Quantitative Characterization of Micro-Scale Pore-Throat Heterogeneity in Tight Sandstone Reservoir

Abstract

Nanoscale pore-throat systems are widely developed in the pore-throat of tight reservoirs. The pore-throat structures of different microscales are complex and diverse with obvious microscale effects. Taking the Chang 6₃ tight sandstone reservoir of the Huaqing area in Ordos basin as an example, under the guidance of information entropy theory, the quantitative characterization model of pore-throat micro-scale heterogeneity in a tight oil reservoir is established based on casting thin sections, physical properties analysis, constant velocity mercury injection, and NMR technology. Moreover, the correlation between pore-throat heterogeneity and porosity, permeability and movable fluid saturation is analyzed. The results show that there are obvious differences in pore-throat heterogeneity between different reservoirs, and the throat uniformity of macro pore-fine-throat reservoir, macro pore–micro throat reservoir, and macro pore–micro throat reservoir becomes worse, successively. There is a negative correlation between porosity uniformity and porosity, permeability and movable fluid saturation. However, there is a positive correlation between throat uniformity and combined pore throat uniformity and porosity, permeability and movable fluid saturation. Therefore, the uniformity of the throat controls the seepage capacity and fluid mobility in the pore system of the Chang 6₃ tight sandstone reservoir in the study area. This has important theoretical and practical significance to enhance oil recovery and promote the efficient development of a tight oil and gas reservoir.

1. Introduction

A tight oil sandstone reservoir is characterized by a complex micro-pore structure, strong heterogeneity, difficulty in predicting reservoir sand bodies, and a complex accumulation mechanism [1,2]. Moreover, the distribution of pore radius and throat radius is low. With the development of the petroleum industry, the methods that are used to describe reservoir heterogeneity are developed from conventional geological statistics to mathematical methods, and some achievements have been made. For example, data envelopment analysis (DEA) is used to calculate the heterogeneity index to quantitatively characterize reservoir heterogeneity [3,4,5]. The nonlinear relationship between reservoir physical property parameters and a combination of sensitive seismic attributes is established by using a probabilistic neural-network algorithm; the direct inversion of reservoir physical property parameters is realized, and a set of research on the flow of reservoir heterogeneity characterization is established [6]. Under the constraints of phase control, the reservoir heterogeneity is quantitatively evaluated by the entropy weight method, and a comprehensive evaluation model of random reservoir heterogeneity under different constraints is established [7]. These research results play an important role in promoting the characterization of reservoir heterogeneity. However, these studies all focus on the macro-scopic characterization of reservoir heterogeneity, and rarely involve the characterization of reservoir heterogeneity at the micro-scale. For parameters of reservoir heterogeneity characterization, “a large number” of test data, which obtain such parameters as inrush coefficient, variation coefficient, sorting coefficient and mean coefficient [8], mainly represents it. Therefore, taking the Chang 6₃ tight sandstone reservoir of the Huaqing area in Ordos basin as an example, micro-scale pore-throat heterogeneity in a different reservoir is quantitatively characterized based on information entropy theory, and its influence on reservoir physical properties is discussed. This has important theoretical and practical significance to enhance oil recovery and promote the efficient development of a tight oil and gas reservoir.

2. Materials and Methods

2.1. Test Method

Six rock samples for the experiment were taken from the Chang 6₃ tight sandstone reservoir of the Huaqing area in Ordos basin. A 2.5 cm diameter plunger sample was drilled from the core for the experiments, such as wash-oil processing, casting-sheet observation [9], the physical testing of rocks [10], and a constant velocity mercury-injection experiment [11].

2.2. Mathematical Theory and Method

Information entropy, first proposed by Shannon, the father of information theory, can be used to measure the uncertainty of information and to represent the complexity of a system [12]. The higher the entropy value of a system, the more complex it is [13,14,15,16,17,18]. The essence of information entropy is the quantitative analysis of distribution uniformity. The steps of establishing a quantitative characterization model of pore-throat micro-scale heterogeneity in a tight sandstone reservoir based on information entropy are as follows:

(1) Pressure and volume of mercury injection in tight sandstone samples are obtained based on the constant velocity mercury injection-experiment;

(2) Experimental data are processed to obtain the distribution data of pore radius and throat radius in a tight sandstone reservoir, and the distribution-frequency spectrum of the pore radius and throat radius in a tight sandstone reservoir are drawn;

(3) The distribution interval of the pore radius or throat radius is intercepted, which is taken as the object, and it is assumed that it contains m pores or throats. The occurrence frequency of different pore radii or throat radii are normalized, and a sequence is generated. According to Formula (1), the information entropy of different pore radius or throat radius intervals is calculated, namely, micro-scale pore-radius entropy [16] and micro-scale throat-radius entropy.

$$H=-{\sum }_{i=1}^m{z}_i\ln z_i$$

(1)

where $z_i$ is the standard value of the occurrence frequency of the ith pore radius or throat radius. In a certain pore or throat interval, when the occurrence frequency of different pore radii or throat radii are the same, namely, $z_1=z_2=\dots =z_m=1/M$, the entropy is at its maximum (lnM). This means that the size distribution of the pores or throat reaches an even state within the pore or throat interval.

In practical applications, due to the differences in the number of pores or throats that are contained in each pore or throat interval, the divided pores or throat intervals may be different, and the information entropy of pores’ radius or throat radius is often not comparable. Therefore, a dimensionless parameter (J) is introduced to represent pore uniformity or throat uniformity. According to Formula (2), the uniformity of pores or throats in different scales can be calculated, which is used to quantitatively characterize the uniformity of pore throat distribution at different scales in a tight sandstone reservoir;

$$J=\frac{-{\sum }_{i=1}^m{z}_i\ln z_i}{M}$$

(2)

(4) The overall distribution uniformity of pore radius or throat radius in a tight sandstone reservoir is calculated;

① In the process of step 4, it is assumed that N pore radius or throat radius intervals are divided, and the total frequency of the pore or throat in each interval is $Q_j$ (j = 1, 2, …, N). According to Formula (3), the percentage of pore or throat in each interval in the total frequency of pores or throats that are obtained from the rock sample test is calculated.

$$P_j=\frac{Q_j}{{\sum }_{j=1}^N{Q}_j}$$

(3)

② According to Formula (4), the overall distribution uniformity of pores or throat is calculated.

$$M={\sum }_{j=1}^N{P}_j{J}_j$$

(4)

where J represents the uniformity of the jth pore or throat;

(5) In order to use information entropy to determine the weight of the pore and throat, and to solve the joint uniformity of the pore and throat, it is necessary to analyze the dispersion degree of the pore and throat. Generally, the dispersion degree of the jth index (pore or throat) depends on $h_j$, and the more dispersed the value distribution of the jth index (pore or throat) is, the greater the corresponding $h_j$ value is, indicating that the significance of the jth index (pore or throat) is also higher. Among all n indexes (pore or throat), the weight of the jth index (pore or throat) can be determined by Equation (5).

$$w_j=\frac{h_j}{{\sum }_{i=1}^n{h}_j}$$

(5)

where $h_j=1-M_j$, j = 1, 2;

(6) Then, the overall distribution uniformity of the pore and throat is combined to generate the combined uniformity of the pore and throat (I), as shown in Formula (6).

$$I=W_1{M}_1+W_2{M}_2$$

(6)

3. Discussions

3.1. Pore Throat Type and Physical Characteristics

Based on the results of a cast thin section analysis of the Chang 6₃ reservoir, it is concluded that the main reservoir spaces are intergranular pores (3.81%), feldspar dissolution pores (0.65%), cuttings dissolution pores (0.23%), intercrystalline pores (0.12%), and micro-fractures (0.03%). According to the analysis of reservoir properties and pore throat capillary-pressure curve characteristics, the porosity distribution range of selected rock samples is 6.99% to 12.41%, the average value is 9.82%, the permeability distribution range is from 0.063 × 10⁻³ μm² to 2.72 × 10⁻³ μm², and the average value is 0.992 × 10⁻³ μm². According to the standards of pore and throat size (

Table 1. Pore and throat size division scheme [19].

Pore Size Classification	Pore Radius (μm)	Throat Size Classification	Throat Radius (μm)
Macro pore	>100	Coarse throat	>4.0
Meso pore	100~50	Medium throat	4.0~2.5
Small pore	50~10	Thin throat	2.5~1.0
Fine pore	10~0.5	Fine throat	1.0~0.5
Micro pore	<0.5	Micro throat	0.5~0.1

), the selected rock samples represent three types of reservoir with different pore and throat combinations (macro pore-thin throat, macro pore-fine throat, macro pore-micro throat), as shown in Figure 1. The throat radius is greater than 1.0 μm, and the storage space is mainly composed of intergranular and dissolved pores in a macro pore-thin throat reservoir with a permeability greater than 0.3 × 10⁻³ μm². The throat radius is between 0.5 μm and 1.0 μm, and the storage space is mainly composed of dissolved pores, a few intergranular pores and micro pores in a macro pore-fine throat reservoir with a permeability between 0.1 × 10⁻³ μm² and 0.3 × 10⁻³ μm². The throat radius is between 0.1 μm and 0.5 μm, and the reservoir space is mainly composed of micro pores and a few dissolution holes in a macro pore-micro throat reservoir with a permeability of less than 0.1 × 10⁻³ μm².

3.2. Quantitative Characterization of Pore Throat Micro-Scale Heterogeneity Based on Information Entropy Theory

Based on the results of the constant velocity mercury-injection experiment and the information entropy theory, six representative rock samples with different types of pore-throat were selected to build quantitative models of microscale pore-throat heterogeneity, which allows to quantitatively characterize the micro-scale pore-throat heterogeneity of a tight sandstone reservoir. The results are shown in

Table 2. Quantitative characterization of pore radius heterogeneity in different pore-throat combination reservoirs.

Sample Number	Reservoir Types	Pore Uniformity	Uniformity of Different Pore Intervals
			Macro Pore	Meso Pore	Small Pore	Fine Pore	Micro Pore
			>100 μm	50~100 μm	10~50 μm	0.5~10 μm	<0.5 μm
1	macro pore-fine throat	0.7249	0.7329	0.1640	0	-	-
2	macro pore-micro throat	0.8224	0.7976	0	-	-	-
3	macro pore-micro throat	0.7639	0.7791	0.0611	-	-	-
4	macro pore-fine throat	0.7269	0.7630	0.2125	0.5436	-	-
5	macro pore-micro throat	0.7304	0.7226	0	-	-	-
6	macro pore-thin throat	0.7324	0.6594	0.0165	-	-	-

and

Table 3. Quantitative characterization of throat radius heterogeneity in different pore-throat combination reservoir.

Sample Number	Reservoir Types	Throat Uniformity	Uniformity of Different Throat Intervals
			Coarse Throat	Medium Throat	Thin Throat	Fine Throat	Micro Throat
			>4.0 μm	4.0~2.5 μm	2.5~1.0 μm	1.0~0.5 μm	0.1~0.5 μm
1	macro pore-fine throat	0.8629	-	-	0.9716	0.9448	0.8625
2	macro pore-micro throat	0	-	-	-	-	0
3	macro pore-micro throat	0	-	-	-	-	0
4	macro pore-fine throat	0.7332	-	0.9363	0.7856	0.9988	0.4863
5	macro pore-micro throat	0.4067	-	-	-	-	0.4067
6	macro pore-thin throat	0.8260	-	-	0.9917	0.5931	0.9308

. It can be seen from Table 2 that the Chang 6₃ reservoir in the study area generally developed macro pores, followed by meso pores, and little small pores. The uniformity of a macro pore-micro throat reservoir is between 0.7304 and 0.8224 and the average is 0.7722. The uniformity of a macro pore-fine throat reservoir is between 0.7249 and 0.7269 and the average is 0.7259. The uniformity of a macro pore-thin throat reservoir is 0.7324. Therefore, the distribution uniformity of pores in a macro pore-micro throat reservoir, macro pore-thin throat reservoir, and macro pore-fine throat reservoir becomes worse successively.

As can be seen from Table 3, the macro pore-micro throat reservoir only develops micro throat, and the average of total throat uniformity is 0.1356, among which the throat radius of the No.2 and No.3 rock samples are concentrated at 0.2 μm, and the uniformity of micro-throat and total throat are both 0, indicating an uneven distribution of throat. The micro-throat uniformity and total throat uniformity of the No.5 rock sample is 0.4067, which indicates that their throat distribution is uniform compared with that of the No.2 and No.3 rock samples. The macro pore-fine throat reservoir is mainly composed of fine throat, and a small number of thin throat and micro-throat. The average of the total throat uniformity is 0.7981, among which the total throat uniformity of the No.1 rock sample is better than that of the No.4 rock sample, but the fine-throat uniformity of the No.4 rock sample is better than that of the No.1 rock sample. The macro pore-thin throat reservoir is mainly composed of thin throat, and a small number of fine throat and micro-throat. The total throat uniformity of the No.6 sample is 0.8260. As a result, the distribution uniformity of throat in macro pore-thin throat, macro pore-fine throat, and macro pore-micro throat reservoirs becomes worse successively.

The concept of “combined pore-throat uniformity” is introduced to characterize the microstructure heterogeneity of pore throat in a tight sandstone reservoir, as shown in

Table 4. The combined pore-throat uniformity of different pore-throat combination reservoir.

Sample Number	Reservoir Types	Porosity (%)	Permeability (10−3 μm2)	Combined Pore-Throat Uniformity
1	Macro pore-fine throat	12.51	0.288	0.7708
2	Macro pore-micro throat	8.44	0.021	0.12408
3	Macro pore-micro throat	9.77	0.031	0.14598
4	Macro pore-fine throat	11.28	0.454	0.7301
5	Macro pore-micro throat	8.98	0.106	0.5078
6	Macro pore-thin throat	11.0	0.31	0.7693

. Among them, the combined pore-throat uniformity of the macro pore-micro throat reservoir (No.2, No.3 and No.5 rock samples) is between 0.1240 and 0.5078, with an average value of 0.2593. The combined pore-throat uniformity of the macro pore-fine throat reservoir (No.1 and No.4 rock samples) is between 0.7301 and 0.7708, with an average value of 0.7504. The combined pore-throat uniformity of the macro pore-fine throat reservoir (No.6 rock sample) is 0.7693. As a result, the combined pore-throat uniformity in macro pore-thin throat, macro pore-fine-throat, macro pore-micro-throat reservoir becomes worse successively. This is consistent with the regularity of throat-uniformity distribution in different pore-throat combinations, indicating that the microscopic pore-throat heterogeneity in the Chang 6₃ reservoir is mainly controlled by the uniformity of throat distribution.

3.3. Effects of Pore Throat Heterogeneity on Reservoir Physical Properties and Fluid Mobility

By analyzing the relationship between physical properties (porosity, permeability) and pore uniformity, throat uniformity, and combined pore-throat uniformity of different pore-throat combination reservoirs (Figure 2), it can be found that the relationship between permeability and pore uniformity, throat uniformity, and combined pore-throat uniformity is better than porosity. There is a negative correlation between porosity uniformity and porosity, and the correlation coefficient (R²) is 0. 525, indicating that the greater the porosity uniformity, the more uniform the development of pores, and the smaller the reservoir porosity. The throat uniformity is positively correlated with porosity, and the correlation coefficient (R²) is 0.653. This indicates that the greater the throat uniformity, the more uniform the throat development, and the greater the porosity. There is a positive correlation between pore-throat joint uniformity and porosity, and the correlation coefficient (R²) is 0.709. It is proved that the greater the combined pore-throat uniformity, the smaller the difference of pore-throat size; the weaker the heterogeneity of pore-throat distribution, the weaker the pore-throat aggregation phenomenon; and the smaller the probability of pore-throat overlap; the larger the effective porosity of the reservoir [20,21]. A comparative analysis shows that the uniformity of throat development controls the effectiveness of reservoir space. The porosity uniformity is negatively correlated with the permeability, and the correlation coefficient (R²) is 0.749. This indicates that the greater the porosity uniformity, the more uniform the development of pores, and the lower the permeability. There is a positive correlation between throat uniformity and porosity, and the correlation coefficient (R²) is 0.9397. The greater the throat uniformity, the more uniform the throat development, and the greater the permeability. There is a positive correlation between the combined pore-throat uniformity and permeability, and the correlation coefficient (R²) is 0.978. This indicates that the greater the combined pore-throat uniformity, the more uniform the radius of pore throat development, and the greater the permeability. Through a comparative analysis, it is found that the uniformity of throat controls the reservoir and seepage capacity of the Chang 6₃ tight sandstone reservoir in the study area.

At the same time, the relationship between movable fluid saturation and pore uniformity, throat uniformity, and pore-throat combination uniformity of different pore-throat combination types was analyzed by using NMR technology (Figure 3). It can be found that the movable fluid saturation is positively correlated with throat uniformity and pore-throat combination uniformity. The porosity uniformity is negatively correlated with movable fluid saturation. Thus, the uniformity of throat development controls fluid mobility in the pore system of the reservoir and restricts oil recovery.

4. Conclusions

(1) Through casting thin section analysis of the Chang6₃ reservoir samples in the research area, it is concluded that the main reservoir spaces are intergranular pores, feldspar dissolution pores, cuttings dissolution pores, intercrystalline pores and micro-fractures, etc. The shape of the orifice throat is mainly a sieve tube shape, strip shape and ball shape, and its quality is successively worse.

(2) Based on the constant velocity mercury-injection technique, the pore and throat radius distribution characteristics of the Chang 6₃ reservoir in the Huaqing area are studied, and it is considered that the pore and throat combination types of the Chang 6₃ reservoir in the study area mainly include macro pore-thin throat, macro pore-fine throat and macro pore-micro throat.

(3) Under the guidance of information entropy theory, the quantitative characterization model of pore-throat microscale heterogeneity in a tight oil reservoir is established. The pore-throat heterogeneity of different reservoirs is obviously different. Moreover, the distribution uniformity of throat in macro pore-thin throat, macro pore-fine-throat and macro pore-micro throat reservoirs becomes worse successively.

(4) The heterogeneity of pore and throat is the key factor to determine the physical property, seepage mechanism and oil recovery of a tight sandstone reservoir. The pore uniformity is negatively correlated with porosity, permeability and movable fluid saturation. However, throat uniformity and combined pore-throat uniformity are positively correlated with porosity, permeability and movable fluid saturation. Therefore, the uniformity of throat development controls the reservoir and seepage capacity of the Chang 6₃ tight sandstone reservoir in the study area and restricts the oil recovery factor.