Relative permeability and transverse relaxation time are both important physical parameters of rock physics. In this paper, a new transformation model between the transverse relaxation time and the wetting phase’s relative permeability is established. The data shows that the cores in the northwest of China have continuous fractal dimension characteristics, and great differences existed in the different pore size scales. Therefore, a piece-wise method is used to calculate the fractal dimension in our transformation model. The transformation results are found to be quite consistent with the relative permeability curve of the laboratory measurements. Based on this new model, we put forward a new method to identify reservoir in tight sandstone reservoir. We focus on the Well M in the northwestern China. Nuclear magnetic resonance (NMR) logging is used to obtain the point-by-point relative permeability curve. In addition, we identify the gas and water layers based on new
The phenomenon of Nuclear Magnetic Resonance (NMR) was discovered in 1946, and since then NMR has been widely used in various fields. NMR logging technology has been rapidly developed in recent years, with confirmed favorable results in the evaluation of reservoir permeability. NMR logging technology has a unique fluid sensitivity and is able to provide information regarding the fluid number of rock pores, fluid properties, and fluid-bearing pore sizes. Since this data cannot be obtained by other conventional logging methods, it thereby provides very important information for reservoir descriptions and evaluations [
The relative permeability refers to the ratio between the effective permeability of each fluid type and the absolute permeability of the rock itself, in the cases of saturated multiphase fluid in the rock pores. The relative permeability is related to the rock’s wettability and fluid saturation, and the relative permeability curve can be obtained by laboratory measurements. Purcell [
In recent years, more and more researches focused on using fractal theory to establish the relationship between the relative permeability and other parameters. The fractal theory, which was developed in the 1970s, is a rational tool used to describe complex and irregular phenomena and processes and provides a good method for research regarding the microscopic pore structure of porous media [
The novelty of this paper is using a combination of the previous research results regarding the links between capillary pressure, resistivity index, relative permeability, and transverse relaxation time; the transformation relationship between the transverse relaxation time and the relative permeability is derived. All experimental cores are taken from tight sandstone reservoir in northwest China. Based on the rock resistivity experiment experimental data and the mercury injection test data, the parameter expression in the transformation relationship is given in order to discuss the control factors and their influences. It is obvious that the transformation results are better than those of the known methods, which thereby provided a theoretical basis for the relative permeability curve with changes over depth through the NMR logging data. The model is applied in the northwest of China to obtain the relative permeability curve with depth, as well as identify the gas and water yield layers. It is a new and reliable reservoir identification method.
In the Archie equation, the relationship between the resistivity index and water saturation is shown as follows:
The capillary pressure can be expressed as follows:
Toledo et al. [
Among these,
The relationship between
In the linear method [
In the equation,
Based on Darcy’s law and Ohm’s law, Li [
Although the relationships between
In the equation,
In accordance with the principle of fractal geometry, the integral was carried out on the above equation in order to obtain the expression of the cumulative pore volume
In the equation,
Through (
Due to
In reservoir physics,
Based on the fractal theory and the relationship between the transverse relaxation time
The parameters in (
In (
It should be noted that the model proposed by Li [
Tight sandstone reservoir samples were selected for the comprehensive laboratory measurements, in order to obtain the capillary pressure curve, relative permeability curve, core nuclear magnetic
Relationship between the resistivity index and the water saturation of the 8 samples.
Figure
Relationship between
As viewed from Figure
Relationship between the pore radius and wetting phase saturation transformed on the basis of a capillary pressure curve.
Table
Basic information of the rock samples.
Core number |
|
|
|
|
|
|
|
---|---|---|---|---|---|---|---|
1 | 6.487 | 0.019 | 2.19 | 0.9924 | 2.9875 | 2.8631 | 1.7245 |
2 | 9.646 | 0.11 | 1.191 | 1.0003 | 2.9123 | 2.6573 | 1.6317 |
3 | 11.791 | 0.097 | 1.25 | 0.9943 | 2.9375 | 2.6445 | 1.2662 |
4 | 12.286 | 9.402 | 1.552 | 1.0210 | 2.8862 | 2.7258 | 1.2623 |
5 | 10.542 | 15.313 | 1.541 | 0.9963 | 2.8944 | 2.6689 | 1.2610 |
6 | 8.588 | 0.036 | 1.223 | 1.0169 | 2.9850 | 2.8330 | 1.6979 |
7 | 4.507 | 0.041 | 2.143 | 1.0245 | 2.9721 | 2.7554 | 1.6070 |
8 | 10.223 | 0.101 | 1.353 | 1.0097 | 2.9425 | 2.8911 | 1.7435 |
Figure
Transformation result contrast of Sample 4.
Transformation result contrast of Sample 5.
Figures
Calculation result contrast of the different equations.
Core number | Equation ( |
Equation ( | ||
---|---|---|---|---|
Mean absolute error |
|
Mean absolute error |
| |
4 | 1.4488 | 0.9939 | 6.6979 | 0.8983 |
5 | 1.0624 | 0.9975 | 3.7613 | 0.9602 |
Nonwetting phase’s relative permeability of Sample 4 calculated by (
Nonwetting phase’s relative permeability of Sample 5 calculated by (
It is worth noting that we get the pseudo relative permeability curve by
The transformation model of the relative permeability and transverse relaxation time is obtained and verified, based on the processing and research of the experimental data, and according to the regional characteristics, the piece-wise method is adopted. This model is applied for the processing of the nuclear magnetic logging data, in order to obtain the relative permeability curve with changes over depth. It must be pointed out that the results we get by this method are pseudo relative permeability curves, as well as using
The processing was carried out on the target segment of Well M in the tight sandstone of the study area. Nuclear magnetic logging data were used to obtain the relative permeability curve with changes over depth. Figure
Comprehensive logging interpretation chart of Well M.
In this study, a transformation model between the transverse relaxation time
It was also determined that a specific problem existed in this model. The
The authors declare that they have no conflicts of interest.
This work is supported in part by the National Natural Science Foundation of China under Grant 41174096 and the Graduate Innovation Fund of Jilin University under Project 2016103.