To address the challenge of reconstructing or designing the three-dimensional microstructure of nanoporous materials, we develop a computational approach by combining the random closed packing of polydisperse spheres together with the Laguerre-Voronoi tessellation. Open-porous cellular network structures that adhere to the real pore-size distributions of the nanoporous materials are generated. As an example, κ-carrageenan aerogels are considered. The mechanical structure-property relationships are further explored by means of finite elements. Here we show that one can predict the macroscopic stress-strain curve of the bulk porous material if only the pore-size distributions, solid fractions, and Young's modulus of the pore-wall fibres are known a priori. The objective of such reconstruction and predictive modelling is to reverse engineer the parameters of their synthesis process for tailored applications. Structural and mechanical property predictions of the proposed modelling approach are shown to be in good agreement with the available experimental data. The presented approach is free of parameter-fitting and is capable of generating dispersed Voronoi structures.