CN104047593B - A kind of method of utilizing speed location drilling well microchip tracer depth - Google Patents

Abstract

The invention belongs to oil exploration and development fields. Especially carry out the method for Depth determination for drilling well microchip tracer. Described tracer moves with flowing of drilling fluid, the method of locating described tracer mine shaft depth is by full well segmentation according to mineshaft annulus inside/outside diameter size, obtain each well section drilling fluid upward velocity and tracer gliding speed according to physical parameter in mud flow rate and well, and obtain thus the actual upward velocity of each well section tracer; According to the running time of this speed and tracer, obtain the moving displacement of tracer, thereby obtain the depth location of tracer in each well section, finally draw the degree of depth of different time tracer, thereby realize location tracer depth. This invention can find that well kick, leakage, the drilling tool friction borehole wall, drilling tool such as pierce through at the drilling well abnormal accident in time, improves drilling efficiency, finds in time and evaluate oil and gas reservoir.

Description

A kind of method of utilizing speed location drilling well microchip tracer depth

Technical field

The invention belongs to oil exploration and development fields. Relate in drilling well in order to improve drilling efficiency and to ensure drilling safetyDetect the research direction of temperature in wellbore and pressure, especially carry out the method for Depth determination for drilling well microchip tracer.

Background technology

1. drilling parameter is measured ensureing that drilling safety has important effect

Oil drilling is a high risk industry, in drilling process, if there is drilling failure, gently causes propertyLoss, heavy cause casualties. Along with the increase of well depth, the particularly exploitation of various Multilateral Wells, horizontal well, drilling failure andThe incidence of complex situations is more and more higher. All there is to some extent the drilling engineering such as well kick, leakage in annual domestic each elephantAccident, and the variation of these accidents and drilling engineering parameter is closely related. Therefore, the variation of Real-Time Monitoring drilling engineering parameter canEffectively to prevent the generation of this type of accident.

2. temperature and pressure is most important two parameters of oil drilling

Drilling fluid temperature and pressure are two important basic datas in drilling engineering. The temperature, pressure on stratum can be anti-Mirror the feature such as the duty of rig and the physical property on stratum. Temperature, pressure to whole pit shaft carry out Real-Time Monitoring, set up withThe speed-raising of drilling engineering is put forward to effect for the temperature of drilling collection, pressure traverse and safety drilling has great significance.

3. the temperature, pressure parameter that routine techniques cannot Quick Acquisition top well

The collection of current temperature parameter generally has two kinds of modes, and one is ground acquisition, and one is that nearly drill bit place gathers.In the time of ground acquisition, due to the migration of drilling fluid, the temperature parameter error gathering is larger, and can not reflect certain point in pit shaftTemperature parameter. While adopting the collection place collection at nearly drill bit place, can only gather near the parameter of bit location. So, so, no matterBe ground acquisition, or nearly drill bit place gathers, and all can not gather the temperature, pressure parameter of top well, lack whole pit shaftThe dynamic change of parameter. With the dark continuous increase of drilling well, the variation of drilling fluid density, Quan the three-dimensional monitoring of pit shaft is even more important.

4. the temperature, pressure parameter gathering is not carried out depth localization

At present, start correlative study both at home and abroad, designed can be used in and detect real-time temperature in wellbore and pressureData collecting system-microchip fluid trace device, Fig. 1 is tracer schematic diagram (pink colour small circle is tracer). This tracerOperation principle be, in drilling process, tracer enters in drilling rod from ground, by circulation of drilling fluid, arrive behind shaft bottom fromThe hydrophthalmia of drill bit enters annular space region, and along with returning to ground on annular space drilling fluid, is finally captured by the special device on ground. ShowTrack device temperature and pressure parameter in real-time collection and continual collection pit shaft in motion process. This tracer is except having recorded temperature, pressure ginsengOutside number, also record time parameter, but do not recorded well depth parameter. Well bore parameter is that in evaluation pit shaft, temperature, pressure is the most directParameter, need to be converted into time parameter well depth parameter, is used for temperature, the pressure of the different well depths of accurate evaluation. At present, domestic and internationalAll do not solve this tracer depth localization problem in well. Because drilling engineer is indifferent to the temperature, pressure parameter in drilling rodChange, be more concerned about the variation of annular space temperature, pressure parameter, so in this patent, only consider that the degree of depth of tracer in annular space is fixedPosition.

Summary of the invention

The present invention is in order to solve the technical problem that in prior art, tracer depth cannot accurately be determined and be evaluated, existingHave in technology, when tracer moves in well, only gathered temporal information, do not have production wells to deeply convince breath,

The present invention has researched and developed a kind of method of utilizing speed location drilling well microchip tracer depth, be by temporal information withCasing programme information combines, and is converted into well depth information, for monitoring the variation of different well depths place parameter, formulates in time construction and arrangesExecute.

Basic research and development thinking of the present invention is: drilling fluid returns in annular space, and tracer is also gone up under the carrying of drilling fluidReturn, meanwhile, because the averag density of tracer is more bigger than drilling fluid, tracer glides relatively with respect to drilling fluid. Obtain drilling wellLiquid upward velocity and tracer gliding speed, the difference of the two is the actual uplink speed of tracer, the taking advantage of of this speed and timeAmass the moving displacement that is tracer, thereby obtain the depth location of tracer, see Fig. 2.

Technical scheme of the present invention is,

A method of utilizing speed location drilling well microchip tracer depth, described tracer is carried and is entered by drilling fluidIn drilling well, to shaft bottom, in well annular space, return to ground, described tracer is for detecting real-time temperature in wellbore and pressureAnd carry out data acquisition;

Described tracer moves with flowing of drilling fluid, and the method for locating described tracer mine shaft depth is according to pit shaftAnnular space dimension of inner and outer diameters, by full well segmentation, obtains returning speed on each well section drilling fluid according to physical parameter in mud flow rate and wellSpend and tracer gliding speed, and obtain thus the actual upward velocity of each well section tracer; Return to ground according to tracer afterwardsThe time of face obtains the moving displacement of tracer, thereby obtains the depth location of tracer in each well section, thereby realizes locationTracer depth.

Because the difference of annular space internal diameter, external diameter will be to returning on this well section drilling fluid and tracer downslide uniform velocity causes shadowRing, therefore need first to distinguish for the inside and outside footpath of different annular spaces in each well section, described according to the inside and outside footpath of mineshaft annulus chiVery little by full well segmentation be according to annular space size by little and large segmentation, the well section of same annular space size is same well section; And carryThe interior physical parameter of well of getting each well section, comprising: internal diameter, external diameter and each well section height.

Each the pit shaft of collection physical parameter is gathered and calculates to the upward velocity of the drilling fluid of each well section,

$V_{\mathrm{un}}=\frac{Q}{\frac{\mathrm{\π}}{4}({D_n}^2-{d_n}^2)},$

In the drilling fluid upward velocity of n well section, wherein,

V_unIt is the upward velocity of n well section; Q-drilling fluid displacement, m³/min

D is this well section annular space external diameter; D is this well section annular space internal diameter.

Same every physical index of each pit shaft of collection physical parameter and tracer is gathered and calculate described inTracer is gliding speed in the annular space of each well section:

$V_d=\frac{4.242d_s{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_d)}^{\frac{2}{3}}}{{{\mathrm{\ρ}}_d}^{\frac{1}{3}}{{\mathrm{\μ}}_e}^{\frac{1}{3}}}$

In formula:

V_dThe gliding speed of-tracer in drilling fluid, m/min; d_s-tracer diameter, cm,

ρ_s-tracer averag density, g/cm³；ρ_d-drilling fluid density, g/cm³，

μ_e-drilling fluid effective viscosity, Pas.

Demarcate for the degree of depth to tracer, need to obtain the upward velocity of actual tracer, described tracer existsThe actual upward velocity of the annular space of each well section is that drilling fluid upward velocity deducts the gliding speed of tracer in annular space, i.e. V=V_un-V_d。

Simultaneously described tracer the run duration of each well section be the height of this well section divided by described tracer at this wellActual upward velocity in section annular space.

Physical parameter obtains slip velocity under each well section drilling fluid upward velocity and tracer according to mud flow rate and wellDegree, and obtain thus after the actual upward velocity of each well section tracer, the time of returning to ground according to tracer is shownTrack device is at the moving displacement of this well section.

If the captive time of described tracer is tracer and arrives time on ground, be designated as 0, tracer in well certainThe moment of some operation is T_i，T_iValue perseverance be less than 0;

Described tracer is described tracer in fact returning in this well section at the move distance in each a certain moment of well sectionSpeed is multiplied by this moment; h_i=V_jT_i, wherein, h_iBe tracer in j well section, the moment is T_iTime distance, V_jAt j wellThe actual upward velocity of tracer when section.

Finally, the degree of depth of tracer is demarcated, described tracer is should in the degree of depth sometime of each well sectionHeight sum and the described tracer of above each well section of well section are the described spike of determining in the move distance sum of this well sectionThe degree of depth of device.

As shown in Figure 2, the method step that a kind of speed of the present invention is located described tracer depth comprises:

1. determine that described tracer arrives the time on ground: described tracer arrives behind ground, received and establish by ground immediatelyStandby catching, the captive time of tracer is the time on tracer arrival ground, is designated as 0, and tracer is certain some operation in wellMoment be T_i，T_iValue perseverance be less than 0;

2. distribute well section step: according to the difference of annular space internal-and external diameter, full well is divided into some well sections, establishes full hole total lengthFor H, i.e. H=h₁+h₂+......+h_n; If each well section annular space internal-and external diameter, length are respectively d from top to bottom₁、D₁、h₁；d₂、D₂、h₂；……,d_n、D_n、h_nn=1,2,3,……；

3. calculate the upward velocity step of each well section drilling fluid at annular space:

At h₁In well section, drilling fluid upward velocity

At h₂In well section, drilling fluid upward velocity

……

At h_nIn well section, drilling fluid upward velocity

Q-drilling fluid displacement, m³/min；

4. calculate the gliding speed step of the described tracer of each well section at annular space:

$V_d=\frac{4.242d_s{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_d)}^{\frac{2}{3}}}{{{\mathrm{\ρ}}_d}^{\frac{1}{3}}{{\mathrm{\μ}}_e}^{\frac{1}{3}}}$

In formula:

V_dThe gliding speed of-tracer in drilling fluid, m/min, d_s-tracer diameter, cm

ρ_s-tracer averag density, g/cm³，ρ_d-drilling fluid density, g/cm³，μ_c-drilling fluid effective viscosity, Pas

5. determine the actual upward velocity step of described tracer at annular space:

At h₁In well section, drilling fluid upward velocity V₁＝V_u1-V_d

At h₂In well section, drilling fluid upward velocity V₂＝V_u2-V_d

……

At h_nIn well section, drilling fluid upward velocity V_n＝V_un-V_d；

6. obtain the run duration step of each well section tracer:

At h₁In well section, section running time of tracer is

At h₂In well section, be the running time of tracer

……

At h_nIn well section, be the running time of tracer

7. calculate each well section tracer sometime section move distance step:

?In time, tracer is at h₁Motion in well section, the move distance of tracer and the pass of run durationBe-V₁T_i

?In time, tracer is at h₂Motion in well section, the move distance of tracer and motionThe pass of time is

……

?In time, tracer is at h_nWell sectionInterior motion, the move distance of tracer and the pass of run duration are

8. determine described tracer depth step sometime:

?In time, tracer is at h₁Motion in well section, T_iThe depth location of moment tracer is h_1i＝V₁T_i?In time, tracer is at h₂Motion in well section, T_iThe depth location of moment tracer is $h_{2i}=h_1+V_2(-\frac{h_1}{V_1}-T_i)$

……

?In time, tracer is at h₃Well sectionInterior motion, T_iThe depth location of moment tracer is

$h_{\mathrm{ni}}=h_1+h_2+......+h_{n-1}+V_n(-\frac{h_1}{V_1}-\frac{h_2}{V_2}-......-\frac{h_{n-1}}{V_{n-1}}-T_i).$

Adopt degree of depth scaling method of the present invention, successfully the time parameter of tracer collection is converted to well depth parameter,Tracer depth location, will carry out depth localization from now on by tracer, can obtain temperature, the pressure ginseng at different depth place in pit shaftCount, realize the real time dynamic tracing of full pit shaft.

1. improve drilling efficiency

Determine after the well depth parameter of tracer, can understand temperature in pit shaft with the degree of depth according to different well depth temperature datasThe gradient increasing, can reflect that drilling liquid flow bulk properties and borehole wall stability change to a certain extent. Press according to different well depthsForce data can be OPTIMIZATION OF DRILLING FLUID density and circulation equivalent, select best casing setting depth etc., carries for formulating technical measuresSupply the foundation of science, improved bit speed and efficiency.

2. ensure drilling safety

In drilling process, in pit shaft, often there is the drilling wells such as well kick, leakage, the drilling tool friction borehole wall, drilling tool pierce through abnormalAccident, if find in time, and takes technical measures in time, can avoid larger drilling failure, if can not find in time Ke NengzaoBecome huge economic loss or casualties. Fig. 4 is certain well drilling tool friction borehole wall tracer temperature curve, due to drilling tool friction wellWall, causes friction point excess Temperature. Determine after the well depth parameter of tracer, according to the variation of tracer temperature, pressure, Neng GoujiAbnormal the occurred position of Shi Faxian drilling well, prevents the accident in drilling engineering in time, has ensured drilling safety.

3. timely discovery and the evaluation of oil and gas reservoir

Oil-gas Layer in stratum, is often accompanied by high temperature, high pressure, and existing technology is mainly to measure on ground, dryThe factor of disturbing is many, is unfavorable for the discovery of oil/gas show. Determine after the well depth parameter of tracer temperature that can be measured according to tracerDegree, pressure change, and find in time oil gas and evaluate to show.

Brief description of the drawings

Fig. 1 is the movement locus figure of tracer at pit shaft;

Fig. 2 is method step flow chart of the present invention;

Fig. 3 is the present invention carries out successively segmentation schematic diagram to full well;

Fig. 4 is certain well drilling tool friction borehole wall tracer temperature profile;

Fig. 5 is the well section schematic diagram in embodiment;

In connection with background technology, summary of the invention and detailed description of the invention describe each width figure

Detailed description of the invention

Demonstration test: see Fig. 5

In order to verify fermentation effect, to verify at K2 well, this well well depth is H=3132.41m, drilling fluid displacement is Q=1.80m³/ min, tracer diameter d_s=0.8cm, tracer averag density is ρ_s=1.60g/cm³, drilling fluid density is ρ_d=1.30g/cm³, drilling fluid effective viscosity is μ_c=0.88Pa·s。

1. determine that tracer arrives the time on ground, be designated as 0, the moment of tracer certain some operation in well is T_i，T_iValuePerseverance is less than 0.

2. the distribution of well section. According to the difference of annular space internal-and external diameter, full well is divided into some well sections. Inside and outside each well section annular spaceFootpath, length are respectively d from top to bottom₁=127.00mm、D₁=220.52mm、h₁=2266.62m；d₂=127.00m、D₂=215.90mm、h₂=650.28m；d₃=177.80mm、D₃=215.90mm、h₃=215.48mm。

3. calculate the upward velocity of each well section drilling fluid at annular space:

[0,2266.65) in well section, drilling fluid upward velocity is:

$V_{u1}=\frac{Q}{\frac{\mathrm{\π}}{4}({D_1}^2-{d_1}^2)}=\frac{1.80}{\frac{\mathrm{\π}}{4}({0.22052}^2-{0.127}^2)}=70.56m/\min$

[2266.65,2916.93) in well section, drilling fluid upward velocity is:

$V_{u2}=\frac{Q}{\frac{\mathrm{\π}}{4}({D_2}^2-{d_2}^2)}=\frac{1.80}{\frac{\mathrm{\π}}{4}({0.2159}^2-{0.127}^2)}=75.24m/\min$

[2916.93,3132.41) in well section, drilling fluid upward velocity is:

$V_{u3}=\frac{Q}{\frac{\mathrm{\π}}{4}({D_3}^2-{d_3}^2)}=\frac{1.80}{\frac{\mathrm{\π}}{4}({0.2159}^2-{0.1778}^2)}=152.88m/\min$

4. calculate the gliding speed of each well section tracer at annular space:

$V_d=\frac{4.242d_s{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_d)}^{\frac{2}{3}}}{{{\mathrm{\ρ}}_d}^{\frac{1}{3}}{{\mathrm{\μ}}_e}^{\frac{1}{3}}}=\frac{4.242*0.8*{(1.60-1.30)}^{\frac{2}{3}}}{{1.30}^{\frac{1}{3}}*{0.88}^{\frac{1}{3}}}=1.357m/\min$

5. calculate the actual upward velocity of tracer at annular space

[0,2266.65) in well section, drilling fluid upward velocity:

V₁＝V_u1-V_d=70.56-1.357=69.20m/min

[2266.65,2916.93) in well section, drilling fluid upward velocity:

V₂＝V_u2-V_d=75.24-1.357=73.88m/min

[2916.93,3132.41) in well section, drilling fluid upward velocity:

V₃＝V_u3-V_d=152.88-1.357=151.52m/min

6. calculate the run duration of each well section tracer

$\frac{h_1}{V_1}=\frac{2266.65}{69.20}=32.755\min$

$\frac{h_2}{V_2}=\frac{650.28}{73.883}=8.801\min$

$\frac{h_3}{V_3}=\frac{215.48}{151.52}=1.442\min$

So:

[0,2266.65) in well section, section running time of tracer be [0 ,-32.755) min

[2266.65,2916.93) in well section, the running time of tracer be [32.755 ,-41.556) min

[2916.93,3132.41) in well section, the running time of tracer be [41.556 ,-42.998) min

7. calculate each well section tracer sometime section move distance

[0 ,-32.755) in the min time, tracer [0,2266.65) motion in well section, the move distance of tracerWith the pass of run duration be:

-V₁T_i=-69.20T_i

[32.755 ,-41.556) in the time, tracer [2266.65,2916.93) motion in well section, tracerMove distance and the pass of run duration be:

$V_2(-\frac{h_1}{V_1}-T_1)=73.88(-32.755-T_i)=-73.88T_i-2419.94$

[41.556 ,-42.998) in the min time, tracer [2916.93,3132.41) motion in well section, spikeThe move distance of device and the pass of run duration are

$V_3(-\frac{h_1}{V_1}-\frac{h_2}{V_2}-T_i)=151.52(-41.556-T_i)=-151.52T_i-6296.57$

8. determine the degree of depth of tracer sometime

[0 ,-32.755) in the min time, tracer [0,2266.65) motion in well section, T_iMoment tracer darkDegree position is:

h_1i-V₁T_i=-69.20T_i

[32.755 ,-41.556) in the time, tracer [2266.65,2916.93) motion in well section, T_iMomentThe depth location of tracer is:

$h_{2i}=h_1+V_2(-\frac{h_1}{V_1}-T_i)=2266.65-73.88T_i-2419.94=-73.88T_i-153.29$

[41.556 ,-42.998) in the min time, tracer [2916.93,3132.41) motion in well section, T_iTimeThe depth location of carving tracer is:

$h_{3i}=h_1+h_2+V_3(-\frac{h_1}{V_1}-\frac{h_2}{V_2}-T_i)=2916.93-151.52T_i-6296.57=-151.52T_i-3379.64$

Can be found out by 3 formula in " 8. determining the degree of depth of tracer sometime ", point at any time, canObtain the degree of depth at tracer place, for example:

Work as T_iWhen=-20min, the position at tracer place is :-V₁T_i=-69.20T_i=1384.0m

Work as T_iWhen=-35min, the position at tracer place is: h_2i=-73.88T_i-153.29=2432.51m

Work as T_iWhen=-42min, the position at tracer place is: h_3i=-151.52T_i-3379.64=2984.20m

The temperature, the pressure data that collect according to tracer are known, and tracer depth contrast locating is more accurate.

Claims (9)

1. a method of utilizing speed location drilling well microchip tracer depth, is characterized in that:

Described tracer is carried and is entered in Oil/gas Well by drilling fluid, to behind shaft bottom along returning to ground on well annular space, described tracerFor detecting temperature in wellbore and pressure and carry out data acquisition real-time;

Described tracer moves with flowing of drilling fluid, and the method for locating described tracer mine shaft depth is according to mineshaft annulusDimension of inner and outer diameters is full well segmentation, according to physical parameter in mud flow rate and well obtain each well section drilling fluid upward velocity andTracer gliding speed, and obtain thus the actual upward velocity of each well section tracer; Return to ground according to tracer afterwardsTime obtains the moving displacement of tracer, thereby obtains the depth location of different time tracer in each well section, thereby realizesLocation tracer depth.

2. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 1, its feature existsIn,

Described according to mineshaft annulus dimension of inner and outer diameters by full well segmentation be according to annular space dimension of inner and outer diameters by little and large segmentation,The well section that is same annular space size is same well section;

And the interior physical parameter of the well that extracts each well section, comprising: internal diameter, external diameter and each well section height.

3. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 2, its feature existsIn,

The upward velocity basis of the drilling fluid of described each well section obtains as follows,

$V_{un}=\frac{Q}{\frac{\mathrm{\π}}{4}({D_n}^2-{d_n}^2)},$

In the drilling fluid upward velocity of n well section, wherein,

V_unIt is the upward velocity of n well section; Q-drilling fluid displacement, m³/min

D is this well section annular space external diameter; D is this well section annular space internal diameter.

4. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 2, its feature existsIn,

Described tracer is gliding speed in the annular space of each well section:

$V_d=\frac{4.242d_s{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_d)}^{\frac{2}{3}}}{{{\mathrm{\ρ}}_d}^{\frac{1}{3}}{{\mathrm{\μ}}_e}^{\frac{1}{3}}}$

In formula:

V_dThe gliding speed of-tracer in drilling fluid, m/min; d_s-tracer diameter, cm,

ρ_s-tracer averag density, g/cm³；ρ_d-drilling fluid density, g/cm³，

μ_e-drilling fluid effective viscosity, Pas.

5. according to a kind of method of utilizing speed location drilling well microchip tracer depth described in claim 3 or 4, its featureBe,

Described tracer is that drilling fluid upward velocity deducts tracer at annular space in the actual upward velocity of the annular space of each well sectionInterior gliding speed, i.e. V=V_un-V_d。

6. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 5, its feature existsIn,

Described tracer in the run duration of each well section be the height of this well section divided by described tracer in this well section annular spaceActual upward velocity.

7. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 6, its feature existsIn,

If the captive time of described tracer is the time on tracer arrival ground, be designated as 0, tracer is certain some fortune in wellThe moment of row is T_i，T_iValue perseverance be less than 0;

Described tracer is the actual upward velocity of described tracer in this well section at the move distance in each a certain moment of well sectionBe multiplied by this moment; h_i＝V_jT_i, wherein, h_iBe tracer in j well section, the moment is T_iTime distance, V_jIn the time of j well sectionThe actual upward velocity of tracer.

8. a kind of method of utilizing speed location drilling well microchip tracer depth according to claim 7, its feature existsIn,

Described tracer the degree of depth sometime of each well section be more than this well section each well section height sum with described inTracer is the degree of depth of the described tracer determined in the move distance sum of this well section.

9. according to a kind of method of utilizing speed location drilling well microchip tracer depth described in claim 1 or 2, its feature existsIn,

The method step that speed is located described tracer depth comprises:

1. determine that described tracer arrives the time on ground: described tracer arrives behind ground, is caught immediately by ground receiving equipmentObtain, the captive time of tracer is tracer and arrives time on ground, is designated as 0, tracer in well certain some operation timeCarve as T_i，T_iValue perseverance be less than 0;

2. distribute well section step: according to the difference of annular space internal-and external diameter, full well is divided into some well sections, establishing full hole total length is H,Be H=h₁+h₂+......+h_n; If each well section annular space internal-and external diameter, length are respectively d from top to bottom₁、D₁、h₁；d₂、D₂、h₂；……,d_n、D_n、h_nn＝1,2,3,……；

3. calculate the upward velocity step of each well section drilling fluid at annular space:

At h₁In well section, drilling fluid upward velocity

At h₂In well section, drilling fluid upward velocity

……

At h_nIn well section, drilling fluid upward velocity

Q-drilling fluid displacement, m³/min；

4. calculate the gliding speed step of the described tracer of each well section at annular space:

$V_d=\frac{4.242d_s{({\mathrm{\ρ}}_s-{\mathrm{\ρ}}_d)}^{\frac{2}{3}}}{{{\mathrm{\ρ}}_d}^{\frac{1}{3}}{{\mathrm{\μ}}_e}^{\frac{1}{3}}}$

In formula:

V_dThe gliding speed of-tracer in drilling fluid, m/min, d_s-tracer diameter, cm

ρ_s-tracer averag density, g/cm³，ρ_d-drilling fluid density, g/cm³，μ_e-drilling fluid effective viscosity, Pas

5. determine the actual upward velocity step of described tracer at annular space:

At h₁In well section, tracer is at the actual upward velocity V of annular space₁＝V_u1-V_d

At h₂In well section, tracer is at the actual upward velocity V of annular space₂＝V_u2-V_d

……

At h_nIn well section, tracer is at the actual upward velocity V of annular space_n＝V_un-V_d；

6. obtain the run duration step of each well section tracer:

At h₁In well section, section running time of tracer is

At h₂In well section, be the running time of tracer

……

At h_nIn well section, be the running time of tracer

7. calculate each well section tracer sometime section move distance step:

?In time, tracer is at h₁Motion in well section, the move distance of tracer and the relation of run durationFor-V₁T_i

?In time, tracer is at h₂Motion in well section, the move distance of tracer and run durationPass be

……

?In time, tracer is at h_nMotion in well section,The move distance of tracer and the pass of run duration are

8. determine described tracer depth step sometime:

?In time, tracer is at h₁Motion in well section, T_iThe depth location of moment tracer is h_1i＝V₁T_i?In time, tracer is at h₂Motion in well section, T_iThe depth location of moment tracer is $h_{2i}=h_1+V_2(-\frac{h_1}{V_1}-T_i)$

……

?In time, tracer is at h₃Motion in well section,T_iThe depth location of moment tracer is

$h_{ni}=h_1+h_2+......+h_{n-1}+V_n(-\frac{h_1}{V_1}-\frac{h_2}{V_2}-......-\frac{h_{n-1}}{V_{n-1}}-T_i).$