Many applications, especially those related to subsurface studies, exhibit complex geometries and heterogeneous data distributions. This complexity is evident in scenarios such as subsurface applications, where permeability can abruptly vary by several orders of magnitude between neighboring cells. The creation of a computational grid faces significant challenges in such cases, often resulting in the generation of poorly shaped cells. This, in turn, adversely affects the quality of numerical solutions, posing a formidable challenge for modern simulation software. Our work is contextualized within the framework of Biot theory for poroelasticity. We introduce a novel approach by allowing grid cells to be of (almost) arbitrary types. To achieve this, we employ the virtual element methods, known for their flexibility in handling diverse scenarios. In addressing the issue of poorly shaped cells, we present various strategies aimed at improving grid quality. These strategies involve solving auxiliary problems that provide insights into how the grid can be effectively deformed. We demonstrate the effectiveness of these algorithms through numerical test cases, evaluating their impact on factors such as condition number and splitting iterations.