Naturally fractured reservoirs are a challenging task for the E&P industry, for both old and new fields. In such systems most of the oil is stored in the matrix blocks, which are surrounded by fractures.<br />The flow of fluids occurs mainly in the fractures, the matrix acts as source or sink to the fractures. Therefore the matrix recovery factor is of special interest and methods to estimate the matrix depletion efficiency should be found. Before simulating the full-field dual-porosity reservoir, small-scale models are used to be able to analyze different matrix recovery mechanisms. For a first assessment of the matrix recovery factor and for the analysis of the influence of different parameters a single matrix block and column models are used. The single matrix block is a fine gridded block in the magnitude of a matrix block used in dual-porosity simulation models, surrounded by fractures. The column models are built of a stack of dual-porosity simulation cells with the properties of the full-field model. In this thesis a general introduction to fractured reservoirs is given.<br />In the scope of a full field study on a dual-porosity oil field in the Middle East investigations on single matrix blocks and column models were carried out and the results are presented. Special emphasis is put on the combination of the wettability of the matrix rock and the production mechanism. To evaluate the influence of different reservoir parameters, sensitivity analysis are performed to demonstrate their impact on the final oil recovery.