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In the past, most of the studies for compressional velocities are based on experimental measurements, which lack the support of field data. The purpose of this study is to estimate the compressional velocities based on well log data of delta front subfacies of Lower Tertiary ages of Ji-Dong oil field, China. At initial stage, we have chosen the well log parameters (effect factors) which strongly influence on compressional velocities and established a new modified equation for compressional velocities, which is based on these effect factors. Then Gardner, De-hua Han and this newly established equation were utilized to calculate the compressional velocities in each well. Finally, Least-square regression was carried out to check the fitting of each equation. Regression results clearly indicate that our purposed equation shows better fitting as compared to Gardner and De-hua Han equations.

Accurate and precise calculation of acoustic velocities can effectively improve the accuracy of processing, inversion and interpretation of seismic data. Different methods for the calculation of acoustic velocities have been studied by a number of scientists.

Wyllie et al. [

Based on the time-average equation, De-hua Han et al. [

where

Gardner et al. [

where ^{3}) is the density,

Equations (1) and (2), which are based on experimental measurements and statistics, have its own limitations. First, there are differences between experimental and subsurface circumstances, such as confining pressure, pore pressure, temperature, and so on. Equations (1) and (2) are purely based on experimental data and do not show good matching with the field measured data. Second, core samples are obtained from different depths and only contain information about those particular interval, not about the whole interval.

Thus, because of the limitations of experimental measurements, this study is based on field well logs, which record continuous variations of the target formations and investigate systematically the calculation method of compressional velocities in delta front subfacies of Lower Tertiary ages of Ji-Dong Oil field.

First we will find the influence factors of compressional velocities and then combine them in equation format, then we use least-squares regression to fit compressional velocities of all wells in the target formations and compare correlation coefficient with Equations (1) and (2).

The target formations can be divided into four sub intervals (Es1, Ed3, Ed2, and Ed1) from bottom to top respectively. Es1 (thickness ranges from 172 m to 455 m) is mainly composed of grey shale, light grey packsand, and light grey siltstone. Ed3 (thickness ranges from 275 m to 487 m) is mainly composed of dark grey shale within grey packsand and siltstone. Ed2 (thickness ranges from 287 m to 540 m) is composed of grey shale within packsand and siltstone, whereas Ed1 (thickness ranges from 230 m to 520 m) is mainly composed of packsand, siltstone, and shale.

Well logs of 19 wells are used as samples. Well names, target formations, type of well logs, and true vertical depths are listed in

No. | Well name | Target formation | Well logs | TVD (m) |
---|---|---|---|---|

1 | G37x3 | Ed1, Ed2, Ed3, Es1 | V_{p}\DEN\GR | 2435.1 - 4254.4 |

2 | GS1 | Ed1, Ed2, Ed3, Es1 | V_{p}\DEN\GR | 2512.0 - 4570.0 |

3 | L166x1 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2493.8 - 3918.2 |

4 | NP2-52 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2499.1 - 3613.9 |

5 | NP2-53 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2548.0 - 3412.0 |

6 | NP2-58 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2532.0 - 3724.5 |

7 | NP4-21 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2407.0 - 3982.7 |

8 | NP4-31 | Ed1, Ed2 | V_{p}\DEN\GR | 2583.8 - 3461.8 |

9 | NP4-32 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2553.3 - 3748.2 |

10 | NP4-33 | Ed1, Ed2 | V_{p}\DEN\GR | 2605.3 - 3582.9 |

11 | NP4-38 | Ed1, Ed2 | V_{p}\DEN\GR | 2500.7 - 3619.8 |

12 | NP4-39 | Ed1, Ed2 | V_{p}\DEN\GR | 2664.6 - 3573.5 |

13 | NP4-65 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2930.0 - 3935.0 |

14 | NP4-66 | Ed1, Ed2, Ed3, Es1 | V_{p}\DEN\GR | 2528.6 - 4076.8 |

15 | NP4-68 | Ed1, Ed2, Ed3, Es1 | V_{p}\DEN\GR | 2619.3 - 4033.4 |

16 | NP43-4704 | Ed1, Ed2, Ed3, Es1 | V_{p}\DEN\GR | 2547.8 - 4125.5 |

17 | NP43-4988 | Ed1, Ed2 | V_{p}\DEN\GR | 2719.6 - 3480.3 |

18 | NP403x1 | Ed1, Ed2, Ed3 | V_{p}\DEN\GR | 2626.4 - 3487.5 |

19 | NP403x2 | Ed1, Ed2 | V_{p}\DEN\GR | 2801.3 - 3712.1 |

V_{p}: P-wave velocity, km/s; DEN: Density, g/cm^{3}; GR: Natural Gamma, API; TVD: True Vertical Depth, m.

formations except Es1 and Ed3. Well logs of compressional velocity, density, and natural gamma are available in all wells. Locations of all these 19 wells are shown in

In this paper, we proposed a new equation to calculate compressional velocities, and compared its correlation coefficient with Equations (1) and (2). The parameters used in the new equation and Equations (1) and (2) have been calculated as follow.

Natural gamma ray log was used to calculate clay content [

where,

No. | Well name | Maximum(API) | Minimum(API) |
---|---|---|---|

1 | G37x3 | 160.4 | 25.7 |

2 | GS1 | 148.0 | 50.5 |

3 | L166x1 | 170.1 | 17.8 |

4 | NP2-52 | 159.8 | 36.0 |

5 | NP2-53 | 153.6 | 45.2 |

6 | NP2-58 | 154.2 | 48.3 |

7 | NP4-21 | 147.3 | 30.5 |

8 | NP4-31 | 179.6 | 49.7 |

9 | NP4-32 | 154.2 | 47.8 |

10 | NP4-33 | 157.4 | 47.4 |

11 | NP4-38 | 168.1 | 49.2 |

12 | NP4-39 | 159.7 | 41.0 |

13 | NP4-65 | 193.6 | 32.6 |

14 | NP4-66 | 145.2 | 41.8 |

15 | NP4-68 | 148.3 | 51.1 |

16 | NP43-4704 | 148.9 | 52.4 |

17 | NP43-4988 | 168.1 | 44.9 |

18 | NP403x1 | 151.8 | 41.7 |

19 | NP403x2 | 163.5 | 47.7 |

spectively, c is a coefficient which is obtained from core data analysis, which is equal to 3.7 in the Tertiary period and 2 for old formations, we choose 2 in this research, and

Density log was used to calculate the porosity. First, we built up a physical model for the target formation. We supposed that the target formation is comprised of sand, shale, and porosity which is filled with water (

Second, setting up a relationship between porosity and density. We supposed the measured density (

Finally, we combined Equations (5) and (6) in order to obtain the porosity expression as follow

The formation pressure is equal to hydrostatic gradient multiplied by the true vertical depth. This simple relationship can be written as

where

Taking well L166x1 as an example, four cross-plots between compressional velocities versus density, porosity, clay content, and formation pressure have been generated as shown in

In this paper, we hold the opinion that the key of establishing an equation of the compressional velocities depends upon choosing the right influence factors and combining them in equation format, rather than obtaining an equation with constant coefficients from experimental measurements of some specific core samples.

At first, exponential functions were used to fit the compressional velocities, and we analyzed seven equation formats: (1) choosing density as the base; (2) Gardner Equation (Equation (2)); (3) choosing porosity as the base;

(4) choosing density and clay content as the bases; (5) choosing porosity and clay content as the bases; (6) choosing density, clay content, and formation pressure as the bases; (7) choosing porosity, clay content, and formation pressure as the bases. The exponential functions, coefficients, and correlation coefficients (Appendix) are listed in

Then, linear functions were used to fit the compressional velocities, and we also analyzed seven equation formats: 1) choosing porosity as variable; 2) choosing density as variable; 3) choosing porosity and clay content as variables; 4) De-hua Han Equation (Equation (1)); 5) choosing density and clay content as variables; 6) choosing porosity, clay content, and formation pressure as variables; 7) choosing density, clay content, and formation pressure as variables. The linear functions, coefficients, and correlation coefficients are listed in

Exponential functions | Coefficients | R | |||
---|---|---|---|---|---|

a | b | c | d | ||

1.47 | 1.02 | 0.4659 | |||

0.4631 | |||||

3.48 | −0.02 | 0.2933 | |||

0.69 | 1.67 | −0.13 | 0.6142 | ||

3.02 | −0.04 | −0.09 | 0.3925 | ||

0.32 | 1.09 | −0.11 | 0.39 | 0.8250 | |

0.65 | −0.03 | −0.09 | 0.45 | 0.7894 |

R: Correlation coefficient.

Linear functions | Coefficients | R | |||
---|---|---|---|---|---|

a | b | c | d | ||

3.92 | −2.19 | 0.4294 | |||

−0.005 | 1.51 | 0.4621 | |||

4.69 | −4.13 | −1.89 | 0.6340 | ||

0.6059 | |||||

−1.94 | 2.50 | −1.67 | 0.6340 | ||

3.01 | −2.68 | −1.45 | 0.04 | 0.8391 | |

−1.29 | 1.63 | −1.30 | 0.04 | 0.8391 |

R: Correlation coefficient.

We conclude from

Equations (1), (2) and (10) were applied to fit the compressional velocities of all wells. The results are listed in

The three equations of

Functions | Coefficients | R | |||
---|---|---|---|---|---|

a | b | c | d | ||

−0.12 | 1.16 | −1.21 | 0.04 | 0.6301 | |

1.83 | 0.77 | 0.3300 | |||

4.42 | −2.15 | −1.57 | 0.4456 |

R: Correlation coefficient.

No. | Well name | |||
---|---|---|---|---|

1 | G37x3 | 0.7426 | 0.5170 | 0.3287 |

2 | GS1 | 0.7992 | 0.4304 | 0.2516 |

3 | L166x1 | 0.8328 | 0.5636 | 0.4628 |

4 | NP2-52 | 0.5486 | 0.4103 | 0.3868 |

5 | NP2-53 | 0.7090 | 0.6606 | 0.5868 |

6 | NP2-58 | 0.5869 | 0.6514 | 0.4607 |

7 | NP4-21 | 0.7814 | 0.3595 | 0.4951 |

8 | NP4-31 | 0.4727 | 0.4358 | 0.4585 |

9 | NP4-32 | 0.5188 | 0.3847 | 0.1171 |

10 | NP4-33 | 0.4778 | 0.5332 | 0.4750 |

11 | NP4-38 | 0.5534 | 0.4462 | 0.4108 |

12 | NP4-39 | 0.2368 | 0.2234 | 0.2372 |

13 | NP4-65 | 0.5429 | 0.5904 | 0.3383 |

14 | NP4-66 | 0.7498 | 0.6967 | 0.5244 |

15 | NP4-68 | 0.5573 | 0.5101 | 0.4322 |

16 | NP43-4704 | 0.3445 | 0.2427 | -0.1645 |

17 | NP43-4988 | 0.4944 | 0.4882 | 0.4657 |

18 | NP403x1 | 0.6491 | 0.5905 | 0.5233 |

19 | NP403x2 | 0.7838 | 0.7956 | 0.6179 |

In the research, we hold the opinion that the key of establishing an equation of the compressional velocities depends upon choosing the right influence factors and combining them in equation format.

The correlation coefficients of the equations for which we have chosen density, clay content, and formation pressure as influence factors are higher than those which depend upon only one, two or three influence factors.

We also found that the fitting results of the compressional velocities by using linear equations are better than the exponential equations for the same influence factors.

Moreover, the fitting results of the compressional velocities through Equation (10) are better than Equations (1) and (2) which are proposed by De-hua Han and Gardner respectively in delta front subfacies of Lower Tertiary ages of Ji-Dong oil field.

Shear-wave velocity is the same important as compressional velocity in processing, inversion and interpretation of seismic data. But it’s expensive to obtain shear-wave velocity in the field and shear-wave data of single well is less than compressional-wave data. In the next step, we are going to transfer our attention to calculate shear-wave velocity.

The authors thank Yanchun Wang and Xueqing Liu for helpful suggestions to start this study. Thanks are also due to Qinghui Mao for collecting well logs of research area. Thanks are also due to Lifang Cheng for extensive reviewing of the final draft.

Feizhou Shi,Yanchun Wang,Xueqing Liu, (2016) Study on Calculation Method of Compressional Velocities Based on Field Well Logs. International Journal of Geosciences,07,928-937. doi: 10.4236/ijg.2016.77069

where

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