Leak-off test (LOT) models
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A leak-off test is one of the most common procedures to test the fracture pressure of the exposed formations. After cementing and drilling out of the casing shoe, the LOT is run to verify that the casing, cement, and formation can withstand the pressure needed to safely drill the next section of the well. The equivalent mud weight obtained from the test is recorded and reported to government agencies as the strength of the casing shoe. Drilling engineers also rely on the reading from the LOT and use it as the maximum pressure that may be imposed on the formation to avoid fracturing. Exceeding the maximum pressure may result in serious consequences such as lost circulation, one of the most costly events in drilling operations. Therefore, accurate determination of formation fracture gradient is critical and can avoid a variety of well control problems. Considerable efforts to model LOT and leak-off behaviors have been done in the past. Altun (2001) and Paknejad (2007) each presented a unique method to estimate leak-off volume by dividing the pressurized system into four sub-systems: mud compression, casing expansion, fluid leakage, and borehole expansion. The volume response from each sub-system is then combined to represent the total volume pumped during a LOT. However, neither model included the expansion volumes of cement sheath and formation rock outside of the casing; these volumes are not trivial and should not be neglected. In addition, both models use only pump pressure to calculate volumes generated during a LOT. The actual downhole pressure and the pressure acting from the outside are ignored. In this study, the volume contributions from cement sheath expansion and formation rock expansion are calculated using single cylinder Lame’s equation. The results are added with Altun’s borehole expansion volume, mud compression volume, and fluid leakage volume to represent the total volume for the enhanced Altun model. Secondly, a Wider Windows mechanical expansion model is developed based on the concentric cylinder theory. This model simulates the compounded effect of casing, cement, and formation expansion along the cased hole based on pressures inside the wellbore and out in the far-field stress region. The volume generated from concentric cylinder expansion is then combined with Altun’s mud compression volume and fluid leakage volume to simulate the total volume pumped during a LOT. The developed models were verified using three sets of field LOT data obtained from literature and compared with the original Altun model. The results confirmed that leak-off volume along the cased hole should be analyzed as a compounded effect of casing, cement, and formation expansion. Overall, the WW models accurately simulate both leak-off volume and leak-off behaviors.