We present and compare three different grid-based inversion methods for estimation of formation parameters and spatial geological feature identification based on pressure transient test (PTT) data from multiple-well locations. The first and second methods employ efficient adjoint schemes to determine the gradient of the objective functions resulting in the most likely set of reservoir parameters and an ensemble of updated realizations of the parameters, respectively. The second method is based on the Langevin equation. The third method uses ensemble Kalman filtering (EnKF) for data assimilation, in which the outcome is an ensemble of updated parameter realizations. These three methods use a grid-independent prior model (in view of the limited prior knowledge of the system expected to be available), described by as few parameters as possible, and consider a non-uniform grid with the highest resolution near the wells. With these methods, the existence of and location of many sub-seismic features such as strong spatial permeability variations, faults, fractures and pinch outs may be determined using exploration and production data. Such features may not be known a priori, particularly in the exploration of heterogeneous carbonate reservoirs.