# Estimation of Sedimentary Rock Porosity Using a Digital Image Analysis
## 1 Introduction  
A number of studies in the past decade have shown that porosity and pore size can significantly affect the physical properties of rocks [1; 2; 3; 4; 5]. Previous research established a few relationships between porosity, Young's modulus, and strength of rock [1; 2; 3; 4; 6; 7]. However, [PERSON] et al. [8] reviewed 31 empirical correlations between rock properties and porosity and noted that the majority of these empirical equations were not sufficiently general as they had strong regional influences, and were unable to account for all available published data on rock strength and physical properties.  
In current practices, laboratory methods are employed to investigate the rock pore space, yet provide different levels of accuracy. Mercury intrusion porosimetry (MIP) is a standardized technique that enables precise estimations of the pore size of rock in the laboratory [9]. However, this experimental procedure is time-consuming, and it requires special equipment that may not be readily available in many laboratories around the world. The scanning electron microscope (SEM) method is an alternative approach that requires minimal sample preparation [10]. Although rock often appears as continuous material, at a microscopic scale, it is composed of a sequence of particles and pores that constitute a rock structure. Thus, using high-quality SEM images, it is possible to identify and quantify the open pore space in rock, which can provide an estimation of the material porosity [11; 12; 13]. Yet, recent works [14; 15; 13] indicated that due to the diversity of rock structures, the quality of digital photographs, and the complexity of the numerical recognition algorithm, it has been extremely challenging to detect and analyse each pore fracture in SEM images to a high level of accuracy. In this regard, the consequential outcome of studies using a digital analysis method of morphological fracture is limited, and only a few practical approaches for the fracture image recognition have been proposed to date [14]. One of them is the pore and crack analysis system (PCAS), which has recently become a popular tool to quantify the fracture and pore space in SEM images [16; 17; 18; 19; 20; 21]. As it provides the advantages ofsimplicity and efficiency over conventional manual procedures, PCAS has successfully been employed to detect cracks, micropores, and mineral particles in rock or soil [22; 23]. However, recent studies indicate some discrepancies between the experimentally measured three-dimensional porosity and the two-dimensional porosity obtained from the digital image analysis. The summary of the previous research presented in Table 1 clearly shows relatively large differences in the porosity values (ranging from 0.56 to 4.6) obtained from the same material using either a direct experimental method or the digital analysis technique. It is clear that more research is necessary to clarify the existing correlations and to develop guidelines on the use of digital analysis for the estimation of rock porosity.  
This article seeks to establish the relationship between the porosity obtained via the MIP and digital analysis methods, which can be widely used for different sedimentary rocks. A series of MIP experiments were carried out on three common sedimentary rocks (sandstone, siltstone, and coal). The porosity and pore size distribution of these rocks were estimated from the high-quality SEM images by employing the PCAS approach. This paper presents and discusses the obtained results.