
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39227728
71433
10.1038/s41598-024-71433-z
Article
The primary porosity heterogeneity characteristics of braided river sandbody and implications for predicting the current physical properties heterogeneities
Yan Yiming 20200007@upc.edu.cn

123
Zhang Liqiang zhanglq@upc.edu.cn

13
Luo Xiaorong 4
1 grid.497420.c 0000 0004 1798 1132 Key Laboratory of Deep Oil & Gas (China University of Petroleum (East China)), Qingdao, 266580 China
2 Shaanxi Key Laboratory of Lacklustre Shale Gas Accumulation and Exploitation, Xian, 710065 China
3 grid.497420.c 0000 0004 1798 1132 School of Geosciences, China University of Petroleum, Qingdao, 266555 China
4 grid.9227.e 0000000119573309 Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029 China
3 9 2024
3 9 2024
2024
14 2042310 10 2023
28 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Understanding the heterogeneity of reservoirs is crucial for enhancing the efficiency of hydrocarbon exploration and development. The primary porosity of samples from modern braided river sands and outcrops of braided river sandstone was calculated using a model previously proposed by the authors. The characteristic parameters (Vx) for calculating primary porosity are closely related to the architectural–elemental configurations (AEC), and the AEC of braided river sand bodies (BRSD) has apparent effects on the distribution of the primary porosity heterogeneities. Analysis of our results has established a simple primary porosity heterogeneity model of BRSD. The center of braided river channel and mid-channel bars have excellent strong primary petrophysical properties with high primary porosity exceeding 38%. The contact areas between the braided river channel and channel bars exhibit relatively low primary porosities of less than 33%. The area between the center and edge of the braided bars and channels displays medium primary porosities. The nonlinear correlation in the Q–Q plot of the primary porosity and present porosity of samples from BRSD in the Ahe Formation is mainly caused by chemical diagenesis. The present porosity heterogeneity of BRSD in the Ahe Formation is less influenced by compaction and cementation, it predominantly arises from the differential of dissolution. Q–Q plots attempt to correlate the geological information from an individual sample with the heterogeneity of present porosity in BRSD. In addition, by utilizing Q–Q plots of the primary and current petrophysical properties of the sand body, the relative extent of heterogeneity modification caused by different diagenetic processes can be assessed. This assessment is crucial for modeling macroscopic models of physical properties during geological history periods.

Keywords

Braided river sandstone
Primary porosity
Heterogeneity
Q–Q plots
Reservoirs
Subject terms

Geology
Sedimentology
National Natural Science Foundation of China42002145 Yan Yiming issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Reservoir heterogeneity presents significant geological challenges to the exploration and development of clastic oil and gas resources, thereby constraining the efficiency of clastic oil and gas development. The present petrophysical heterogeneities of clastic reservoirs reflect a comprehensive outcome of the primary sedimentary (original) heterogeneities and diagenetic evolution1,2. Several researchers have conducted systematic and comprehensive studies on the impact of different diagenetic pathways on reservoir heterogeneity in sandstone reservoirs, including the influence of sandstone compositions on diagenesis and the evolution of petrophysical properties of reservoirs3. Additionally, investigations have been carried out on the effects of various diagenetic processes on reservoir heterogeneities4–6. Studies on present heterogeneities of fluvial sandstone bodies are abundant and diverse, such as diagenesis, porosity distribution. However, research specifically addressing primary porosity heterogeneity is relatively scarce.

Towards the end of the twentieth century, research started to focus on understanding the strong heterogeneities of the primary petrophysical properties of sandstone reservoirs, which has a strong bearing the process of reservoir diagenetic evolution7–11. In previous studies focused on reservoir architectural configurations and petrophysical properties of braided sandstone reservoirs, it has been found that the petrophysical properties of sand bodies vary significantly and are related to microfacies or lithofacies9. Microfacies or Lithofacies controlled the grain size distribution and affected the primary petrophysical properties12. For example, the petrophysical properties of braided channel and bar reservoirs gradually become worsening from the center to the edge13; the petrophysical properties of channel sand bodies have distinct directionality and is closely related to the lithofacies14. The influence of the heterogeneities of primary porosity on the petrophysical heterogeneities of reservoirs is rarely quantitative discussed.

The primary porosity of braided river sandstone reservoirs is closely related to its grain size distribution and grain packing texture, which is also mainly controlled by microfacies or lithofacies. For example, King pointed out that the primary porosity of coarse sandstone was 34%, and the primary porosity of well-sorted fine sandstone was 38%15. Rogers and Head stated that the primary porosities of well-sorted sandstones were higher than those of the poorly-sorted sandstones16, and the primary porosity was significantly affected by the sorting coefficient17.

The primary porosity of sands or sandstone can be obtained using the following methods: (1) The empirical formula between sorting coefficient and primary porosity which is proposed by Scherer12. (2) Xu et al. fitted the mathematical model between primary porosity, sorting coefficient, and median particle size based on experimental data18. (3) A mathematical model which is based on grain packing texture and grain size distribution curve proposed by Yan et al.19,20. However, limited research has focused on the primary porosity heterogeneities of braided sand bodies and their architectural elements, such as braided channels, braided bars, and channel edges. Attention on the influence of primary porosity heterogeneities on present petrophysical heterogeneities of braided sand bodies is lacking. Lunt et al. point out that the primary porosity of braided river sands is related to sediment texture, and the sands facies have the highest porosities (range 17–30%), followed by open-framework gravels (range 16–24%), and then sandy gravels (range 14–26%)21, the porosities of braided river can be predicted using sedimentary facies. Similar work related to permeability has been reported by Ritzi et al.22. However, there is limited discussion on the evolution relationship between primary porosity and present porosity under the constraint of sedimentary facies, which is crucial for studying the distribution of reservoir petrophysical properties during geological historical periods.

This paper aims to establish a primary porosity heterogeneity model for braided sand bodies, based on the primary porosity calculation model of Yan et al.19, using samples from modern braided rivers and ancient braided sand outcrops. By the application of the similarity solution between primary porosity and present porosity, an attempt is made to quantitatively characterize the heterogeneity of sand bodies using diagenetic information from single sample. This has great significance in establishing the heterogeneity of sand bodies by using geostatistics. The nonlinear correlation in the Q–Q plot of the primary porosity and present porosity of samples from braided sandstone bodies in the Ahe Formation is primarily attributed to chemical diagenesis. Q–Q plots can verify whether the porosity distribution map records the heterogeneous information from different diagenetic process. This approach can be employed to assess the impact of different types of diagenesis on the macroscopic heterogeneity of reservoir physical properties, establishing a connection between the diagenetic information of single samples and macroscopic physical properties heterogeneity of reservoir properties, which is highly significant for studying the macroscopic paleoproperties of reservoir during geological historical periods.

Primary porosity calculation function

Previous studies have proposed that the primary porosity of sandstone is primarily influenced by factors such as grain size distribution, grain shape, and grain packing texture, which represent the spatial overlay of grains, the relationship of grain contacts, and grain filling model of sandstone12,17,23–25. Therefore, recent research has indicated that relying solely on Trask sorting coefficients26 to calculate the primary porosity of sandstone might result in significant errors. Grain packing texture and grain shape have been introduced into the quantitative calculation of the primary porosity of sandstone, instead of qualitative analysis of their correlation19,20.

In general, based on the characteristics of grain size distribution, the grain packing texture of sandstone can be categorized into three types: one-component grain packing texture (O-GPT), binary grain packing texture (B-GPT), and ternary or multiple grain packing texture (T-GPT)19,20,27–29. The primary porosity of sandstone with O-GPT is influenced by grain shape and the specific type of O-GPT. Specifically, sand composed of round or sub-round grains exhibiting O-GPT tends to have a primary porosity of around 40%12,17. The packing texture of sandstone with B-GPT can be divided into two types based on the proportion of fine grains. When the content of fine grains is small (< 30%), the packing texture of sandstone is referred to as coarse-grain dominant binary packing texture (C-B-GPT); when the content of fine grains is large (> 30%), the packing texture of sandstone is referred to as fine-grain dominant binary packing texture (F-B-GPT). Consequently, the primary porosity of sandstone with B-GPT is influenced by grain shape, the proportion of fine grains, and the diameter ratio between coarse and fine grains. The same pattern is also observed in T-GPT, and the primary porosity is influenced by grain shape, the diameter ratio between coarse, medium, and fine grains, and the content of fine grains and medium grains.

The variations in grain size within modern deposited sands are typically continuous, and the theoretical grain packing texture model of nature deposited sands can be calculated by disassembling it into multiple binary packing texture based on the grain size distribution. There are several theoretical models for grain size distribution characteristics of modern braided river sands (Fig. 1). Type A sandstone is predominantly developed in the center of braided bars and channel, or the fine sediments in the upper braided channel. Type B–D sandstone are mainly developed in the transitional area between the braided channel and braided bars or the edge of the braided channel, which are influenced by two forms of hydrodynamic forces.Fig. 1 Theoretical models of particle size distribution for four types sands (modified form Yan et al.19).

The primary porosity calculation formulas for four types of sands in braided rivers proposed by the authors (more detailed instructions are available in Yan et al.19), are as follows:

For type A sands, the primary porosity can be calculated by Eqs. (1) and (2), as following:1 φj=ej1+ej,

2 ej=em·Cm+ec·Cc+ef·Cf-a0·(1+ef)·Cf-b0·ec·Cc.

For type B and C sands, the primary porosity can be calculated by Eqs. (1) and (3), as following:3 ej=em1·Cm1+em2·Cm2+ef1·Cf1-b1·em2·Cm2-a2·(1+ef1)·Cf1.

For type D sands, the primary porosity can be calculated by Eqs. (1) and (4), as following:4 ej=em1·Cm1+em2·Cm2+ef1·Cf1-a1·(1+em1)·Cm1-a2·(1+ef1)·Cf1,

where the meaning of parameters used in Eqs. (1)–(4) can be found in Table 1.Table 1 Meaning of parameters used in calculating the primary porosity of braided river sands.

Φj	Primary porosity of sandstone	ej	Primary void ratio of sandstone	
R	The grain size of the peak in grain size distribution curve of type A sandstone	Cm2	The content grains with diameter between (R1 + R2)/2 and 2R2 of type B sandstone	
Cf	The content grains with diameter between 0 and R/2 of type A sandstone	ec	The void ratio of O-GPT sands with grain diameter between 2R and + ∞	
Cm	The content of grains with diameter between R/2 and 2R of type A sandstone	em	The void ratio of O-GPT sands with grain diameter between R/2 and 2R of type A sands	
Cc	The content of grains with diameter between 2R and + ∞ of type A sandstone	ef	The void ratio of O-GPT sands with grain diameter between 0 and R/2 of type A sands	
R1	The grain size of the first peak in grain size distribution curve of type A sandstone	em1	The void ratio of O-GPT sands with grain diameter between R1/2 and (R1 + R2)/2 of type B sands	
R2	The grain size of the two peak in grain size distribution curve of type A sandstone	em2	The void ratio of O-GPT sands with grain diameter between (R1 + R2)/2 and 2R2 of type B sands	
Cf1	The content grains with diameter between 0 and R1/2 of type B sandstone	ef1	The void ratio of O-GPT sands with grain diameter between 0 and R1/2 of type B sands	
Cm1	The content grains with diameter between R1/2 and (R1 + R2)/2 of type B sandstone	a0, b0, a1, a2, b2	a0, a1, and a2 are filling coefficient; b0, and b2 are embedment coefficient	

Samples and methods

Samples

All samples in this study were collected from the northern part of the Tarim Basin in China (Fig. 2A). To investigate the reliability of the calculated primary porosity of braided river sandstone, this study selected a modern braided river with a similar sedimentary background to the outcropping braided river sandstone. Therefore, the samples in this study are from two areas, one from a modern braided river, and the other from the outcropping braided river sandstone. The details of these samples are as follows:Fig. 2 The location of study area. (A,B) Is the location of Kuqa River Agexiang Section and braided river sandstone outcrops; (D,F) is characteristics of sedimentary facies and the position of samples in modern braided river (N42.123256°–N42.123 086°, E83.159711°–E83.160719°); (C,E) multi-order bounding interface according Miall30 and architectural-elemental configurations (AEC) of braided river sandstone outcrops of Ahe Formation.

Modern braided river samples

Samples of modern braided river sediment are collected using a cylindrical sampler, extracting from approximately 10 cm below the surface. 72 samples were collected from braided river located in the Agexiang section within the Kuqa River, Tarim Basin, China (N42.123256°–N42.123 086°, E83.159711°–E83.160719°) (Fig. 2B). Out of these, 35 samples were extracted from the braided channel, 17 samples originated from gravel-braided bars, and 20 samples were collected from sands-braided bars (Fig. 2D,F).

Braided river sandstone outcrop samples

The outcrop studied came from the tight sandstone reservoir of the Lower Jurassic Ahe Formation, Kuqa depression, Tarim Basin (Fig. 2A,B). The sandstone of the Ahe Formation mainly comprises braided sand bodies (Zhang et al.10, Fig. 2B). The digital outcrop model of braided river sandstone outcrops of Ahe Formation was obtained using the unmanned aerial vehicle (UAV) (Fig. 2B,C). The digital outcrops were used to create a vertical section to avoid the distortion of the two-dimensional photos. Twenty-four samples were obtained at the top, middle and bottom of braided bar or channel (Fig. 2E).

Methods

Sample pretreatment for particle size distribution and morphological analysis

To determine the particle size distribution and morphological properties of the sample, the following pretreatment steps were carried out:

First, 0.2–0.3 g of loose sample was taken and placed in a beaker. 10 ml of 10% H2O2 solution as added to the beaker. The beaker was then transferred to a hot plate within a fume hood and heated to allow for a slow and thorough reaction. During the heating process, a wash bottle filled with distilled water was used to continuously rinse the inner walls of the beaker to prevent the solution from splashing or drying out. This process was continued until the solution became clear and no fine bubbles were formed, ensuring complete removal of organic matter from the sample.

Then, 10 ml of 10% HCL solution was added to the beaker. The beaker was reheated to ensure a slow and thorough reaction until no visible bubbles were formed and removal of carbonates from the sample was assured. During this heating process, the inner walls of the beaker were also rinsed with distilled water to prevent the solution from splashing or drying out. The beaker was then filled with distilled water and taken from the fume hood to the lab-oratory, where the samples were arranged neatly and left undisturbed for approximately 12 h.

After allowing to stand, the supernatant was carefully removed with a rubber tube so that approximately 20 ml of solution remained in the beaker. Then 10 ml of dispersant solution was added to the beaker, and it was placed in an ultrasonic cleaner. The beaker was stirred for 5 to 7 min, removed from the cleaner, and subjected to the drying process.

Particle size distribution and morphological analysis method

To accurately analyze the particle size distribution and morphology of the sample, Bettersize’s Laser Image Grain Size Shape and Shape Analysis system was used.

Laser diffraction method

The pretreated sample is introduced into the laser diffraction module of the Bettersize analyzer. As the laser beam penetrates the sample, it measures the scattering angle of the light at different particle sizes. By analyzing the distribution of the scattering angles and the light intensity, the particle size distribution curve of the sample is determined.

Image analysis method

Using the Bettersize device’s image analysis module, high-resolution images of the particles are captured using a sophisticated camera. Image processing software analyzes these images to calculate morphological parameters such as aspect ratio, roundness and surface roughness. These parameters provide a detailed description of the particle shape properties.

The grain size distribution curve and grain shape of the 72 modern braided river samples were evaluated using the Image Grain Size Shape and Shape Analysis system (Bettersize, China, 2002). The grain shape of modern samples was analyzed using the Image Grain Size Shape and Shape Analysis system is shown in Fig. A1 (Supplementary Appendix 1). The primary porosity of 41 modern braided river samples was measured using the Diagenetic Analog instrument (developed by China University of Petroleum (East China)) (details and design drawings of the Diagenetic Analog instrument can be seen in Fig. A2 (Supplementary Appendix 1) and Yan et al.27), while the primary porosity of 44 samples was calculated using mathematical model (Eqs. 1–4) (Fig. 2D, Table 1).

The grain shape and grain size distribution of the outcrop samples were also measured using Image Grain Size and Shape Analysis system. The primary porosity of all the samples from the digestion is calculated by Eqs. (1)–(4) (calculated results in Tables 2 and 3). The present porosity of the outcrop samples was determined using the gas porosity meter based on Boyle’s law developed by China University of Petroleum (East China). In addition, thin sections of samples C0–C8 were extracted to analyze diagenesis and porosity evolution.Table 2 Porosity calculated results of the braided sand outcrops.

Sample	Type	Primary porosity/%	Present porosity/%	Sample	Type	Primary porosity/%	Present porosity/%	Sample	Type	Primary porosity/%	Present porosity/%	
C0	D	32.5	2.30	B0	D	33.40	3.10	A0	C	34.1	3.2	
C1	B	33.2	1.80	B1	C	36.10	3.60	A1	B	31	1.3	
C2	C	38.5	4.80	B2	C	38.20	4.40	A2	C	38.5	4.4	
C3	C	36.2	4.60	B3	C	38.60	4.80	A3	C	39.3	6.8	
C4	C	36.8	8.70	B4	B	32.10	4.10	A4	C	39.7	4.3	
C5	B	37.5	5.70	B5	C	39.50	9.30	A5	D	34.1	5	
C6	D	31.2	2.50	B6	B	34.20	7.70	A6	B	38.8	0.2	
C7	C	37.8	0.54	B7	D	31.30	0.76	–	–	–	–	
C8	–	–	0.30	–	–	–	–	–	–	–	–	
Type A, B, C and D is proposed by Yan et al.19, using to calculated the primary porosity.

Table 3 Porosity results and particle size parameters for the braided sand.

Sample	φ5	φ16	φ25	φ50	φ75	φ84	φ95	Md	MZ	σ1	SK1	KG	S0	Sedimentary faices	Pri-Por/%	Type	
S1	 − 1.00	 − 0.38	 − 0.06	0.64	1.47	0.27	0.15	1.69	1.25	1.02	0.12	0.64	0.71	Braided channel	36.00	C	
S2	 − 1.32	0.03	0.54	1.36	2.06	0.19	0.12	1.71	1.32	1.18	 − 0.17	1.37	1.27	Braided channel	40.63	C	
S3	 − 2.00	 − 1.06	 − 0.60	0.30	1.25	0.30	0.15	1.90	1.51	1.05	0.03	0.30	0.33	Gravel-braided bars	33.57	B	
S4	 − 2.00	0.03	0.58	1.32	1.94	0.20	0.12	1.62	1.39	1.50	 − 0.21	1.31	1.22	Gravel-braided bars	37.14	C	
S5	 − 2.79	 − 1.97	 − 1.18	0.15	1.22	0.31	0.15	2.29	1.82	0.95	 − 0.11	0.15	 − 0.04	Braided channel	35.71	B	
S6	 − 2.07	 − 0.74	 − 0.19	0.71	1.47	0.29	0.16	1.78	1.41	1.17	 − 0.16	0.71	0.59	Braided channel	37.14	C	
S7	 − 0.19	0.23	0.60	1.25	1.79	0.24	0.15	1.51	1.07	1.00	 − 0.05	1.25	1.18	Braided channel	40.00	C	
S8	0.25	0.76	1.00	1.47	2.06	0.20	0.13	1.43	0.87	1.06	0.06	1.49	1.52	Braided channel	40.71	C	
S9	 − 1.58	 − 0.42	0.15	1.06	1.74	0.24	0.15	1.73	1.33	1.12	 − 0.22	1.07	0.89	Braided channel	39.29	C	
S10	 − 2.81	 − 1.74	 − 0.96	0.64	1.74	0.22	0.12	2.56	1.91	0.89	 − 0.19	0.64	0.37	Sands-braided bars	31.43	B	
S11	 − 0.23	 − 0.20	0.10	0.76	1.40	0.31	0.19	1.57	1.04	0.83	0.13	0.75	0.75	Braided channel	39.29	C	
S12	 − 1.93	 − 0.24	0.25	1.12	1.89	0.21	0.13	1.76	1.49	1.24	 − 0.17	1.12	1.04	Gravel-braided bars	37.14	C	
S13	 − 1.58	 − 0.59	 − 0.07	0.84	1.64	0.25	0.14	1.82	1.38	1.05	 − 0.10	0.84	0.75	Braided channel	33.71	B	
S14	 − 1.58	 − 0.81	 − 0.33	0.60	1.43	0.28	0.15	1.84	1.39	1.00	 − 0.04	0.59	0.53	Gravel-braided bars	40.00	B	
S15	 − 1.58	 − 0.59	 − 0.14	0.74	1.43	0.31	0.22	1.73	1.18	0.98	 − 0.19	0.73	0.61	Braided channel	40.87	B	
S16	 − 2.17	 − 1.44	 − 1.10	 − 0.16	0.89	0.38	0.16	1.99	1.55	1.00	0.14	 − 0.17	 − 0.07	Gravel-braided bars	32.86	D	
S17	 − 0.23	 − 0.08	0.23	0.86	1.56	0.26	0.14	1.57	1.13	0.96	0.17	0.86	0.90	Braided channel	35.71	C	
S18	 − 1.12	0.23	0.58	1.22	1.94	0.20	0.11	1.61	1.22	1.29	 − 0.02	1.23	1.26	Braided channel	40.71	C	
S19	 − 2.58	 − 1.65	 − 1.38	 − 0.57	0.32	0.59	0.25	1.80	1.39	1.11	0.11	 − 0.57	 − 0.49	Gravel-braided bars	32.86	D	
S20	 − 2.32	 − 1.61	 − 1.21	 − 0.16	0.71	0.44	0.20	1.96	1.51	0.98	0.02	 − 0.16	 − 0.20	Braided channel	35.71	D	
S21	 − 1.26	 − 0.29	0.12	0.79	1.43	0.29	0.16	1.57	1.20	1.23	 − 0.05	0.79	0.76	Braided channel	38.57	C	
S22	 − 2.17	 − 1.23	 − 0.64	0.32	1.09	0.37	0.21	1.81	1.47	1.05	 − 0.14	0.32	0.18	Braided channel	34.86	B	
S23	 − 2.17	 − 1.93	 − 1.48	 − 0.01	1.79	0.19	0.10	3.07	1.99	0.69	0.17	 − 0.01	0.16	Sands-braided bars	30.71	D	
S24	 − 1.26	 − 0.10	0.30	1.06	1.69	0.25	0.16	1.62	1.22	1.15	 − 0.14	1.05	0.98	Braided channel	34.29	C	
S25	 − 3.12	 − 1.31	 − 0.72	0.45	1.51	0.25	0.13	2.16	1.79	1.12	 − 0.13	0.46	0.38	Sands-braided bars	35.71	B	
S26	 − 0.58	0.17	0.47	1.09	1.69	0.25	0.15	1.53	1.05	1.11	 − 0.02	1.10	1.09	Sands-braided bars	37.14	C	
S27	 − 2.54	 − 1.46	 − 0.97	 − 0.04	0.86	0.37	0.16	1.88	1.59	1.16	0.03	 − 0.04	 − 0.02	Braided channel	36.43	B	
S28	 − 1.63	 − 0.86	 − 0.46	0.17	0.86	0.42	0.19	1.58	1.22	1.25	0.06	0.17	0.19	Braided channel	39.71	B	
S29	 − 2.70	 − 1.79	 − 1.23	 − 0.31	0.49	0.50	0.18	1.82	1.59	1.23	0.01	 − 0.31	 − 0.37	Gravel-braided bars	35.71	D	
S30	 − 1.93	 − 1.00	 − 0.42	0.34	0.97	0.40	0.23	1.62	1.30	1.19	 − 0.14	0.34	0.22	Braided channel	40.86	B	
S31	 − 1.54	 − 0.95	 − 0.54	0.36	1.36	0.27	0.13	1.92	1.45	0.98	0.11	0.36	0.42	Braided channel	37.57	B	
S32	 − 3.00	 − 1.88	 − 1.26	 − 0.14	0.81	0.40	0.17	2.04	1.73	1.10	 − 0.06	 − 0.14	 − 0.24	Gravel-braided bars	35.14	D	
S33	 − 1.32	 − 0.18	0.15	0.84	1.60	0.24	0.12	1.66	1.34	1.23	0.05	0.84	0.91	Braided channel	39.29	C	
S34	 − 1.81	 − 1.06	 − 0.68	0.20	1.15	0.33	0.17	1.89	1.41	0.97	0.07	0.19	0.25	Gravel-braided bars	30.00	D	
S35	 − 3.12	 − 2.20	 − 1.94	 − 0.49	1.25	0.25	0.12	3.01	2.03	0.80	0.17	 − 0.49	 − 0.22	Sands-braided bars	30.71	D	
S36	 − 2.32	 − 2.03	 − 1.82	 − 0.95	0.09	0.71	0.41	1.94	1.27	0.77	0.19	 − 0.95	 − 0.83	Sands-braided bars	37.14	D	
S37	 − 2.61	 − 2.01	 − 1.56	 − 0.11	1.51	0.21	0.11	2.92	1.98	0.77	0.12	 − 0.11	0.04	Sands-braided bars	33.57	D	
S38	 − 1.00	0.18	0.58	1.22	1.79	0.24	0.15	1.53	1.17	1.25	 − 0.15	1.23	1.17	Braided channel	41.43	C	
S39	 − 2.32	 − 1.84	 − 1.42	 − 0.36	0.62	0.42	0.16	2.03	1.61	0.99	0.12	 − 0.35	 − 0.31	Sands-braided bars	37.71	D	
S40	 − 1.56	 − 0.70	 − 0.23	0.56	1.25	0.33	0.19	1.68	1.24	1.08	 − 0.08	0.55	0.49	Braided channel	35.71	B	
S41	 − 1.93	 − 1.42	 − 1.21	 − 0.65	0.23	0.63	0.30	1.65	1.22	1.04	0.28	 − 0.65	 − 0.47	Braided channel	39.86	D	
Md is the mean particle size; Mz is the median particle size; σ1 is the standard deviation; SK1 is the skewness; Pri-Por is the primarity porosity, S0 is the Trask sorting coefficient; and φ5, φ16, φ25, φ50, φ75, φ84 and φ95 correspond to the particle sizes when the grain size probability curve reaches 5, 16, 25, 50, 75, 84 and 95, respectively.

This article follows Miall’s30 concept of a hierarchy of interfaces and elementary architectural units. The architectural–elementary configurations (AEC) of the outcrops were analyzed and the interfaces are shown in Fig. 2E.

Results

Grain size distribution and primary porosity heterogenetic characteristics of modern braided river sands

The grain size characteristics of modern braided river sands

There are two peaks in the grain size distribution curve (GSDC) of samples in modern braided river sands, and the skewness of the peaks are different. Based on the GSDC, all the samples are divided into three types, and named as type B, C, and D (Fig. 3a are the GSDC of all the samples; and Fig. 3b–d are the grains size distribution curve of 41 samples).Fig. 3 The types of grain size distribution curve of the modern braided river sands. (a) The grain size distribution curve (GSDC) of sands in modern braided river; (b–d) is the type of GSDC of sands in modern braided river, (b) is type C, (c) is type D, (d) is type B. (e) Is the distribution of sands type in different microfacies.

Nineteen samples from modern braided river were categorized as type B classification, with an average grain content between 0.21 and 1.414 at around 63.14%, an average grain content between 0 and 0.21 at about 13.89%, and an average grain content between 1.414 and 2 at around 22.97%. Twenty-nine samples from modern braided river were categorized as type C sands, with an average grain content between 0.21 and 1.414 at around 70.16%, an average grain content between 1.414 and 2 at about 17.06%, and an average grain content between 0 and 0.21 at around 12.78%. In addition, twenty-four samples from modern braided river were identified as type D sands, with an average grain content between 0.21 and 1.414 at around 29.95%, an average grain content between 0 and 0.21 at about 6.52%, and an average grain content between 1.414 and 2 at around 63.55% (Fig. 3c, Tables 3, 4). Table 4 The type and sedimentary microfacies of sands from modern braided river.

Sample	Facies	Type	Sample	Facies	Type	Sample	Facies	Type	Sample	Facies	Type	
S1	Braided channel	C	S19	Gravel-braided bars	D	S37	Sands-braided bars	D	S55	Sands-braided bars	D	
S2	Braided channel	C	S20	Gravel-braided bars	D	S38	Braided channel	C	S56	Braided channel	C	
S3	Gravel-braided bars	B	S21	Braided channel	C	S39	Sands-braided bars	D	S57	Braided channel	C	
S4	Gravel-braided bars	C	S22	Braided channel	B	S40	Braided channel	B	S58	Braided channel	B	
S5	Braided channel	B	S23	Sands-braided bars	D	S41	Braided channel	D	S59	Sands-braided bars	D	
S6	Braided channel	C	S24	Braided channel	C	S42	Braided channel	B	S60	Sands-braided bars	D	
S7	Braided channel	C	S25	Sands-braided bars	B	S43	Sands-braided bars	C	S61	Braided channel	B	
S8	Braided channel	C	S26	Sands-braided bars	C	S44	Braided channel	B	S62	Braided channel	B	
S9	Braided channel	C	S27	Braided channel	B	S45	Sands-braided bars	D	S63	Gravel-braided bars	C	
S10	Sands-braided bars	B	S28	Braided channel	B	S46	Sands-braided bars	D	S64	Gravel-braided bars	C	
S11	Braided channel	C	S29	Gravel-braided bars	D	S47	Sands-braided bars	D	S65	Sands-braided bars	C	
S12	Gravel-braided bars	C	S30	Braided channel	B	S48	Braided channel	B	S66	Sands-braided bars	D	
S13	Braided channel	B	S31	Braided channel	B	S49	Gravel-braided bars	C	S67	Sands-braided bars	C	
S14	Gravel-braided bars	B	S32	Gravel-braided bars	D	S50	Sands-braided bars	D	S68	Gravel-braided bars	C	
S15	Braided channel	B	S33	Braided channel	C	S51	Gravel-braided bars	B	S69	Sands-braided bars	D	
S16	Gravel-braided bars	D	S34	Gravel-braided bars	D	S52	Sands-braided bars	D	S70	Sands-braided bars	D	
S17	Braided channel	C	S35	Sands-braided bars	D	S53	Gravel-braided bars	C	S71	Braided channel	C	
S18	Braided channel	C	S36	Sands-braided bars	D	S54	Braided channel	C	S72	Sands-braided bars	D	

For samples from braided river, the GSDC and types of sands are different when the microfacies or architectural elements changed. In the center of the braided channel, 45.45% samples are types B sands, 51.52% samples are type C sands, and 3.03% are type D sands. In the mid-channel bars with coarse sands, the percentage of type B, C and D are 4.55%, 18.18%, and 77.27%, respectively. In the mid-channel bars with sands, the percentage of type B, C and D are 17.65%, 47.06%, and 35.29%, respectively. In the contact area between the braided channels and braided bars or the contact area between two braided channels, the sand type is quite diverse, but mainly type B (Fig. 3a). Thus, type B and C sands dominant in the braided channels; type D sands dominant in the braided bars with coarse sands; and type C and D sands dominant in the braided bars with sands (Fig. 3e).

The heterogeneities characteristics of primary porosity in modern braided river

The parameters in Eqs. (2)–(4) are given by Yan et al.19, and the results are ef1 = eF = 0.60, eC = em1 = em2 = 0.78, a0 = a1 = 0.39, a2 = 0.40, b0 = b1 = 0.41, b2 = 0.34, the primary porosity of samples from outcrops are calculated using these parameters. The results show that the maximum error of the calculated primary porosity is about 3%, and the calculated results have high reliability (The details can be found in Supplementary Appendix 2). The primary porosity of samples S42–S72 were calculated by using formulas (1)–(4). The primary porosity of the 72 sands samples are plotted on the sedimentary facies map (Fig. 4). The results reveal significant heterogeneity in the primary porosity of samples from braided river, with notable variations in the values of primary porosities. The maximum, minimum, average, and main distribution interval of the primary porosity are 41.43%, 28.51%, 36.60%, and 34–40%, respectively.Fig. 4 Primary porosity heterogeneities of modern braided river channel sands.

The regions with high primary porosity of braided river sediments were mainly concentrated in the central part of both the braided bars and braided channels. There are obvious low primary porosity areas at the edge of the braided bar and channel. The characteristics of primary porosity heterogeneities of braided river sediments can be summarized as follows (Fig. 4):The primary porosity variation of braided river sands is large and the heterogeneity of primary porosity is greatly affected by sedimentary microfacies or grain size with a maximum value of 41.43%, minimum value of 35.71%, and average value of 37%.

Most of the primary porosity is above 35% in the braided channel. The high primary porosity zone in the center of the braided channel is obviously related to strong hydrodynamic conditions which is conducive to the differentiation of grains and improving the sorting of sands.

The primary porosity increases from the edge to the center of the braided bar; the porosity at the edge of the gravel braided bar is obviously low (< 30%). The high primary porosity area in the central part of the braided bar, almost > 35%, is also related to strong hydrodynamic conditions.

The contact area of the braided bar and channel has a low primary porosity. The formation of this low primary porosity area may be related to the blocking effect of the braided bar on water flow in the braided channel.

Grain size distribution and primary porosity heterogenetic characteristics of braided sandstone outcrops

Grain size distribution of braided sandstone outcrops

Following Miall’s30 concept of a hierarchy of bounding surfaces and architectural elemental units, gray-white trough cross-bedded coarse sandstone and gravelly sandstone dominate the bottom of the braided sandstone outcrop; gray-white cross-bedded or parallel-bedded siltstone and medium-grained sandstone are dominant in the middle and upper; and a 0.3 m layer of gray-dark mudstone is distributed at the top (Fig. 2E). This constitutes a relatively complete sequence of braided river deposits. Gray-white trough cross-bedded coarse sandstone and gravelly sandstone were mainly deposited in the braided river bar; while gray-white cross-bedded medium-grained sandstone was mainly deposited in the braided channel. Parallel-bedded or corrugated bedding fine-grain sandstone and mudstone were mainly deposited in abandoned channel (Figs. 2E, 5a). The bottom and top of this outcrop were determined to 5th-order bounding surfaces; the surfaces between the abandoned channel and braided channel were determined to 4th–order bounding surfaces; and the surfaces between the braided river bar and braided channel were determined to 3th-order bounding surfaces.Fig. 5 Architectural-elemental configurations and grain size distribution curve of BRSD.

The GSDC of the 23 samples is shown in Fig. 5b. The median grain size of the samples decreases gradually from the bottom to top of the BRSD. The median grain sizes of samples at the bottom of individual braided channels or bars are slightly higher than those at the top (such as B2 and B3 in Fig. 5b), but with local variations (e. g. the median grain sizes of C2 and C3 are greater than C1). The GSDC of the 23 samples has two peaks, and the skewness of peaks are different. Gray-white trough-cross-bedded coarse sandstone and gravelly sandstones are dominant in the braided flow zone under the 4th-order bounding surface in the middle and bottom of the outcrop. The sorting coefficient is larger, and the GSDC shows twin negative skewness peaks. In the middle and upper parts of BRSD, the GSDC of samples shows positive skewness or normal twin peaks. The sandstone upper 4th-order bounding surface consist of fine grains, and the GSDC shows positive skewness twin peaks.

Primary porosity heterogeneities of braided sandstone outcrops

Samples C1, C5, B4, B6, A1, and A6 belong to Type B sandstone, samples C2, C3, C4, C7, B1, B2, B3, B5, A0, A2, A3, and A4 belong to Type C sandstone, and samples C0, C6, B0, B7, and A5 belong to Type D sandstone. The primary porosity of 24 samples were calculated by Eqs. (1)–(4), and the results are shown in Fig. 6 and Table 3. The GSDC of outcrops are similar as the GSDC of sample from modern braided river. The primary porosity of samples C0–C8 are 32.50%, 33.20%, 38.50%, 36.20%, 36.80%, 37.50%, 31.20%, 37.80%, and 32.3%, respectively. The primary porosities of samples B0–B7 are 33.40%, 36.10%, 38.20%, 38.20%, 32.10%, 39.50%, 34.20%, and 31.30%, respectively. The primary porosities of samples A0–A6 are 34.10%, 31.00%, 38.50%, 39.30%, 39.70%, 34.10%, and 38.80%, respectively. The range of primary porosity is 31–40% and the main range of primary porosity is 34–39%.Fig. 6 Primary porosity heterogeneities of braided sandstone outcrops.

Discussion

Primary porosity heterogeneity model of BRSD

Equations (1) to (4) show that the primary porosity of sandstone were mainly dominant by eX × VX. Where, ex is the primary void ratio of O-GPT with grains whose diameter varies within a given range; VX is the content of grains whose diameter varies within a given range. ex is influenced by the grain shape, VX is closely related to sedimentary hydrodynamic conditions and is also an important criterion to classify lithofacies and AEC. This indicates that if the particle size is the same and the particle shape changes little, then the primary porosity is related to the content of grain with different grain size (Vx). In other words, the primary porosity may be closely related to AEC. The results of the sample analysis in Fig. 7a show that characteristic parameters (Vx) for calculating the primary porosity are closely related to the AEC; here, Vx can refer to either Vf1, Vm1, or Vm2. Thus, the variogram of AEC and primary porosity is extracted (Fig. 7b).Fig. 7 (a) is the relationship between characteristic parameters (Vx) and architectural–elemental configurations; (b) is the variogram of primary porosity and architectural–elemental configurations.

The range and arch height of the variogram of sedimentary microfacies and primary porosity are similar; this proves that there is a good correspondence between the AEC and the distribution of primary porosity (Fig. 7b). Based on the analysis of the results, the plane distribution map of modern braided river is drawn (Fig. 4).

The same analysis process is being used for braided river sandstone outcrops. The map of primary porosity distribution is shown in Fig. 6. The primary porosity characteristics of BRSD show that: (1) The primary porosity in the upper parts of the 5th, 4th, and 3rd-order bounding surfaces is lower with a range of 30–33%; (2) A low primary porosity area is locally distributed in the upper part of the 2nd-order bounding surface. The 1st and 0th-order bounding surfaces have little influence on the primary porosity heterogeneities of the BRSD, which are affected by the river swing and braided river bar migration. The bottom and edge of the braided bar and braided channel are characterized by an area with low primary porosity. The distribution of high primary porosity areas in the center of the BRSD is influenced by 3rd-order bounding surface but is not restricted by the 2nd-order bounding surface (Fig. 6).

The primary porosity of braided river sands which is shown in Fig. 4, and braided river sandstone outcrop (Fig. 6) show that the AEC of braided sandstone bodies have an obvious control on the primary porosity distribution. The primary porosity heterogeneity is strong in the BRSD, which is confined by the 5th-order bounding surface. The distribution of high primary porosity areas is controlled by the 4th and 3rd-order bounding surfaces.

Grain shape is another important factor influencing primary porosity of braided river sandstone. Grain shapes are directly related to the distance between the deposition area and area of provenance. The roundness and sphericity of grains are high, when the distance between the area of deposition and that of provenance is long, and low, when this distance is short. Considering the general principles applicable to the primary porosity heterogeneity model, the primary porosity areas are divided into three segments: high porosity area (> 38%), medium porosity area (33–38%) and low porosity area (< 33%). In addition, the primary porosity of mudstone is generally high, but its calculation method is different from that for sandstone. The present porosity of mudstone is low (< 1%), and mudstone is generally impermeable. Therefore, the primary porosity of mudstone is not discussed in this paper.

A simple configuration model of braided river was proposed by Miall31, the primary porosity heterogeneity model of BRSD is summarized based on this model (Fig. 8a). Based on the analysis of the primary porosity in the modern braided river sands and braided river sandstones (outcrops), the heterogeneity model of the primary porosity for BRSD can be summarized as follows:In the center of the braided river bars and channels, which are constrained by 4th order bounding surfaces, type C sandstone is dominant, the GSDC show twin peaks with negative skewness, and the primary porosity is high (> 38%) (Fig. 8).

In the surfaces between the braided river bars and channels, which are 3rd order bounding surface attachments, type D is dominant, the GSDC show twin peaks with positive skewness, and primary porosity is low (< 33%) (Fig. 8a).

The areas between the center and edge of the braided river bars and channels are mainly type B sandstone with a moderate primary porosity (between 33 and 38%), the GSDC show symmetric twin peaks.

The braided river architecture model used in the model is only the simplest model. As the architecture model of river becomes more complex, the grain size distribution will become more complex, and the primary porosity model will become more complex. The porosity distribution in the single bar and braided channel should be similar, although every river has a different architecture.

Fig. 8 Sedimentary heterogeneity model of braided river sandstone bodies.

Influence of primary porosity heterogeneity and diagenesis on porosity heterogeneity in braided sand bodies

The correlation between primary porosity and present porosity

The present porosity of the 24 samples of BRSD of the Ahe Formation were measured by Boyle’s law (Table 2). The present porosities of samples C0–C8 are 2.30%, 1.80%, 4.80%, 4.60%, 8.7%, 5.70%, 2.50%, 0.54%, and 0.30%, respectively; that of samples B0–B7 are 3.10%, 3.60%, 4.40%, 4.80%, 4.10%, 9.30%, 7.70%, and 0.76%; that of samples A0–A6 are 3.20%, 1.30%, 4.40%, 6.80%, 4.30%, 5.00%, and 0.20%, respectively. The present porosities of all samples are less than 10%, mostly less than 5% (Table 2). The present porosities of all samples are plotted at the location of the sample on the outcrop (Fig. 5a). The fracture and secondary porosity are the main reservoir spaces of sandstone (Fig. 9). The porosity of fine-sandstone and siltstone is lower with a range of 0–1%, which are rich in ductile debris or calcite cements in the upper area of 4th-order bounding surface (Figs. 9b-C7,C8, 10). The porosity of coarse or medium sandstone in the upper parts of the 5rd and 3rd-order bounding surfaces is lower with a range of 1–3%; this sandstone have little calcite cement (about 4%) (Figs. 9b-C0, 10). The distribution of high present porosity areas in the center of the BRSD is influenced by 3rd-order bounding surface but is not restricted by the 2nd-order bounding surface (Fig. 5b).Fig. 9 Microscopic characteristics of outcrop samples of braided river sand body. (S-p is the secondary porosity; Fra is the fracture; Fe-cal is ferrocalcite; Fe-dol is ankerite).

Fig. 10 The composition and lithofacies of outcrop samples of braided river sand body in Ahe formation.

The main frequency distribution regions of present and primary porosities are 2–5% and 36–39%, respectively (Fig. 11a). Q–Q plots of present and primary porosities show that the primary porosity and the present porosity share similar probability distribution when the primary porosity is less than 35%, or the present porosity is less than 4%. The probability distribution of present and primary porosities is different when the present porosity is over 5%, giving two different linear relationships (Fig. 11b). Figure 11c plot the present and primary porosities of sandstone, and there is positive correlation between the present porosity and the primary porosity. However, there are also some significant differences in some of type C and B sand samples. The Q–Q plots of type B, C, and D show that the probability distribution of the present and primary porosities having different linear relationships mainly come from type C (Fig. 11d–f).Fig. 11 Relationship between primary porosity and present porosity of outcrop of braided sand bodies in Ahe Formation (a is distribution of primary and present porosity of braided sandstone in Ahe formation; b is Q–Q plot of primary and present porosity of braided sandstone in Ahe Formation; c plot primary and present porosity of braided sandstone in Ahe Formation; d,e, and f Q–Q plot of primary and present porosity of type C, B, and D in the outcrops, respectively).

If compaction is the only diagenesis considered, the relationship between the present porosity and primary porosity can be written as formula (5).5 Φ=Φ0×e-cz,

where Φ0 is primary porosity, Φ is porosity at depth z, e is the base of the Napierian logarithms, and c is the constant dimension (length−1) (proposed by Rubey and Hubbert16).

If the data set of the primary porosity is:6 Φ01,Φ02,Φ03,…Φ0x.

Thus, the data of present porosity can be denoted as:7 [Φ01×e-cz,Φ02×e-cz,Φ03×e-cz,…Φ0x×e-cz].

The probability distributions of [Φ01, Φ02, Φ03, ……Φ0x] and [Φ01 × e−cz, Φ02 × e−cz, Φ03 × e−cz, ……Φ0x × e−cz] are similar. This means that Q–Q plots of present and primary porosity has a linear correlation (Fig. 12). In other words, the nonlinear correlation of the present and primary porosities (broken lines in Fig. 11b) is influenced by chemical diagenesis, such as cementation and dissolution.Fig. 12 Q–Q plot of primary and compaction porosity of sandstone (X1 is minimum of [Φ01, Φ02, Φ03, ……Φ0x]; Xn is maximum of [Φ01, Φ02, Φ03, ……Φ0x]; Y1 is minimum of [Φ01 × e−cz, Φ02 × e−cz, Φ03 × e−cz, ……Φ0x × e−cz]; Yn is maximum of [Φ01 × e−cz, Φ02 × e−cz, Φ03 × e−cz, ……Φ0x × e−cz]).

The diagenetic process of sandstone and porosity evolution

The diagenetic sequence and porosity evolution model have been established by previous studied (details in Zhang et al.10,32), and the porosity evolution curve of samples C0–C8 can be established based on the analysis of diagenetic pathway and the statistics of authigenic minerals and pores. The carbon and oxygen isotopic values of C0–C8 samples were measured to determine the diagenetic pathway of different samples. The 13C value of Fe-calcite and ankerite in sample C0–C6 were ranged from − 5.8 to − 18.9‰. This indicates that a carbon source from the decarboxylation of organic matter (Morad30). The 13C value of calcite in sample C7 is about − 0.8‰, and the 13C value of Fe-calcite in sample C8 is about − 3.7‰. These indicate that the carbonate cement in sample C7 and C8 may in an early period, may even be the stage of deposition (Fig. 13).Fig. 13 Carbon and oxygen isotopic characteristics of samples C0–C8.

In addition, the oil inclusions with yellow and white fluorescent were observed in the fracture of quartz grains, and absorbed oils with yellow fluorescent were observed in the pore with clay of sample C4 (Fig. 14). This is similar to previous studies10,32, which confirms that samples from outcrop and subsurface may have experienced similar hydrocarbon charging processes. By using the lithofacies classification of Zhang et al.32, samples C0–C6 are identified as ductile-lean sandstone; samples C7 is identified as ductile-rich sandstone; and samples C8 is identified as calcite-cement sandstone (Fig. 13).Fig. 14 Thin section images of pore bitumens and oil inclusions of samples C4.

Combining with on the diagenetic sequence proposed by Zhang et al.10,32, the diagenetic sequence of Ahe Formation can be described as follows:Eodiagenetic process main include: grain sliding and ductile grain deformation during compaction; calcite cement; initial dissolution of framework and early hydrocarbon charge.

Mesodiagentic process main include: later dissolution of framework, later Fe-calcite cement, hydrocarbon charge.

On the basis of these analysis, the porosity evolution process of C0–C8 samples was restored (Fig. 15). During the eodiagenetic and mesodiagentic process, the porosity loss due to ductile grains deformation is large in C7 than that in other samples, and the porosity loss due to early carbonate cementation is large in C8 than that in other samples. The porosity loss due to compaction in samples C0–C6 almost the same and relative smaller than that of C7, some minor differences cause from differences in primary porosity and ductile grain content. The cementation which caused by Fe-calcite and ankerite resulted in relative low porosity of C0 and C1. The fracture and dissolution which caused by organic acids resulted in relative high porosity of C2–C5.Fig. 15 The process of porosity evolution of tight sandstones (samples C0–C8).

The similarity solution between primary porosity and present porosity

In the study of the heterogeneity of tight sandstone bodies, the above diagenetic pathway and porosity evolution anatomy is the most commonly used method. In general, most researchers use cartoons to illustrate the pore evolution pattern of different parts of the sandstone body or different lithofacies32,33. However, it has always been a problem how to apply geological information from single-point analysis in geological modeling, especially in heterogeneous characterization.

Figure 12 shows that the distribution probability of primary and present porosity should be linear, when the chemical diagenesis isn’t considered. However, Fig. 14 shows that chemical diagenesis generally plays a very important role in the porosity evolution of tight sandstone. The evolution process of porosity can be expressed as follows:8 Φ=Φ0×e-cz+Φd-Φc,

where the meaning of Φ, Φ0 and c is same as that in Eq. (5); Φd is the increased porosity by dissolution; Φc is the porosity loss by cementation.

Thus, the data of present porosity can be denoted as:9 Φ01×e-cz+Φd1-Φc1,Φ02×e-cz+Φd2-Φc2,Φ03×e-cz+Φd3-Φc3,……Φ0n×e-cz+Φdn-Φcn.

Here, Φd1 and Φc1 have effects at different stages of porosity evolution.

The data (6), (7) and (9) was normalized, as follows:10 Z=∑i=0n(Φ0i×e-cz+Φdi-Φci)=∑i=0n(Φ0i×e-cz)-∑i=0n(Φdi)+∑i=0n(Φci),

11 σ=∑(Φ0i×e-cz+Φdi-Φci)-Z)n-12,

12 Qxi=(Φ0i×e-cz+Φdi-Φci)-Zσ,

where Z is the average of present porosity or primary porosity; σ is the standard deviation of the present porosity or primary porosity; Qxi is the normalized value of (Φ0i × e−cz + Φdi − Φci) or (Φ0i). Formula (10)–(12) refers to the process of normalizing a data set, and Z, σ and Qxi changes with the normalized object, the above instructions are only examples.

Equations (10)–(12) is used to solve the Q-Q diagram of cement content, porosity reduction caused by compaction, porosity increase caused by dissolution, primary porosity and present porosity, the results are shown in Figs. 16 and 17. Figure 16a,b shows that the Q–Q plot of primary and present porosity is similar to that of secondary and primary porosity; Fig. 16c show that there is a linear relationship between secondary porosity and present porosity; Fig. 16d show that the Q–Q plot of secondary porosity and present porosity is nearly linear. The Q–Q plot of porosity reduction caused by compaction and primary porosity is almost not linear; the Q–Q plot of porosity reduction caused by compaction and present porosity is almost not linear; the Q–Q plot of cement content and primary porosity is almost not linear; the Q–Q plot of cement content and present porosity is almost not linear. These proved that the present heterogeneity of BRSD in Ahe Formation mainly come from the differential of dissolution.Fig. 16 (a) is the Q–Q plot of normalized data from primary and present porosity of samples from braided sandstone outcrops; (b) is the Q–Q plot of normalized data from secondary and primary porosity of samples from braided sandstone outcrops; (c) plot of secondary and primary porosity of samples from braided sandstone outcrops; (d) is the Q–Q plot of normalized data from secondary and present porosity of samples from braided sandstone outcrops.

Fig. 17 (a) is the Q–Q plot of normalized data from compaction porosity loss and primary porosity of samples from braided sandstone outcrops; (b) is the Q–Q plot of normalized data from cement and primary porosity of samples from braided sandstone outcrops; (c) plot of normalized data from compaction porosity loss and present porosity of samples from braided sandstone outcrops; (d) is the Q–Q plot of normalized data from cement and present porosity of samples from braided sandstone outcrops.

This analysis process is very important for the application of geological information obtained from single sample to geological modeling, and can also be used for the verification of geological models. Figures 5a and 6 are the profiles of present and primary porosity distribution of braided sandstone outcrops according to the geological laws, the Q–Q plot of present and primary porosity distribution of braided sandstone outcrops which data come from Figs. 5a and 6 is similar as that of sample data (Figs. 16a, 18). This confirms that the profile of porosity distribution which is plotted by the present and primary porosity information from samples records the heterogeneity of the porosity distribution.Fig. 18 Connection between the heterogeneity of present and primary porosity of outcrop of braided sand bodies in Ahe Formation (a is gray map of primary and present porosity of braided sandstone outcrop in Ahe Formation (Figs. 5a, 6); b is Q–Q plot of digital primary and present porosity image).

The application of geological information from single-point analysis to geological modeling, especially in heterogeneous characterization, is a very difficult study. However, it is important for us to recover the physical properties of sand bodies for critical periods in geological history. The above method is only a small experiment. This is a small step, but an indispensable step for a long journey. To fully understand the heterogeneous characterization of sand bodies for critical periods in geological history, more approaches are being tried by the authors and will be published in the future.

Conclusions

The characteristic parameters (Vx) for calculating the primary porosity are closely related to the AEC, and the range and arch height of the variogram of sedimentary microfacies and primary porosity are similar. Thus, the AEC of braided sand bodies have a strong effect on the distribution of the primary porosity heterogeneities of the sand bodies.

A simple primary porosity heterogeneity model of braided river sandstone bodies is summarized. In the center of the braided bar and channel, which is constrained by the 4th order bounding surface, type C sandstone is dominant, the GSDC show twin peaks with negative skewness, and primary porosity is high (> 38%). In the surface between the braided bar and channel, which is the 3rd order bounding surface attachment, type D becomes dominant, the GSDC show twin peaks with positive skewness, and primary porosity is low (< 33%). The area between the center and edge of the braided bars and channels are dominated by type B sandstone, the GSDC show symmetric twin peaks, and the primary porosity is between 33 and 38%. The braided river architecture model used in the model is only the simplest model. As the architecture model of river becomes more complex, the grain size distribution will become more complex, and the primary porosity model will become more complex.

Eodiagenetic process of sandstone in Ahe Formation mainly include: grain sliding and ductile grain deformation during compaction; calcite cement; initial dissolution of framework and early hydrocarbon charge; Mesodiagentic process of sandstone in Ahe Formation main include: later dissolution of framework, later Fe-calcite cement, hydrocarbon charge.

The reservoir quality prediction models established shed light on the porosity evolution process of three lithofacies are different.

Q–Q plot of the primary porosity and present porosity are nonlinear correlation caused by chemical diagenesis. The present porosity heterogeneity of BRSD in Ahe Formation less affected by compaction and cementation; the present porosity heterogeneity of BRSD in Ahe Formation mainly come from the differential of dissolution.

Supplementary Information

Supplementary Information.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-71433-z.

Acknowledgements

This study is supported by Funded by Open Foundation of Shanxi Key Laboratory of Lacustrine Shale Gas Accumulation and Exploitation, National Natural Science Foundation of China (42002145), China Postdoctoral Science Foundation funded project (2020M672173), Qingdao Applied Basic Research, National Science and Technology Major Project (2017ZX05008-004), Key Technology of Efficient Exploration and Development of Deep Oil and Gas in Tarim Basin (ZD2019-183) and the Fundamental Research Funds for the Central Universities (22CX06003A).

Author contributions

Yiming Yan: Funding acquisition, Methodology, Data curation, Writing—review & editing; Liqiang Zhang: Conceptualization, Investigation, Funding acquisition; Review & editing; Xiaorong Luo: Conceptualization, Methodology, Investigation, Supervision. Chenyu Liu: Writing—review & editing.

Data availability

All data generated or analysed during this study are included in this published article [and its Supplementary Information files].

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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