## 1 Introduction  
Steam-assisted gravity drainage (SAGD) is widely applied to recover bitumen and heavy oil resources [1, 2]. In a typical SAGD configuration, a pair of horizontal wells are positioned near the bottom of a reservoir. The steam is injected through the upper horizontal well, while heated oil and condensed water are produced through the lower production well [3]. With the continuous injection of the steam, the steam chamber grows vertically and then laterally. Uniform development of the steam chamber is crucial to SAGD performance. The economics of a SAGD project is closely related to the geological parameters, such as reservoir thickness, vertical permeability, oil saturation, and porosity [4, 5, 6]. Increasing the reservoir heterogeneity continues to challenge the application of SAGD technology in bitumen or heavy oil formations. Shale barriers are one of the common heterogeneous features in oil sand reservoirs [7; 8; 9; 10; 11] and are reported in various SAGD projects [12; 13; 14; 15]. These shale barriers usually consist of alternate pairs of sand and mudstone [16; 17], resulting in low permeability [18]. Therefore, the presence of shale barriers in oil sand reservoirs tends to impede the development of steam chambers and adversely affects SAGD performance [19]. A considerable number of studies have been conducted to understand the impact of shale barriers on SAGD performance. Because of the limited information regarding shale barriers in reservoirs, extensive numerical studies have been performed considering shale locations and shale characteristics. [PERSON] and [PERSON] (2009) generated various shale barriers in a two-dimensional simulation model. They examined the sizes and the vertical locations of the shale barriers [20]. The shale barriers were either positioned above the injection or between the injector and the producer. It was found that the vertical distance of shale barriers was essential to affect SAGD production. [PERSON] et al. (2021) established a numerical model containing shale barriers to evaluate the SAGD process, including steam chamber evolution, production evaluation, and economic evaluation. In real reservoirs, the information on shale barriers is usually unknown. [PERSON] et al. (2018) integrated artificial intelligence and production data to interpret shale characteristics [21]. Similarly, [PERSON] and [PERSON] (2021) applied machine learning to investigate the impact of random shale barriers [22]. Except for numerical investigation, experimental efforts have also been made to understand the effects of shale layers on SAGD performance. [PERSON] and [PERSON] (1992) were among the first to design physical experiments considering reservoir heterogeneity [23]. They provided an initial understanding of the effects of shale barriers on SAGD performance. In recent years, researchers have extended the previous work and considered multiple shale barriers in the physical experimental model. [PERSON] et al. (2019) experimentally investigated the steam chamber and production characteristics of SAGD, considering multiple barrier layers [24; 25]. Multiple impermeable and parallel shale barriers were considered in the physical sand pack model. Different flow characteristics were identified with variations in shale location and length. Similarly, [PERSON] et al. (2022) performed multiple experiments to study the effect of different distributed interlayers on SAGD performance. Steam chamber development was well illustrated based on the temperature data measured by thermocouples [26]. They provided guidance to place wells to minimize the effects of shale barriers on SAGD performance. Although previous researchers investigated the effects of shale layers on SAGD performance [16; 24; 26], limited effective strategies have been provided to improve the production performance in reservoirs with multiple shale layers. [PERSON] et al. (2011) investigated the potential injection strategies to reduce the impact of the shale barrier on the SAGD process.