CN103064118A - Method of acoustic logging and quantifying cavern filling degree - Google Patents

Abstract

The invention relates to a method of acoustic logging and quantifying a cavern filling degree and belongs to the field of petroleum and geology. The method comprises the following steps that 1 a stratum model is established: a real environment of an actual shaft acoustic wave instrument is imitated, wherein a stratum is made of limestone, the longitudinal wave time difference is 154 microseconds per meter and the density is 2.7g/cm<3>; 2 acoustic numeral is simulated: acoustic wave whole wave train data and an imitated acoustic wave whole wave train curve with the different filling degrees are obtained; 3 acoustic wave interval transit time is extracted and the transversal and longitudinal wave acoustic wave interval transit time with the different filling degrees are calculated; 4 response regularity of the interval transit time and the filling degree is analyzed; and 5 a quantification calculation model of the cavern filling degree is established and response characteristics of the acoustic wave interval transit time caused by the different filling degrees and the regulation of the response characteristic are analyzed. According to the numerical simulation to a sound field in a barefoot well, the filling degree calculation model is established to quantifying and assessing the different filling degrees in a cavern type reservoir stratum so that practicality is high and popularization and application value is good.

Description

A kind of method of utilizing the quantitative cavern filling degree of acoustic logging

Technical field

The present invention relates to a kind of method of utilizing the quantitative cavern filling of acoustic logging, utilize Sonic Logging Data to carry out the quantitative calculation of cavern filling degree, to promote the log interpretation technology of cave type reservoir, belong to oil and geology field.

Background technology

In recent years, along with Marine Carbonate Rocks oil-gas exploration deepens continuously, showed a collection of large-scale or especially big groove part hole type carbonate rock hydrocarbon reservoir in basinal facies secondary such as China Sichuan, Bohai Sea Gulf and Tarim Basins, made the research of seam hole type carbonate reservoir become a new focus.

Cave type carbonate reservoir is the important type of preserving of a class of carbonate reservoir.Facts have proved that such reservoir is the important leverage of carbonate rock hydrocarbon reservoir stable yields and volume increase.In the evaluating reservoir of carbonatite, generally with the be called duck eye of footpath, hole less than 0.02 meter, the footpath, hole is called middle hole between 0.02～0.1 meter, and the hole directly is large hole of 0.1～1 meter be called, footpath, hole 〉=1 meter be called giant void.On geology, according to the different origin causes of formation, the cave there is different classification.The hydrodynamic condition that the people such as D.C Ford formed according to the cave the eighties in 20th century (being origin cause of formation classification) is divided into the cave four classes such as vadose zone cave, underground water table cave, phreatic zone cave and dark phreatic zone cave, and tells two kinds of special cave--types: isolated bag-shaped cave and gravity flow cave.Since Tarim Basin backlands district found Early Hercynian emergence karst cave type reservoir, many impressive progresses had been got in domestic research to the cave reservoir.Guo Jianhuas etc. have been set up distinguishing mark and the genetic model of taking turns southern regional cave layer.Xiao Yuru etc. take the ancient cave of Tahe Oilfield of The Tarim Basin Ordovician system type reservoir as the example systematic analysis with concluded response characteristic and the distinguishing mark of such reservoir on the data such as drilling well, well logging, well logging, well testing, earthquake.The cave is divided into top, cave phase, cave filling facies composed and the bottom phase that collapses vertical, and thinks that top, cave phase and the bottom relative oil gas that collapses preserves very favourable.Result of study shows, storage and collection performance preferably paleocave carbonate reservoir is not filling cave reservoir and large-scale cavern filling porous sandstone reservoir.

Because the nonuniformity that underground karst cavity is grown and distribute is extremely strong, the filling in cave and fluid properties complicated and changeable logs well in addition that it is unclear that the Response Mechanism of cavern filling also is familiar with, and at present the logging evaluation of cave type reservoir still is in the qualitative evaluation stage.Because the greatest differences of the rock physical property of cave and inner filling material and country rock has obvious response characteristic at logging trace.Obvious emptying does not appear in the filling cave in boring the chance process, and serious mud loss and hole diameter enlargement phenomenon occur.On Logging Curves, the type gamma ray curve value up and down country rock slightly increases or remain unchanged (being generally less than 15API), CAL has obvious increase, depth al-lateral resistivity log value is lower, be generally less than 200 Ω m, even low to several ohm meters, and positive separation appears, namely the deep lateral resistivity value is greater than shallow side direction resistivity value.The density logging curve values generally up and down country rock larger reduction is arranged, the acoustic travel time logging value shows as the high time difference, generally greater than 50 μ s/ft, have in addition greater than 100 μ s/ft, the neutron porosity value also shows as high value, generally all more than 3%.Unusually as distinguishing feature, and the gamma logging value is at the solution cavity place normal " being anti-arc " take the natural gamma height in sand shale full-filling cave, and its value is probably between 30～135API, but the hole enlargement phenomenon is generally not obvious, and the tri-porosity logging curve has obvious fluctuating; And the electrical property feature in sand shale part filling cave also shows hole diameter enlargement phenomenon to a certain degree simultaneously between between the two.

In recent years, by the fine variation of high resolving power electric imaging logging commercial measurement borehole wall formation resistivity, borehole wall surface is carried out imaging, for the feature of the ancient solution cavity of Study of The Underground directly perceived and stuff thereof provides the important channel.Under rock core demarcation and conventional logging constraint, utilize electric imaging logging image identification palaeokarst, and set up thus the electric imaging logging qualitative interpretation template of ancient solution cavity and inner filling thing thereof.On the electric imaging logging image, the filling solution cavity generally is not black, and the filling solution cavity then can present the shades of colours such as black, brown, yellow, white, and this depends on the type and character of stuff; Show as solution cavity borderline " people " font striped at the reflected Stoneley-wave variable density figure of DSI, larger decay also will occur in the energy of Stoneley wave.

Along with the exploration and development of a large amount of caves type carbonatite, will be more and more higher to the evaluation requirement of cavern filling degree.Because the theoretical research to cave type reservoir log response mechanism still is in the stage of fumbling at present, especially blank to quantitatively remaining of cave type reservoir cavern filling degree, caused the logging evaluation level of cave type reservoir can not satisfy the needs of produced on-site, and then evaluation and the exploitation in hydrocarbon-bearing pool later stage caused harmful effect.

Summary of the invention

The objective of the invention is in order to overcome the prior art deficiency: the state of the art that does not have the quantitative evaluation means for present cave type carbonate reservoir cavern filling degree, a kind of method of utilizing the quantitative cavern filling of acoustic logging is proposed, utilize the method for sound wave numerical simulation to draw the quantitative relationship of different filling operations and interval transit time, and its rule is applied in the real data, foundation utilizes Sonic Logging Data to calculate the computation model of cavern filling degree, realization improves the logging evaluation level of cave type reservoir to the quantitative evaluation of cavern filling degree.

For achieving the above object, technical scheme of the present invention is:

A kind of method of utilizing the quantitative cavern filling of acoustic logging of the present invention, its method may further comprise the steps:

1, set up stratigraphic model: simulate the true environment of actual pit shaft acoustic wave apparatus, the stratum is that its compressional wave time difference of limestone is 154 μ s/m, and density is 2.7g/cm ³One solution cavity is wherein arranged, and diameter is 0.6m, and well is passed solution cavity, and FIH is water, and density is 1g/cm ³, filling shale in the solution cavity, shale compressional wave time difference are set as 400 μ s/m, and density is 2.3g/cm ³

2, sound wave numerical simulation: in order to obtain the sonic wavetrain information of the different filling operations in cave, consider that filling operation is respectively 25%, 50%, the cave of four kinds of situations such as 75% and 100%, cave model to different filling operations adopts the finite difference method of staggered-mesh that wave equation is carried out numerical simulation, speed (stress) is converted into stress (speed) to the derivative in space to the odd-order higher derivative of time, thereby under the prerequisite that does not increase the required memory amount, staggered-mesh and HIGH-ORDER DIFFERENCE METHOD are organically combined, apply to and find the solution in transverse isotropy (TI) medium one-order velocity-stress equations for elastic waves; Finite difference is found the solution partial differential equation and is surely separated problem, at first will will surely separate the zone with mesh lines and turn to discrete point set, on this basis, turns to difference equation partial differential equation is discrete, by the Solving Algebraic Equation group,

$\mathrm{\&rho;}\frac{{\&PartialD;v}_x}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xx}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yx}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zx}}}{\&PartialD;z}---\left(\text{1}\right)$

$\mathrm{\&rho;}\frac{{\&PartialD;v}_{\mathrm{yx}}}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xy}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yy}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;z}---\left(\text{2}\right)$

$\mathrm{\&rho;}\frac{{\&PartialD;v}_z}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zx}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zz}}}{\&PartialD;z}---\left(\text{3}\right)$

And

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xx}}}{\&PartialD;t}=(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_x}{\&PartialD;x}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_y}{\&PartialD;y}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(4\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yy}}}{\&PartialD;t}=\mathrm{\&lambda;}\frac{{\&PartialD;v}_x}{\&PartialD;x}+(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_y}{\&PartialD;y}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(5\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zz}}}{\&PartialD;t}=\mathrm{\&lambda;}\frac{{\&PartialD;v}_x}{\&PartialD;x}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_y}{\&PartialD;y}+(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(\text{6}\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xy}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_x}{\&PartialD;y}+\frac{{\&PartialD;v}_y}{\&PartialD;x})---\left(7\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xz}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_x}{\&PartialD;z}+\frac{{\&PartialD;v}_z}{\&PartialD;x})---\left(8\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_y}{\&PartialD;z}+\frac{{\&PartialD;v}_z}{\&PartialD;y})---\left(9\right)$

Obtain numerical solution, namely obtain the sound wave full-wave train data of different filling operations and the sound wave full-wave train curve of simulation.

3, the extraction of interval transit time data: window when utilizing slowness time coherence in one group of all-wave wave train, to offer, window is sought compressional wave, shear wave and Stoneley wave when mobile with certain slowness (time difference), simulate the related coefficient of resulting series of waves graphic data by evaluation, the computing formula of its related coefficient is as follows:

${\mathrm{\&rho;}}^2(s,\mathrm{\&tau;})=\frac{\frac{1}{M}{\&Integral;}_0^{\mathrm{Tw}}{\left\{\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{r}_m\right[t+s(m-1)\mathrm{\&Delta;z}+\mathrm{\&tau;}\left]\right\}}^2\mathrm{dt}}{\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;}_0^{\mathrm{Tw}}{\left\{r_m\right[t+s(m-1)\mathrm{\&Delta;z}+\mathrm{\&tau;}\left]\right\}}^2\mathrm{<figure-callout\; id="0"\; label="dt"\; filenames="130108091346.png"\; state="\{\{state\}\}">dt</figure-callout>}}$ 0≤ρ≤1（10）

Calculate thus the sound wave P-wave And S time difference of different filling operations.

4, the response pattern analysis of interval transit time and filling operation: the interval transit time data of processing the different filling operations that obtain according to STC, analyze the relation between cavern filling degree and the interval transit time, set up the response pattern of interval transit time and cave filling extent, find that the cave of different filling operations and the length of sound wave curve abnormal section have preferably correlativity.

5, set up the quantitative calculation of cavern filling degree: according to numerical simulation interval transit time and cavern filling degree response pattern, utilize actual Sonic Logging Data, acoustic logging to different filling operations, extract interval transit time abnormal section length, the difference of the Abnormal acoustic wave segment length when defining Abnormal acoustic wave segment length that Abnormal acoustic wave section relative value is cave 100% filling and cave part filling here is again divided by the Abnormal acoustic wave segment length of cave 100% filling.Set up the computation model of the cavern filling degree of practical logging curve:

I=-0.8404×D+92.806?（11）

Utilize said method to carry out the sound wave numerical simulation to the cave model of different filling operations, analyze different filling operations to response characteristic and the rule thereof of interval transit time.

Advantage of the present invention: 1, this method has been analyzed the quantitative relationship of interval transit time from the different filling operations in cave by the numerical simulation to sound field in the uncased hole, and the filling operation computation model of setting up on this basis, has preferably theoretical foundation; 2, the method is simple to operate, and precision is higher, the different filling operations of quantitative evaluation cave type reservoir, and practicality is stronger, and preferably application value is arranged.

Description of drawings

Fig. 1 is a kind of acoustic logging numerical simulation stratigraphic model synoptic diagram that utilizes the method for the quantitative cavern filling of acoustic logging of the present invention.

Fig. 2 is the sound wave full-wave train squiggle figure of the filling operation that obtains of sound wave numerical simulation of the present invention.

Fig. 3 is the filling operation that obtains of numerical simulation of the present invention and the graph of a relation of interval transit time abnormal section length.

Fig. 4 is interval transit time abnormal section relative value of the present invention and filling operation graph of a relation.

Among the figure: 1. stratum, 2. well, 3. cave, 4. instrument, 5. the sound wave full-wave train curve of simulation.

Embodiment:

Such as Fig. 1, Fig. 2, Fig. 3, shown in Figure 4, a kind of method of utilizing the quantitative cavern filling of acoustic logging of the present invention, its method may further comprise the steps:

(1) set up stratigraphic model: as shown in Figure 1, in order to simulate the true environment of actual pit shaft acoustic wave apparatus 4, the stratigraphic model of setting up simulation is as follows: stratum 1 is 154 μ s/m for its compressional wave time difference of limestone, and density is 2.7g/cm ³One solution cavity is wherein arranged, and diameter is 0.6m, and well 2 is passed solution cavity, and FIH is water, and density is 1g/cm ³, filling shale in the solution cavity 3, shale compressional wave time difference are set as 400 μ s/m, and density is 2.3g/cm ³

(2) sound wave numerical simulation: as shown in Figure 2, in order to obtain the sonic wavetrain information of cave 3 different filling operations, utilize the finite difference method of staggered-mesh, consider that filling operation is respectively the cave 3 of four kinds of situations such as 25%, 50%, 75% and 100%, cave model to different filling operations carries out numerical simulation, obtains the sound wave full-wave train data of different filling operations and the sound wave full-wave train curve 5 of simulation.

(3) extraction of interval transit time data: utilize slowness-time matching method that the sound wave full-wave train data of four kinds of different filling operations obtaining by numerical simulation are processed, the sound wave that obtains different filling operations is the ripple time difference data in length and breadth.

(4) the response pattern analysis of interval transit time and filling operation: as shown in Figure 3, process the interval transit time data of the different filling operations that obtain according to STC, analyze the relation between cave 3 filling operations and the interval transit time, set up the response pattern of interval transit time and cave 3 filling extents, think, find that the cave 3 of different filling operations and the length of sound wave curve abnormal section have preferably correlativity, namely for the cave 3 of shale filling, along with increasing of filling operation, the length of interval transit time curve exception response section can increase thereupon.

(5) set up the quantitative calculation of cave 3 filling operations: as shown in Figure 4, according to numerical simulation interval transit time and cave 3 filling operation response patterns, utilize actual Sonic Logging Data, acoustic logging to different filling operations, extract interval transit time abnormal section length, the difference of the Abnormal acoustic wave segment length when defining Abnormal acoustic wave segment length that Abnormal acoustic wave section relative value is cave 3100% filling and cave 3 part filling here is again divided by the Abnormal acoustic wave segment length of cave 3100% filling.Along with the increase of filling operation, interval transit time abnormal section relative value reduces gradually.Utilize regression analysis, the computation model of cave 3 filling operations of setting up the practical logging curve is as follows:

I=-0.8404×D+92.806?（11）

In the formula: I is filling operation, %; D is interval transit time abnormal section relative value, %.

The material point of above-mentioned formula derives from real logging data, because the actual measurement data is subjected to the impact of well 2, country rock, can there be certain error in its value.By with the error analysis (seeing Table 1) of theoretical value, error can satisfy the error requirements of present cave 3 filling operation quantitative evaluations in 10%.Utilize this model, just can realize the quantitative calculating to cave 3 filling operations.

The theoretical filling operation of table 1 and model calculate filling operation error analysis table

Claims (1)

1. method of utilizing the quantitative cavern filling of acoustic logging is characterized in that method may further comprise the steps:

1. set up stratigraphic model: in order to simulate the true environment of actual pit shaft acoustic wave apparatus (4), the stratigraphic model of setting up simulation is as follows: stratum (1) is 154 μ s/m for its compressional wave time difference of limestone, and density is 2.7g/cm ³One solution cavity is wherein arranged, and diameter is 0.6m, and well (2) is passed solution cavity, and FIH is water, and density is 1g/cm ³, filling shale in the solution cavity, shale compressional wave time difference are set as 400 μ s/m, and density is 2.3g/cm ³

2. sound wave numerical simulation: in order to obtain the sonic wavetrain information of the different filling operations in cave (3), utilize the finite difference method of staggered-mesh, consider that filling operation is respectively 25%, 50%, the cave (3) of four kinds of situations such as 75% and 100%, cave model to different filling operations adopts the finite difference method of staggered-mesh that wave equation is carried out numerical simulation, speed (stress) is converted into stress (speed) to the derivative in space to the odd-order higher derivative of time, thereby under the prerequisite that does not increase the required memory amount, staggered-mesh and HIGH-ORDER DIFFERENCE METHOD are organically combined, apply to and find the solution in transverse isotropy (TI) medium one-order velocity-stress equations for elastic waves; Finite difference is found the solution partial differential equation and is surely separated problem, at first will will surely separate the zone with mesh lines and turn to discrete point set, on this basis, turns to difference equation partial differential equation is discrete, by the Solving Algebraic Equation group,

$\mathrm{\&rho;}\frac{{\&PartialD;v}_x}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xx}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yx}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zx}}}{\&PartialD;z}---\left(\text{1}\right)$

$\mathrm{\&rho;}\frac{{\&PartialD;v}_{\mathrm{yx}}}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xy}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yy}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;z}---\left(\text{2}\right)$

$\mathrm{\&rho;}\frac{{\&PartialD;v}_z}{\&PartialD;t}=\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zx}}}{\&PartialD;x}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;y}+\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zz}}}{\&PartialD;z}---\left(\text{3}\right)$

And

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xx}}}{\&PartialD;t}=(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_x}{\&PartialD;x}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_y}{\&PartialD;y}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(4\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yy}}}{\&PartialD;t}=\mathrm{\&lambda;}\frac{{\&PartialD;v}_x}{\&PartialD;x}+(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_y}{\&PartialD;y}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(5\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{zz}}}{\&PartialD;t}=\mathrm{\&lambda;}\frac{{\&PartialD;v}_x}{\&PartialD;x}+\mathrm{\&lambda;}\frac{{\&PartialD;v}_y}{\&PartialD;y}+(\mathrm{\&lambda;}+2\mathrm{\&mu;})\frac{{\&PartialD;v}_z}{\&PartialD;z}---\left(\text{6}\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xy}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_x}{\&PartialD;y}+\frac{{\&PartialD;v}_y}{\&PartialD;x})---\left(7\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{xz}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_x}{\&PartialD;z}+\frac{{\&PartialD;v}_z}{\&PartialD;x})---\left(8\right)$

$\frac{{\&PartialD;\mathrm{\&tau;}}_{\mathrm{yz}}}{\&PartialD;t}=\mathrm{\&mu;}(\frac{{\&PartialD;v}_y}{\&PartialD;z}+\frac{{\&PartialD;v}_z}{\&PartialD;y})---\left(9\right)$

Obtain numerical solution, namely obtain the sound wave full-wave train data of different filling operations and the sound wave full-wave train curve (5) of simulation;

3. the extraction of interval transit time data: window when utilizing slowness-time matching method in one group of all-wave wave train, to offer, window is sought compressional wave, shear wave and Stoneley wave when mobile with certain slowness (time difference), simulate the related coefficient of resulting series of waves graphic data by evaluation, the computing formula of its related coefficient is as follows:

${\mathrm{\&rho;}}^2(s,\mathrm{\&tau;})=\frac{\frac{1}{M}{\&Integral;}_0^{\mathrm{Tw}}{\left\{\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{r}_m\right[t+s(m-1)\mathrm{\&Delta;z}+\mathrm{\&tau;}\left]\right\}}^2\mathrm{dt}}{\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{\&Integral;}_0^{\mathrm{Tw}}{\left\{r_m\right[t+s(m-1)\mathrm{\&Delta;z}+\mathrm{\&tau;}\left]\right\}}^2\mathrm{dt}}$ 0≤ρ≤1（10）

Calculate thus the sound wave P-wave And S time difference of different filling operations;

4. the response pattern analysis of interval transit time and filling operation: the interval transit time data of processing the different filling operations that obtain according to STC, analyze the relation between cave (3) filling operation and the interval transit time, set up the response pattern of interval transit time and cave (3) filling extent, think, find that the cave (3) of different filling operations and the length of sound wave curve abnormal section have preferably correlativity, namely for the cave (3) of shale filling, along with increasing of filling operation, the length of interval transit time curve exception response section can increase thereupon;

5. set up the quantitative calculation of cave (3) filling operation: according to numerical simulation interval transit time and cave (3) filling operation response pattern, utilize actual Sonic Logging Data, acoustic logging to different filling operations, extract interval transit time abnormal section length, the difference of the Abnormal acoustic wave segment length when defining Abnormal acoustic wave section relative value here and be the Abnormal acoustic wave segment length of cave (3) 100% fillings and cave (3) part filling is again divided by the Abnormal acoustic wave segment length of cave (3) 100% fillings; Along with the increase of filling operation, interval transit time abnormal section relative value reduces gradually; Utilize regression analysis, the computation model of cave (3) filling operation of setting up the practical logging curve is as follows:

I=-0.8404×D+92.806?（11）

In the formula: I is filling operation, %; D is interval transit time abnormal section relative value, %.

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