CN103576196B - A kind of pressure-dependent pore media S-Wave Velocity Predicted Method - Google Patents

Abstract

A kind of pressure-dependent pore media S-Wave Velocity Predicted Method, carries out matching and weighting to measuring ligancy, obtains ligancy C_p, by ligancy C_pSubstitution considers that the Digby formula that pressure changes obtains K_dry, by ligancy C_pIn the Mindlin formula that substitution consideration pressure changes, obtain μ_dry, by K_dryWith μ_dryIn the deformation formula of substitution Gassmann equation, calculate prediction velocity of longitudinal waveObtain thus weight coefficient W; By weight coefficient W substitution formula (2), obtain ligancy C_p, obtain C_pAfterwards, C_pIn value substitution formula (8), obtain the shear modulus μ of dry rock_dry, and then by μ_dryIn the deformation formula of substitution Gassmann equation, calculate prediction shear wave velocityAccording to pressure-dependent shear wave velocityCan set up and comprise four-dimensional AVO model and elastic impedance model etc., and then the oil-gas reservoir attribute of prediction development phase reservoir pressure variation; The more realistic reservoir situation of change of pressure-dependent shear wave velocity that this prediction obtains.

Description

A kind of pressure-dependent pore media S-Wave Velocity Predicted Method

Technical field

The invention belongs to rock physics field in seismic prospecting, be specifically related to a kind of pressure-dependent shear wave velocity predictionMethod.

Background technology

Analyze by AVO, Geophysicist can assess Reservoir rocks attribute better, comprise porosity, density,Lithology and fluid properties, and shear wave velocity is an indispensable elasticity ginseng of setting up in AVO model, converted wave analytic processNumber. In most cases study work area and there is no Shear Wave Velocity Well Logging data; People are constant with p-and s-wave velocity ratio conventionallyReplace shear wave velocity, but more different than being for different medium p-and s-wave velocities, such hypothesis is unreasonable. ThereforeA lot of geophysicists is in the Forecasting Methodology of studying shear wave velocity. There is experience formula, also have based on rock physics theory.

Pickett has provided limestone ripple in length and breadth in 1963 is related to Vs=Vp/1.9, and for dolomite, he has provided Vs=Vp/1.8. The people such as Castagna revised this formula in 1993, and limestone is Vs=-0.055Vp2+1.017Vp-1.031, dolomite is Vs=0.583Vp-0.078, and the p-and s-wave velocity relational expression that he has also proposed clastic rock is simultaneously Vs=0.804Vp-0.856。

More famous empirical equation comprises that the famous mud stone line that the people such as Castagna proposed in 1985 is Vs=0.862Vp-1.172. Gardner has provided the relation of the velocity and density between different lithology in 1974, wherein itAverage formula is ρ=0.23V^0.25, this average formula is the best fit of the velocity and density relation to all lithology,It is suitable for all lithology, not only uses certain lithology. And Castagna carried out the formula of Gardner in 1993Expansion, obtained the relation between the velocity and density of different lithology: have for sandstoneFor shaleHaveHave for limestoneHave for dolomiteTo anhydriteBeThe people such as Wyllie were in 1958 and within 1963, proposed successively the hole of the pore media that is full of salt solutionEmpirical relation between degree and speed: 1/V=(1-φ)/V_ma+φ/V_f1, the bulk velocity that wherein V is rock, V_maFor rock boneThe speed of frame, V_f1For the speed of pore-fluid, φ is porosity. This formula also can be write as the expression of interlayer whilst on tour conventionallyFormula: Δ t=(1-φ) Δ t_ma+φΔt_f1, wherein Δ t represents the whilst on tour of whole rock stratum, Δ t_maFor the whilst on tour of skeleton, and Δt_f1For the whilst on tour of pore-fluid, and this time-average relationship of Wyllie also comprises many hypothesis and restriction, as: this sideJourney will be used for the situation that pore-fluid is salt solution, the rock that is less than 2700 meters for the degree of depth, and the degree of consolidation of this rockFine with the degree of consolidation, and porosity is medium. In the time of some log disappearance, or seismic amplitude extremely allCan apply these time limits and carry out quality monitoring, but these formula are very strong for the dependence of lithology, and depend on local barPart, and the people such as Mavko repeatedly mention in their book: " these relation formulas are all empirical equations, thus strictly speaking theyCan only be used on the rock of research at that time ", therefore these empirical equations do not have generality.

Perfect along with rock physics theory, the S-Wave Velocity Predicted Method based on rock physics theory becomes research graduallyMain flow. As Greenberg and Castagna utilized Biot-GassmannTheory(BGT in 1992) carry out shear wave velocityPrediction, namely suppose between p-and s-wave velocity, exist a firm relation to suppose between solid particles of rock composition simultaneouslyMixing rule is linear.Carried out shear wave speed in 1999 according to the Effective medium theory based on inclusion Deng peopleThe prediction of degree, and reach a conclusion, even if Effective medium theory is more complicated than regression and statistical method, but it still has superiorityBecause it can be embodied in the impact of the impact of mud stone and pore shape in formula. Many Geophysicist like usingThe prediction of Gassmann equation process shear wave velocity, this is because the most parameters of Gassmann equation becomes mould as the body of particleAmount Kma and shear modulus μ_maDeng being all fine acquisition, therefore no matter a lot of providing of method are for sandstone or to carbonic acidSalt is all based on Gassmann equation. But in Gassmann equation the body of dry rock become modulus and shear modulus be individual veryScabrous problem, therefore a lot of Geophysicist has provided the computational methods of dry lithosome change modulus and shear modulus,The body of having known dry rock becomes modulus and shear modulus, and the p-and s-wave velocity of rock is with regard to fine acquisition. Xu and White are by KusterWithThe theoretical combination of the theory of setting up in 1974 and difference Effective medium, carries out the calculating of elastic modulus of rock, concreteShow as and utilize hole recently to characterize in length and breadth the relation between sand mud composition. Nolen-Hoeksema and WangZhijing inThe shear wave velocity of the dry rock that record for 1996 end of the year according to laboratory, utilizes Gassmann equation to calculate the springform of dry rockAmount, and then use in the shear wave velocity prediction of fluid saturated rock. What in 2006, Lee proposed contacts with consolidation parametersRelation between matrix elastic modelling quantity and skeleton elastic modelling quantity, by relatively drawing of actual measurement velocity of longitudinal wave and prediction velocity of longitudinal waveConsolidation parameters, then utilize consolidation parameters to calculate shear wave velocity. The people such as Sun Fuli in 2008 utilize the side of actual data to LeeMethod is verified, and has been proposed the span of consolidation parameters.

But these methods all reckon without the impact of pressure on media property. Such as in actual production, along with oil fieldNo matter the carrying out of exploitation, be water filling or gas injection, and reservoir pressure can change. And CCS(carbon capture with seal up for safekeeping) skillIn art, we know at CO₂Inject the process of underground and CO2-EOR, the large and pressure of production well point of the pressure that injects well pointLess. Along with CO₂Continuous injection, be included in CO₂The different phase of geological storage (in injection process, inject complete and injectedAfter becoming, considerable time is interior), reservoir inner pore pressure can great changes will take place, can make differential pressure change, therebyThe body of dry rock becomes modulus and variation has also occurred shear modulus, and p-and s-wave velocity also can be along with changing so. Utilize fourDimension seismic monitoring CO₂In underground state procedure of sealing up for safekeeping, be no matter four-dimensional seismic interpretation or four-dimensional AVO inverting, elasticity resistanceAnti-inverting, all needs to utilize pressure-dependent shear wave velocity just can carry out.

Summary of the invention

A kind of method that the object of the present invention is to provide pressure-dependent pore media shear wave velocity prediction, utilization is adoptedThe data of collection are carried out the prediction of reservoir shear wave velocity, and the shear wave velocity of prediction tallies with the actual situation more.

For achieving the above object, the present invention adopts following technical scheme:

The present invention includes following steps:

1) image data: gather the porosity φ of rock, the bulk density ρ of rock, the body of fluid becomes modulus K_f, actual verticalWave velocity Vp_measured, the body of rock matrix becomes modulus K_ma, the shear modulus μ of rock matrix_ma, differential pressure p, measures ligancyC_p', the radius a of contact area and the radius R of rock particles before rock particles distortion;

To measuring ligancy C_p' be weighted, obtain ligancy C_pFormula (2), in formula, W is weight coefficient:

C_p=W*C_p'（2）

2) utilize ligancy C_pAnd Digby formula obtains the body change modulus K of dry rock_dry, utilize ligancy C_pAndMindlin formula obtains the shear modulus μ of dry rock_dry, then become modulus K according to the body of the dry rock obtaining_dry, dry rockShear modulus μ_dryAnd the deformation formula of Gassmann equation, obtain the prediction velocity of longitudinal wave that contains weight coefficient WAccording toThe velocity of longitudinal wave of predictionEqual the actual velocity of longitudinal wave Vp measuring_measured, obtain weight coefficient W;

3), according to weight coefficient W and Mindlin formula, obtain the shear modulus μ of dry rock_dry, by the shear of dry rockModulus μ_dryIn the deformation formula of substitution Gassmann equation, obtain predicting shear wave velocity

4) according to prediction shear wave velocitySet up four-dimensional AVO model and elastic impedance model, prediction development phase reservoirThe oil-gas reservoir attribute that pressure changes.

In described step 1), measure ligancy C_p' obtain by following process: to C_p' and e^1-φCarry out linear fitObtain measuring the relation of ligancy and porosity, as shown in Equation (1):

C_p'=11.759e^1-φ-12.748（1）。

Described step 2) in weight coefficient W obtain by following process:

Utilize the deformation formula of Gassmann equation to carry out the prediction of p-and s-wave velocity, formula (3)-(5) are GassmannThe deformation formula of equation:

$V_{p_{\mathrm{sat}}}=\sqrt{\frac{K_{\mathrm{dry}}+\frac{{(1-\frac{K_{\mathrm{dry}}}{K_{\mathrm{ma}}})}^2}{\frac{\mathrm{\φ}}{K_f}+\frac{1-\mathrm{\φ}}{K_{\mathrm{ma}}}-\frac{K_{\mathrm{dry}}}{K_{\mathrm{ma}}^2}}+\frac{4}{3}{\mathrm{\μ}}_{\mathrm{sat}}}{\mathrm{\ρ}}}---\left(3\right)$

μ_sat=μ_dry（4）

$V_{s_{\mathrm{sat}}}=V_{\mathrm{dry}}=\sqrt{\frac{{\mathrm{\μ}}_{\mathrm{sat}}}{\mathrm{\ρ}}}=\sqrt{\frac{{\mathrm{\μ}}_{\mathrm{dry}}}{\mathrm{\ρ}}}---\left(5\right)$

WhereinWithBe respectively velocity of longitudinal wave, the shear wave velocity of prediction, μ_satFor the shear modulus of pore media, μ_dryFor the shear modulus of dry rock; K_dryFor the body of dry rock becomes modulus, K_maFor the body of rock matrix becomes modulus; φ is the hole of rockGap degree; K_fFor the body of fluid becomes modulus, the bulk density that ρ is rock;

By ligancy C_pIn substitution Digby formula, obtain

$K_{\mathrm{dry}}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}b}{3\mathrm{\πR}(1-v)}---\left(7\right)$

By ligancy C_pIn substitution Mindlin formula, obtain:

${\mathrm{\μ}}_{\mathrm{dry}}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ})}{20\mathrm{\πR}}(\frac{4{\mathrm{\μ}}_{\mathrm{ma}}b}{1-v}+\frac{12{\mathrm{\μ}}_{\mathrm{ma}}a}{2-v})---\left(9\right)$

In formula, the Poisson's ratio that ν is rock matrix, μ_maFor the shear modulus of rock matrix; φ is the porosity of rock; C_pForLigancy; C_p' for measuring ligancy; A is the rock particles distortion radius of contact area before, and b is after rock particles is out of shapeThe radius of contact area, the radius that R is rock particles;

The body of dry rock is become to modulus K_dryShear modulus μ with dry rock_dryThe deformation formula of substitution Gassmann equationIn obtain predicting velocity of longitudinal waveEqual the velocity of longitudinal wave value of actual measurement according to the velocity of longitudinal wave value of prediction, obtain weighting systemNumber W.

Described Mindlin formula is:

${\mathrm{\μ}}_{\mathrm{dry}}=\frac{C_p(1-\mathrm{\φ})}{20\mathrm{\πR}}(\frac{4{\mathrm{\μ}}_{\mathrm{ma}}b}{1-v}+\frac{12{\mathrm{\μ}}_{\mathrm{ma}}a}{2-v})---\left(8\right).$

In described Mindlin formula (9)

$\frac{b}{R}={[d^2+{\left(\frac{a}{R}\right)}^2]}^{\frac{1}{2}}---\left(10\right)$

$d^3+\frac{3}{2}{\left(\frac{a}{R}\right)}^{2}d-\frac{3\mathrm{\π}(1-v)p}{{2C}_p(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}}=0---\left(12\right)$

Wherein p is differential pressure.

Described Digby formula is:

$K_{\mathrm{dry}}=\frac{C_p(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}b}{3\mathrm{\πR}(1-v)}---\left(6\right).$

The invention has the beneficial effects as follows: the present invention has considered that in reality, pressure, for the impact of p-and s-wave velocity, utilizesThe body that Digby, Mindlin formula calculate dry rock becomes modulus and shear modulus, in Digby, Mindlin formula, and existing skillIn art, suppose ligancy C_pFor constant, and the structure on stratum is being all laterally still longitudinally vicissitudinous, so be assumed to be C_pConstant does not meet actual. The present invention, according to the result of Murphy, carries out linear fit and has obtained porosity and ligancy C_pBetween relation, wherein, ligancy C_pFor variable, and closely related with the structure on stratum, obtain ligancy C_pAfterwards, just canThe body that substitution Digby, Mindlin formula calculate dry rock becomes modulus and shear modulus, then utilizes Gassmann equationDeformation formula obtains pressure-dependent pore media prediction shear wave velocity.

The present invention carries out the prediction of reservoir shear wave velocity according to the log data gathering, and the shear wave velocity that prediction obtains moreTally with the actual situation. According to the shear wave velocity obtaining, can set up AVO model, carry out converted wave analysis, and then can be betterAnalyze and identification of hydrocarbon Tibetan rock properties, comprise porosity, density, lithology and fluid content.

Brief description of the drawings

Fig. 1 is for measuring ligancy C_p' and e^1-φThe result of linear fit.

Fig. 2 is C programmer flow chart.

Fig. 3 is the contrast of the shear wave velocity of the shear wave velocity predicted under the identical porosity of different pressures and actual measurement, Qi ZhongshiLine is actual measurement shear wave velocity, and dotted line is prediction shear wave velocity.

Fig. 4 predicts shear wave velocity and surveys the right of shear wave velocity under same pressure different depth (being different aperture degree)Ratio, wherein solid line is actual measurement shear wave velocity, dotted line is prediction shear wave velocity.

Detailed description of the invention

Below in conjunction with accompanying drawing, the present invention is described in detail; * in formula of the present invention represents multiplication sign.

The present invention utilizes the deformation formula of Gassmann equation to carry out the prediction of the shear wave velocity of pore media,In the deformation formula of Gassmann equation, the body of dry rock becomes modulus K_dryWith shear modulus μ_dryUnknown. And in production processIn, the pressure of reservoir will change, and the deformation formula of Gassmann equation cannot embody pressure to p-and s-wave velocityImpact. The body that the present invention utilizes Digby, Mindlin formula to carry out dry rock becomes modulus K_dryWith shear modulus μ_dryPrediction,This is because Digby, Mindlin formula have considered that pressure is for K_dryAnd μ_dryImpact. And at Digby, Mindlin formulaIn, conventionally suppose ligancy C_pFor constant, this is obviously irrational. Step of the present invention is as follows:

1) image data: the body that gathers rock matrix becomes modulus K_ma, the shear modulus μ of rock matrix_ma, the hole of rockThe body of degree φ, fluid becomes modulus K_fAnd the bulk density ρ of rock, measurement ligancy C_p', the distortion of differential pressure p, rock particlesThe radius a of contact area, the radius R of rock particles before, actual velocity of longitudinal wave Vp_measured；

According toCalculate the Poisson's ratio v of rock matrix, wherein K_maFor the body of rock matrixBecome modulus, μ_maFor the shear modulus of rock matrix.

The present invention carries out linear fit according to the empirical value of Murphy, and in table 1, table 1 is porosity and measurement ligancy C_p'Correspondence table, utilize these group data to carry out linear fit and obtain formula (1):

C_p'=11.759e^1-φ-12.748（1）

Wherein C_p' for measuring ligancy, the porosity that φ is rock.

Table 1 porosity and measurement C_p' corresponding table

Porosity	Cp
		0.20	14.007
0.25	12.336
		0.30	10.843
0.35	9.5078
		0.40	8.3147
0.45	7.2517
		0.50	6.3108
0.55	5.4878
		0.60	4.7826
0.65	4.1988
		0.70	3.7440

Actual saturated rock ligancy C in the situation such as different depth, lithology_p(Coordinationnumber)Size should be different, but also should meet this rule. Therefore the present invention proposes the ligancy in actual conditionsC_pFormula, see formula (2), wherein W is weight coefficient, weight coefficient W has comprised the degree of depth, lithology etc. to actual ligancy C_p'sCombined influence:

C_p=W*C_p'（2）

When utilizing Digby, Mindlin formula in prior art, just suppose ligancy C_pFor constant, and the present inventionThe proposition of middle formula (2) is by ligancy C_pConnect with the porosity of reservoir, see Fig. 1, more tally with the actual situation, this is thisOne of key of invention.

2) suppose that medium is uniform pore media, can utilize the deformation formula of Gassmann equation to carry out velocity of wave in length and breadthThe prediction of degree, the following is the distortion of Gassmann equation:

$V_{p_{\mathrm{sat}}}=\sqrt{\frac{K_{\mathrm{dry}}+\frac{{(1-\frac{K_{\mathrm{dry}}}{K_{\mathrm{ma}}})}^2}{\frac{\mathrm{\φ}}{K_f}+\frac{1-\mathrm{\φ}}{K_{\mathrm{ma}}}-\frac{K_{\mathrm{dry}}}{K_{\mathrm{ma}}^2}}+\frac{4}{3}{\mathrm{\μ}}_{\mathrm{sat}}}{\mathrm{\ρ}}}---\left(3\right)$

μ_sat=μ_dry（4）

$V_{s_{\mathrm{sat}}}=V_{\mathrm{dry}}=\sqrt{\frac{{\mathrm{\μ}}_{\mathrm{sat}}}{\mathrm{\ρ}}}=\sqrt{\frac{{\mathrm{\μ}}_{\mathrm{dry}}}{\mathrm{\ρ}}}---\left(5\right)$

WhereinWithThe compressional wave that is respectively prediction hastens, shear wave velocity, μ_satFor the shear modulus of pore media, μ_dryFor the shear modulus of dry rock, shear modulus convection cell is insensitive, therefore μ_sat=μ_dry；K_dryFor the body of dry rock becomes modulus, K_maFor the body of rock matrix becomes modulus, the shear modulus μ of rock matrix_ma; φ is the porosity of rock; K_fFor the body of fluid becomes mouldAmount, the bulk density that ρ is rock; Wherein the body of rock matrix becomes modulus K_ma, rock the body of porosity φ, fluid become modulus K_fAnd the bulk density ρ of rock is the data of collection;

Body for dry rock becomes modulus K_dry, utilize and considered that the Digby formula that pressure changes calculates; For dryThe shear modulus μ of rock_dryUtilize and considered that the Mindlin formula that pressure changes calculates.

Calculate pressure-dependent compacting closely dry rock body become modulus Digby formula into:

$K_{\mathrm{dry}}=\frac{C_p(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}b}{3\mathrm{\πR}(1-v)}---\left(6\right)$

By the ligancy C in formula (2)_pSubstitution formula (6) obtains

$K_{\mathrm{dry}}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}b}{3\mathrm{\πR}(1-v)}---\left(7\right)$

The Mindlin formula that calculates pressure-dependent dry shearing of rocks modulus is:

${\mathrm{\μ}}_{\mathrm{dry}}=\frac{C_p(1-\mathrm{\φ})}{20\mathrm{\πR}}(\frac{4{\mathrm{\μ}}_{\mathrm{ma}}b}{1-v}+\frac{12{\mathrm{\μ}}_{\mathrm{ma}}a}{2-v})---\left(8\right)$

By the ligancy C in formula (2)_pSubstitution formula (8) obtains

${\mathrm{\μ}}_{\mathrm{dry}}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ})}{20\mathrm{\πR}}(\frac{4{\mathrm{\μ}}_{\mathrm{ma}}b}{1-v}+\frac{12{\mathrm{\μ}}_{\mathrm{ma}}a}{2-v})---\left(9\right)$

Wherein

$\frac{b}{R}={[d^2+{\left(\frac{a}{R}\right)}^2]}^{\frac{1}{2}}---\left(11\right)$

$d^3+\frac{3}{2}{\left(\frac{a}{R}\right)}^{2}d-\frac{3\mathrm{\π}(1-v)p}{{2C}_p(1-\mathrm{\φ}){\mathrm{\μ}}_{\mathrm{ma}}}=0---\left(12\right)$

Wherein, v and μ_maBe respectively Poisson's ratio and the shear modulus of rock matrix; φ is the porosity of rock; C_pFor coordinationNumber (Coordinationnumber); C_p' for measuring ligancy; The variation of differential pressure p is embodied inIn, i.e. formula (11)In, no matter be in formula (11), to try to achieve differential pressure differential pressure value or utilization variance in Digby, Mindlin formulaPressure p value is calculated, in Practical CalculationDo as a whole; A is contact area before rock particles distortionRadius, b is the rock particles distortion radius of contact area afterwards, the radius that R is rock particles. The dry lithosome of above-mentioned calculating becomes mouldThe parameter of amount and shear modulus, except weight coefficient W, the porosity φ of rock, measurement ligancy C_p', differential pressure p, rockBefore particle deformation, the radius a of contact area, the radius R of rock particles are the data that collect; According to formulaCalculate the Poisson's ratio v of rock matrix, wherein K_maFor the body of rock matrix becomes modulus, μ_maForThe shear modulus of rock matrix.

The body of dry rock is become to modulus K_dryShear modulus μ with dry rock_dryThe deformation formula of substitution Gassmann equationIn obtain calculate prediction velocity of longitudinal waveExpression formula, in this expression formula, only have a unknown number W, i.e. the weighting of ligancy systemNumber. In log data data due to actual acquired data, have velocity of longitudinal wave, the velocity of longitudinal wave value of prediction will approach actual measurementVelocity of longitudinal wave value, therefore utilizing formula (13) is actual measurement velocity of longitudinal wave value Vp_measuredDeduct prediction velocity of longitudinal wave valueEqual zero (shear wave velocity of prediction is wanted the shear wave velocity of infinite approach reality in theory, and actually, infinite approachCannot practical operation, therefore suppose actual measurement velocity of longitudinal wave value Vp_measuredWith prediction velocity of longitudinal wave valueCompletely equal),Obtain weight coefficient W:

${\mathrm{VP}}_{\mathrm{measured}}-V_{\mathrm{Psat}}\→0---\left(13\right)$

WhereinFor the prediction velocity of longitudinal wave that contains unknown number W, Vp_measuredThe actual compressional wave speed obtaining for image dataDegree.

Specifically being implemented as follows of pressure-dependent pore media S-Wave Velocity Predicted Method, by formula (2) substitutionDigby, Mindlin formula obtain dry lithosome and become modulus K_dryWith dry shearing of rocks modulus μ_dryExpression formula, this expression formulaIn to only have weight coefficient W be unknown number, then dry lithosome is become to modulus K_dryWith dry shearing of rocks modulus μ_drySubstitutionThe deformation formula of Gassmann equation obtains the expression formula of velocity of longitudinal wave, similarly, only has one in the expression formula of velocity of longitudinal waveUnknown weight coefficient W, can obtain weight coefficient W according to formula (13). This process realizes by C Programming with Pascal Language, seesFig. 2, utilizes this flow process written-out program can obtain weight coefficient W, and detailed description of the invention is: porosity, the rock of input rockThe body of the shear modulus of skeleton, the Poisson's ratio of rock matrix, rock matrix become modulus, rock bulk density, differential pressure thisA little parameters; Utilize circulation to try to achieve weight coefficient W, initial value 0(of first given weight coefficient W first defines weight coefficient W=0), then weight coefficient W is added to 0.1 obtains new W value (being new W=W+0.1), by this new W value together with before inputThe Poisson's ratio of the porosity of rock, the shear modulus of rock matrix, rock matrix, the body of rock matrix become the body of modulus, rockPrediction velocity of longitudinal wave is calculated in long-pending density, differential pressure substitutionFormula, will predict velocity of longitudinal waveDeduct actual compressional wave speedDegree Vp_measuredZero (if result is), this new W value is exactly adding under this porosity soWeight coefficient W, if non-vanishing, continue W is added to 0.1, repeat said process untilDeduct Vp_measuredResult is till zero,Be that W cumulative 0.1 is until accumulated value is satisfiedDeduct Vp_measuredResult is till zero, and this cumulative W is exactly at this porosityUnder weight coefficient W.

W value under table 2 uniform pressure different aperture degree

The degree of depth (m)	Porosity	W
			1398	0.141589	23
1398.1	0.152161	23.5
			1398.2	0.161756	20.7
1398.3	0.167833	21.9
			1398.4	0.168482	22.2
1398.5	0.168241	22.5

1398.6	0.167943	22.4
			1398.7	0.170837	22.1
1398.8	0.175003	22.2
			1398.9	0.181451	22.6
1399	0.189306	26.2
			1399.1	0.197517	22.9
1399.2	0.206004	23.6
			1399.3	0.213971	23.8
1399.4	0.221924	24.2
			1399.5	0.2307	24.6
1399.6	0.241194	24.8
			1399.7	0.253885	24.8
1399.8	0.266761	24.5
			1399.9	0.279295	23.6
1400	0.289936	22.7
			1400.1	0.299826	21.9
1400.2	0.308263	21.1
			1400.3	0.314609	20.2
1400.4	0.319537	19.4
			1400.5	0.320876	18.5
1400.6	0.318931	17.6
			1400.7	0.31625	16.6
1400.8	0.312713	16.2
			1400.9	0.306305	15.8
1401	0.297617	15.7
			1401.1	0.285234	15.7
1401.2	0.273926	15.7
			1401.3	0.266078	15.7
1401.4	0.259892	15.8
			1401.5	0.257437	16.2
1401.6	0.25944	16.6
			1401.7	0.262708	16.8
1401.8	0.267011	17
			1401.9	0.272578	16.9
1402	0.278568	16.6
			1402.1	0.284364	16.2
1402.2	0.286848	16
			1402.3	0.287378	15.9 8 -->
1402.4	0.283574	15.6
			1402.5	0.278016	15.5
1402.6	0.272875	15.6
			1402.7	0.270568	15.8
1402.8	0.271379	15.9
			1402.9	0.275682	16.1

1403	0.280734	16.4
			1403.1	0.286579	16.3
1403.2	0.286618	16
			1403.3	0.284568	15.6
1403.4	0.280121	15.1
			1403.5	0.276038	14.9
1403.6	0.272641	14.9
			1403.7	0.271467	15.3
1403.8	0.273295	15.7
			1403.9	0.276155	16.1
1404	0.280596	16.2
			1404.1	0.287741	16.2
1404.2	0.295395	16.1
			1404.3	0.300905	16
1404.4	0.301144	15.9
			1404.5	0.295262	15.4
1404.6	0.288593	14.7
			1404.7	0.281516	14.3
1404.8	0.275032	14.9
			1404.9	0.267789	16.5
1405	0.257688	18.4

The weight coefficient W of table 2 for obtaining under same pressure different depth (being different aperture degree), utilizes in table 2Weight coefficient W under different aperture degree carries out the result of shear wave velocity prediction. W value under table 2 uniform pressure different aperture degree,Utilize the weight coefficient W of the log data predicting reservoir ligancy of actual acquisition. In same reservoir, differential pressure is identical, andThe different corresponding porositys of the degree of depth also can change, and are therefore the W values under uniform pressure different aperture degree.

3) utilizing after programming calculates weight coefficient W, by weight coefficient W substitution formula (2), can obtain one and beBe listed as the ligancy C relevant with porosity_p, obtaining ligancy C_pAfterwards, suppose that medium is uniform pore media, utilizes coordinationNumber C_pAnd Digby formula obtains the body change modulus K of dry rock_dry, by ligancy C_pValue substitution Mindlin formula is formula (8)In obtain the shear modulus μ of dry rock_dry, then by μ_dryIn the deformation formula of substitution Gassmann equation, be in substitution formula (5)Calculate prediction shear wave velocitySimilarly, this process is (being specially of completing by the C programmer in Fig. 2Become modulus, rock by the porosity of W value, rock, the shear modulus of rock matrix, the Poisson's ratio of rock matrix, the body of rock matrixThe bulk density of stone, differential pressure obtain predicting shear wave velocity, then prediction of output shear wave velocity).

Shear wave velocity and weight coefficient W value under table 3 different pressures

Table 3 is shear wave velocity and W value under different pressures, as can be seen from Table 3, under different pressures, pre-by the present inventionThe shear wave velocity of surveying and survey to such an extent that the absolute error of shear wave velocity is all less than 5%, illustrates shear wave that the present invention the records comparison operators that hastensClose reality.

Fig. 3 is the contrast of the shear wave velocity of the shear wave velocity predicted under the identical porosity of different pressures and actual measurement, Qi ZhongshiLine is actual measurement shear wave velocity, and dotted line is prediction shear wave velocity. The actual measurement shear wave velocity of different pressures, prediction shear wave velocity in Fig. 3And error is all visible in table 3. Fig. 4 is prediction shear wave velocity and actual measurement under same pressure different depth (being different aperture degree)The contrast of shear wave velocity, wherein solid line is actual measurement shear wave velocity, and dotted line is prediction shear wave velocity, and its mean error is 6.288%,The result of utilizing the weight coefficient W under the uniform pressure in table 2 to carry out shear wave velocity prediction.

4) according to pressure-dependent prediction shear wave velocityCan set up and comprise four-dimensional AVO model and elastic impedance mouldType etc., and then the oil-gas reservoir attribute of prediction development phase reservoir pressure variation; The pressure-dependent shear wave that this prediction obtainsThe more realistic reservoir situation of change of speed; According to pressure-dependent shear wave velocity, except setting up AVO model, all rightBe used for carrying out converted shear wave analysis, can better assess the dynamic reservoir attribute of oil-gas reservoir, comprise oil-gas field development different phasePorosity, density, lithology and fluid content etc.

Claims (6)

1. a pressure-dependent pore media S-Wave Velocity Predicted Method, is characterized in that, comprises the following steps:

1) image data: gather the porosity φ of rock, the bulk density ρ of rock, the body of fluid becomes modulus K_f, actual compressional wave speedDegree Vp_measured, the body of rock matrix becomes modulus K_ma, the shear modulus μ of rock matrix_ma, differential pressure p, measures ligancy C_p'，The radius a of contact area and the radius R of rock particles before rock particles distortion;

To measuring ligancy C_p' be weighted, obtain ligancy C_pFormula (2), in formula, W is weight coefficient:

C_p＝W*C_p'(2)

2) utilize ligancy C_pAnd Digby formula obtains the body change modulus K of dry rock_dry, utilize ligancy C_pAnd MindlinFormula obtains the shear modulus μ of dry rock_dry, then become modulus K according to the body of the dry rock obtaining_dry, dry rock shear mouldAmount μ_dryAnd the deformation formula of Gassmann equation, obtain the prediction velocity of longitudinal wave that contains weight coefficient WAccording to what predictVelocity of longitudinal waveEqual the actual velocity of longitudinal wave Vp measuring_measured, obtain weight coefficient W;

3), according to weight coefficient W and Mindlin formula, obtain the shear modulus μ of dry rock_dry, by the shear modulus of dry rockμ_dryIn the deformation formula of substitution Gassmann equation, obtain predicting shear wave velocity

4) according to prediction shear wave velocitySet up four-dimensional AVO model and elastic impedance model, prediction development phase reservoir pressureThe oil-gas reservoir attribute changing;

Wherein, formula (3)-(5) are the deformation formula of Gassmann equation:

$V_{p_{sat}}=\sqrt{\frac{K_{dry}+\frac{{\left(1-\frac{K_{dry}}{K_{ma}}\right)}^2}{\frac{\mathrm{\φ}}{K_f}+\frac{1-\mathrm{\φ}}{K_{ma}}-\frac{K_{dry}}{K_{ma}^2}}+\frac{4}{3}{\mathrm{\μ}}_{sat}}{\mathrm{\ρ}}}---\left(3\right)$

μ_sat＝μ_dry(4)

$V_{s_{sat}}=V_{dry}=\sqrt{\frac{{\mathrm{\μ}}_{sat}}{\mathrm{\ρ}}}=\sqrt{\frac{{\mathrm{\μ}}_{dry}}{\mathrm{\ρ}}}---\left(5\right)$

WhereinWithBe respectively velocity of longitudinal wave, the shear wave velocity of prediction, μ_satFor the shear modulus of pore media, μ_dryFor dryThe shear modulus of rock; K_dryFor the body of dry rock becomes modulus, K_maFor the body of rock matrix becomes modulus; φ is the porosity of rock;K_fFor the body of fluid becomes modulus, the bulk density that ρ is rock.

2. the pressure-dependent pore media S-Wave Velocity Predicted Method of one according to claim 1, is characterized in that,Described step 1) the middle ligancy C that measures_p' obtain by following process: to C_p' and e^1-φCarrying out linear fit is measuredThe relation of ligancy and porosity, as shown in formula (1):

C_p'＝11.759e^1-φ-12.748(1)。

3. the pressure-dependent pore media S-Wave Velocity Predicted Method of one according to claim 1, is characterized in that,Described step 2) in weight coefficient W obtain by following process:

While utilizing the deformation formula of Gassmann equation to carry out p-and s-wave velocity prediction, by ligancy C_pIn substitution Digby formulaArrive:

$K_{dry}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ}){\mathrm{\μ}}_{ma}b}{3\mathrm{\π}R(1-\mathrm{\ν})}---\left(7\right)$

By ligancy C_pIn substitution Mindlin formula, obtain:

${\mathrm{\μ}}_{dry}=\frac{W*{C_p}^{\′}(1-\mathrm{\φ})}{20\mathrm{\π}R}\left(\frac{4{\mathrm{\μ}}_{ma}b}{1-\mathrm{\ν}}+\frac{12{\mathrm{\μ}}_{ma}a}{2-\mathrm{\ν}}\right)---\left(9\right)$

In formula, the Poisson's ratio that ν is rock matrix, μ_maFor the shear modulus of rock matrix; φ is the porosity of rock; C_pFor coordinationNumber; C_p' for measuring ligancy; A is the rock particles distortion radius of contact area before, and b is rock particles distortion contact afterwardsThe radius in region, the radius that R is rock particles;

The body of dry rock is become to modulus K_dryShear modulus μ with dry rock_dryIn the deformation formula of substitution Gassmann equationTo prediction velocity of longitudinal waveThe velocity of longitudinal wave value that equals actual measurement according to the velocity of longitudinal wave value of prediction, obtains weight coefficient W.

4. the pressure-dependent pore media S-Wave Velocity Predicted Method of one according to claim 3, is characterized in that,Described Mindlin formula is:

${\mathrm{\μ}}_{dry}=\frac{C_p(1-\mathrm{\φ})}{20\mathrm{\π}R}\left(\frac{4{\mathrm{\μ}}_{ma}b}{1-\mathrm{\ν}}+\frac{12{\mathrm{\μ}}_{ma}a}{2-\mathrm{\ν}}\right)---\left(8\right).$

5. the pressure-dependent pore media S-Wave Velocity Predicted Method of one according to claim 4, is characterized in that,In described Mindlin formula (9)

$\frac{b}{R}={\[d^2+{\left(\frac{a}{R}\right)}^2\]}^{\frac{1}{2}}---\left(10\right)$

$d^3+\frac{3}{2}{\left(\frac{a}{R}\right)}^{2}d-\frac{3\mathrm{\π}(1-\mathrm{\ν})p}{2C_p(1-\mathrm{\φ}){\mathrm{\μ}}_{ma}}=0---\left(12\right)$

Wherein p is differential pressure.

6. the pressure-dependent pore media S-Wave Velocity Predicted Method of one according to claim 3, is characterized in that,Described Digby formula is:

$K_{dry}=\frac{C_p(1-\mathrm{\φ}){\mathrm{\μ}}_{ma}b}{3\mathrm{\π}R(1-\mathrm{\ν})}---\left(6\right).$