Rock density prediction method considering stratum shale content

Abstract

The invention discloses a rock density prediction method considering stratum shale content, and relates to the technical field of determination of stratum rock density through petroleum drilling and completion calculation, and the rock density prediction method comprises the following steps: S1, obtaining the shale content of a target stratum by using natural gamma of well logging information of drilled wells of the target stratum; s2, obtaining the rock density of the target stratum containing an undetermined coefficient by using the shale content of the target stratum and the logging longitudinal wave time difference; s3, correcting the rock density undetermined coefficient of the target stratum by using a least square method to obtain a rock density prediction method considering the shale content of the stratum; and S4, predicting the rock density of the target stratum by using a rock density prediction method. The stratum rock density is predicted only through the logging longitudinal wave time difference and the shale content, the density prediction precision is improved, meanwhile, the method has the advantages of being simple and easy to use, and the method can be used for calculating and determining the stratum rock density in the technical field of petroleum drilling and completion.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil drilling and completion calculation determining formation rock density, and more particularly to a rock density prediction method considering formation shale content. BACKGROUND

[0002] In oil exploration and development, formation density is a necessary parameter for rock physics analysis, rock mechanics parameters, rock physical property analysis and ground stress calculation. Formation density is usually obtained through density logging, but for some well sections or formations, density logging is not carried out, and rock density needs to be predicted by other logging parameters. The most commonly used method is Gardner's empirical formula using logging compressional wave time to predict rock density, but this formula predicts high density for pure sandstone formation and low density for pure mudstone formation. In view of the problem that Gardner's empirical formula is prone to errors when used in sand-shale interbedded complex formations, Castagna (1985), Ma Zhonggao (2005) and others established an empirical formula of density and compressional wave, shear wave velocity based on Gardner's empirical formula. However, due to the many influencing factors of shear wave measurement and the difficulty of obtaining it, conventional logging is difficult to obtain shear wave time, and although the density prediction method based on compressional wave and shear wave velocity has relatively high reliability, its application is limited.

[0003] Gardner's empirical formula also shows that density is closely related to formation lithology, and a more accurate prediction result can be obtained by establishing an empirical relationship between density and compressional wave velocity of different lithologies. However, lithology identification also needs to rely on rich logging data, and if there is an error in lithology identification, it will be difficult to obtain accurate and reliable density prediction. Formation lithology is closely related to the shale content and particle composition of the rock itself, and the rock density is also a reflection of the composition of various minerals in the rock. Therefore, rock density prediction considering the influence of shale content can help improve the reliability and accuracy of density prediction, and can also reflect the influence of different lithologies on density. SUMMARY

[0004] In order to overcome the defects in the prior art, the present application discloses a rock density prediction method considering formation shale content, so as to solve the problems in the prior art. In the present application, the natural gamma of the drilled well logging data of the target formation is used to obtain the shale content of the target formation; then the shale content of the target formation and the logging compressional wave time difference are used to obtain the rock density of the target formation containing undetermined coefficients; then the least square method is used to determine the undetermined coefficient of the rock density of the target formation, so as to obtain the rock density prediction method considering the formation shale content; finally, the rock density prediction method is used to predict the rock density of the target formation. The present application only needs to predict the formation rock density through the logging compressional wave time difference and the shale content, which helps to improve the density prediction accuracy and has the characteristics of simplicity and easy use. The method can be used in the technical field of oil drilling and completion to calculate and determine the density of the formation rock.

[0005] In order to achieve the above object, the technical scheme adopted by the present application is:

[0006] A rock density prediction method considering formation shale content, comprising the following steps:

[0007] I. Formation shale content calculation

[0008] S1, the natural gamma of the drilled well logging data of the target formation is used to obtain the shale content of the target formation;

[0009] Preferably, the step S1 comprises:

[0010]

[0011]

[0012] Wherein, SH is the relative value of natural gamma, dimensionless; GR is the measured natural gamma of logging, GAPI; GR max , GR min is the maximum and minimum natural gamma of the target formation, GAPI; V SH is the formation shale content, percentage; GCUR is the HILCHI index, 3.7 for new formation and 2 for old formation.

[0013] II. Target formation density calculation

[0014] S2, the shale content of the target formation and the logging compressional wave time difference are used to obtain the rock density of the target formation containing undetermined coefficients;

[0015] Preferably, in the step S2, the rock density of the target formation is:

[0016]

[0017] Wherein, p b is the rock density, g / cm3 ; Δt p is the logging compressional wave slowness, us / ft; a, b, c are undetermined coefficients, which are determined by fitting regression of adjacent well logging data; V SH is the shale content of the formation, percentage.

[0018] III. Correcting the undetermined coefficients of the formula

[0019] S3, using the least square method, correcting the undetermined coefficients of the rock density of the target formation, to obtain a rock density prediction method considering the shale content of the formation;

[0020] Preferably, in the step S3, the undetermined coefficients of the rock density of the target formation are determined by fitting regression of adjacent well logging data and the least square method, to obtain a rock density prediction method containing only two parameters of the logging compressional wave slowness and the shale content of the formation.

[0021] Preferably, the step S3 comprises the following steps:

[0022] S31, taking natural logarithm on both sides of the calculation formula of the rock density of the target formation;

[0023] Preferably, the step S31 comprises:

[0024]

[0025] wherein, ln represents taking natural logarithm; ρ b is the rock density, g / cm 3 ; Δt p is the logging compressional wave slowness, us / ft; a, b, c are undetermined coefficients; V SH is the shale content of the formation, percentage.

[0026] S32, using the letters of independent variables and dependent variables to perform substitution processing on part of the items in the calculation formula after taking natural logarithm;

[0027] Preferably, the substitution processing in the step S32 comprises:

[0028]

[0029] wherein, y represents the dependent variable after substitution, x1 and x2 represent the independent variables after substitution.

[0030] S33, substituting the independent variables and dependent variables after substitution into the calculation formula after taking natural logarithm on both sides of the step S31, to obtain a substitution formula;

[0031] Preferably, in the step S33, the substitution formula is:

[0032] y = ln a + bx1 + cx2;

[0033] Wherein, y represents the dependent variable after substitution, x1 and x2 represent the independent variables after substitution.

[0034] S34, according to the well logging data of the drilled well, the dependent variable and the independent variable in the substitution formula are calculated.

[0035] Preferably, the step S34 comprises:

[0036]

[0037] Wherein, y1, y2, …, y n are the natural logarithms of n calculated densities; x 11 , x 12 , …, x 1n are n corresponding independent variables x1; x 21 , x 22 , …, x 2n are n corresponding independent variables x2.

[0038] S35, according to the least square principle, a group of undetermined coefficients are found in the calculation of step S34 to make the multiple regression residual sum of squares minimum.

[0039] Preferably, the step S35 comprises: according to the least square principle, a group of undetermined coefficients lna, b, c are found in the calculation of step S34 to make the multiple regression residual sum of squares minimum.

[0040] Preferably, in the step S35, the multiple regression residual sum of squares is:

[0041]

[0042] Wherein, M is the multiple regression residual sum of squares; y i is the natural logarithm lnρ b，i of the i-th calculated density; is the natural logarithm of the i-th corresponding logging measured density

[0043] S36, the found undetermined coefficients are substituted into the calculation formula of the rock density of the target formation in the step S2 to obtain a rock density prediction formula considering the formation shale content.

[0044] Four, rock density prediction

[0045] S4, the rock density of the target formation is predicted by using the rock density prediction method.

[0046] The beneficial effects of the present application are:

[0047] The rock density prediction method considering formation shale content provided by the application obtains the formation shale content of a target formation by using the natural gamma of the well logging data of the drilled well of the target formation, obtains the rock density of the target formation containing undetermined coefficients by using the formation shale content of the target formation and the logging compressional wave time difference, corrects the undetermined coefficient of the rock density of the target formation by using the least square method to obtain the rock density prediction method considering the formation shale content, and finally predicts the rock density of the target formation by using the rock density prediction method. BRIEF DESCRIPTION OF DRAWINGS

[0048] Figure 1 The steps of the rock density prediction method considering formation shale content of the application;

[0049] Figure 2 The rock density prediction example result considering formation shale content of the application. DETAILED DESCRIPTION

[0050] The concept, specific structure and generated technical effects of the application will be described clearly and completely in combination with the embodiments and the drawings to fully understand the purpose, features and effects of the application.

[0051] Embodiment 1

[0052] The rock density prediction method considering formation shale content, as shown in Figure 1 , comprises the following steps:

[0053] S1, obtaining the formation shale content of a target formation by using the natural gamma of the well logging data of the drilled well of the target formation;

[0054] S2, obtaining the rock density of the target formation containing undetermined coefficients by using the formation shale content of the target formation and the logging compressional wave time difference;

[0055] S3, obtaining the rock density prediction method considering formation shale content by correcting the undetermined coefficient of the rock density of the target formation by using the least square method;

[0056] S4, predicting the rock density of the target formation by using the rock density prediction method.

[0057] Embodiment 2

[0058] This embodiment is further described on the basis of the embodiment 1. In the step S1, for the target formation, the formation shale content V is calculated according to the natural gamma of the well logging data of the drilled well. SH .

[0059]

[0060]

[0061] Wherein, SH is the natural gamma relative value, dimensionless; GR is the measured natural gamma in well logging, GAPI; GR max , GR min is the maximum and minimum natural gamma of the target formation, GAPI; V SH is the formation shale content, percentage; GCUR is the Hilchie index, taking 3.7 for new formation and 2 for old formation.

[0062] Example 3

[0063] This example is based on example 2, and further describes the S2 step. In the S2 step, the formation density is calculated by using the longitudinal wave time difference and the shale content V SH The following formula is used to calculate the density of the target formation:

[0064]

[0065] Wherein, p b is the rock density, g / cm 3 ; At p is the logging longitudinal wave time difference, us / ft; a, b, c are the undetermined coefficients, which are determined by fitting regression of the logging data of the adjacent well; V SH is the formation shale content, percentage.

[0066] Example 4

[0067] This example is based on example 3, and further describes the S3 step. In the S3 step, the undetermined coefficients of the rock density of the target formation are determined by fitting regression and least square method of the logging data of the adjacent well, and a rock density prediction method containing only two parameters of the logging longitudinal wave time difference and the formation shale content is obtained. The S3 step includes the following steps:

[0068] S31, taking the natural logarithm of both sides of the calculation formula of the rock density of the target formation;

[0069] S32, using the independent variable and dependent variable letters, performing substitution processing on part of the items in the calculation formula after taking the natural logarithm;

[0070] S33, substituting the independent variable and dependent variable letters after substitution into the calculation formula after taking the natural logarithm of both sides of the S31 step, to obtain a substitution formula;

[0071] S34, calculating the independent variable and the dependent variable in the substitution formula according to the n measured density values of the logging data of the drilled well;

[0072] S35, according to the least square principle, finding a set of undetermined coefficients in the calculation of the S34 step to make the residual sum of squares of the multiple regression minimum;

[0073] S36, the found pending coefficient is substituted into the calculation formula of the target formation rock density in the S2 step to obtain a rock density prediction formula considering the formation shale content.

[0074] Specifically as follows:

[0075] In the S3 step, the natural logarithm of both sides of the formula in Example 3 is taken to obtain:

[0076]

[0077] The above formula is substituted into the formula after taking the natural logarithm of both sides to obtain:

[0078]

[0079] The above formula is substituted into the formula after taking the natural logarithm of both sides to obtain:

[0080] y = ln a + bx1 + cx2;

[0081] According to the n measured density values of the drilled well logging data, the formula for calculating y and two independent variables x1 and x2 is as follows:

[0082]

[0083] wherein y1, y2, …, y n are the natural logarithms of n calculated densities; x 11 , x 12 , …, x 1n are n corresponding independent variables x1; x 21 , x 22 , …, x 2n are n corresponding independent variables x2.

[0084] According to the least square principle, a set of coefficients ln a, b, c is found to make the multiple regression residual sum of squares M minimum, and the calculation formula of M is as follows:

[0085]

[0086] wherein M is the multiple regression residual sum of squares; y i is the natural logarithm ln p b，i of the i-th calculated density; is the natural logarithm ln p

[0087] For a certain rock density prediction formula considering the formation shale content, a set of coefficients ln a = -1.6539, b = 0.2833, c = 0.08136 obtained after the above analysis is adopted.

[0088] The numerical values of ln a, b, c are brought into the formula in Example 3, and a certain example prediction formula of rock density prediction considering formation shale content is obtained:

[0089]

[0090] Wherein, p b is the rock density, g / cm 3 ; Δt p is the logging compressional wave slowness, us / ft; V SH is the formation shale content, percentage.

[0091] Figure 2 A certain example result of rock density prediction considering formation shale content is shown, and it can be known from comparison that the rock density prediction formula considering formation shale content established by the present application is more in line with the measured density than the Gardner empirical formula, and the density prediction precision is significantly improved. In the above certain example prediction formula, only two parameters of logging compressional wave slowness and formation shale content are contained, and therefore the present application can only predict the formation rock density through the logging compressional wave slowness and the formation shale content, which is helpful to improve the density prediction precision, and has the characteristics of being simple and easy to use.

[0092] The embodiments of the present application are specifically described above, but the present application is not limited to the above examples, and those skilled in the art can make various equivalent modifications or replacements without departing from the spirit of the present application, and these equivalent modifications or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A method of rock density prediction taking into account shale content of a formation, characterized in that, The method comprises the following steps: S1, obtaining the shale content of the target formation by using the natural gamma ray of the well logging data of the drilled well in the target formation; S2, obtaining the rock density of the target formation containing undetermined coefficients by using the shale content of the target formation and the logging compressional wave time difference; S3, correcting the undetermined coefficients of the rock density of the target formation by using the least square method to obtain a rock density prediction method considering the shale content of the formation; S4, predicting the rock density of the target formation by using the rock density prediction method.

2. The rock density prediction method of claim 1, wherein, In the step S3, the undetermined coefficients of the rock density of the target formation are determined by using the well logging data fitting regression and the least square method to obtain the rock density prediction method containing only two parameters of the logging compressional wave time difference and the shale content of the formation.

3. The method of predicting rock density as claimed in claim 1, wherein, The step S3 comprises the following steps: S31, taking the natural logarithm of both sides of the calculation formula of the rock density of the target formation; S32, using the independent variable and the dependent variable letters to perform substitution processing on some terms in the calculation formula after taking the natural logarithm; S33, substituting the independent variable and the dependent variable letters after the substitution into the calculation formula after taking the natural logarithm of both sides in the step S31 to obtain a substitution formula; S34, calculating the dependent variable and the independent variable in the substitution formula according to the n measured density values of the well logging data of the drilled well; S35, finding a set of undetermined coefficients in the calculation in the step S34 according to the least square principle to make the residual sum of squares of the multiple regression minimum; S36, substituting the found undetermined coefficients into the calculation formula of the rock density of the target formation in the step S2 to obtain a rock density prediction formula considering the shale content of the formation.

4. The method of predicting rock density as claimed in claim 1, wherein, The step S1 comprises: Where SH is the relative value of natural gamma, dimensionless; GR is the measured natural gamma in well logging, GAPI; GR max GR min For the target formation's maximum and minimum natural gamma, GAPI; V SH The value represents the mud content of the formation, as a percentage; GCUR is the Hillch index, with 3.7 for new formations and 2 for old formations.

5. The method of predicting rock density as recited in claim 1, wherein, In the step S2, the rock density of the target formation is: wherein, p b is the rock density, g / cm 3 ; Δt p is the logging longitudinal wave time, us / ft; a, b, c are respectively undetermined coefficients, which are determined by fitting regression through adjacent well logging data; V SH is the formation shale content, percentage.

6. The method of predicting rock density as claimed in claim 3, wherein, The step S31 comprises: wherein, ln represents taking natural logarithm; p b is the rock density, g / cm 3 ; Δt p is the logging longitudinal wave time, us / ft; a, b, c are undetermined coefficients respectively; V SH is the formation shale content, percentage.

7. The method of predicting rock density as claimed in claim 6, wherein, The substitution processing in the step S32 comprises: Wherein, y represents the dependent variable after the substitution, x1 and x2 represent the independent variables after the substitution.

8. The method of predicting rock density as claimed in claim 7, wherein, In the step S33, the substitution formula is: y = lna + bx1 + cx2; Wherein, y represents the dependent variable after the substitution, x1 and x2 represent the independent variables after the substitution.

9. The method of predicting rock density as claimed in claim 8, wherein, The step S34 comprises: where y1, y2,..., yn are the n dependent variables; x1, x2,..., xn are the n independent variables; and f1, f2,..., fn are the n functions. n ln is the natural logarithm of the n computed densities; x 11 , x 12 ,..., x 1n are the n corresponding independent variables x1; x 21 , x 22 ,..., x 2n are the n corresponding independent variables x2.

10. The method of predicting rock density as claimed in claim 9, wherein, The step S35 comprises: finding a set of undetermined coefficients lna, b, c in the calculation in the step S34 according to the least square principle to make the residual sum of squares of the multiple regression minimum; wherein, the residual sum of squares of the multiple regression is: where M is the multiple regression residual sum of squares; y i ln p is the natural logarithm of the i-th calculated density b，i ; ln p is the natural logarithm of the i-th calculated density

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