Calculate the absolute permeability of a cylindrical core plug in milli-Darcy (m
ID: 234079 • Letter: C
Question
Calculate the absolute permeability of a cylindrical core plug in milli-Darcy (mD), when a fluid with kinematic viscosity of 5 cst (centistokes) and density of 0.95 gr/cc is flowing through a core plug of 5 cm long with a diameter of 1 inch at a constant rate of 150 cc/min. The flow was conducted using a horizontal core flooding apparatus and was measured at the upstream pressure of 2.5 MPa (absolute pressure) and downstream pressure of 0 MPa (gauge pressure). After the flooding test in part (a), the core holder is turned to vertical position such that the circular cross section of the cylindrical sample is facing the ground. Then the same fluid is supplied to the top of the rock sample at 0 psig, and the bottom of the sample is also exposed to atmospheric pressure. Knowing that the porosity of the sample is 20 %, and considering only vertical linear flow along the axis of the core plug, calculate how long it takes to flow one pore volume through the sample. Considering all the assumptions in part (b), now assume that the core holder is held in an inclined position, such that the angle between the sample's axis and the horizon is 70 degrees. Recalculate the time it takes to flow one pore volume through the sample. Formulate the time calculation and plot the flowing time (for one pore volume) versus sample's inclination angle ranging from 90 to 0 degrees.Explanation / Answer
a) Q = K * A * (P1 - P2) / (u * L)
Where:
Q = flow rate
K = permeability
A = area
P1 - P2 = pressure drop
L = path length
u = dynamic viscosity (aka absolute viscosity or viscosity)
from the above formula we calculate K= 295.91 mD