Reasonability judgment method for nuclear magnetic resonance power function relational expression

Abstract

The invention relates to the technical field of oil and gas field development, in particular to a method for judging reasonability of a nuclear magnetic resonance power function relational expression. The invention discloses a rationality judgment method for a nuclear magnetic resonance power function relational expression. The method comprises the following steps: respectively constructing a value interval of a power exponent n and a value interval of a conversion coefficient C; and if the power exponent n value and the conversion coefficient C value obtained by other methods fall into the value interval correspondingly, indicating that the power exponent n value and the conversion coefficient C value obtained by other methods are reasonable, otherwise, indicating that the power exponent n value and the conversion coefficient C value are not reasonable. The method disclosed by the invention has a relatively high application value.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to a method for judging the rationality of a nuclear magnetic resonance power function relationship. Background Art

[0002] The nuclear magnetic resonance core experiment is based on the nuclear magnetic resonance phenomenon. By measuring the nuclear magnetic resonance signals of hydrogen nuclei in fluids (such as oil, gas, and water) in rock pores, key parameters such as porosity, pore size distribution, movable fluid saturation, and permeability of rock pore structures are obtained. It has been widely used in oil and gas reservoir evaluation, oil and gas field exploration and development, etc. In order to convert the transverse relaxation time measured by nuclear magnetic resonance into the nuclear magnetic resonance pore throat radius, existing studies have proposed that there is a power function relationship between the transverse relaxation time and the pore throat radius. Only by obtaining the conversion coefficient and the power exponent, the transverse relaxation time distribution can be converted into the nuclear magnetic resonance pore throat radius distribution.

[0003] The conversion coefficient and power exponent jointly determine the accuracy of converting the transverse relaxation time into the pore throat radius; however, there are currently few related studies in this field. If we can use the correlation between the transverse relaxation time distribution and the pore throat radius distribution measured by high-pressure mercury injection to construct a method that can determine the rationality of the conversion coefficient and power exponent in the nuclear magnetic resonance power function relationship, the reliability of the pore structure analysis results can be effectively improved. Summary of the invention

[0004] The present invention aims to solve the above problems and propose a method for judging the rationality of a nuclear magnetic resonance power function relationship.

[0005] The technical solution of the present invention is: According to the basic principles of nuclear magnetic resonance, the transverse relaxation process of fluid in the pore throat is affected by the combined effects of three mechanisms: free relaxation, diffusion relaxation and surface relaxation. The transverse relaxation time is expressed as: 1 / T 2=1 / T 2B +1 / T 2D +1 / T 2S (1) Where: T 2 is the transverse relaxation time, with the dimension of ms; T 2B is the transverse free relaxation time, with the dimension of ms; T 2D is the lateral diffusion relaxation time, with the dimension of ms; T 2S is the transverse surface relaxation time, with the dimension of ms.

[0006] When the fluid in the core pore throat is a wetting phase, its transverse free relaxation time T 2B Much longer than the transverse relaxation time T 2, 1 / in formula (1) T 2B The term can be ignored; when the magnetic field gradient is small and the echo interval is short enough, the transverse diffusion relaxation time T 2D Usually longer, 1 / T 2D The term can be ignored. For NMR experiments, the fluid used in the experiment is usually simulated formation water, the magnetic field is weak and the echo interval is short, so equation (1) can be approximately written as: 1 / T 2≈1 / T 2S = ρ 2 S / V (2) Where: ρ 2 is the transverse surface relaxation intensity, with the dimension of μm / ms; S is the pore throat surface area, dimension is μm 2 ; V is the pore throat volume, dimension is μm 3 ; make S / V = F S / r , substituting into formula (2), we get: r ≈ ρ 2 F S T twenty three) Where: F S is the pore throat shape factor, dimensionless; r is the pore throat radius, with the dimension of μm.

[0007] Due to ignoring 1 / T 2B and 1 / T 2D 1 / T 2, so both Equation (2) and Equation (3) are approximate equations. For the convenience of solution, it is assumed that the pore throat radius r and transverse relaxation time T The equation relationship between 2 is: r= ( ρ 2 F S+ δ ) T twenty four) Where: δ is the correction factor of transverse free relaxation time and transverse diffusion relaxation time, with the dimension of μm / ms; Introducing into formula (4) δ Transform equation (3) into Eq.

[0008] because ρ 2 F S and δ The changing rules of the pore throat radius are unknown and difficult to obtain accurately. r and transverse relaxation time T The correlation between the 2 is unknown.

[0009] If you C =( ρ 2 F S + δ ) T 2 1-1 / n , substituting into formula (4), we get: r=CT 2 1 / n (5) Where: C is the conversion coefficient, the dimension is μm / ms, n is a power exponent, dimensionless.

[0010] The conversion factor of the same core C is regarded as a constant, and formula (5) is the pore throat radius r and transverse relaxation time T 2 is the power function relationship between .

[0011] According to formula (5), the power function relationship contains two unknown parameter conversion coefficients: C Sum power index n , usually taking the transverse relaxation time T 2 and pore throat radius r The combined approach resulted in a variety of calculation methods, but the conversion factors obtained by these calculation methods C Sum power index n Whether it is reasonable remains to be demonstrated.

[0012] High-pressure mercury injection pore throat radius determined by high-pressure mercury injection experiments r pc The distribution does not represent the complete pore throat radius r Distribution, according to NMR T 2 NMR pore throat radius obtained by conversion r T2The distribution represents a nearly complete range of pore throat radii. r distribution, for which there is a "NMR pore throat radius r T2 The distribution includes the pore throat radius of high-pressure mercury injection r pc The objective fact of "distribution".

[0013] According to the "NMR pore throat radius r T2 The distribution includes the pore throat radius of high-pressure mercury injection r pc The objective fact of "distribution" is that the minimum pore throat radius of high-pressure mercury injection r pc,min Two constraints must be met: ① The minimum pore throat radius of NMR is less than the minimum pore throat radius of high pressure mercury injection r pc,min ; ② Volume proportion of minimum pore throat radius in high-pressure mercury injection γ ( r pc,min )≤ from the minimum transverse relaxation time T 2min Transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection T 2( r pc,min )’s cumulative volume share.

[0014] Since the measurement results of high-pressure mercury injection and nuclear magnetic resonance are both discrete data points, the transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection is T 2( r pc,min ) has a lower limit: T 2( r pc,min )≥ T 2min * (6) Where: r pc,min is the minimum pore throat radius of high-pressure mercury injection, with the dimension of μm; T 2( r pc,min ) is the transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection, with the dimension of ms; T 2min * for T 2( r pc,min ), that is, the lower limit of the transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection; From the minimum transverse relaxation timeT 2min Starting from the transverse relaxation time T 2, there must be a certain transverse relaxation time to satisfy the minimum pore throat radius of high-pressure mercury injection. r pc,min The constraint condition ②, then the transverse relaxation time at this moment is T 2min * .

[0015] Minimum pore throat radius of high pressure mercury injection r pc,min and its corresponding T 2( r pc,min ) satisfies formula (5), that is, T 2( r pc,min ) = r pc,min n / C n ; Substitute it into formula (6) and derive the conversion coefficient C Upper limit: C ≤ r pc,min / ( T 2min * ) 1 / n (7).

[0016] Similarly, according to the “NMR pore throat radius r T2 The distribution includes the pore throat radius of high-pressure mercury injection r pc The objective fact of "distribution" is that the maximum pore throat radius of high-pressure mercury injection r pc,max Two constraints must be met: ① Maximum pore throat radius of NMR ≥ maximum pore throat radius of high pressure mercury injection r pc,max ; ② From any high-pressure mercury injection pore throat radius r pc Maximum pore throat radius for high pressure mercury injection r pc,max The cumulative volume proportion is ≤ from any high-pressure mercury injection pore throat radius r pc The corresponding transverse relaxation time to the maximum transverse relaxation time T 2max The cumulative volume share of .

[0017] Since the measurement results of high-pressure mercury injection and nuclear magnetic resonance are both discrete data points, the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection has a lower limit: T 2( r pc,max )≤ T 2max * (8) Where: r pc,max is the maximum pore throat radius of high-pressure mercury injection, with the dimension of μm; T 2( r pc,max ) is the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection, with the dimension of ms; T 2max * for T 2( r pc,max ), that is, the upper limit of the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection; From the maximum transverse relaxation time T 2max Starting from the transverse relaxation time T 2 decreases, there must be a certain transverse relaxation time to satisfy the maximum pore throat radius of high-pressure mercury injection. r pc,max The constraint condition ②, then the transverse relaxation time at this moment is T 2max * .

[0018] Maximum pore throat radius of high pressure mercury injection r pc,max and its corresponding T 2( r pc,max ) satisfy formula (5), that is, T 2( r pc,max )= r pc,max n / C n ; Substitute it into formula (8) and derive the conversion coefficient C The lower limit is: C ≥ r pc,max / ( T 2max * ) 1 / n (9).

[0019] According to equations (7) and (9), the conversion coefficient is establishedC The value range of is: r pc,max / ( T 2max * ) 1 / n ≤ C ≤ r pc,min / ( T 2min * ) 1 / n (10).

[0020] In formula (10), the conversion coefficient C The upper and lower limits contain the power index n , and the power index n is an unknown parameter, so the parameter interval [ r pc,max / ( T 2max * ) 1 / n , r pc,min / ( T 2min * ) 1 / n ] Verify the conversion coefficients obtained by other methods C When the value is reasonable, it is necessary n The value is known. Therefore, we also need to establish the power index n Method for judging the rationality of .

[0021] According to formula (10), the power index n Satisfies the following inequality: r pc,max / ( T 2max * ) 1 / n ≤ r pc,min / ( T 2min * ) 1 / n (11) By deducing formula (11), we can get the power exponent n Upper limit: n ≤ln( T 2max * / T 2min * ) / ln( r pc,max / r pc,min ) (12) According to the basic principle of nuclear magnetic resonance, whether the linear correlation or the power function relationship is used, the pore throat radius r and transverse relaxation time T 2 should satisfy a positive correlation, that is, the pore throat radius r With the transverse relaxation time T 2 increases. Formula (5) is a power function relationship. r and transverse relaxation time T 2 need to satisfy a positive correlation, so it is required n >0. It should be noted that the power function relationship also requires the conversion coefficient C >0, but according to formula (10) we can see that the conversion coefficient C >0 must be true.

[0022] According to formula (12) and n >0, the power exponent of the power function relationship is established n The value range of is: 0< n ≤ln ( T 2max * / T 2min * ) / ln ( r pc,max / r pc,min ) (13) According to formula (13), the power exponent n The value range of (0, ln( T 2max * / T 2min * ) / ln( r pc,max / r pc,min )] is a half-open, half-closed interval, which can be used to verify the power index obtained by other methods n The rationality of the value.

[0023] Combining equations (10) and (13) to evaluate the conversion coefficient C Sum power index n , we can judge the rationality of the power function relationship obtained by other methods: if the conversion coefficient obtained by other methods C The value satisfies formula (10), and the power exponent nIf the value satisfies formula (13), it means that the power function relationship obtained by other methods is reasonable, otherwise it is unreasonable.

[0024] The technical effects of the present invention are: The present invention is based on the transverse relaxation time T 2 and pore throat radius r The power function relationship between them is used to construct the conversion coefficients using the minimum pore throat radius of high-pressure mercury injection and its corresponding transverse relaxation time, as well as the maximum pore throat radius of high-pressure mercury injection and its corresponding transverse relaxation time. C Sum power index n The value range of can be used to judge the rationality of the power function relationship obtained by other methods, and has high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is the cumulative volume percentage distribution curve of high-pressure mercury injection pore throat radius.

[0026] Figure 2 is the cumulative volume share distribution curve of the transverse relaxation time.

[0027] Figure 3 for T 2max M =816.26ms, the cumulative volume share distribution curve of the NMR pore throat radius.

[0028] Figure 4 for Figure 1 and Figure 3 .

[0029] Figure 5 for T 2max M =29.72ms, the cumulative volume share distribution curve of the NMR pore throat radius.

[0030] Figure 6 for Figure 1 and Figure 5 . DETAILED DESCRIPTION

[0031] A method for judging the rationality of a nuclear magnetic resonance power function relationship is as follows: Step 1: Obtain the high-pressure mercury injection pore throat radius through high-pressure mercury injection experiment r pc The distribution data of high-pressure mercury injection can be used to obtain the minimum pore throat radius r pc,min , Maximum pore throat radius of high pressure mercury injection r pc,max and the volume proportion of the minimum pore throat radius of high-pressure mercury injection γ ( r pc,min ); Step 2: Obtain transverse relaxation time by NMR experiment T 2 distribution data, and then obtain the maximum transverse relaxation time T 2max and minimum transverse relaxation time T 2min ; Step 3: Obtain the upper limit of the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection T 2max * The lower limit of transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection T 2min * ; The specific process is: (1) Define the first intermediate parameter T 2max M and the second intermediate parameter T 2min M ; (2) T 2max M = T 2max Start using r T2 =( r pc,max / T 2max M )× T 2 Nuclear Magnetic Resonance T 2Convert to r T2 ; Construct the first judgment condition: r T2 Are all the cumulative volume share distribution curves located in r pc The right side of the cumulative volume proportion distribution curve; if the first judgment condition is met, the current T 2max M As T 2max * Otherwise, reduce T 2max M The value taking starts again until the first judgment condition is met; (3) T 2min M = T 2minStart, if you meet the " r pc,max / T 2max * ≤ r pc,min / T 2min M "and" γ ( r pc,min )≤From T 2min arrive T 2min M The second judgment condition of "the cumulative volume proportion of T 2min M As T 2min * Otherwise, increase T 2min M The value taking starts again until the second judgment condition is met; Step 4: Construct the power index n The value range of (0, ln( T 2max * / T 2min * ) / ln( r pc,max / r pc,min )] and conversion factor C The value range of [ r pc,max / ( T 2max * ) 1 / n , r pc,min / ( T 2min * ) 1 / n ]; Step 5: If the power index is obtained by other methods n and conversion factor C All of them fall into the above value range, which means that the power index obtained by other methods n and conversion factor C The value of is reasonable, otherwise it is unreasonable.

[0032] Specific application cases A method for judging the rationality of a nuclear magnetic resonance power function relationship is as follows: High-pressure mercury injection pore throat radius determined by high-pressure mercury injection experiments r pc The distribution data of is shown in Table 1; the transverse relaxation time measured by NMR experiment T The distribution data of 2 is shown in Table 2; Table 1 High-pressure mercury injection pore throat radius r pc Distribution data ; Table 2 Transverse relaxation time T 2 Distribution data .

[0033] Step 1: According to the data in Table 1, the maximum pore throat radius of high-pressure mercury injection is obtained. r pc,max =0.1508 μm, minimum pore throat radius of high-pressure mercury injection r pc,min =0.0036 μm; Volume proportion of the minimum pore throat radius of high-pressure mercury injection γ ( r pc,min ) = 0.24%; Draw the cumulative volume distribution curve of high-pressure mercury injection pore throat radius ( Figure 1 ).

[0034] Step 2: According to the data in Table 2, the maximum transverse relaxation time is obtained. T 2max =816.26ms, minimum transverse relaxation time T 2min = 0.04ms; draw the cumulative volume distribution curve of transverse relaxation time ( Figure 2 ).

[0035] Step 3: Obtain the upper limit of the transverse relaxation time corresponding to the maximum pore throat radius of high-pressure mercury injection T 2max * The lower limit of transverse relaxation time corresponding to the minimum pore throat radius of high-pressure mercury injection T 2min * ; The specific process is: (1) Define the first intermediate parameter T 2max M and the second intermediate parameter T 2min M ; (2) T 2max M = T2max =816.26ms, using r T2 =( r pc,max / T 2max M )× T 2=0.000184745× T 2. NMR T 2Conversion to NMR pore throat radius r T2 , the conversion results are shown in Table 3; Table 3 T 2max M =816.26ms, NMR pore throat radius r T2 Data ; According to the data in Table 3, the T 2max M =816.26ms NMR pore throat radius cumulative volume distribution curve ( Figure 3 ); let the pore throat radius r = NMR pore throat radius r T2 , and the pore throat radius r = High-pressure mercury injection pore throat radius r pc ,Will Figure 1 and Figure 3 Plotted onto a graph ( Figure 4 ) for comparison; T 2max M = T 2max =816.26ms, r T2 The cumulative volume share distribution curves are not all located in r pc If the cumulative volume ratio distribution curve is on the right side, the first judgment condition is not met; therefore, reduce T 2max M Get value; Until T 2max M =29.72ms, using r T2 =( r pc,max / T 2maxM )× T 2 = 0.005074024× T 2. NMR T 2Conversion to NMR pore throat radius r T2 , the conversion results are shown in Table 4; Table 4 T 2max M =29.72ms, NMR pore throat radius r T2 Data According to the data in Table 4, the T 2max M =29.72ms NMR pore throat radius cumulative volume distribution curve ( Figure 5 ); let the pore throat radius r = NMR pore throat radius r T2 , and the pore throat radius r = High-pressure mercury injection pore throat radius r pc ,Will Figure 1 and Figure 5 Plotted onto a graph ( Figure 6 ) for comparison; when T 2max M =29.72ms, r T2 The cumulative volume share distribution curves are all located in r pc If the cumulative volume proportion distribution curve is on the right side, the first judgment condition is met; then T 2max * = T 2max M =29.72ms; (3) T 2min M = T 2min = 0.04ms, according to the data in Table 2, from T 2min arrive T 2min M Cumulative volume fraction = 0.006% (transverse relaxation time T 2 is the volume proportion at 0.04ms), and the second judgment condition is judged. The result shows: r pc,max / T 2max * = 0.005074024 μm / ms, r pc,min / T 2min M =0.09μm / ms, satisfying the r pc,max / T 2max * ≤ r pc,min / T 2min M ”; γ ( r pc,min ) = 0.24%, from T 2min arrive T 2min M The cumulative volume share = 0.006%, which does not meet the " γ ( r pc,min )≤From T 2min arrive T 2min M The second judgment condition is not met; therefore, the cumulative volume proportion of T 2min M Get value; Until T 2min M =0.12ms, r pc,min / T 2min M = 0.03μm / ms, satisfying the r pc,max / T 2max * ≤ r pc,min / T 2min M ”; γ ( r pc,min ) = 0.24%, from T 2min arriveT 2min M The cumulative volume share = 0.344%, satisfying the γ ( r pc,min )≤From T 2min arrive T 2min M The second judgment condition is met; therefore T 2min * = T 2min M =0.12ms.

[0036] Step 4: Create the power index n and conversion factor C The value range of ; the specific process is: ln( T 2max * / T 2min * ) / ln( r pc,max / r pc,min )=1.48, so the power exponent n The value range of is (0, 1.48]; r pc,max / ( T 2max * ) 1 / n =0.1508 / (29.72) 1 / n , r pc,min / ( T 2min * ) 1 / n = 0.0036 / (0.12) 1 / n , so the conversion factor C The value range is [0.1508 / (29.72) 1 / n , 0.0036 / (0.12) 1 / n ].

[0037] Step 5: If the power index is obtained by other methods n Located at (0, 1.48] and the conversion factor C Located at [0.1508 / (29.72) 1 / n , 0.0036 / (0.12) 1 / n], it means that the power index obtained by this method n and conversion factor C The value of is reasonable, otherwise it is unreasonable.

Claims

1. A method for judging the rationality of a nuclear magnetic resonance power function relationship, characterized in that: Here’s how: Build n The value range of (0, ln( T 2max * / T 2min * ) / ln( r pc,max / r pc,min )]; Build C The value range of [ r pc,max / ( T 2max * ) 1 / n , r pc,min / ( T 2min * ) 1 / n ]; If obtained by other means n Value and C If the values ​​fall within the above range, it means that the n Value and C The value is reasonable, otherwise it is unreasonable; in, T 2max * and T 2min * The specific process of obtaining is: (1) Definition T 2max M and T 2min M ; (2) T 2max M = T 2max Start using r T2 =( r pc,max / T 2max M )× T 2 Nuclear Magnetic Resonance T 2Convert to r T2 ; Construct the first judgment condition: r T2 Are all the cumulative volume share distribution curves located in r pc The right side of the cumulative volume proportion distribution curve; if the first judgment condition is met, the current T 2max M As T 2max * Otherwise, reduce T 2max M The value taking starts again until the first judgment condition is met; (3) T 2min M = T 2min Start by building the second judgment condition: r pc,max / T 2max * ≤ r pc,min / T 2min M "and" γ ( r pc,min )≤From T 2min arrive T 2min M If the second judgment condition is met, the current T 2min M As T 2min * Otherwise, increase T 2min M The value taking starts again until the second judgment condition is met; in, C is the conversion coefficient, the dimension is μm / ms; n is the power exponent, dimensionless; r pc,max is the maximum pore throat radius of high-pressure mercury injection, with the dimension of μm; r pc,min is the minimum pore throat radius of high-pressure mercury injection, with the dimension of μm; T 2max * for r pc,max The corresponding upper limit of the transverse relaxation time is in ms; T 2min * for r pc,min The corresponding lower limit of transverse relaxation time is in ms; T 2max M is the first intermediate parameter, with the dimension of ms; T 2min M is the second intermediate parameter, with the dimension of ms; T 2 is the transverse relaxation time, with the dimension of ms; T 2max is the maximum transverse relaxation time, with the dimension of ms; T 2min is the minimum transverse relaxation time, with the dimension of ms; r T2 is the NMR pore throat radius, dimension is μm; r pc is the high-pressure mercury injection pore throat radius, with the dimension of μm; γ ( r pc,min )for r pc,min The volume percentage of , dimensionless.

2. The method for judging the rationality of the nuclear magnetic resonance power function relationship according to claim 1, characterized in that: Said r pc , r pc,max , r pc,min and γ ( r pc,min ) were obtained through high-pressure mercury injection experiments.

3. The method for judging the rationality of the nuclear magnetic resonance power function relationship according to claim 1, characterized in that: Said T 2max and T 2min All were obtained through nuclear magnetic resonance experiments.

4. The method for judging the rationality of the nuclear magnetic resonance power function relationship according to claim 1, characterized in that: Also includes reducing T 2max M When taking the value, the transverse relaxation time measured by NMR experiment is T 2 The distribution data of is correspondingly reduced; Increase T 2min M When taking the value, the transverse relaxation time measured by NMR experiment is T 2 The distribution data increases accordingly.

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