Leak-off test (LOT) models combining wellbore and near-wellbore mechanical and thermal behaviors

Considerable efforts to model leak-off test (LOT) and leak-off behaviors have been carried out in the past. Altun presented a model to estimate leak-off volume by dividing the wellbore system into four sub-systems: mud compression, casing expansion, fluid leakage, and borehole expansion (Altun 2001). The volume response from each sub-system is then combined to represent the total volume pumped during a LOT. Most existing leak-off models do not account for mechanical behavior of cement and rock formations around the wellbore. While their compressibilities are small, the cement and rock formation volume changes can be significant. In this research, a mechanical expansion model has been developed, based on a linearly elastic, concentric cylinder theory developed by Norris (Norris 2003). The model is an extension of Lamé equations for multi concentric cylinders and assumes the horizontal stresses on the system’s boundary are applied equally in all directions, i.e., the horizontal, far-field stresses around the system are isotropic. The resulting model simulates the compound radial displacements of casing, cement, and formation along the cased hole, based on pressures inside the wellbore and in the far-field stress region. The volume generated from concentric cylinder expansion is then combined with Altun’s model to simulate the total volume pumped during a LOT. One use of the model is the estimation of minimum horizontal far field stress. Since the model consists of concentric cylinders, the pressure on the outside boundary can approximate the minimum horizontal far field stress, which in turn is related to overburden pressure. The pressure inside the most inner cylinder is calculated from known mud weight. With an initial estimation for the far field stress and iterative methods, the minimum horizontal stress can be estimated. The developed models were then applied to field LOT data from Gulf of Mexico. The results show that leak-off volume along the cased hole should be analyzed as a compound expansion of casing, cement, and formation.