Does Gassmann Fluid Substitution Work in Complex Carbonates?

Obtaining or monitoring fluid saturation from elastic properties (such as quantitative seismic interpretation) is of great importance to oil and gas industry as well as gas storage applications (Avseth et al. 2000; Fawad et al., 2020; Dvorkin et al. 2014; Fawad and Mondol, 2022). The most commonly used formulations for linking fluid content/saturation and elastic properties is Gassmann (Gassmann 1951). Gassmann theory has been used extensively in rock-physics related literature to either test the feasibility of time lapse seismic (forward modeling) or to invert for changes in fluid saturation based on time lapse seismic (Avseth et al. 2000; Mavko et al., 2009; Dvorkin et al. 2014; Fawad et al., 2020; Fawad and Mondol, 2022). Such applications have gained popularity especially in sandstone reservoirs while the applicability of Gassmann in carbonates have been a debate for over a decade. Carbonate rocks are frequently characterized by heterogeneous microstructure and properties as complicated by their variable pore types and geometry (e.g., Eberli et al., 2003; Fournier et al., 2014; 2018; Neto et al., 2014; El Husseiny and Vanorio, 2015; 2017; El-Husseiny et al., 2019; 2022; Regnet et al., 2015; Jaballah et al., 2021; Salih et al., 2021, Reijmer et al., 2021). Such heterogeneity combined with the reactivity of calcite and dolomite minerology have raised questions about whether Gassmann theory can be used in carbonates or not (Adam et al., 2006; Vega et al., 2010; Sharma et al., 2013; Vanorio et al., 2011). Large body of literature, including mainly laboratory measurements at ultrasonic frequencies indicated that Gassmann formulations tend to underestimate the changes in velocities associated with saturation changes (Baechle et al., 2005; Rogen et al., 2005; Khodja et al., 2022). Nevertheless, an overestimation by Gassmann's prediction has been observed for some cases/samples (Wang, 2000; Baechle et al., 2005; Vega et al., 2010; El-Husseiny et al., 2019). Due to the scarcity of well log data and the feasibility of lab measurements, most studies conducted to evaluate the applicability of Gassmann have utilized the laboratory ultrasonic measurements and core samples (Vega et al., 2010; Sharma et al., 2013; Baechle et al., 2005; Vanorio et al., 2011; Khodja et al., 2022). The conventional approach is to measure elastic properties before (i.e., dry) and after saturation with a fluid and then compare Gassmann predictions with the measured saturated values. One fundamental issue with this approach is that ultrasonic measurements of saturated rock samples are prone for dispersion (i.e., dependent of velocity on frequency) which is not present at low frequency (at which Gassmann is applicable). Many studies have discussed this dispersion and its impact on velocity (e.g., Mavko and Jizba, 1991; Borgomano et al., 2017) which is not applicable to seismic frequency and is not considered in Gassmann. Another fundamental issue with many studies is the use of a fluid that is not at equilibrium with the rock (like distilled or deionized water) which then results in dissolution for example and shear weakening (Adam et al., 2006; Baechle et al., 2005; Vanorio et al., 2011). Such weakening clearly would violate Gassmann condition for constant shear modulus during the fluid substitution. In avoiding the above issues, this work investigates the applicability of Gassmann in carbonates using low frequency laboratory measurements published in literature in addition to combining ultrasonic laboratory measurements from dry cores (should not suffer from dispersion) with well log data. In particular, this study aims to answer the following questions: 1. Does Gassmann provide accurate prediction in carbonates when dealing with fluids that are not reactive (i.e., like oil or brine in equilibrium with the rock frame)? 2. Can Gassmann be used in rock-physics modeling of carbonates to build the velocity-porosity relationship considering different fluid content?.