## 1 Introduction  
China is a major wheat-growing country, and the annual production output of wheat is over 130 million tons [1]. The safe storage of wheat is crucial for national security. This requirement has become more important with the intensification of the Russia-Ukraine conflict and the current Palestinian-Israeli conflict [2, 3]. However, when the moisture content of wheat is above the safe level of 14% during storage, the number of pests and mold will sharply increase. This can result in local mold and heating in the wheat pile, which can contribute to quality degradation [4]. To ensure wheat quality during storage, the wheat pile must be kept below a safe moisture level and at an appropriate temperature [5]. A viable solution to counteract these problems is the application of low-temperature ventilation drying [6]. This approach reduces the temperature and humidity of the air around the grain particles by forming airflow circulation within the grain pile. Then, the air undergoes heat and humidity exchange with the grain particles to achieve the goal of reducing the temperature and moisture content of the grain pile [7]. Therefore, studying the drying behaviors of the low-temperature drying of wheat grain piles is crucial for the safe storage of wheat. The distribution of porosity inside the grain pile is a key parameter that affects the heat and water transfer inside the grain pile during the process of drying. The airflow circulation inside the grain pile is mainly carried out through the connected pores between particles [8; 9; 10]. As the depth of the grain pile increases, the vertical pressure increases, which makes this phenomenon more obvious [11]. Previous studies have shown that the porosity will gradually decrease as the depth of the grain pile increases, which indicates that the resistance of the airflow passing through this area will increase [12; 13; 14], reducing the drying efficiency. Simply treating the porosity of the grain pile as a uniform distribution will lead to inaccurate predictions of the grain pile temperature and moderation during numerical simulation [15]. Moreover, compared with the cooling results of grain with a uniformly distributed porosity inside the pile, it has been demonstrated that the cooling time for grain with a non-uniform porosity increased by 55% [16]. In addition, as the depth of the grain pile increases, the effect of self-compaction also increases, resulting in the air velocity decreasing [17]. Although researchers have provided many contributions in terms of the distribution of non-uniform porosity, most scholars have focused on the influence of porosity on the distribution of airflow velocity and airflow resistance; the effect on the heat and moisture transfer inside the grain pile is rarely reported. Considering the influence of non-uniform porosity in the simulation of the low-temperature drying of a wheat grain pile is not enough for prediction accuracy, and the selection of the drying model is more important. However, the heat and moisture transfer inside the grain pile during the drying process is complex [18]. For this reason, many drying models have been used to study the drying process for wheat grain piles [19]. There are more than 100 different thin-layer drying models based on semi-theoretical models and the empirical models used in grain piles under different drying conditions [20]. For the semi-theoretical models, researchers have usually proposed the drying models based on [PERSON]'s law of cooling, [PERSON]'s second law of diffusion [21; 22; 23; 24; 25; 26], and relevant experiments. For the empirical models, scholars have derived models from relevant experimental data, such as the Wang and Singh model, the Thompson model, the Weibull distribution models, etc. [27; 28; 29]. Compared with the empirical models, the semi-theoretical models consider the fundamentals of the drying process, so they do not require assumptions regarding the geometry of a typical grain and are more suitable for the drying of porous media [30].