In this work, we describe limitations of the free-field propagation model for designing broadband beamformers for microphone arrays on a rigid surface. Towards this goal, we describe a general framework for quantifying the microphone array performance in a general wave-field by directly solving the acoustic wave equation. The model utilizes Finite-Element-Method (FEM) for evaluating the response of the microphone array surface to background 3D planar and spherical waves. The effectiveness of the framework is established by designing and evaluating a representative broadband beamformer under realistic acoustic conditions.