2 | Material and methods
2.2.6 Porosity & permeability measurements
The equipment used to measure porosity (φ) and permeability (K) is an AP-608 Automated pulse decay Porosimeter-Permeameter (Figure 2.8 using Nitrogen gas. Porosity is determined according to Boyle’s laws (equations 2.30-2.32) and permeability is measured using unsteady-state techniques.
In practice, each sample is first cleaned from drilling mud with distilled water and dried for 24 hours in an oven at 50◦C. In case samples would contain hydrocarbons, a specific cleaning procedure using solvents should be applied, but it was not necessary in this study.
Secondly, dry samples are weighted, and this parameter is inserted in the AP-608 software.
Plug length and diameter are measured using a digital caliper directly connected to the program, and the latter three parameters are used to calculate automatically bulk volume of the samples (Vb) according to:
Vb =πr2h (2.1)
Vb = bulk volume [cm3]
r = rayon of the plug sample [cm]
h = height of the plug sample [cm]
2.2. Cores 41
20 seconds0 seconds0 seconds40 seconds
a
c
b
d
e f
g h
Figure 2.6: Artefacts caused by the polishing, sample ER-100 (Well Savoie-107, Calcaires de Tabalcon Formation), and effect of etching after 20 and 40 seconds. (a) Nannoparticles dropped on large calcite crystals surfaces (b) Zoom on an accumulation of residual nanno-micrite formed during polishing (c) and (d) Nanno-nanno-micrite accumulated in a pore (e) and (f) the same sample after 20 seconds etching (g) and (h) after 40 seconds etching, the nanno-micrite has almost entirely disappeared.
42 Chapter 2. Material and methods
e c a
f d b
Figure 2.7: Artefacts caused by glue on SEM samples. (a) Glue drops along clivage plans of large calcite crystals. (b) Glue accumulates preferentially on crystals edges and clivage plans.
(c) Micrite entirely covered with glue. (d) Slight glue artefact on micrite, which crystals show rough surfaces. (e) Clean micrite for comparison. (f) Detail on clean micro-crystals, which surfaces are smooth compared to picture (d).
2.2. Cores 43 Then, Boyle’s law defines the porosity as:
φ= Vp
Vb = Vb−Vg
Vb (2.2)
φ = porosity [vv]
Vp = pore volume [cm3] Vb = bulk volume [cm3] Vg = grain volume [cm3]
According to ideal gas properties and monitored gas pressure entrance (Pi) and exit (Po) in a reference cell (here the core holder) whose volume is calibrated, Boyle’s law states:
PiVr =Po(Vr+VL+Vp) =Po(Vr+VL+Vb −Vg) (2.3) It can be simplified and directly solved by the porometer according to:
Vp = PiVb
Po (2.4)
Pi = gas pressure entrance
Vr = volume of the reference cell [cm3] Po = gas pressure exit
VL = volume of connecting tubing [cm3] Vp = pore volume [cm3]
Vb = bulk volume of the sample [cm3] Vg = grain volume [cm3]
Another way to calculate Vp requires to determine preliminarily the grain volume, which can directly be performed on additional equipment of the same instrument. The grain density of samples (ρg) can be calculated from theVg and helps defining large lithological categories such as limestone, sandstone, dolomite, anhydrite or shale, which show characteristic density values:
ρg = sampleweight
Vg (2.5)
φ = porosity [vv]
ρg = grain density [g/cm3] Vg = grain volume [cm3]
Comparing φ values from grain volume and direct pore volume measurements provides mainly quality control values, which allow the identification of residual contaminants in pores.
Permeability is measured with unsteady-state techniques. On one hand, this method shortens the time of measurement in tight rocks particularly compared to steady-state tech-niques, but on the other hand, it overestimates results by propagating numerical and me-chanical errors compared to the latter method (Rushing et al., 2004). Uncertainties increase
44 Chapter 2. Material and methods as permeability decreases, particularly for values lower than 0.01mD. This remark is partic-ularly important for very tight gas reservoir studies, where even additional corrections should be applied (Knudsen’s correction, (Ziarani and Aguilera, 2012)). However, the present study focuses on geothermal reservoirs, and because rock units showing such poor permability val-ues were not considered as potential geothermal target, these methodological uncertainties had no major impact on the results.
Permeability is calcualted according to Darcy’s law (equation 2.24) corrected for non-Darcy effects caused by the use of gas instead of liquid. The gas slippage effect relates to gas molecules acceleration along the pore throat wall when the radius of the latter approaches the mean free path of the gas molecules. This effect is linked to the mean core pressure, and the following equation (Klinkenberg, 1941) is applied to provide Klinkenberg corrected permeability values according to fixed gas slippage factor (b) and measured p:
K =K∞(1 + b
p) (2.6)
K = permeability [mD]
K∞ = Klinkenberg-corrected permeability [mD]
b = gas slippage factor
p = average mean core pressure = p1+p2 2 [atm]
The inertial effect is marked by an increasing pressure difference while no fluid accelera-tion is detected. It occurs usually at high flow rate, when gas molecules accelerate through the narrow pore throats and decelerate in larger pores, inducing convective flow movement.
These inertial forces were defined by Forchheimer’s experimentations (Forchheimer, 1901), modifying Darcy’s law as:
∆p
∆dx = µ
kv+βρv2 (2.7)
∆p= pressure difference [atm]
∆x= length of the flow path [cm]
µ= fluid viscosity [P a∗s]
k = permeability [mD]
v = intersitial gas velocity along the core plug length β = Forchheimer’s inertial resistance coefficient [cm−1] ρ = gas density [g/cm3]
This equation reveals that the inertial effect (right term in the equation) is negligeable with viscous fluids, and is more pronounced with gas (low viscosity) and particularly when the gas velocity increases.
In this study, φ, k and ρg measurements were carried out on plug samples, the length of which (h) ranges between 2.5 to 4 cm (minimum length for consistent analysis is 1 inch).
Results presented in appendix C.1 show the average of three measurements on each sample at a confining pressure of 500 psi.
2.2. Cores 45
Figure 2.8: Porosimeter-permeameter Core test AP608 used to measure porosity, perme-ability and grain density at the RT lab of University of Geneva.
Poroperm measurements at different confining pressure were realized on three samples showing different microfacies, in order to give an idea of modifications which could occur at reservoir conditions. Obviously, the pore network decreases following a logarithmic regression curve decay while pressure increases. However, the decrease of φ and k was small, and no monitoring of the rock internal changes could be available on the equipment used (such as axial pressure). For these reasons, this procedure was not applied in routine.