Abstract
The hydraulic diffusivity and permeability of a rock mass can be measured with a double packer permeameter, placed in a long bore hole. If the flow is steady, the relation between supply pressure and flux is a measure of the permeability whereas if the flow is transient, the relation is a measure of both the hydraulic diffusivity of the rock and the elasticity of the equipment. If the equipment is effectively rigid and the distance between the packers is much bigger than the size of the packers, an approximate closed solution is characterized bytwo parameters: the distance between the packers divided by the radius of the hole and the width of the packers divided by the radius of the hole. The flow is fully 3-D if the hydraulic diffusion distance far exceeds the distance between the packers. If the elasticity of the equipment is not negligible, the transient solution is characterized byone parameter including the elasticity coefficient of the equipment the conductivity of the rock and the radius of the hole. The relations between pressure and flux is given as a closed formula, suitable for engineering practice.
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Abbreviations
- a ≈ 0.8905:
-
numerical constant
- B(r,ξ):
-
auxiliary function
- c(t):
-
dimensionless potential between the packers
- ċ(t):
-
dimensionless time derivative ofc(t)
- f(z):
-
auxiliary function
- F(τ):
-
auxiliary function
- g :
-
gravity acceleration
- G(τ):
-
auxiliary function
- K :
-
conductivity
- m :
-
auxiliary variable
- N(t):
-
integration limit
- p :
-
pore pressure
- p 0 :
-
reference pressure
- P(r, m, t):
-
auxiliary function
- Q′(t′),Q′ p(t′):
-
fluxes
- Q(t),Q p(t):
-
dimensionless fluxes
- Q st :
-
dimensionless stationary flux
- (r′, θ, z′):
-
cylindrical coordinates
- t :
-
dimensionless time
- z′ 0 :
-
distance between the packers
- z 0 :
-
dimensionless distance between the packers
- β :
-
dimensionless rise rate of the potential between the packers
- β 0 :
-
dimensionless second rise rate of the potential between the packers
- γ′ :
-
coefficient of elasticity
- γ :
-
dimensionless coefficient of elasticity
- Δ′ :
-
axial length of a packer
- Δ :
-
dimensionless axial length of a packer
- ξ(t):
-
integration limit
- θ :
-
dimensionless rise rate of the potential between the packers
- κ :
-
hydraulic diffusivity
- ϱ :
-
density of water
- (r,θ,z):
-
dimensionless cylindrical coordinates
- R(τ):
-
auxiliary function
- r 0 :
-
radius of the hole
- S 0 :
-
specific storativity
- s :
-
auxiliary variable
- t′ :
-
time
- τ :
-
dummy variable
- φ′(r′,θ,z′):
-
potential
- φ(r,θ,z):
-
dimensionless potential
- φ 0 :
-
reference potential
- φ∞ :
-
undisturbed potential
- ξ :
-
dummy variable
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Rehbinder, G. The double packer permeameter with narrow packers. Analytical solution for non steady flow. Appl. Sci. Res. 56, 255–279 (1996). https://doi.org/10.1007/BF02251034
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DOI: https://doi.org/10.1007/BF02251034