Reservoir Characterization. Группа авторов
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Название: Reservoir Characterization

Автор: Группа авторов

Издательство: John Wiley & Sons Limited

Жанр: Физика

Серия:

isbn: 9781119556244

isbn:

СКАЧАТЬ modulus:

      (2.2)image

      The usual process is initiated by replacing the primary fluid with a fluid with similar sets of velocities and rock densities, compared with the primary fluid. These velocities are usually obtained from logs, but sometimes they may also be the results of theoretical models. In this study, the velocity of the wave that has passed through the primary fluid (in our case, supercritical dioxide is injected into the water) is obtained through laboratory measurements. But the removal of the existing fluid effects and replacing it by the common fluid (brine) has been achieved through the following steps (Dvorkin, 2003):

      In the first stage the effective bulk modulus of pore fluid composition, (image) is calculated using:

      (2.3)image

      where, ϕ is porosity and Kmineral is the apparent modulus in the mineral phase (Thomsen, 1986). The bulk modulus of rock saturated with brine (Kcommon) is determined by:

      (2.6)image

      where, Kcf is the bulk modulus. The compressional wave modulus of the rock saturated with brine (Mcommon) is calculated using the following formula:

      (2.7)image

      The compressional wave velocity after removal of the primary fluid and replacing it with brine is obtained by:

      (2.8)image

      In this case, when the shear wave data is not available, compressional wave modulus (Mlog) is calculated from charts (logs) using the following relation:

      (2.9)image

      The compressional wave modulus of the dry rock (Mdry) is also calculated using compressional wave modulus of the rock’s minerals:

      (2.10)image

      (2.11)image

      where, ϕ is porosity, μmineral is shear modulus and Kmineral is the apparent modulus in the mineral phase. The changes in the elastic modules of different minerals as a whole have been estimated [28]. Finally, the compressional wave modulus of the brine saturated rock (Mcommon) is calculated as follows:

      (2.12)image

      Greenberg - Castagna formula is defined for rocks completely saturated with brine. In this paper, the apparent modulus (Kcf) of 2/25 is assumed for brine saturated cases.

      It is worth mentioning that the fluid changes have no effect on shear wave modulus, which is the same before and after complete saturation with brine.

      2.2.2 Estimating Geomechanical Parameters

      Here to determine the bulk modulus, shear modulus, and Young’s modulus of rocks, we assumed that they are elastic, homogeneous and isotropic and used the following formula:

      (2.13)image

      (2.14)image

      (2.15)image

Schematic illustration of the placement of the test device.