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SOLUTION TO CHAPTER PROBLEMS CHAPTER 2 1. Given the following survey data, calculate the ΔTVD, ΔNorth and ΔEast using the average angle and radius of curvature methods. MD1 = 1000 feet MD2 = 2000 feet I1 = 0º I2 = 40º A1 = S42W A2 = S42W Solution: Average angle method: ΔMD = MD2 − MD1 ΔMD = 2000 − 1000 = 1000 feet Azimuth = 180 + 42 = 222º ⎛I +I ⎞ ΔTVD =
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  SOLUTION TO CHAPTER PROBLEMS CHAPTER 2 1. Given the following survey data, calculate the  Δ TVD ,  Δ North  and  Δ East   using the average angle and radius of curvature methods. MD 1  = 1000 feet MD 2   = 2000 feet I  1  = 0º I  2   = 40º  A 1  = S42W  A 2   = S42W Solution:  Average angle method: feet100010002000 12 =−=Δ −=Δ MDMDMDMD   Azimuth = 180 + 42 = 222º feet69.939 240010002 21 =⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ CosTVDI I CosMDTVD  feet17.254 22222222400100022 2121 −=⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ CosSinNorth A ACosI I SinMDNorth  feet86.228 22222222400100022 2121 −=⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ SinSinEast  A ASinI I SinMDEast   Radius of Curvature: If the azimuths or inclinations are equal, you must add a small amount to one of the azimuths or inclinations so that the radius of curvature equations will work. Otherwise, the eqation will be divided by zero. o 001.222001.0222 001.0 212 =+=+=  A A A   Copyright © 2007 OGCI/PetroSkills. All rights reserved. 1    Horizontal and Directional Drilling Solutions To Chapter Problems ( )( )( )( )( )( )( )( ) feet73.920 0400401000180 180 1212 =−π−=Δ−π−Δ=Δ SinSinTVDI I I SinI SinMD TVD   ( ) ( )( )( )( )( )( ) ( )( )( )( )( ) feet04.249 222001.222040 222001.2224001000180 180 221212 21221 2 −=−−π−−=Δ−−π−−Δ=Δ SinSinCosCos North A AI I   ASin ASinI CosI CosMD North   ( )( )( )( )( )( )( )( )( )( ) feet24.224 222001.222040 001.2222224001000180 180 221212 22121 2 −=−−π−−=Δ−−π−−Δ=Δ CosCosCosCos East  A AI I   ACos ACosI CosI CosMD East   The answers are not the same both methods because the distance between surveys is too great for the average angle method. That is why radius of curvature is generally used to calculate the position of the wellbore when planning a directional well. 2 Copyright © 2007 OGCI/PetroSkills. All rights reserved  Horizontal and Directional Drilling Solutions To Chapter Problems 2. Given the following rectangular coordinates, calculate the vertical section of the survey point if the vertical section azimuth is 215º. North  = -1643.82 feet and East   = -822.16 feet Solution: o 57.2682.164316.822  11 =⎟ ⎠ ⎞⎜⎝ ⎛ −−=⎟ ⎠ ⎞⎜⎝ ⎛ = −− TanDirectionClosureNorthEast TanDirectionClosure  Since the well is in the southwest (both the north and east are negative), 180º must be added to the Closure Direction . Closure Direction  = 26.57º +180º = 206.57º ( ) ( )( ) ( ) feet96.183716.82282.1643   2222 =−+−= += DistanceClosureEast NorthDistanceClosure   ( ) ( )( ) ( ) feet10.181896.183757.206215   =×−= ×−= CosVSDistanceClosure Az  Az CosVS cl vs   Copyright © 2007 OGCI/PetroSkills. All rights reserved. 3    Horizontal and Directional Drilling Solutions To Chapter Problems 3 Given the following survey data, calculate the  Δ TVD ,  Δ North  and  Δ East   using the average angle, radius of curvature and minimum curvature methods. MD 1  = 100 feet MD 2   = 200 feet I  1  = 1º I  2   = 1º  A 1  = 0º  A 2   = 180º Solution:  Average angle method: feet100100200 12 =−=Δ −=Δ MDMDMDMD   feet98.99 2111002 21 =⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ CosTVDI I CosMDTVD   feet00.0 2180021110022 2121 =⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ CosSinNorth A ACosI I SinMDNorth   feet75.1 2180021110022 2121 =⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×=Δ⎟ ⎠ ⎞⎜⎝ ⎛  +×⎟ ⎠ ⎞⎜⎝ ⎛  +×Δ=Δ SinSinEast  A ASinI I SinMDEast   Radius of Curvature: If the azimuths or inclinations are equal, you must add a small amount to one of the azimuths or inclinations so that the radius of curvature equations will work. Otherwise, the eqation will be divided by zero. o 001.1001.01 001.0 212 =+=+= I I I    ( )( )( )( )( )( )( )( ) feet98.99 1001.1 1001.1100180 180 1212 =−π−=Δ−π−Δ=Δ SinSinTVDI I I SinI SinMD TVD   4 Copyright © 2007 OGCI/PetroSkills. All rights reserved
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