Geophysical Monitoring for Geologic Carbon Storage. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: География
Год издания: 0
isbn: 9781119156840
Скачать книгу
here on, we will use Cartesian coordinates with the 3 axis aligned with the core axis. First, we compute low‐frequency Young's modulus for a jacketed cylindrical core with a radius a and a height H, containing a single fracture along its axis. Conservation of fluid mass in the core requires that the fluid volume exchanged between the fracture and the matrix be in balance:

      Note that this indicates that large fracture compliances result in K *K U α 2 M = K D , that is, E para E D (drained Young's modulus). In contrast, when the fracture compliances are very small, K *K U and E para E U (undrained Young's modulus). What this equation reveals is that for large drained normal fracture compliance η D , substitution of fluids within the fracture, which increases η M , may not result in significant changes in the Young's modulus.

      Next, we examine the case when a core contains a fracture perpendicular to the axis. The conservation of fluid mass requires

      Note that upper B overTilde is a Skempton‐coefficient‐like parameter, providing the ratio between −p f and τ 33. Also, the effect of fluid substitution in the fractured core affects the effective Young's modulus only through this parameter. Small fracture compliances result in upper B overTilde right-arrow upper B slash 3 equals alpha upper M slash 3 upper K Subscript upper U , that is, E norm E U (undrained Young's modulus). Large drained fracture compliance results in upper B overTilde right-arrow 1 minus eta Subscript upper M Baseline slash eta Subscript upper D . Therefore,