 0.9

** Please remember that single d exponent or corrected d exponent valve does not help identify abnormal pressure. The trend of d exponent will help drilling personnel detect high formation pressure zones while drilling.

## D Exponent Calculation

D exponent is an extrapolation of drilling parameters to get a trend while drilling into over-pressured zones. Usually, mud logger will correct all data, calculate d-exponent and plot the d exponent valve on the curve. The d-exponent can be utilized to detect transition from normal pressure regime to abnormal formation pressure. While drilling, if the change of trend is observed, rig supervisors must be cautious about this situation because this is one of the possible well control indications.

The “d” exponent described from the equation below:

d = log (R ÷ 60N) ÷ log (12W ÷ 1000D)

Where; R = penetration rate in feet per hour

d = exponent in drilling equation, dimensionless

N = rotary speed in rpm

W = weight on bit in kilo pound

D = bit size in inch

** Note: this equation is is valid for constant drilling fluid weight.

Example: Determine the d-exponent from following information.

Rate of penetration (R) = 90 ft/hr

Rotary drilling speed (N) = 110 rpm

Weight on bit (W) = 20 klb

Bit Diameter (D) = 8.5 in.

Solution: d = log [90÷ (60 x 110)] ÷ log [(12 x 20) ÷ (1000 x 8.5)] d = 1.20

Please find the Excel Sheet for calculating d-exponent.

References

(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.

Grace, R. and Cudd, B. (1994). Advanced blowout & well control. 1st ed. Houston: Gulf Publishing Company.

Watson, D., Brittenham, T. and Moore, P. (2003). Advanced well control. 1st ed. Richardson, Tex.: Society of Petroleum Engineers.