# Acoustic Propagation Characteristics of Unsaturated Porous Media Containing CO\({}_{2}\) and Oil
## 1 Introduction  
With the intensification of the greenhouse effect, carbon capture and storage (CCS) and carbon capture, utilization, and storage (CCUS) have attracted much attention in recent years [1]. Carbon dioxide (CO\({}_{2}\)) geological utilization and storage (CGUS) is one of the most common methods to achieve CCUS. However, it requires careful monitoring to ensure the security of CGUS [2]. Seismic monitoring is an essential technology with the advantages of a wide detection range and high accuracy [3]. For seismic monitoring, it is vital to clarify the physical nature of acoustic wave propagation with varying environmental parameters, which can be used in identifying CO\({}_{2}\) migration status, spatial distribution, and providing guidance for CGUS strategy. Most underground formations can be classified as porous media; the fluid-holding capacity of pore space is the basis for CGUS. When CO\({}_{2}\) is injected into the reservoir, the pore fluid is replaced by CO\({}_{2}\), accompanying the dissolution effect, which affects the energy exchange of the acoustic wave [4]. Thus, understanding the changes of seismic attributes form the foundations for successful monitoring. Therefore, analyzing the wave propagation in the reservoir filled with supercritical CO\({}_{2}\) and other fluids is crucial. In particular, changes in CO\({}_{2}\) injection in pore fluid parameters via different temperatures and pressures significantly impact how waves propagate. Formations in CGUS are typical unsaturated porous media, composed of a solid grain and two fluids (usually CO\({}_{2}\) and oil in the oil reservoir), where acoustics theories for multi-phase porous media are appropriate for studying wave propagations [5]. To date,many models have described the porous media saturated by two immiscible fluids, such as Biot-Gassmann-Wood (BGW) theory [6; 7; 8], [PERSON]'s model [9], [PERSON]'s model [10], the Biot-Rayleigh (BR) theory [11], [PERSON]'s model [12] and [PERSON]'s model [13; 14]. Among them, the BGW theory is based on the effective media theory, which can be used at low frequencies [15]. The BR, [PERSON], and [PERSON]'s models describe patchy saturation's mesoscopic dissipation mechanisms [16]. [PERSON] and [PERSON]'s models are the theory of the unsaturated porous media, considering both changes in capillary pressure and inertial and viscous coupling. [PERSON]'s model is derived on the Lagrangian description, and [PERSON]'s model is deduced on the Eulerian description. Compared with [PERSON]'s model, [PERSON]'s model derives from basic equations of the dynamic problem and the equation of state, and provides a detailed mathematical description of viscous coupling parameters, so that the parameters have clearer physical meaning. Currently, the BGW theory is commonly used in the seismic monitoring of CGUS [17]. However, the essence of this model is still a fluid-solid porous media, which replaces the parameters in Biot theory with the equivalent parameters of the mixed fluid. As a result, the BGW theory ignores fluid-fluid interactions [18]. In contrast, [PERSON]'s model considers the coupling of fluid-fluid, which is more suitable to match the actual situation of unsaturated porous media in CGUS. [PERSON] [13; 14] validated the correctness by degenerating the model into the fully saturated porous media ([PERSON] [6; 7]; [PERSON] [19]) and the unsaturated porous media ([PERSON] [12]; [PERSON] [20]). [PERSON] [21] used [PERSON]'s model to analyze the acoustic propagation in the unsaturated porous media. The fluid type, CO\({}_{2}\) content, and dissolution are the key factors causing changes in pore fluid parameters [22]. In the monitoring of CGUS, many scholars used [PERSON]'s model [23] to describe the gas dissolution effect on fluid parameters [17]. [PERSON]'s model was proposed for hydrocarbon gases. The influence of hydrocarbon gases and CO\({}_{2}\) on oil, however, are different [24]. Therefore, it is inaccurate to treat CO\({}_{2}\) as a hydrocarbon gas.