Modeling of Rock Permeability Damage and Repairing Dynamics Due to Invasion and Removal of Particulate from Drilling Fluids

Asymptotics of the Filtration Problem With Almost Constant Coefficients

“…In the domain Ω = {0 ≤ x ≤ 1, t ≥ 0}, consider the system of first-order differential equations Here the blocking filtration function Λ(S) is smooth and positive at 0 ≤ S < S m , S m > 0; Λ(S) = 0 at S ≥ S m ; the functions g(S) and f(S) are positive at 0 ≤ S ≤ S m ; C(x,t), S(x,t) -the unknown volumetric concentrations of suspended and retained particles [21]. For the uniqueness of the solution to the system (1), (2), the initial and boundary conditions are set Condition (3) means that a suspension of variable concentration is injected at the inlet of the porous medium; by condition (4), at the initial moment of time, the porous medium does not contain any suspended and retained particles. The concentrations front of the suspended and retained particles given by the formula x = vt, v = f(0)/g(0) moves with a speed v from the inlet to the outlet of the porous medium.…”

“…Filtration of suspensions and colloids in porous media occurs in many natural and technological processes: the spread of microorganisms in the aquatic environment, filtration of water in rocks, treatment of industrial and domestic wastewater, a decrease in oil production due to the deposition of small particles entrained in water near the well, and much more [1][2][3]. During the construction of tunnels and underground storage facilities for hazardous toxic and radioactive waste, a liquid grout is pumped into the rock under pressure to create watertight walls.…”

Impurity Effects on the Mechanical Properties and Permeability Characteristics of Salt Rock

“…Many experiments have been conducted to investigate the short-term mechanical properties, long-term creep behavior and gas sealing capacity of pure salt rock, indicating that salt rock is a typical type of soft rock with low strength and permeability [9][10][11][12][13][14]. Underground energy storage in pure salt rock has been proven to be highly feasible, according to extensive experimental results and existing salt cavern construction, which is of great importance for the large demands of the national energy reserves for China.…”