Hollow fiber heat exchangers offer several benefits over the conventional metal heat exchangers, such as reduced carbon footprint, lower weight and potentially cheaper manufacturing. One of the necessary tools of heat exchangers R&D is numerical modeling. However, the typical hollow fiber heat exchanger has a complex geometry, which makes numerical analysis challenging. The idea is to implement and utilize still rather unconventional CFD approach: the Lattice Boltzmann method. This method is known for its good scalability to complex geometry problems due to its inherently explicit and local nature and therefore suitability for massive parallelization. We present here an initial stage of the research: the mesh convergence study and the comparison with pressure drop correlations for cross-flow heat exchangers with small diameter tubes.