Method for Calculating Saturation of Natural Gas Hydrate Based on Wood Wave Impedance Method

20200333313 ยท 2020-10-22

    Inventors

    Cpc classification

    International classification

    Abstract

    In a method for calculating saturation of a natural gas hydrate based on a Wood wave impedance method a compressional wave impedance Z.sub.b of a deposit containing the natural gas hydrate can be obtained by compressional wave impedance inversion, and a compressional wave impedance Z.sub.w of the fluid and a compressional wave impedance Z.sub.h of the pure natural gas hydrate can be calculated by measuring relevant elastic parameters in a laboratory, a compressional wave impedance Z.sub.m of a matrix can be calculated on the basis of drilling data and measurement data of the relevant elastic parameters measured in the laboratory, and a porosity can be obtained by utilizing a logging interpretation technique, and the saturation of the natural gas hydrate can be calculated.

    Claims

    1. A method for calculating saturation of a natural gas hydrate based on a Wood wave impedance method, the method comprising: (1) using a Wood method to predict a saturation of the natural gas hydrate utilizing an equation and an equation 1 b .Math. V b 2 = ( 1 - S h ) w .Math. V p .Math. w 2 + .Math. S h h .Math. V p .Math. h 2 + 1 - m .Math. V p .Math. m 2 and an equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m, wherein V.sub.b, V.sub.pw, V.sub.ph, and V.sub.pm represent a compressional wave velocity of a deposit containing the natural gas hydrate, compressional wave velocity of a fluid, a compressional wave velocity of a pure natural gas hydrate and a compressional wave velocity of a matrix of the deposit, respectively; represents porosity; S.sub.h represents a proportion of the natural gas hydrate in a pore space, and .sub.b, .sub.w, .sub.h and .sub.m represent a bulk density of the deposit containing the natural gas hydrate, a density of the fluid, a density of the pure natural gas hydrate, and a density of the matrix of the deposit, respectively; (2) calculating the density of the matrix of the deposit utilizing a formula m = .Math. i = 1 n .Math. f i .Math. i , and calculating the compressional wave velocity of the matrix of the deposit utilizing a formula V p .Math. m = K + 4 3 .Math. G m ; wherein f.sub.i is a volume percentage of an i-th substance in the matrix of the deposit, .sub.i is a density of the i-th substance in the matrix of the deposit, n represents the kinds of a substances forming the matrix of the deposit, K represents a substance bulk modulus, G represents a substance shear modulus, K = 1 2 [ .Math. i = 1 n .Math. f i .Math. K i + ( .Math. i = 1 n .Math. f i K i ) - 1 ] , .Math. G = 1 2 [ .Math. i = 1 n .Math. f i .Math. G i + ( .Math. i = 1 n .Math. f i G i ) - 1 ] , wherein K.sub.i is a bulk modulus of the i-th substance in the matrix of the deposit, and G.sub.i is a shear modulus of the i-th substance in the matrix of the deposit; (3) calculating the compressional wave velocity of a pure natural gas hydrate utilizing a formula V p .Math. h = E ( 1 - ) ( 1 + ) .Math. ( 1 - 2 .Math. ) , wherein E is a Young's modulus of the pure natural gas hydrate, is a density of the pure natural gas hydrate, and is a Poisson's ratio of the pure natural gas hydrate; wherein the Young's modulus is obtained by a formula E = 9 .Math. K .Math. G 3 .Math. K + G , and the Poisson's ratio is obtained by a formula = 3 .Math. K - 2 .Math. G 2 .Math. ( 3 .Math. K + G ) ; (4) multiplying both sides of the equation by 1 b .Math. V b 2 = ( 1 - S h ) w .Math. V p .Math. w 2 + .Math. S h h .Math. V p .Math. h 2 + 1 - m .Math. V p .Math. m 2 by 1 b to obtain an equation 1 ( b .Math. V b ) 2 = ( 1 - S h ) b .Math. w .Math. V p .Math. w 2 + .Math. S h b .Math. h .Math. V p .Math. h 2 + 1 - b .Math. m .Math. V p .Math. m 2 ; wherein a compressional wave impedance of the deposit containing the natural gas hydrate is Z.sub.b=.sub.bV.sub.b, the compressional wave impedance of the fluid is Z.sub.w=.sub.wV.sub.pw, a compressional wave impedance of the pure natural gas hydrate is Z.sub.h=.sub.hV.sub.ph, a compressional wave impedance of the matrix of the deposit is Z.sub.m=.sub.mV.sub.pm, and then the equation 1 ( b .Math. V b ) 2 = ( 1 - S h ) b .Math. w .Math. V p .Math. w 2 + .Math. S h b .Math. h .Math. V p .Math. h 2 + 1 - b .Math. m .Math. V p .Math. m 2 can be expressed as an equation 1 ( Z b ) 2 = ( 1 - S h ) ( b / w ) .Math. ( Z w ) 2 + .Math. S h ( b / h ) .Math. ( Z h ) 2 + 1 - ( b / m ) .Math. ( Z m ) 2 ; multiplying both sides of an equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m by 1 w to obtain an equation .sub.b/.sub.w=(1S.sub.h)+S.sub.h.sub.h/.sub.w+(1).sub.m/.sub.h, multiplying both sides of an equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m by 1 h to obtain an equation .sub.b/.sub.h=(1S.sub.h).sub.w/.sub.h+S.sub.h+(1).sub.m/.sub.h, and multiplying both sides of an equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m by 1 m to obtain an equation .sub.b/.sub.m=(1S.sub.h).sub.w/.sub.m+S.sub.h.sub.h/.sub.m+(1), and setting C.sub.bw=.sub.b/.sub.w, C.sub.bh=.sub.b/.sub.h, C.sub.bm=.sub.b/.sub.m, and C.sub.bhcustom-characterC.sub.bwcustom-character1custom-characterC.sub.bm; (5) substituting C.sub.bw, C.sub.bh and C.sub.bm into an equation 1 ( Z b ) 2 = ( 1 - S h ) ( b / w ) .Math. ( Z w ) 2 + .Math. S h ( b / h ) .Math. ( Z h ) 2 + 1 - ( b / m ) .Math. ( Z m ) 2 , to obtain a formula 1 ( Z b ) 2 = ( 1 - S h ) C b .Math. w ( Z w ) 2 + .Math. S h C b .Math. h ( Z h ) 2 + 1 - C b .Math. m ( Z m ) 2 for calculating the saturation of the natural gas hydrate by using a Wood wave impedance method, wherein the compressional wave impedance Z.sub.b of the deposit containing the natural gas hydrate is obtained by compressional wave impedance inversion, and the compressional wave impedance Z.sub.w of the fluid and the compressional wave impedance Z.sub.h of the pure natural gas hydrate are calculated by measuring relevant elastic parameters in a laboratory; the compressional wave impedance Z.sub.m of the matrix is calculated on the basis of drilling data and measurement data of the relevant elastic parameters measured in the laboratory, and the porosity is obtained by utilizing a logging interpretation technique.

    2. A method for estimating saturation of a natural gas hydrate contained in a deposit, the method comprising: obtaining a compressional wave impedance Z.sub.b of the deposit containing the natural gas hydrate by compressional wave impedance inversion; calculating a compressional wave impedance Z.sub.h of the natural gas hydrate in a pure state by laboratory measurement of at least one elastic parameter; calculating a compressional wave impedance Z.sub.w of a fluid by laboratory measurement of at least one elastic parameter; calculating a compressional wave impedance Z.sub.m of the deposit on the basis of drilling data and laboratory measurement data of at least one elastic parameter; obtaining a porosity of the deposit utilizing a logging interpretation technique; calculating the saturation of the natural gas hydrate in the deposit utilizing a formula 1 ( Z b ) 2 = ( 1 - S h ) C b .Math. w ( Z w ) 2 + .Math. S h C b .Math. h ( Z h ) 2 + 1 - C b .Math. m ( Z m ) 2 , wherein S.sub.h represents a proportion of the natural gas hydrate in a pore space of the deposit, C.sub.bw=.sub.b/.sub.w, C.sub.bh=.sub.b/.sub.h, and C.sub.bm=.sub.b/.sub.m, wherein .sub.b represents a bulk density of the deposit containing the natural gas hydrate, .sub.w represents a density of fluid contained in the deposit, .sub.h represents a density of the natural gas hydrate in a pure form, and .sub.m represents a density of the deposit as a matrix, and wherein C.sub.bhcustom-characterC.sub.bwcustom-character1custom-characterC.sub.bm; and outputting the calculated saturation of the natural gas hydrate in the deposit.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0020] To describe the technical solutions in the embodiments of the present invention or in the prior art more clearly, the following briefly describes the accompanying drawings required for describing the embodiments or the prior art. Apparently, the accompanying drawings in the following description show some embodiments of the present invention, and a person of ordinary skill in the art may still derive other drawings from these accompanying drawings without creative efforts.

    [0021] FIG. 1 shows elastic parameters of a deposit matrix composition of a natural gas hydrate-enriched zone in the Shenhu sea area.

    DETAILED DESCRIPTION OF EMBODIMENTS

    [0022] The following describes technical solutions of one or more embodiments of the present invention with reference to the accompanying drawing(s). Apparently, the described embodiment(s) are merely a part rather than all of the embodiments of the present invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

    [0023] Taking the calculation of saturation of a natural gas hydrate in the Shenhu sea area of China as an example, a method for calculating saturation of a natural gas hydrate based on a Wood wave impedance method includes the following steps:

    [0024] Step (1): a Wood method for obtaining saturation of the natural gas hydrate consists of an equation

    [00018] 1 b .Math. V b 2 = ( 1 - S h ) w .Math. V p .Math. w 2 + .Math. S h h .Math. V p .Math. h 2 + 1 - m .Math. V p .Math. m 2

    and an equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m, where V.sub.b, V.sub.pw, V.sub.ph, and V.sub.pm represent the compressional wave velocity of a deposit containing the natural gas hydrate, the compressional wave velocity of a fluid, the compressional wave velocity of a pure natural gas hydrate and the compressional wave velocity of a matrix, respectively; represents porosity; S.sub.h represents the proportion of the natural gas hydrate in a pore space, and .sub.b, .sub.w, .sub.h and .sub.m represent the density of the deposit containing the natural gas hydrate, the density of the fluid, the density of the pure natural gas hydrate, and the density of the matrix, respectively.

    [0025] Step (2): since the matrix is often composed of many substances, a formula for calculating the matrix density can be expressed as

    [00019] m = .Math. i = 1 n .Math. f i .Math. i ,

    and a formula for calculating the compressional wave velocity of the matrix is

    [00020] V p .Math. m = K + 4 3 .Math. G m ;

    where f.sub.i is the volume percentage of an i-th substance in the matrix, .sub.i is the density of the i-th substance in the matrix, n represents the kind of a substance forming the matrix, K represents a substance bulk modulus, G represents a substance shear modulus,

    [00021] K = 1 2 [ .Math. i = 1 n .Math. f i .Math. K i + ( .Math. i = 1 n .Math. f i K i ) - 1 ] , G = 1 2 [ .Math. i = 1 n .Math. f i .Math. G i + ( .Math. i = 1 n .Math. f i G i ) - 1 ] ,

    where K.sub.i is the bulk modulus of the i-th substance in the matrix, and G.sub.i is the shear modulus of the i-th substance in the matrix.

    [0026] Step (3): a formula for calculating the compressional wave velocity of a pure natural gas hydrate is

    [00022] V p .Math. h = E ( 1 - ) ( 1 + ) .Math. ( 1 - 2 .Math. ) ,

    where E is the Young's modulus of the pure natural gas hydrate, is the density of the pure natural gas hydrate, and is the Poisson's ratio of the pure natural gas hydrate; where the Young's modulus is obtained by a formula

    [00023] E = 9 .Math. K .Math. G 3 .Math. K + G ,

    and the Poisson's ratio is obtained by a formula

    [00024] = 3 .Math. K - 2 .Math. G 2 .Math. ( 3 .Math. K + G ) .

    [0027] Step (4): multiply both sides of the equation

    [00025] 1 b .Math. V b 2 = ( 1 - S h ) w .Math. V p .Math. w 2 + .Math. S h h .Math. V p .Math. h 2 + 1 - m .Math. V p .Math. m 2

    by

    [00026] 1 b

    to obtain an equation

    [00027] 1 ( b .Math. V b ) 2 = ( 1 - S h ) b .Math. w .Math. V p .Math. w 2 + .Math. S h b .Math. h .Math. V p .Math. h 2 + 1 - b .Math. m .Math. V p .Math. m 2 ;

    where the compressional wave impedance of the deposit containing the natural gas hydrate is Z.sub.b=.sub.bV.sub.b, the compressional wave impedance of the fluid is Z.sub.w=.sub.wV.sub.pw, the compressional wave impedance of the pure natural gas hydrate is Z.sub.h=.sub.hV.sub.ph, the compressional wave impedance of the matrix is Z.sub.m=.sub.mV.sub.pm, and then the equation

    [00028] 1 ( b .Math. V b ) 2 = ( 1 - S h ) b .Math. w .Math. V p .Math. w 2 + .Math. S h b .Math. h .Math. V p .Math. h 2 + 1 - b .Math. m .Math. V p .Math. m 2

    can be expressed as an equation

    [00029] 1 ( Z b ) 2 = ( 1 - S h ) ( b / w ) .Math. ( Z w ) 2 + .Math. S h ( b / h ) .Math. ( Z h ) 2 + 1 - ( b / m ) .Math. ( Z m ) 2 .

    [0028] The deposit matrix of a natural gas hydrate-enriched zone in the Shenhu sea area is mainly composed of silt, sand and clay, and also includes seawater and pure methane hydrate. FIG. 1 shows elastic parameters of a deposit matrix composition actually measured. Two sides of the equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m are multiplied by

    [00030] 1 w

    simultaneously to obtain an equation .sub.b/.sub.w=(1S.sub.h)+S.sub.h.sub.h/.sub.w+(1).sub.m/.sub.w, and .sub.b/.sub.w(1S.sub.h)+0.87S.sub.h+0.97(1).sub.m=0.97(1).sub.m+0.13S.sub.h can be obtained by substituting elastic parameters in FIG. 1.

    [0029] Both sides of the equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m are multiplied by

    [00031] 1 h

    simultaneously to obtain an equation .sub.b/.sub.h=(1S.sub.h).sub.w/.sub.h+S.sub.h+(1).sub.m/.sub.h, and .sub.b/.sub.h1.15(1S.sub.h)+S.sub.h+1.11(1).sub.m=1.11(1).sub.m+1.15+0.15S.sub.h can be obtained by substituting the elastic parameters in FIG. 1.

    [0030] Both sides of the equation .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m are multiplied by

    [00032] 1 m

    simultaneously to obtain an equation .sub.b/.sub.h=(1S.sub.h).sub.w/.sub.m+S.sub.h.sub.h/.sub.m+(1), and .sub.b/.sub.m(1)+1.03/.sub.m0.13S.sub.h/.sub.m can be obtained by substituting the elastic parameters in FIG. 1.

    [0031] Set C.sub.bw=.sub.b/.sub.w, C.sub.bh=.sub.b/.sub.h, C.sub.bm=.sub.b/.sub.m, and C.sub.bhcustom-characterC.sub.bwcustom-character1custom-characterC.sub.bm, since .sub.b is generally greater than 1.5 g/cm.sup.3 and the maximum matrix density generally does not exceed 3 g/cm.sup.3, the smallest coefficient C.sub.bm is greater than 0.5, and S.sub.h generally is about 0.1. Relative to the value greater than 0.5, the value of S.sub.h is negligible, and then C.sub.bw0.97(1).sub.m+, C.sub.bh1.11(1).sub.m+1.15, C.sub.bm(1)+1.03/.sub.m, C.sub.bw, C.sub.bh, and C.sub.bm can be considered as a coefficient related to porosity and matrix density.

    [0032] Step (5): substitute C.sub.bw, C.sub.bh and C.sub.bm into an equation

    [00033] 1 ( Z b ) 2 = ( 1 - S h ) ( b / w ) .Math. ( Z w ) 2 + .Math. S h ( b / h ) .Math. ( Z h ) 2 + 1 - ( b / m ) .Math. ( Z m ) 2 ,

    to obtain a formula

    [00034] 1 ( Z b ) 2 = ( 1 - S h ) C b .Math. w ( Z w ) 2 + .Math. S h C b .Math. h ( Z h ) 2 + 1 - C b .Math. m ( Z m ) 2

    for calculating the saturation of the natural gas hydrate by using a Wood wave impedance method, where the compressional wave impedance Z.sub.b of the deposit containing the natural gas hydrate can be obtained by compressional wave impedance inversion, and the compressional wave impedance Z.sub.w of the fluid and the compressional wave impedance Z.sub.h of the pure natural gas hydrate can be calculated by measuring relevant elastic parameters in a laboratory; the compressional wave impedance Z.sub.m of the matrix can be calculated on the basis of drilling data and measurement data of the relevant elastic parameters measured in the laboratory, and the porosity can be obtained by utilizing a logging interpretation technique.

    [0033] In order to verify the reliability of the method of the present invention, an error analysis is performed on the above method:

    [0034] First, some basic data assumptions are made. It is assumed that the matrix of natural gas hydrate deposit in the sea area is composed of siltstone and clay, and their proportions in the matrix is 75% and 25%, respectively; the natural gas hydrate in a suspension mode is generally less than 50%, it is assumed that the saturation of the natural gas hydrate for the study is 30%; and it is assumed that the porosity of the natural gas hydrate deposit is 40%.

    [0035] From FIG. 1 and the formula

    [00035] m = .Math. i = 1 n .Math. f i .Math. i ,

    the density of the matrix can be calculated to be about 2.63 g/cm.sup.3. From FIG. 1 and the formulas

    [00036] K = 1 2 [ .Math. i = 1 n .Math. f i .Math. K i + ( .Math. i = 1 n .Math. f i K i ) - 1 ] .Math. .Math. and G = 1 2 [ .Math. i = 1 n .Math. f i .Math. G i + ( .Math. i = 1 n .Math. f i G i ) - 1 ] ,

    the bulk modulus and shear modulus of the matrix can be calculated to be about 33.94 GPa and 19.32 GPa, respectively; and from the matrix density and the bulk modulus and the shear modulus, the compressional wave velocity of the matrix can be calculated to be 4762.34 m/s using a formula

    [00037] V p .Math. m = K + 4 3 .Math. G m .

    [0036] From FIG. 1 and the formulas

    [00038] E = 9 .Math. K .Math. G 3 .Math. K + G .Math. .Math. and = 3 .Math. K - 2 .Math. G 2 .Math. ( 3 .Math. K + G ) ,

    the Young's modulus and Poisson's ratio of the natural gas hydrate can be calculated to be about 6.3 GPa and 0.31, respectively. The compressional wave velocity of the natural gas hydrate can be calculated from FIG. 1 and the formula

    [00039] V p .Math. h = E ( 1 - ) ( 1 + ) .Math. ( 1 - 2 .Math. )

    to be 3126.94 m/s; the coefficients C.sub.bw, C.sub.bh and C.sub.bm are further calculate to be 1.93, 2.21 and 0.76 respectively; the density of the deposit containing the natural gas hydrate can be calculated to be about 1.97 g/cm.sup.3 according to the formula .sub.b=(1S.sub.h).sub.w+S.sub.h.sub.h+(1).sub.m, and it can be calculated according to the formula

    [00040] 1 b .Math. V b 2 = ( 1 - S h ) w .Math. V p .Math. w 2 + .Math. S h h .Math. V p .Math. h 2 + 1 - m .Math. V p .Math. m 2

    that the compressional wave velocity of the deposit containing the natural gas hydrate is about 1855.96 m/s. It can be known in combination with the calculated data that the compressional wave impedance Z.sub.b of the deposit containing the natural gas hydrate, the compressional wave impedance Z.sub.w of the fluid, the compressional wave impedance Z.sub.h of the pure natural gas hydrate, and the compressional wave impedance Z.sub.m of the matrix are about 3651.61 (m.Math.g)/(s.Math.cm.sup.3), 12536.88 (m.Math.g)/(s.Math.cm.sup.3), 1527.36 (m.Math.g)/(s.Math.cm.sup.3), and 2814.25 (m.Math.g)/(s.Math.cm.sup.3) respectively; and it is further calculated according to the formula

    [00041] 1 ( Z b ) 2 = ( 1 - S h ) C b .Math. w ( Z w ) 2 + .Math. S h C b .Math. h ( Z h ) 2 + 1 - C b .Math. m ( Z m ) 2

    that the saturation of the natural gas hydrate is 28.5%.

    [0037] The accurate saturation of the natural gas hydrate obtained by the actual measurement is 30%, and it can be seen that the saturation value of the natural gas hydrate calculated by the method of the present invention is very close to the actual value, and the error is small.

    [0038] In conclusion, the method of the present invention forms a novel prediction method by deriving and analyzing the existing Wood method, and clearly shows the relationship between the compressional wave impedance of the natural gas hydrate reservoir and the saturation of the natural gas hydrate, and the method has a small error and has a certain promotion and application value.

    [0039] The above-mentioned contents are merely preferred embodiments of the present invention, and are not used to limit the present invention, and wherever within the spirit and principle of the present invention, any modifications, equivalent replacements, improvements, and the like shall be all contained within the protection scope of the present invention.