# A Multi-Level Approach for Simulation of Storage and Respiration of Produce
## 1 Introduction
The basic unit cube model [7] is possibly the simplest three-dimensional geometric idealization of a porous material comprised of spheres and is created by placing a sphere inside a cube, and then increasing its diameter until the desired porosity is achieved. The geometry is extremely simple and can be used for either spherical void materials or for packed spheres (if the sphere diameter is set equal to the cube side length and the sphere is assumed solid). The model makes it easy to analytically calculate parameters such as porosity and interstitial surface area, but [PERSON] et al. [7] found that estimates of the permeability led to pressure drops that were unrealistically low, mainly due to the ordered orientation that the model produces. Other authors also used simple cubic packing to build a channel containing a large number of particles to study heat transfer and pressure drop [8; 9]. Moving away from ordered geometric idealizations, a study undertaken by [PERSON] [10] computed the flow and heat transfer in a saturated REV micromodel, which was obtained from a 3D micro-CT image following the procedure described in [11]. [PERSON] and [PERSON] [1] developed a model that creates a region of variable-sized spheres randomly arranged to produce a foam structure with a specified pore-size and porosity. This model incorporates YADE (Yet Another Development Engine) [12] and produces geometric models that yield far superior simulated results in terms of pressure drop and convective heat transfer compared to prior work [12]. YADE is an open source discrete element modelling (DEM) framework, which is commonly used to study solid particle packing problems. The particles may deform or interact together based on kinematics and force analysis. Herein, and similar to the work of [PERSON] and [PERSON] [1], it is used to create packing of objects that results in a porous media representative elemental volume. Because of the generic nature of the model by [PERSON] and [PERSON] [1], it is also possible to incorporate porosity gradient and shape effects, which makes it an attractive tool for the present study. To this end,the digital geometry generation model developed by [PERSON] and [PERSON] [1] is extended herein to generate packing arrangements suitable for produce modelling. To simulate metabolic processes that occur under storage conditions, consideration of the produce-to-air interaction is also required. In essence, this requires that an inner-produce model be implemented to characterize gas respiration processes; i.e., CO\({}_{2}\)/O\({}_{2}\) gas exchange and heat exchanges that occur between the produce and surrounding air during respiration and transpiration [13; 14; 15; 16]. It is also important to characterize other gas exchanges like ethylene (C\({}_{2}\)H\({}_{4}\)) due to its major role in the ripening of some fruits and vegetables [17; 18]. The metabolic process of respiration and gas emission in fruits and vegetables is a function of many factors, including the nature of the crop itself--i.e., whether it is climacter (ripens after harvest) or non-climacteric fruits (does not ripen further after harvest) [17; 18; 19; 20]--however, it is mainly dependent upon the composition of the atmosphere around the fruit in terms of concentrations of oxygen and carbon dioxide (mainly) and the temperature of storage [21; 22; 23]. Predictions of ethylene emission from fruits and vegetables is important and affects the process of ripening and shelf-life significantly [18; 19; 24]. This article presents an approach to model respiration and transpiration processes for stored produce. The work is considered an application/extension of porous media modelling tools; however, it is specifically directed towards produce, which necessitates revisiting of shape idealization and packing to achieve a proper REV and exchange process modelling.