###### Abstract
In this regard, [PERSON] [17] established an empirical model by fitting experimental data of pressure drop \(\Delta P\) across the grain bulk and airflow velocity \(v_{a}\) for several grain types using a logarithmic scale. \(v_{a}\) referred to the hypothetical airflow velocity calculated from the volume flow rate in the free bulk cross-section area, also known as superficial velocity. However, [PERSON]'s model was limited to a narrow range of airflow velocities, which was further enhanced by the model of [PERSON] and [PERSON] [18]. Due to their ease of handling and simplicity, these models have been used in several studies [19; 20; 21]. In addition, [PERSON] [22] developed a lumped polynomial-based model capable of accurately anticipating the relationship of \(\Delta P\) vs. \(v_{a}\), but lacked insight into parameters affecting the airflow resistance. A modified version was proposed by [PERSON] et al. [23] that included the moisture content as an input parameter. As these models were empirical in nature, they were tied to the same grain-air conditions and bin configurations for which they were created and therefore can outperform when those conditions vary widely. To overcome the shortcomings of empirical models, semi-empirical models which use the grain's physical characteristics and air properties have been developed. [PERSON] [24] conducted a thorough data analysis to describe the relationship between \(\Delta P\) and \(v_{a}\) of uniform spherical particles and developed a semi-empirical model based on the Kozeny-Carman [25] and Burke-Plummer relationships [26], making this model one of the most commonly analyzed and used in the literature. However, the [PERSON] model lacked adaptability to non-spherical shapes of particles, thus [PERSON] [27] and [PERSON] and [PERSON] [28] suggested quantitative improvements to account for irregular and random-sized shapes of grains. A simplification of these models was proposed by [PERSON] and [PERSON] [29]. In addition, [PERSON] [30] developed a semi-empirical model based on the Hagen-Poisseuille law for isothermal flow that contained a modified friction factor for the state-of-flow and a shape factor for non-spherical particles, while [PERSON] and [PERSON] [31] established another model for high grain bulks. Due to their theoretical underpinning, the semi-empirical models were able to determine the effect of different grains, moisture contents, filling methods, impurity concentration and airflow directions on the airflow resistance [12; 13; 23; 32]. They were also viable in isolating and quantifying the grain bulk pore volume. A summary of the above-mentioned models for describing the relationship of \(\Delta P\) vs. \(v_{a}\) in grain bulks is presented in Table 1. So far, the known models are limited to depicting the complexity and diversity of bulk pore structures [29]. During storage, grain bulk undergoes burden pressures imposed by its dead weight, contributing to self-compaction [33; 34; 35]. Hence, the bulk characteristics may change depending on the degree of compaction. According to [PERSON] et al. [36], the airflow resistance in aeration systems is significantly increased with the increase of compaction when higher pressures are applied. Therefore, the misestimation of airflow resistance due to compaction can lead to ineffective aeration strategies and grain quality problems [35]. To date, the literature offers limited coverage on the effect of compaction on the airflow resistance of stored grain bulks where controlled compaction systems or filling methods were used [36; 37; 38]. However, the influence of spontaneous temporal and spatial self-compaction on the airflow resistance of practical storage systems has not been considered so far.