By E Buforn; Carmen Pro; Agustin Udias Vallina
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The aim of utilized Geothermics for Petroleum Engineers is to offer in a transparent and concise shape equipment of using the knowledge of temperature surveys in deep boreholes in addition to the result of box, laboratory and analytical investigations in geothermics to a large viewers. even though a few elements of the topic of this publication were mentioned in numerous past books and diverse papers, utilized Geothermics for Petroleum Engineers is the 1st ebook in this subject on hand to the petroleum engineering neighborhood.
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20 a3 M 4 ¼ M1 ¼ pð5r À rÞ 3 2 2 and for the inverse of the distance 1/q we use the approximation a 2 1 À Á 1 1 a ¼ 1 þ cos y þ 3cos2 y À 1 q r 2r 2r 2 ! Then, the total gravitational potential is V ¼ Á GM 3 a 1 a2 À þ cos y þ 3cos2 y À 1 r 2 4r 16 r ! The total potential U is the sum of the gravitational potential V plus the potential of rotation F, where 1 F ¼ r2 o2 sin2 y 2 and using the coefﬁcient m = o2a3/GM = 1/8, we have U¼ ! Á r 3 m 2 GM 3 a 1 a2 À þ cos y þ 3cos2 y À 1 þ sin y r 2 4r 16 r a 2 At the North Pole, y = 0 and r ¼ a, and the value of the potential is !
R 3 m 2 GM 3 a 1 a2 À þ cos y þ 3cos2 y À 1 þ sin y r 2 4r 16 r a 2 At the North Pole, y = 0 and r ¼ a, and the value of the potential is ! GM 3 1 1 15GM Up ¼ þ þ ¼ a 2 4 8 8a Earth’s gravity ﬁeld and potential 37 The form of the equipotential surface is found by putting U ¼ Up: Á r 3 m 2 15GM GM 3 a 1 a2 À ¼ þ cos y þ 3cos2 y À 1 þ sin y 8a r 2 4r 16 r a 2 ! Putting r ¼ a inside the square brackets and solving for r we ﬁnd ! 4 1 1 r ¼ a 1 þ cos y þ cos2 y 5 6 12 (b) The deviation of the vertical with respect to the radial direction is given by the angle i: tan i ¼ gy gr To ﬁnd this value we have to calculate the two components of gravity gr ¼ !
28 (a) The gravity anomaly produced by an inﬁnite horizontal cylinder buried at depth d, with centre at x ¼ 0 (Fig.