## Drilling Formula Calculation Sheet v1

When you one the file Drilling-formulas-Calculation-shee-V1.xls, you will see the fist page call index page which shows you all of formulas like this.

## What is slug mud? How much volume and weight of slug mud should be?

Slug Mud: It is heavy mud which is used to push lighter mud weight down before pulling drill pipe out of hole. Slug is used when pipe became wet while pulling out of hole.

Normally, 1.5 to 2 PPG over current mud weight is a rule of thumb to decide how much weight of slug should be. For example, current mud weight is 10 PPG. Slug weight should be about 11.5 to 12 PPG.

Normally, slug is pumped to push mud down approximate 200 ft (+/2 stands) and slug volume can be calculated by applying a concept of U-tube (see a figure below)

Volume of slug can be calculated by this following equation:

This equation expresses that the higher slug volume, the deeper of dry in drill pipe is met. As per the above equation, length of dry pipe can be substituted by 200 ft.

In normal practice, slug volume pumped to clean drill pipe is around 15-25 bbl depending on drillpipe size. Moreover, it also depends on situations because sometime mud in annulus side may be heavier than measured MW due to cutting, drilling solid contaminated in mud, hence more slug volume is needed.

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.

## 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.

## Pressure in a well

In a static condition

• Pressure at any depth = Hydrostatic Pressure (HP) + Surface Pressure (SP)
• Pressure between 2 points is HP between these points

The diagram below demonstrates the relationship of pressure in a well.

At point 1, Pressure@1 = Surface Pressure (SP) + Hydrostatic Pressure @ 1 (HP1)

At point 1, Pressure@2 = Surface Pressure (SP) + Hydrostatic Pressure@1 (HP1) + Hydrostatic Pressure@2 (HP2)

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.

## Dilution of Mud System to Control Low Gravity Solid by Adding Mud

Adding bbl of  drillingfluid can help control low gravity solid (LGS) in mud system. However, this is different from the way to control LGS by adding base fluid as base oil or water because mud that is added into system has some Low Gravity Solid (LGS). Hence, when we calculate it, we need to account for Low Gravity Solid (LGS) of new mud into the calculation as well. This post will demonstrate you how to determine barrels of drilling fluid required to achive the desired Low Gravity Solid (LGS).

Formula, used to calculate dilution of mud system, is listed below;

Vwm = Vm x (Fct – Fcop) ÷ (Fcop – Fca)

Where; Vwm = barrels of dilution water or base fluid

Vm = total barrels of mud in circulating system

Fct = percent low gravity solids in system

Fcop = percent total low gravity solids desired

Fca = percent low gravity solids bentonite and/or chemicals added in mud

Example: Determine how much barrels of oil base mud to diluate total 2000 bbl of mud in system from total LGS = 7 % to desired LGS of 3.5 %. The oil base mud has 2% of bentonite slurry.

Vwm = Vm x (Fct – Fcop) ÷ (Fcop – Fca)

Vwm = 2000 x (7 – 3.5) ÷ (3.5-2)

Vwm = 4667 bbl

In order to dilute total of 2000 bbl of the original mud with 7% LGS down to 3.5% LGS, 4667 bbl of mud that has 2% bentonite is requied to add into the system.

Please find the excel sheet used to calculate how much barrel of drilling fluid to control Low Gravity Solid (LGS) in mud system.