PERMEABILITY . Some slides in this section are from NExT PERF Short Course Notes, 1999. Some slides appear to have been obtained from unknown primary sources that were not cited by NExT. Note that some slides have a notes section.
Permeability Definition (ABW, Ref: API 27) … permeability is a property of the porous medium and is a measure of the capacity of the medium to transmit fluids … a measure of the fluid conductivity of the particular material Permeability is an INTENSIVE property of a porous medium (e.g. reservoir rock) 1. Classification a) Primary permeability—originates at the time of deposition and lithification. Generally reduced by compaction and cementation, but increased by fracturing and solution. b) Secondary permeability—results from alteration of the rock matrix by: compaction, cementation, fracturing, and solution.
Sources for Permeability Determination Core analysis Well test analysis (flow testing) RFT (repeat formation tester) provides small well tests Production data production logging measures fluid flow into well Log data MRI (magnetic resonance imaging) logs calibrated via core analysis Permeability is an important parameter that controls the reservoir performance. Its importance is reflected by the number of available techniques typically used to estimate it. These different techniques provide formation permeability that represents different averaging volumes. The quality of the reservoir, as it relates to permeability can be classified as follows k < 1 md poor 1 < k < 10 md fair 10 < k < 50 md moderate 50 < k < 250 md good 250 md < k very good This scale changes with time, for example 30 years ago k< 50 was considered poor.
Examples, Typical Permeability- Porosity Relationship Factors affecting the magnitude of permeability Shape and size of pore system Sorting Cementation Fracturing and solution Lithology or rock type From Tiab and Donaldson, 1996
Darcy’s Apparatus for Determining Permeability WATER h1-h2 q A h1 h2 (Sand Pack Length) L Permeability is a property of the rock to transmit fluids. As such it is a derived property (like electric resistivity). Permeability can not be measured in the absence of flow. Flow is Steady State q = KA (h1-h2)/L K is a constant of proportionality h1>h2 for downward flow q WATER
PERMEABILITY Darcy’s “K” was determined to be a combination of k, permeability of the sand pack (porous medium, e.g. reservoir rock) , viscosity of the liquid Permeability, k, is a measure of the fluid conductivity of a porous material (analogous to electrical resistivity of a material). Permeability usually correlates with other rock properties such as porosity and saturation. Absolute permeability - the permeability of a porous medium with only one fluid present (single-phase flow). When two or more fluids are present permeability of the rock to a flowing fluid is called effective permeability (ko, kg, kw). Relative permeability is the ratio of absolute and effective permeabilities kro=ko/k, krg=kg/k, krw=kw/k. Effective and relative permeability will be discussed in more detail in a later section of this course.
Review - Derived Units Consider Newton’s 2nd Law for constant mass, F=ma SI Units are Absolute and Coherent Absolute: Force is a derived unit, 1 N = 1 (kg*m/s2) Coherent (consistent): No conversion constants needed So: F[N] = m[kg]*a[m/s2]
Review - Derived Units What if we want F to be in [lbf ]? Then, F[lbf]*4.448[ N/lbf] = m[kg]*a[m/s2] Adding the conversion factor restores the original formula (a true statement in SI units)
Review - Derived Units For: F in [lbf ], m in [lbm ], a in [ft/s2] Then, F[lbf ]*4.448222[N / lbf] = m[lbm ]*0.4535924[kg/lbm] * a[ft/s2]*0.3048[m/ft] Or, F[lbf ] = m[lbm ] * a[ft/s2] / 32.17405[(lbmft)/(lbf s2)] Remember: 1[N] / 1[kg*m/s2] = 1; dimensionless
Permeability Dimensions & Units Permeability is a derived dimension From Darcy’s equation, the dimension of permeability is length squared This is not the same as area, even though for example, it is m2 in SI units See handout: Darcy, {SI}, and [Oilfield] units In Darcy and SI Units, this equation is coherent Oilfield units are non-coherent, a unit conversion constant is required
Darcy Units Permeability is a derived dimension based on Darcy’s Equation k = (q m L) / (A Dp) The unit of permeability is the Darcy [d] The oilfield unit is millidarcy [md] The Darcy is defined from Darcy’s Equation, where: q [cm3/s] m [cp] L [cm] A [cm2] Dp [atm]
Differential Form - Darcy’s Law Darcy’s Equation rearranged as Darcy velocity (volumetric flux) vs = q/A = (k/m) (Dp/L) This equation applies for any L, as L0 vs = q/A = -(k/m) (dp/ds) where, vs Darcy velocity, (volumetric flux) s distance along flow path (0s L), in the direction of decreasing pressure (note negative sign) The differential form is Darcy’s Law vs, the “Darcy velocity”, is not the fluid particle velocity. It is literally the volumetric flow rate [volume/time] divided by the cross-sectional area along the flow path.
Flow Potential The generalized form of Darcy’s Law includes pressure and gravity terms to account for horizontal or non-horizontal flow The gravity term has dimension of pressure / length Flow potential includes both pressure and gravity terms, simplifying Darcy’s Law = p - gZ/c ; Z+; Z is elevation measured from a datum has dimension of pressure The gravitational conversion constant, c, is needed to convert the gravity term to units of pressure gradient [pressure/length] A clear way to determine the sign of the gravity term (+ or -) is to consider the static case. If no fluid is flowing, then there is no potential gradient (potential is constant), while pressure changes with elevation, due to fluid density (dp=(g/c)dZ).