Method for predicting fish falling position of logging cable in vertical well

Abstract

The invention provides a method for predicting the fish position of a logging cable in a vertical well, and the method comprises the steps: determining the total length of a dropped cable through the length of the cable before and after the cable is broken when a logging instrument is blocked to form a fish in a logging process; calculating the axial pressure of the cable distributed along the well depth according to the total length of the falling cable and the weight of the cable in the liquid; according to different axial pressures of the cable distributed along the well depth and bending deformation of the cable under the action of self weight, the intervals of the bending deformation of the cable in a spiral section, a sine section and a linear section are determined, and the axial deformation amounts of the cable in the spiral section, the sine section and the linear section are calculated respectively; the top well depth position of the fish is determined; through comprehensive analysis, the position of the cable falling into the well is accurately calculated for guiding construction of cable salvage operation, the cable salvage efficiency can be greatly improved, the cable salvage time is shortened, and risks existing in the cable salvage operation are reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical exploration and relates to a method for predicting the position of a logging cable fish in a vertical well. Background Art

[0002] Currently, for the judgment of the falling position of the cable, an estimation method is usually adopted. By subtracting the length of the broken cable in the wellbore from the depth in the wellbore, the shallowest depth of the cable is obtained. Based on this depth, instruments are used for detection, or fishing tools are gradually lowered to fish for the fallen cable. Due to the complexity of the environment such as the liquid and pipe string in the well, the detection by instruments often has poor effects, especially inside the tubing or casing, where effective detection often cannot be achieved, resulting in the only way of gradually lowering the fishing tool to fish for the cable. By taking the shallowest depth of the cable as the benchmark and gradually lowering the fishing tool to fish for the cable, in the case of a deeper wellbore and a longer length of the fallen cable, it will cause too long fishing time, or due to operational reasons, too much cable is fished at one time and forms a ball, thus triggering secondary accidents and increasing the complexity of cable fishing in the well. Summary of the Invention

[0003] Aiming at the problems existing in the prior art, the present invention provides a method for predicting the position of a logging cable fish in a vertical well, thereby solving the problems of low efficiency, long time consumption, and high risk of cable fishing in the current blind fishing method by gradually lowering the fishing tool.

[0004] A method for predicting the position of a logging cable fish in a vertical well includes:

[0005] S1. During the logging process, when the logging instrument gets stuck and the cable is pulled and broken to form a fish, the total length of the fallen cable is determined through the cable lengths before and after the break;

[0006] S2. Calculate the axial pressure of the cable distributed along the well depth through the total length of the fallen cable and the weight of the cable in the liquid;

[0007] S3. According to the different magnitudes of the axial pressure of the cable distributed along the well depth and the bending deformation of the cable under the action of its own weight, determine the intervals of the helical section, sine section, and straight section where the cable undergoes bending deformation;

[0008] S4. Respectively calculate the axial deformation amounts of the cable in the helical section, sine section, and straight section through the intervals of the helical section, sine section, and straight section where the cable undergoes bending deformation;

[0009] S5. Determine the well depth position L of the top of the fish through the axial deformation amounts of the cable in the helical section, sine section, and straight section

[0010] p . ​

[0011] Preferably, the calculation formula for the total length of the dropped cable is:

[0012] L c = L d - L t

[0013] In the formula: L c is the total length of the dropped cable, in m; L d is the total length of the cable lowered into the well, in m; L t is the length of the cable pulled onto the ground after being pulled off, in m.

[0014] Preferably, the expression for the axial pressure of the cable distributed along the well depth is:

[0015] F Z = q l ·Z

[0016] In the formula: F Z is the axial pressure, in N; q l is the weight of the cable in the liquid, in N / m; Z is the length along the well depth at the fracture position, in m;

[0017] where Z = L c + L g ;

[0018] In the formula, L g is the length of the tool string, in m; L c is the total length of the dropped cable, in m.

[0019] Preferably, the weight of the cable in the liquid is calculated from the well fluid density and the weight of the cable in air, and its expression is:

[0020]

[0021] In the formula: q l is the weight of the cable in the liquid, in N / m; ρ l is the well fluid density, in kg / m 3 ; q s is the weight of the cable in air, in N / m; d is the cable diameter, in m; g is the acceleration due to gravity, in m / s 2 .

[0022] Preferably, the specific process for determining the bending deformation in the helical section in S3 is:

[0023] When the dimensionless axial pressure , the cable is helically deformed;

[0024] Then the critical pressure F of the helical section hel is:

[0025]

[0026] In the formula, q l is the weight of the cable in the liquid, with the unit of N / m; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, I = πd 4 / 64, with the unit of m 4 ;

[0027] The corresponding position Z of the helical section cable hel is:

[0028]

[0029] The length L of the helical section hel is:

[0030] L hel = L c - Z hel

[0031] Then the corresponding helical section interval is [Z hel , L c ; L c is the total length of the dropped cable, with the unit of m.

[0032] Preferably, the specific process of determining the bending deformation in the sine section interval in S3 is:

[0033] When the dimensionless axial pressure is, the cable is in a sine shape;

[0034] According to the function expression of the dimensionless axial pressure and the dimensionless length is:

[0035]

[0036] In the formula: ξ c is the dimensionless axial pressure of the cable, q l is the weight of the cable in the liquid, with the unit of N / m; F Z is the axial pressure of the cable along the well depth, with the unit of N; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, I = πd 4 / 64, with the unit of m 4 ;

[0037] By obtaining the dimensionless length γ i , then the actual sine critical length l i is:

[0038]

[0039] Then the critical pressure F of the sine segment sin is:

[0040]

[0041] In the formula, The corresponding cable position Z of the sine segment sin is:

[0042]

[0043] Then the length L of the sine segment sin is:

[0044] L sin = Z hel - Z sin ;

[0045] The corresponding sine segment interval is [Z sin , Z hel ; Z hel is the cable position of the helical segment.

[0046] Preferably, the specific process of determining the bending deformation in the sine segment interval in S3 is:

[0047] When the dimensionless axial pressure , the cable is in a straight shape, and the length L of the straight segment s is:

[0048] L s = Z sin

[0049] Then the straight segment interval is [0, Z sin ; Z sin is the cable position of the sine segment.

[0050] Preferably, the specific process of S4 is:

[0051] The axial deformation Δl of the cable in the straight segment s is:

[0052]

[0053] In the formula: A is the cross-sectional area of the cable, A = πd 2 / 4, m 2 ; E is the elastic modulus of the cable, with the unit of Pa; q l is the weight of the cable in the liquid, with the unit of N / m; L s is the length of the straight segment, with the unit of m;

[0054] The axial deformation Δl of the cable in the sine segmenti is:

[0055] According to the arc length integral formula, the arc length s of the sine function in the sine segment is obtained i Expression:

[0056]

[0057] For the same infinitesimal segment, s should satisfy the following in terms of length i = l i Let

[0058]

[0059] Let the equation f(x) = 0, and calculate the axial deformation Δl of the sine segment i .

[0060] The axial deformation Δl of the cable in the helical segment m is:

[0061] Δl m = l m - P m ;

[0062] In the formula: k m is the helical length, with the unit of m; p m is the pitch, with the unit of m.

[0063] Preferably, the expression of the pitch P m is:

[0064]

[0065] In the formula: m is the number of helices from top to bottom; p m is the pitch, with the unit of m; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, I = πd 4 / 64, m 4 ; q l is the weight of the cable in the liquid, with the unit of N / m;

[0066] According to the parametric equation of the cylindrical helix, the relationship between the pitch P m and the helical length l m can be obtained:

[0067]

[0068] In the formula: m is the number of helices from top to bottom; R is the wellbore radius, with the unit of m.

[0069] Preferably, the specific process of S5 is:

[0070] The axial deformation amounts of the cable in the spiral section, sine section, and straight section are accumulated to obtain the total deformation amount Δl.

[0071] Δl = Δl s + ∑Δl i + ∑Δl m ;

[0072] Then the well depth position L at the top of the fish p is:

[0073] L p = L b -(L c + L g ) + Δl;

[0074] In the formula: L b is the well depth where the tool string gets stuck, with the unit of m; L g is the length of the tool string, with the unit of m; L c is the total length of the dropped cable, with the unit of m.

[0075] Compared with the prior art, the present invention has the following beneficial technical effects:

[0076] The present invention provides a method for predicting the position of a logging cable fish in a vertical well. During the logging process, when the logging instrument gets stuck and the cable is pulled and broken to form a fish, the total length of the dropped cable is determined through the cable lengths before and after the break; the axial pressure distribution of the cable along the well depth is calculated through the total length of the dropped cable and the weight of the cable in the liquid; according to the different magnitudes of the axial pressure distribution of the cable along the well depth and the bending deformation of the cable under its own weight, the intervals of the cable bending deformation in the spiral section, sine section, and straight section are determined, and the axial deformation amounts of the cable in the spiral section, sine section, and straight section are calculated respectively, so as to determine the well depth position at the top of the fish; through comprehensive analysis, the position of the dropped cable is accurately calculated, which is used to guide the construction of the cable fishing operation, can greatly improve the cable fishing efficiency, shorten the cable fishing time, and reduce the risks existing in the cable fishing operation. Brief Description of the Drawings

[0077] Figure 1 is the flowchart for predicting the position of a logging cable fish in a vertical well;

[0078] Figure 2 is the coordinate establishment diagram of the axial pressure of the cable along the well depth in the embodiment;

[0079] Figure 3 is the schematic diagram for calculating the sine buckling deformation in the embodiment;

[0080] Figure 4 is the schematic diagram of the spiral buckling deformation in the embodiment. Detailed Embodiment

[0081] The present invention will be further described in detail below in conjunction with specific embodiments, which are explanations of the present invention rather than limitations.

[0082] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative work shall fall within the scope of protection of the present invention.

[0083] Currently, the position judgment of the downhole cable mainly adopts the empirical method, and blind fishing is carried out by gradually lowering the fishing tool. The cable fishing efficiency is low, the time consumption is long, and the risk is high. The present invention provides a method for predicting the position of the logging cable fish in a vertical well, as Figure 1 shown:

[0084] (1) Determine the length of the dropped cable

[0085] During the logging process, when the logging instrument gets stuck, both pulling up and lowering cannot release the stuck state, and finally the cable is pulled off to form a fish. The well depth where the instrument string gets stuck is the stuck position L b . The length L g of the tool string can be obtained from the instrument string information. The total length L c of the dropped cable is

[0086] L c = L d - L t (1)

[0087] In the formula: L c is the total length of the dropped cable, m; L d is the total length of the cable lowered into the well, m; L t is the length of the cable pulled onto the ground after being pulled off, m.

[0088] (2) Calculate the axial pressure of the cable distributed along the well depth

[0089] The cable fish in the vertical well is mainly affected by its own weight and buoyancy. According to the density of the well fluid and the weight of the cable in the air, the weight of the cable in the liquid is calculated:

[0090]

[0091] In the formula: q l is the weight of the cable in the liquid, N / m; ρ l is the density of the well fluid, kg / m 3 ; qs is the weight of the cable in air, N / m; d is the cable diameter, m; g is the acceleration of gravity, m / s 2 .

[0092] Establish a coordinate system OXYZ at the fracture position, with the X-axis pointing due north, the Y-axis pointing due east, and the Z-axis pointing in the direction of the well depth, as Figure 2 shown. Then the axial pressure F of the cable along the well depth Z is

[0093] F Z = q l ·Z (3)

[0094] where: F Z is the axial pressure, N; Z is the length along the well depth at the fracture position, m.

[0095] (3) Determine the intervals of the helical section, sine section, and straight section

[0096] Assume that the downhole instrument is rigid and does not deform. The cable bends under its own weight. According to the magnitude of the axial pressure on the cable, the deformation can be divided into helical, sine, and straight shapes.

[0097] ① When the dimensionless axial pressure , the cable is helically deformed. The pitch p of the m-th helical turn m is

[0098]

[0099] where: m is the number of helical turns from top to bottom; p m is the pitch, m; E is the elastic modulus of the cable, Pa; I is the moment of inertia of the cable cross-section, I = πd 4 / 64, m 4 . The critical pressure of the helical section is

[0100]

[0101] where The corresponding cable position is

[0102]

[0103] The length of the helical section

[0104] L hel = L c - Z hel (7)

[0105] The corresponding helical section interval is [Z hel , L c .

[0106] ②When the dimensionless axial pressure is applied, the cable is in a sine shape. According to the functional expression of the dimensionless axial pressure and the dimensionless length

[0107]

[0108] where: ξ c is the dimensionless axial pressure of the cable, the dimensionless length γ i is obtained, and then the actual critical length

[0109]

[0110] The critical length l of the first segment is calculated 1 and then all the critical lengths l are calculated sequentially from bottom to top i . The critical pressure of the sine segment is

[0111]

[0112] where the corresponding cable position is

[0113]

[0114] The sine segment length

[0115] L sin = Z hel - Z sin (12)

[0116] The corresponding sine segment interval is [Z sin , Z hel .

[0117] ③When the dimensionless axial pressure is applied, the cable is in a straight line shape and the length is

[0118] L s = Z sin (13)

[0119] The straight line segment interval is [0, Z sin .

[0120] (4) Calculate the axial deformation of the cable

[0121] ①Deformation of the straight line segment

[0122] For the straight line shape, the axial deformation amount is

[0123]

[0124] where: A is the cross-sectional area of the cable, A = πd2 / 4, m 2 。

[0125] ② Sine segment deformation

[0126] For the sine axial deformation within a critical length, establish a coordinate system as shown in Figure 3 The function expression for this segment is

[0127]

[0128] where R is the wellbore radius, m; Δl i is the axial deformation, m.

[0129] According to the arc length integral formula, the arc length s of the sine function for this segment can be obtained i Expression

[0130]

[0131] For the same infinitesimal segment, s should satisfy s i = l i , let

[0132]

[0133] Solve the equation f(x) = 0 to find the sine axial deformation Δl for this segment i 。

[0134] ③ Helical segment deformation

[0135] For the axial deformation of one helix, the helix of the cable in the well is as shown in Figure 4 According to the parametric equation of the cylindrical helix, the relationship between the pitch P m and the helix length l m can be obtained

[0136]

[0137] Then the axial deformation for this segment is

[0138] Δl m = l m - P m (19)

[0139] (5) Calculate the position of the fish top

[0140] After finding the axial deformations of each helical, sine, and straight-line segment, sum them up to obtain the total deformation Δl,

[0141] Δl = Δl s + ∑Δl i + ∑Δl m(20)

[0142] Then the well depth position L at the top of the fish p

[0143] L b = L b -(L c + L g ) + Δl (21)

[0144] Example 1:

[0145] (1) Determine the length of the dropped cable

[0146] Assume the stuck position L b = 2500m, the length of the tool string L g = 25m, the total length of the cable lowered into the well L d = 2000m, the length of the cable pulled to the ground after being pulled off L t = 500m. Calculate the total length L of the dropped cable according to formula (1) c = L d - L t = 2000 - 500 = 1500m.

[0147] (2) Calculate the axial pressure of the cable distributed along the well depth

[0148] Assume the cable model of the cable manufacturer is W7F46F40CF - EEHS - 12.4, the cable diameter d = 12.4mm, and the cross - sectional area of the cable A = πd 2 / 4 = 1.207×10 -4 m 2 , the weight of the cable in air is 580kg / km, that is q s = 5.684N / m. The elongation rate is 0.8m / km / 5kN, and the equivalent elastic modulus of the cable where Δl is the cable elongation, taking 0.8m; F is the tensile force, 5kN. Assume the well fluid density ρ l = 1300kg / m 3 , then the weight of the cable in the liquid Then the axial pressure F of the cable along the well depth Z = q l Z = 4.145Z.

[0149] (3) Determine the intervals of the spiral section, sine section, and straight section

[0150] Assume the downhole instrument is rigid and does not deform. The cable bends under its own weight. According to the different magnitudes of the axial pressure on the cable, the deformation can be divided into spiral shape, sine shape, and straight shape.

[0151] ① Helical section length

[0152] The moment of inertia of the cable cross-section I = πd 4 / 64 = 1.16×10 -9 m 4 , and the corresponding non-dimensional critical axial pressure of the helical section Critical pressure of the helical section The corresponding cable position is The helical section range is 4.101m to 1500m, and the helical section length L hel = L c -Z hel = 1495.9m.

[0153] ② Sine section length

[0154] Non-dimensional axial pressure of the sine section Corresponding axial pressure The corresponding cable position at this time is The sine section range is 2.654m to 4.101m, and the sine section length L sin = Z hel -Z sin = 1.477m.

[0155] ③ Straight section length

[0156] When the axial pressure is reached, the cable is in a straight shape. The straight section range is 0m to 2.654m, and the straight section length L s = 2.654m.

[0157] (4) Calculate the axial deformation of the cable

[0158] ① Deformation of the straight section

[0159] For the straight shape, the axial deformation

[0160] ② Deformation of the sine section

[0161] The sine section length L sin = Z hel -Z sin = 1.447m, ξ c = ξ sin starting from 1.086, ∑l i = Substitute into formulas (8), (9), (17), and calculate successively until ∑l i ≥ L sin , and calculate the total deformation of the sine section ∑l i = 0.13m.

[0162] ③ Deformation of the spiral section

[0163] Take the length L of the spiral section hel = 1495.9 m, substitute it into formulas (4), (18), and (19), and calculate the pitch p of each spiral in sequence starting from m = 1 m , the length l of each section of the spiral line m , the axial deformation amount Δl of each section of the pitch m , until ∑l m ≥L hel . Calculate the total deformation ∑l of the spiral section m = 269.16 m..

[0164] (5) Calculate the position of the fish top

[0165] The total deformation amount Δl = Δl s +∑Δl i +∑Δl m = 269.29 m.

[0166] The well depth position L of the fish top p = L b -(L c +L g )+Δl = 1244.29 m.

[0167] The above is only the preferred embodiment of the present invention, and it is not intended to limit the present invention in any form; any ordinary technician in the industry can smoothly implement the present invention according to the illustrations in the specification and the above description; however, any equivalent changes such as slight modifications, decorations, and evolutions made by those skilled in the art within the scope of the technical solution of the present invention by using the technical content disclosed above are all equivalent embodiments of the present invention; at the same time, any equivalent changes, modifications, and evolutions made to the above embodiments based on the essential technology of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for predicting the position of a logging cable fish in a vertical well, characterized in that, it includes, S1. During the logging process, when the logging instrument gets stuck and the cable is broken to form a fish, the total length of the dropped cable is determined by the cable lengths before and after the break; S2. The axial pressure of the cable distributed along the well depth is calculated through the total length of the dropped cable and the weight of the cable in the liquid; S3. According to the different magnitudes of the axial pressure of the cable distributed along the well depth and the bending deformation of the cable under its own weight, the intervals of the cable's bending deformation in the spiral section, sine section, and straight section are determined; S4. Through the intervals of the cable's bending deformation in the spiral section, sine section, and straight section, the axial deformation amounts of the cable in the spiral section, sine section, and straight section are respectively calculated; S5. Through the axial deformation amounts of the cable in the spiral section, sine section, and straight section, the well depth position of the top of the fish is determined.

2. The method for predicting the position of a logging cable fish in a vertical well according to claim 1, characterized in that, the calculation formula for the total length of the dropped cable is: L c = L d - L t Where: L c is the total length of the dropped cable, in m; L d is the total length of the cable lowered, in m; L t is the length of the cable pulled onto the ground after being broken, in m.

3. The method for predicting the position of a logging cable fish in a vertical well according to claim 2, characterized in that, the expression for the axial pressure of the cable distributed along the well depth is: F Z = q l · Z Where: F Z is the axial pressure of the cable along the well depth, with the unit of N; q l is the weight of the cable in the liquid, with the unit of N / m; Z is the length along the well depth at the fracture position, with the unit of m.

4. The method for predicting the position of a logging cable fish in a vertical well according to claim 3, characterized in that, the weight of the cable in the liquid is calculated through the well fluid density and the weight of the cable in the air, and its expression is: Where: q l is the weight of the cable in the liquid, in N / m; ρ l is the density of the well fluid, in kg / m 3 ; q s is the weight of the cable in air, in N / m; d is the diameter of the cable, in m; g is the acceleration due to gravity, in m / s 2 .

5. The method for predicting the position of a logging cable fish in a vertical well according to claim 1, characterized in that, the specific process for determining the interval of the bending deformation in the spiral section in S3 is: When the dimensionless axial pressure is applied, the cable is helically deformed; Then the critical pressure F of the spiral section hel is as follows: In the formula, q l is the weight of the cable in the liquid, with the unit of N / m; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, with the unit of m 4 ; The corresponding spiral section cable position Z hel is as follows: The length L of the spiral section hel is as follows: L hel = L c - Z hel Then the helical section interval is [Z hel , L c ; L c is the total length of the dropped cable, in m.

6. The method for predicting the position of a logging cable fish in a vertical well according to claim 5, characterized in that, the specific process for determining the interval of the bending deformation in the sine section in S3 is: When the dimensionless axial pressure is applied, the cable assumes a sinusoidal shape; According to the function expression of the dimensionless axial pressure and the dimensionless length: where: ξ c is the dimensionless axial pressure of the cable, q l is the weight of the cable in the liquid, with the unit of N / m; F Z is the axial pressure of the cable along the well depth, with the unit of N; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, with the unit of m 4 ; By obtaining the dimensionless length γ i , the actual sine critical length l i is as follows: Then the critical pressure F of the sine segment sin is as follows: In the formula, The corresponding sine-segment cable position Z sin is: Length L of the sine segment sin is as follows: L sin = Z hel -Z sin ; Then the sine segment interval is [Z sin , Z hel ; Z hel is the position of the helical section cable.

7. The method for predicting the position of a logging cable fish in a vertical well according to claim 6, characterized in that, the specific process for determining the interval of the bending deformation in the straight section in S3 is: When the dimensionless axial pressure is applied, the cable is in a straight shape, and the length L of the straight section s is as follows: L s = Z sin Then the straight-line segment interval is [0, Z sin ; Z sin is the position of the sine-segment cable.

8. The method for predicting the position of a logging cable fish in a vertical well according to claim 7, characterized in that, the specific process of S4 is: Axial deformation Δl of the cable in the straight section s is as follows: Where: A is the cross-sectional area of the cable, A = πd 2 / 4, m 2 ; E is the elastic modulus of the cable, with the unit of Pa; q l is the weight of the cable in the liquid, with the unit of N / m; L s is the length of the straight segment, with the unit of m; The axial deformation Δl of the cable in the sine segment i is as follows: According to the arc length integral formula, the arc length s of the sine function in the sine segment is obtained i Expression: For the same infinitesimal segment, it should satisfy s i = l i Let Let the equation be f(x) = 0, and calculate the sine axial deformation Δl of the sine segment i ; Axial deformation Δl of the cable in the helical section m is as follows: Δl m = l m - P m ; where: l m is the length of the helix, in m; p m is the pitch, in m.

9. The method for predicting the position of a logging cable fish in a vertical well according to claim 8, characterized in that, The pitch P m is expressed as: where: m is the number of helices from top to bottom; p m is the pitch, with the unit of m; E is the elastic modulus of the cable, with the unit of Pa; I is the moment of inertia of the cable cross-section, I = πd 4 / 64, m 4 ; q l is the weight of the cable in the liquid, with the unit of N / m; According to the parametric equation of the cylindrical helix, the pitch P can be obtained m and the relationship with the helix length l m is as follows: In the formula: m is the number of spirals from top to bottom; R is the radius of the wellbore, with the unit of m.

10. The method for predicting the position of a logging cable fish in a vertical well according to claim 8, characterized in that, the specific process of S5 is: Through the axial deformation amounts of the cable in the spiral section, sine section, and straight section, the total deformation amount Δl is obtained by cumulative summation, and the expression is: Δl = Δl s + ∑Δl i + ∑Δl m ; The well depth position L at the top of the fish p is: L p = L b -(L c + L g ) + Δl; Where: L b is the well depth where the tool meets the obstruction, in m; L g is the length of the tool string, in m; L c is the total length of the dropped cable, in m.

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