We present a lattice computer simulation study on the geometrical confinement effect of polymer solutions in a wide range of concentrations. Polymer chains were equilibrated for a system that consists of a bulk solution and a slit between two parallel walls. The partition coefficient of the polymer was determined and found to increase as the bulk concentration phi increased, confirming the theoretical predictions. We applied the blob picture to analyze the partition coefficient data in the semidilute regime where the partitioning is considered to be controlled by the ratio of the blob size to the slit width, rather than by the ratio of the chain dimension to the slit width. Our simulation data and earlier experimental data support the application of the blob theory. Furthermore, we found it is possible to estimate the blob size in the bulk solution directly from the partition coefficient data by assuming that the confinement entropy of the blob depends on the blob size in the same way as the confinement entropy of the individual chain depends on the chain dimension at infinite dilution. The blob size thus determined confirms the scaling prediction; namely, the blob size proportional to phi(-3/4). Some deviations from this simple picture, however, exist when the slit is narrow and the solution is concentrated.