Research on the normalisation method of logging curves: taking XJ Oilfield as an example

The frequency histogram method can intuitively reflect the frequency distribution of the curve between each well and the standard layer of the standard well and facilitate comparison between them. The frequency histogram divides the standard layer of each well into several sections according to the logging value and counts each. Draw the frequency histogram of the logging frequency of the logging value of each well in the standard layer and compare it with the standard well. This method considers that the standard layer is stable, and the peak value and frequency distribution of frequency histogram in the standard layer remain unchanged. Each well is calibrated to a uniform range according to the standard well. The correction amount of each well is determined by histogram [4]. Two points need to be avoided in the application of frequency histogram method: (1) No suitable standard layer can be found in the whole area. (2) The standard layer is thin, and there are a few data points in the standard layer. When drawing the frequency histogram, the data is scattered and there is no obvious rule.

Trend surface analysis [5] is a commonly used method for standardisation. In the oilfield, the geological parameters are not stable in the formation but have certain change rules. These geological parameters combined with the logging response reflecting the formation characteristics show regular changes in spatial distribution, showing a certain natural trend, which can be fitted as a curved surface, called trend surface.

The trend surface divides a concrete or abstract surface of spatial distribution into two parts [6]. The first part changes slowly, and the other part changes quickly. The slow-changing part is the component that reflects the change law of the entire study area, which is called the trend component. The fast-changing part reflects the local change law, which is called the residual component. In the analysis of the trend surface, the most commonly used methods are polynomials and Fourier series. The mathematical surface that we obtain through multivariate analysis technology will only be affected by regional values to eliminate the influence of regional outliers or interference values and complete the standardisation of logging curves.

In the formation, the logging response value that can reflect the characteristics of the formation usually has a certain relationship with its spatial distribution and conforms to the corresponding law. The trend surface we make is to simulate the natural trend value of the formation [7], and the principle of fitting is to make the trend value that is closer to the true value of the formation. The following formulas are usually used to express the trend value and the remaining value: (1)z(x,y)=z^(x,y)+ez(x,y) = \hat z(x,y) + e

Among them, z^(x,y)\hat z(x,y) and e in the formula are the trend value and the residual value, respectively. Substituting the known data, using regression analysis to find the regression equation f(x,y), satisfying: (2)Q=∑i=1n[zi-f(xi,yi)]Q = \sum\nolimits_{i = 1}^n {[{z_i} - f({x_i},{y_i})]}

Take the minimum value and get the regression surface: (3)z^=f(xi,yi)\hat z = f({x_i},{y_i})

Therefore, the trend value is z^=f(xi,yi)\hat z = f({x_i},{y_i}) residual value zi-z^{z_i} - \hat z . The logging value can be corrected according to the trend value and residual value.

The mean variance method is also called the normal distribution method [8]. After we select the standard wells of the standard wells, we obtain the logging data a1,a2,a3···,an. After obtaining this set of data, their expectation can be calculated as Ea, and the variance is S²(a). After we complete the standard layer data of the standard well, we need to calibrate this layer of other wells and take the data of other wells as b1,b2,b3. . . ..bn, this set of data needs to be corrected. The corrected data have a linear relationship with the previous data. Assuming that the corrected data are c1,c2,c3,. . . ,cn, this set of data meets the data before correction (4)cn=kb+dcn = kb + d

After correction, the expectation and variance of CN and an are equal (5)E(a)=E(c), s2(a)=s2(c)E(a) = E(c),\,{s^2}(a) = {s^2}(c)(6)Ea=kEb+ds2(a)=k2s2(b)Ea = kEb + d{s^2}(a) = {k^2}{s^2}(b)(7)k=[s2(a)/s2(b)]1/2k = {[{s^2}(a)/{s^2}(b)]^{1/2}}(8)d=E(a)-[s2(a)/s2(b)]1/2Ebd = E(a) - {[{s^2}(a)/{s^2}(b)]^{1/2}}Eb

The correction equation can be found (9)c=[s2(a)/s2(b)]1/2b+Ea-[s2(a)/s2(b)]1/2Ebc = {[{s^2}(a)/{s^2}(b)]^{1/2}}b + Ea - {[{s^2}(a)/{s^2}(b)]^{1/2}}Eb

The quality of the logging curve is a prerequisite to ensure the reliability of logging interpretation results. In the process of logging data processing, the computer takes out the logging data of each sampling point according to the depth point by point for quantitative calculation, so there are very strict requirements on the quality of the logging curve. The pre-processing of logging data in logging project mainly includes [9]: logging quality inspection, logging curve environment correction, curve depth matching, GR curve splicing, data repair of expanding section, resistivity inversion, normalisation processing, and so on. After logging quality inspection, depth matching, GR curve splicing, borehole expansion repair, resistivity inversion and other preprocessing research work, the system error of various curves is reduced, the reliability of curve use is improved, and standardisation can be guaranteed. The accuracy of the results.

In normal applications, using a method for normalisation often fails to achieve the expected results. As shown in Figure 5, the frequency histogram method or the mean variance method alone cannot be consistent with the standard well. Several methods are needed to work together to make the correction accurate. In the process of standardisation of the XJ oilfield, the entire region has stable stratum deposition and no trend surface correction is required. Due to the difference in logging companies and measurement methods, the abnormalities in the logging environment after correction have been combined. The frequency histogram method and the mean variance method are used for correction. Combining the two methods has achieved good results.

Fig. 4

Fig. 5

Before correction, it is necessary to determine the correction method for each well [10, 11, 12, 13, 14]. The curve shape of some wells is similar to that of standard wells, which can be corrected directly by frequency histogram method. For some curves with a large difference in distribution frequency and different shapes of curves, it is necessary to use frequency histogram together with mean variance method. In this project, multiplication factor and addition factor are used to characterise them Correction amount.

For the XJ oilfield, most wells in the same area have similarity in the shape of the curve, conform to the same law and perform stable in the standard layer. Therefore, most wells can be processed by the frequency histogram method, and a few wells require A curve corrected by the mean-variance method after the mean-variance processing. The shape of the curve can be made to conform to the laws of geology. Figure 7 shows the changes in the shape of the curve before and after normalisation by the mean square error method.

Fig. 6

Fig. 7

After the correction of the mean variance of the curve, the correction amount of all curves [11] is statistically analysed, as shown in Table 1. If only frequency histogram method is needed to correct, then only the additive factor correction amount is needed. If the mean variance method is used for correction, the addition factor and multiplication factor exist.

After the correction amount is counted, the wells in the XJ block can be standardised. According to the method mentioned above, the contrast map before and after GR before and after standardisation can be obtained.

From the normalised GR curve, it can be seen that the frequency histogram method and the mean variance method can be used in combination to obtain a better standardisation effect than using one method alone, which is suitable for multi-well standardisation research.

In the actual processing process, the gamma, density and neutron curves were all standardised, and the standardised curves were used for logging interpretation, and the shale content and porosity logging interpretation of the whole area were counted. According to the statistics of the whole well section of shale interpretation, the shale content of sandstone section is about 5% (Figure 10), with good consistency; according to the statistics of porosity of sandstone reservoir HB layer, the porosity is between 24 and 29% (Figure 11), and the porosity consistency of the sandstone section is better.

Fig. 8

Fig. 9

Fig. 10

Fig. 11

The interpretation result is shown in Figure 12. From the well diagram, there is no obvious lithological change in the formation. The HB layer at the high part still has a pure oil layer of 3 m thick, and the thickest part of the H1B layer has about 10 m oil layer. It is recommended to continue to pay attention. The newly obtained interpretation result is compared with the actual production data, which is more in line with the actual production situation. After the logging curve is standardised, the accuracy of the logging interpretation is improved.

Fig. 12