Browsing by Subject "Porosity--Mathematical models"
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Item Fine scale sandstone acidizing coreflood simulation(2004) Li, Chunlou; Hill, A. D., (A. Daniel)Contrary to the traditional understanding of matrix acidizing of sandstone that the acid front propagates in the formation with a piston-like style, some wormhole like structures were observed in lab tests under certain conditions. Most current models treat the rock as a homogeneous porous medium to describe the matrix acidizing in sandstone. The most sophisticated design models divide the formation into a series of layers with constant properties (minerals, permeability, etc.) in each layer. However, sandstones invariably have small – scale heterogeneities in minerals and flow properties that may cause the effects of injected acids to differ greatly from what is predicted by a model based on a homogeneous formation. A fine-scale model of the sandstone core acid flooding is developed based on mass balance and the chemical reactions between acids and minerals that occur during sandstone acidizing. This mathematical model is numerically solved to predict the permeability response and demonstrate the distributions of acids, precipitates, flow velocity and porosity in the core during acidizing. Cores are divided into 8000 grid blocks to simulate the fine-scale structure of sandstone. Using standard geostatistical techniques at the beginning of simulations can generate heterogeneous porosity or/and minerals. The permeability response to acidizing is predicted using a model in which not only the porosity, but also the minerals, tortuosity, and statistical parameters of the particle size are considered. Application of the new model to typical acidizing conditions shows that acid tends to channel through a heterogeneous sandstone, with the most efficient acidizing occurring when the rock has a layered structure. A layered structure is simulated by assuming a correlated permeability field in the main flow direction, as occurs in sandstones having horizontal laminations. The model shows that acid can stimulate the matrix permeability two to three times farther into the rock than would be predicted with a standard acidizing model, which takes the rock as homogeneous porous medium.Item Mechanical behavior of concentric and eccentric casing, cement, and formation using analytical and numerical methods(2008-12) Jo, Hyunil, 1977-; Gray, Kenneth E., Ph. D.The first main goal of this research is to develop comprehensive analytical and numerical models for the stress distribution around an inclined cased wellbore by considering all wellbore processes and to amend erroneous models of most previous work. The second main goal is to apply the developed models to explain near wellbore phenomena such as cement failure and sand production. To achieve these goals, this work checked the eligibility of using simple elastic approaches for the system by using a poroelastic undrained condition and a steady state condition for stresses induced by wellbore temperature variation. It utilized the generalized plane strain to compensate for the limitation of the plane strain which most previous work had used. In addition, this research developed comprehensive models to improve previous work by using superposing principles. For applying the developed models to cement failure, Mogi-Coulomb criterion for shear failure instead of Mohr-Coulomb and Drucker-Prager criteria was used to properly consider the intermediate stress. Additionally, ABAQUSr was utilized for numerical models with the "model change" option to simulate and combine all individual wellbore processes while MATLABr was used for analytical models. For predicting sand production, fully coupled poroelastic solutions for an inclined open wellbore were modified to obtain the stress distribution around a perforation tunnel after perforating. Then, modified Lade failure criterion was used to calculate the critical drawdown when sand production occurs, that is, when the perforation tunnel starts failure. This research obtained the following results. For developing models, the analytical models improved the previous research. However, the numerical results under a vertical tectonic stress showed discrepancies because of the difference between the generalized plane strain and numerical models. For cement failure, Young's modulus of cement, wellbore pressure and wellbore temperature variation could affect shear failure more significantly than the other factors. The numerical results showed closer to the failure envelopes than the analytical results. For predicting sand production, well completion affected sand production near wellbore and the critical drawdown converged to asymptotic values. In addition, perforating along the minimum horizontal stress direction was most preferable in a vertical cased wellbore under a normal stress regime.