8.9 Basic Maths For Well Planning

Quartz School for Well Site Supervisors Module – 8 Directional Drilling

Section – 9 Basic Mathematics for DD Calculations

The Basics What is the relationship between Circumference, Radius & π? We know that :

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Circumference = 2πR= πD = 360°ARC Therefore: 360 = 2πR 360 / 2 = πR 180 = πR 180 / π= R 1 unit of Radius = 1 Radian (Ra) 180 / π = Ra = 57.2958°

Build Up Rate Where does the equation for Build Up Rate come from? Build Up Rate is the Arc of a circle divided by the Circumference:

360° / Circumference = BUR 360 / (2 x π x Rc) = BUR 180 / (π x Rc) = BUR

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Because we prefer to work in whole numbers, we need to multiply this value by the unit length. For feet we use a 100’ length as a unit (i.e. degrees per 100’)

Build Up Rate Where does the equation for Build Up Rate come from? This now makes our BUR equation:

BUR (in °/ 100’)= 180 x 100 / (π x Rc) With Metric wells the unit length is usually 30m. For this type of well:

BUR (in °/ 30m)= 180 x 30 / (π x Rc) A derivative of this equation can be used to find Radius from a BUR: 4

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Rc= 180 x 100’ / (π x BUR)

Build Up Rate Be aware of the units you are working in!!!! Some clients use °/ 10m. PAY ATTENTION TO DETAIL!! See Quest below! Quest no. : 20070123194025 DD had not noticed that the required doglegs in the plan were 2.5º/10m but thought it was 2.5º/30m. Therefore the needed doglegs were not achieved and the well was not landed horizontal with in the target boundaries. Non-Productive Time Total 480.0 K 5

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Arc Lengths & Angles Given that we know :

Circumference = 2πR = 360° Arc Arc AB will be a fraction of the circumference, the ratio of this fraction will be the Arc angle divided by the Circumference Arc (360°): Arc AB = 2πR x θ/ 360° Arc AB = π R x θ/180° With: BUR (in °/ 100’)= 180 x 100 / (π x Rc) We can derive:

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Arc AB = θ x 100’ / BUR

Radius of Curvature Projection We need Radius of Curvature Projection primarily when we are landing horizontal wells. This gives a relationship between Inclinations, BURs and either ∆TVD or ∆Displacement. If we consider the Arc AD we know that: CD = Rc (radius of curvature) We can find ∆TVD: ∆TVD = BD = Rc x Sin θ And the ∆Displacement 7

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∆Disp = AB = Rc-Rc x Cos θ = Rc(1 – Cos θ)

Radius of Curvature Projection When we compare two points on the curve: If we consider the Arc DF we know that: ∆TVD = XF = EF -BD =Rc x Sin I2 –Rc x Sin I1 = Rc (Sin I2 -Sin I1) = (180 x 100) x (Sin I2 -Sin I1) / ( π x BUR ) And the ∆Displacement ∆Disp = DX = CB -CE = (Rc x CosI1)-(Rc x Cos I2 ) = Rc (CosI1- CosI2) = (180 x 100 ) x (CosI1- CosI2) /( π x BUR) 8

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Radius of Curvature Projection When we compare two points on the curve: If we consider the Arc DF we know that:

Arc DF = θ x 100’ / BUR θ is the difference between the two inclinations so:

Arc DF = ( I2 - I1 ) x 100’ / BUR

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