CN108509675B - Method for calculating hole diameter and clearance by density logging while drilling - Google Patents

Method for calculating hole diameter and clearance by density logging while drilling Download PDF

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CN108509675B
CN108509675B CN201810125774.5A CN201810125774A CN108509675B CN 108509675 B CN108509675 B CN 108509675B CN 201810125774 A CN201810125774 A CN 201810125774A CN 108509675 B CN108509675 B CN 108509675B
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于华伟
陈翔鸿
周悦
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China University of Petroleum East China
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
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    • E21B49/005—Testing the nature of borehole walls or the formation by using drilling mud or cutting data
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Abstract

The invention discloses a method for calculating a hole diameter and a clearance by density logging while drilling, which belongs to the technical field of oil field logging and specifically comprises the following steps: first, X is obtainedLAnd XLA functional relation; secondly, the gap size t is obtainedm(ii) a Finally, the radius D of the borehole is obtained. The invention can cover the measuring blind area of the hole diameter measured by ultrasonic waves in the range of calculating the clearance, and has wider application range to mud than the ultrasonic measuring clearance and hole diameter; in addition, from the engineering point of view, the invention solves the problems of inconvenient maintenance, high maintenance cost, very expensive instrument cost and the like of the ultrasonic instrument.

Description

Method for calculating hole diameter and clearance by density logging while drilling
Technical Field
The invention belongs to the technical field of oil field logging, and particularly relates to a method for calculating a hole diameter and a gap by density logging while drilling.
Background
In the logging while drilling, the change of the borehole diameter (borehole size) influences the measurement precision of the instrument, not only is an important parameter for eliminating the influence of porosity logging and lithologic density logging boreholes eliminated, but also the amount of cement required by well cementation can be estimated by utilizing the borehole diameter information, the position of a fracture zone in the oil exploitation process is positioned, and the stability of the borehole wall, such as shrinkage, collapse and drill jamming, borehole expansion and the like in the drilling process, is intuitively and vividly reflected. The traditional cable logging is to measure the borehole diameter after drilling, and the size of the borehole is measured by contacting the wall of the borehole by a pushing arm in the process of lifting the instrument. While logging while drilling is to measure underground information in the rotary advancing process of drilling, which is greatly different from the instrument structure and construction mode of cable logging and the measurement environment, so that a non-contact measurement mode is required for measuring the size of a borehole in logging while drilling.
At present, ultrasonic well diameter measurement is generally used in well logging while drilling, the distance between an instrument and a well wall is determined by utilizing ultrasonic echo time difference, and the well diameter size is calculated, but the ultrasonic signal is seriously attenuated due to the increase of mud specific gravity, the measurement reliability is reduced, so that the conventional measurement technology is only suitable for the mud specific gravity smaller than 1.3g/cm3And when the specific gravity of the slurry is more than 1.3g/cm3The reliability of the measurement under (1) is extremely poor. In addition, when the ultrasonic caliper works, aftershocks can be generated on the probe and the casing of the caliper, and a dead zone is generated during measurement of the caliper due to the fact that current of a circuit is very strong instantly when the ultrasonic waves are reflected, and the dead zone is basically within 3 cm. Thus, the accuracy of measuring parameters such as density, neutron porosity and the like is reduced. There is therefore a great limitation in measuring the hole diameter using ultrasonic waves.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a method for calculating the hole diameter and the clearance by density logging while drilling, which has reasonable design, overcomes the defects of the prior art and has good effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating the hole diameter and the clearance by density logging while drilling specifically comprises the following steps:
step 1: determining the weight X of the slurryLAnd XLThe functional relation specifically includes the following steps:
step 1.1: simulating the logging-while-drilling density by using Monte Carlo simulation to obtain the far density rhofarFormation density ρbMud density ρmAnd a gap dimension tmA value of (d);
step 1.2: using formula XL＝(ρb-ρfar)/(ρb-ρm) Calculating XLA value of (d);
step 1.3: varying the gap dimension tmFormation density ρbAnd mud density ρmMultiple experiments are carried out to obtain the scatter combination (X)L1，(ρb-ρm)2，tm1)、(XL2，(ρb-ρm)2，tm2)……(XLi，(ρb-ρm)i，tmi) Wherein i is the number of measurements;
step 1.4: to obtain XL＝f(ρb-ρm，tm) A functional relation;
step 2: determining the gap size tmThe method specifically comprises the following steps:
step 2.1: mixing XL＝f(ρb-ρm，tm) The functional relation is deformed to obtain tm＝g(XL，ρb-ρm)；
Step 2.2: calculating the gap size t by using a multiple linear regression analysis methodmThe concrete formula is as follows:
tm＝aXL+bXL 2+c(ρb-ρm)+d(ρb-ρm)2+eXL(ρb-ρm)
wherein a, b, c, d, e are coefficients, respectively;
and step 3: the method for obtaining the radius D of the borehole specifically comprises the following steps:
step 3.1: the sizes of three gaps are arbitrarily taken at positions of every 120 degrees;
step 3.2: the distance S between the axis of the instrument and the well wall is calculated by the following formula1、S2、S3；
S1＝r+tm1；
S2＝r+tm2；
S3＝r+tm3；
Wherein, tm1、tm2、tm3Is the gap size, r is the radius of the instrument, S1、S2、S3The included angle between every two is 120 degrees,
for 3 three corners with d as a common edge, the following 3 trigonometric functions can be listed:
Figure GDA0003245412620000021
Figure GDA0003245412620000022
Figure GDA0003245412620000023
wherein d is the distance between the axis of the well and the axis of the instrument, and alpha is S1And d;
solving the equation system to obtain the radius D of the borehole, wherein the result is as follows:
Figure GDA0003245412620000024
Figure GDA0003245412620000025
where T is a temporary variable.
The following description is given of the basic principles of the invention:
the basic principle of the invention is a method for calculating the hole diameter and the clearance size based on the density logging while drilling. Mud weight XLIs determined by the formation density ρbAnd gap-filled mud density ρmDifference of (D) and gap thickness tmDetermined, mud weight XLDifference from formation density and mud density (p)b-ρm) And gap thickness tmFunctional relationship between:
XL∝(ρb-ρm)tm
where ρ isbIs the formation density value, ρmIs the mud density value, tmIs the size of the gap.
Wherein, for the weight X of the slurryLThe explanation of (a) is as follows:
in density logging while drilling, dual detectors are used to make measurements, the density measured by the detector that is farther from the source is called the far density, and the density measured by the detector that is closer to the source is called the near density. Because of the influence of the gap and the filling mud, the calculated far density and near density are not equal to the real density of the stratum, and the corresponding far density and near density are weighted values of the stratum density and the mud density at the moment.
ρfar＝XLρm+(1-XL)ρb
Weight of mud deformed by XLComprises the following steps:
XL＝(ρb-ρfar)/(ρb-ρm)
where ρ isfarIs a remote sonde measuring the density value of the formation.
The invention has the following beneficial technical effects:
according to the invention, on the basis of density logging while drilling, compared with a method of using ultrasonic distance measurement, the calculation of the clearance and the hole diameter can cover a blind area measured by using ultrasonic waves in the size range of the calculated clearance, and the application range of mud is improved; in addition, from the engineering point of view, the invention solves the problems of inconvenient maintenance, high maintenance cost, very expensive instrument cost and the like of the ultrasonic instrument.
Drawings
FIG. 1 is a schematic view of the geometry of the gap and the wellbore and instrumentation.
Wherein, 1-well wall; 2-the apparatus wall; 3-well axis; 4-instrument axis; 6-detecting the position of the stratum; 8-distance S from instrument axis to well wall1And the included angle of the distance from the axis of the well to the axis of the instrument; 9-distance S from the instrument axis to the borehole wall1(ii) a 10-distance S from the instrument axis to the borehole wall2(ii) a 11-distance S from the instrument axis to the borehole wall3。
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the geometrical relationship between the gap and the borehole and the instrument is shown in figure 1.
A method for calculating the hole diameter and the clearance by density logging while drilling specifically comprises the following steps:
step 1: determining the weight X of the slurryLAnd XLThe functional relation specifically includes the following steps:
step 1.1: simulating the logging-while-drilling density by using Monte Carlo simulation to obtain the far density rhofarFormation density ρbMud density ρmAnd a gap dimension tmA value of (d);
step 1.2: using formula XL＝(ρb-ρfar)/(ρb-ρm) Calculating XLA value of (d);
step 1.3: varying the gap dimension tmFormation density ρbAnd mud density ρmMultiple experiments are carried out to obtain the scatter combination (X)L1，(ρb-ρm)2，tm1)、(XL2，(ρb-ρm)2，tm2)……(XLi，(ρb-ρm)i，tmi) Wherein i is the number of measurements;
step 1.4: to obtain XL＝f(ρb-ρm，tm) A functional relation;
step 2: determining the gap size tmThe method specifically comprises the following steps:
step 2.1: mixing XL＝f(ρb-ρm，tm) The functional relation is deformed to obtain tm＝g(XL，ρb-ρm)；
Step 2.2: calculating the gap size t by using a multiple linear regression analysis methodmThe concrete formula is as follows:
tm＝aXL+bXL 2+c(ρb-ρm)+d(ρb-ρm)2+eXL(ρb-ρm)
wherein a, b, c, d, e are coefficients, respectively;
and step 3: the method for obtaining the radius D of the borehole specifically comprises the following steps:
step 3.1: the sizes of three gaps are arbitrarily taken at positions of every 120 degrees;
step 3.2: the distance S between the axis of the instrument and the well wall is calculated by the following formula1、S2、S3；
S1＝r+tm1；
S2＝r+tm2；
S3＝r+tm3；
Wherein, tm1、tm2、tm3Is the gap size, r is the radius of the instrument, S1、S2、S3The included angle between every two is 120 degrees,
for 3 three corners with d as a common edge, the following 3 trigonometric functions can be listed:
Figure GDA0003245412620000041
Figure GDA0003245412620000042
Figure GDA0003245412620000043
wherein d is the distance between the axis of the well and the axis of the instrument, and alpha is S1And d;
solving the equation system to obtain the radius D of the borehole, wherein the result is as follows:
Figure GDA0003245412620000044
Figure GDA0003245412620000045
where T is a temporary variable.
The platform of the experiment is Monte Carlo simulation software, data is simulated, the clearance and the well diameter processed by the calculation method of the invention are compared with the designed clearance and well diameter (such as tables 1 and 2), the feasibility of the invention is determined by analyzing errors, the table 1 is the comparison of the designed clearance and the calculated clearance, and the table 2 is the comparison of the designed well radius and the calculated radius.
TABLE 1 comparison of design gap to calculated gap
Figure GDA0003245412620000046
Figure GDA0003245412620000051
TABLE 2 comparison of design radius to calculated radius
Serial number Design radius cm Angle of rotation/degree Gap size/cm Calculating radius/cm Error of the measurement
1 12.9 0 0.093188 12.99319 0.09
2 12.9 22.5 0.310813 13.05561 0.16
3 12.9 45 0.542498 12.83261 0.07
4 12.9 67.5 1.358426 12.92321 0.02
5 12.9 90 1.9991 12.64862 0.25
6 12.9 112.5 3.032269 12.68757 0.21
7 12.9 135 3.976884 12.73243 0.17
8 12.9 157.5 4.691901 12.81796 0.08
9 12.9 180 5.011733 12.91173 0.01
From the above table 1, it can be seen that the difference between the calculated clearance value and the designed clearance value is 0.323794 (i.e. error) at most, the average error is 0.1641107cm, and the difference is almost the same as the accuracy of determining the clearance by using the ultrasonic echo time difference, but the range of the calculated clearance covers the measurement blind area of the ultrasonic caliper, and the limitation on the requirement of mud performance is relatively reduced; it can be seen from table 2 that the errors in the hole diameters calculated by the present invention are small, substantially approaching the designed wellbore size. As can be seen from tables 1 and 2, the method provided by the invention can effectively calculate the gap thickness and the hole diameter size, and therefore, the method provided by the invention can meet the requirement of obtaining the calculation result in engineering.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.

Claims (1)

1. A method for calculating the hole diameter and the clearance by density logging while drilling is characterized in that: the method specifically comprises the following steps:
step 1: determining the weight X of the slurryLAnd XLThe functional relation specifically includes the following steps:
step 1.1: simulating the logging-while-drilling density by using Monte Carlo simulation to obtain the far density rhofarFormation density ρbMud density ρmAnd a gap dimension tmA value of (d);
step 1.2: using formula XL＝(ρb-ρfar)/(ρb-ρm) Calculating XLA value of (d);
step 1.3: varying the gap dimension tmFormation density ρbAnd mud density ρmMultiple experiments are carried out to obtain the scatter combination (X)L1，(ρb-ρm)2，tm1)、(XL2，(ρb-ρm)2，tm2)……(XLi，(ρb-ρm)i，tmi) Wherein i is the number of measurements;
step 1.4: to obtain XL＝f(ρb-ρm，tm) A functional relation;
step 2: determining the gap size tmThe method specifically comprises the following steps:
step 2.1: mixing XL＝f(ρb-ρm，tm) The functional relation is deformed to obtain tm＝g(XL，ρb-ρm)；
Step 2.2: calculating the gap size t by using a multiple linear regression analysis methodmThe concrete formula is as follows:
tm＝aXL+bXL 2+c(ρb-ρm)+d(ρb-ρm)2+eXL(ρb-ρm)
wherein a, b, c, d, e are coefficients, respectively;
and step 3: the method for obtaining the radius D of the borehole specifically comprises the following steps:
step 3.1: the sizes of three gaps are arbitrarily taken at positions of every 120 degrees;
step 3.2: the distance S between the axis of the instrument and the well wall is calculated by the following formula1、S2、S3；
S1＝r+tm1；
S2＝r+tm2；
S3＝r+tm3；
Wherein, tm1、tm2、tm3Is the gap size, r is the radius of the instrument, S1、S2、S3The included angle between every two is 120 degrees,
for 3 three corners with d as a common edge, the following 3 trigonometric functions can be listed:
Figure FDA0003245412610000011
Figure FDA0003245412610000012
Figure FDA0003245412610000013
wherein d is the distance between the axis of the well and the axis of the instrument, and alpha is S1And d;
solving the equation system to obtain the radius D of the borehole, wherein the result is as follows:
Figure FDA0003245412610000014
Figure FDA0003245412610000021
where T is a temporary variable.
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