**1. Introduction**

The organic-rich shale reservoirs have gained increasing attention in the last decades due to the depletion of conventional reservoirs [1,2]. For reliable volumetric calculation of the reserve, the porosity and water saturation are the most critical parameters to estimate [3–6]. The shale reservoirs contain free and adsorbed gases. The free gas associates within the pore spaces whereas the adsorbed gas is usually linked with the clay minerals and organic matter [2,4,7–10]. However, the complex pore system and organic matter together with inorganic mineral constituents affect the well logging tool responses needing to take them into account during petrophysical evaluation. Previous studies demonstrate that the porosity can be overestimated by using empirical equations without applying

kerogen corrections. Therefore, the conventional approaches for porosity estimation are not feasible for organic-rich shale reservoirs. Many authors selected petrophysical models based on wireline logs to generate a set of simultaneous equations to estimate the kerogen content, mineral volume, and pore volume [7,11–13]. The introduced methods are most suitable for composition computation; however, it is hard to accurately determine all the required coefficients. Similarly, few authors standardised the well logs by multiplying the log data with defined coefficients to match the results with the core-derived porosity [12]. However, such equations were limited to a specific area and data set due to heterogeneity of shale in terms of thermal maturity, mineral composition, and organic matter content. Moreover, the organic-rich shales consist of the organic as well as matrix porosities [5,10,14–16]. In this study, the porosity for the shale reservoir is estimated by using a kerogen corrected density log, and the kerogen porosity is calculated by using a mass balance method based on original total organic carbon (TOCo) and kerogen maturity. The core-based total organic carbon (TOC) and porosity were used to validate the results.

Similarly, the accurate estimation of water saturation also plays a key role in economic evaluations of shale reservoirs. However, the investigations of the water saturation determination methods did not ge<sup>t</sup> much attention in the literature. Already available water saturation equations, e.g., Archie and Simandoux work better for conventional reservoirs (e.g., sandstone and shaly sands) [17,18]. However, the accurate determination of the unknown parameters such as formation water resistivity (Rw), cementation exponent (m), and saturation exponent (n) is very challenging for shale reservoirs [2,4,19–21]. The shale reservoir is a mixture of inorganic material (e.g., clays and detrital grains), kerogen, clay bound water, free and capillary held water, free and adsorbed gas [2,4]. However, the resistivity tool measures a reflection of constituent minerals and fluids of shales. Therefore, it is very critical to correct the resistivity log for shale and kerogen effects. In this research, a water saturation equation independent of water resistivity and Archie's parameters is introduced. Based on core derived water saturation validation, this equation worked very well as compared to other equations. However, it is always hard to take and interpret pressurised core samples from shale reservoirs. Therefore, sometimes it is impractical to measure water saturation through core samples in shale.

A case study from organic-rich Ordivician Goldwyer Formation (Goldwyer-III shale unit), Canning Basin, Western Australia is presented to verify both techniques for porosity and water saturation estimations. The Goldwyer Formation of Lower to Middle Ordovician age has an average thickness of almost 400 m, whereas, it's the thickest encounter (740 m) is recorded in Blackstone 1, a Lennard Shelf Sub-basin well. The Goldwyer shale is deposited in an open marine setting [22] having thin laminations of quartz silt and carbonates bands with alternating black shale layers. The mineral composition of Goldwyer shale includes quartz, carbonates, clay minerals, and pyrite [14]. The illite is a more abundant clay mineral in this shale. The Goldwyer shale is thermally mature having kerogen types-II and III and the total organic carbon content (TOC) varies from 0.35 to 4.5 wt% [23,24]. The results indicate a good match between core-based and corrected well logs-based estimations. Archie equation overestimated the water saturation, however, the proposed modified equation provided us better results. [25,26].

#### **2. Materials and Methods**

As illustrated in the simple shale reservoirs petrophysical model (Figure 1), the organic-rich shales are composed of kerogen and non-kerogen parts. A systematic workflow is developed to estimate the porosity and water saturations by considering the organic matter and matrix of the shale.

**Figure 1.** A typical conceptual petrophysical model for shale reservoirs showing kerogen porosity Øk and non-kerogen Ønk (inorganic matrix) porosity, modified from Yu et al. [5].
