Page | 159
And so:
(𝑫 𝒌+𝟏 −𝑫 𝒌 )𝒄𝒐𝒔𝑰 𝒌+𝟏 𝒄𝒐𝒔𝑨 𝒌+𝟏 (𝑫 𝒌+𝟏 −𝑫 𝒌 )𝒄𝒐𝒔𝑰 𝒌+𝟏 𝒔𝒊𝒏𝑨 𝒌+𝟏 −(𝑫 𝒌+𝟏 −𝑫 𝒌 )𝒔𝒊𝒏𝑰 𝒌+𝟏
[ −𝒔𝒊𝒏𝑰 𝒌 𝒄𝒐𝒔𝑨 𝒌 −𝒔𝒊𝒏𝑰 𝒌+𝟏 𝒄𝒐𝒔𝑨 𝒌+𝟏 −𝒔𝒊𝒏𝑰 𝒌 𝒔𝒊𝒏𝑨 𝒌 −𝒔𝒊𝒏𝑰 𝒌+𝟏 𝒔𝒊𝒏𝑨 𝒌+𝟏 −𝒄𝒐𝒔𝑰 𝒌 −𝒄𝒐𝒔𝑰 𝒌+𝟏
−(𝑫 𝒌+𝟏 −𝑫 𝒌 )𝒔𝒊𝒏𝑰 𝒌+𝟏 𝒔𝒊𝒏𝑨 𝒌+𝟏 (𝑫 𝒌+𝟏 −𝑫 𝒌 )𝒔𝒊𝒏𝑰 𝒌+𝟏 𝒄𝒐𝒔𝑨 𝒌+𝟏 𝟎 ]
𝒅∆𝒓 𝒌+𝟏 𝒅𝒑 𝒌
𝟏 𝟐
=
So in summary, we have now calculated the 3x3 matrix equations which describe the change in the wellbore position, in the nev-co-ordinate frame caused by changes to the survey measurement at any preceding given station, k . For the last survey station of interest, only the preceding interval is applicable and equation (A.1) becomes:
𝒅∆𝒓 𝒌 𝒅𝒑 𝒌
𝝏𝒑 𝒌 𝝏𝜺 𝒊
𝒆 𝒊,𝒍,𝒌 ∗
𝒊,𝒍 (
)
= 𝝈
Made with FlippingBook flipbook maker