Analytical solution for the dynamic behavior of surface casing

In order to develop the Pre-Salt reservoirs located in the Santos Basin off Brazil, Petrobras is drilling very deep subsea wells, which means that the casing strings deployed in the Pre-Salt wells are much longer and heavier compared to subsea wells from other offshore provinces. A casing string is installed and cemented into well to give stability to wellbore and avoid any leakage from or into the formations. In the scenario of low petroleum price, the reduction of the development cost is necessary. One cost reduction alternative is to eliminate one phase of the well drilling, which may save operational time of the floating drilling platform and avoid the use of a whole casing string. However, in this alternative, the other casing strings installed into the well need to be even longer. This article intends to verify the effect of the length on the axial dynamic behavior of the surface casing comparing the results of typical surface casing strings used in Post-Salt, Pre-Salt and a hypothetical longer string. The analytical solution for the surface casing is obtained assuming a vertical oscillating motion on the top end of the surface casing. The results show that the natural frequency in the axial direction approaches the wave frequency when the surface casing gets longer.