Sentence examples for diffusion of pressure from inspiring English sources
It is shown that the hydraulic resistance gives rise to a powerful agency (diffusion of pressure) capable of driving the combustion wave both at fast subsonic and at supersonic velocities.
Post-shut-in pressure evolution is characterized by further diffusion of pressure deeper into the medium as compared to the pressure front at the moment of shut-in.
The needle was then held in position for a further 30 min to allow the diffusion of pressure before retracting the injection needle to minimise back spill along the injection tract.
For example, Deming (1994a) provided a solution to the one-dimensional (1D) groundwater flow equation that can be used to estimate permeability, 5 where z is overburden thickness, α is the compressibility of bedrock, t is the timescale for diffusion of pressure, and μ is the viscosity of water.
The diffusion of pressure is obtained by taking the divergence operation on both sides of equation (5), and combined with equation (6): (7) 0 = ∇ 2 p + (n - λ a ) χ Ω V - λ N χ Ω N p | ∂ Ω = 0 In the implementation, the finite element method is used to solve PDEs with diffusion item ∇ 2 [ 28].
This leads to apply non-equilibrium condition in which, mass transfer phenomena, in addition to the concentration diffusion, will be a function of pressure diffusion, external force diffusion and thermal diffusion (Bird et al. 2002).
Moreover, based on the precisely determined hypocenters during the 2009 Hakone unrest, Yukutake et al. (2011) demonstrated that swarm earthquakes were triggered by the diffusion of highly pressured fluids within a preexisting plane-like structure.
In this paper, an attempt is made to clarify the intricate links between transport processes (e.g. hydraulic flow, osmosis, diffusion of ions and pressure), physical change (e.g. loss of hydraulic overbalance due to mud pressure penetration) and chemical change (e.g. ion exchange, alteration of shale water content, changes in swelling pressure) that govern shale stability.
Equation 24 is the dimensionless form of pressure diffusion equation of laminar fluid flow in a sample with initial pore pressure of (P_{i}) and constant boundary pressures of (P_{1} = P_{i}) and (P_{2} = 0).
Equation 18 shows the linear form of pressure diffusion equation in porous media (Donnez 2012): frac{{partial P}}{{partial t}} = alpha ^{2} frac{{partial ^{2} P}}{{partial x^{2} }};,t ge 0,quad0 le x le L (18) (alpha^{2}) is called hydraulic diffusivity and is equal to fluid mobility divided by fluid storability (Donnez 2012): alpha^{2} = frac{k}{{varphi mu c_{text{t}} }} (19).
The radial form of pressure diffusion equation in porous media is shown in Eq. 28 (Dake 1978): frac{1}{R}frac{partial }{partial R}left( {Rfrac{partial P}{partial R}} right) = frac{{varphi mu c_{text{t}} }}{k}frac{partial P}{partial t}, quad t ge 0, quad R_{text{w}} le R le R_{text{e}} (28).
