Artificial lift systems become more and more important for the oil sector in the future as Brown Field Development increases and natural reservoirs reach maturity stage. While Electric Submersible Pumps and Sucker Rod Pumps clearly dominate the global market, Hydraulic Pumping systems are highly underrepresented and only contribute a few percent to it. At the Montanuniversitaet Leoben a new hydraulic pump was designed and manufactured, which consists of a double plunger/barrel system and comprises only a few moving parts downhole, bringing along all benefits these lift systems are known for. For instance, a reduction of potential failure sources can be achieved due to the omission of electric cables or rods. Further, no over- and under-traveling is possible and wellbore inclination is no limiting factor. Also, by installing the system as a concentric tubular installation, inhibitors can be easily injected, and free gas can be vented to the surface. This makes the pump to an excellent alternative in Enhanced Oil Recovery applications. For the validation of the pump concept a numerical study is conducted by utilizing OpenFOAM, an open-source software toolbox, and the additional library swak4Foam. Thereby an incompressible solver with the ability to handle dynamic meshes is applied for this Computational Fluid Dynamic simulation. The model includes OpenFOAM’s Arbitrary Coupled Mesh Interface as a deforming mesh region to describe the motion of the moving pump assembly. The displacement of the pump is derived from the forces acting on the piston. These forces are calculated every time step of the simulation and the new position of the pump, respectively of the mesh points, is updated for the next time step. The study, its results and the model setup itself give a good insight into the behavior of the pump at certain operation conditions and can be used for the further development and optimization of the pump assembly.