Introduction to Relative Permeability AFES Meeting Aberdeen 28 th March 2007 Dave Mogford ResLab UK Limited
Outline 1. Introduction 2. Basic Concepts 3. Overview of Test Methods 4. Interpretation
Introduction What is Relative Permeability? Relative Permeability is a concept used to describe the movement of more than one fluid in a porous medium.
Introduction Why Measure? Important in many reservoir engineering calculations Provides a basic description of how fluids move through the reservoir Assists in determining many aspects of reservoir economics and influences top level decision making by allowing prediction of hydrocarbon recovery rate total recoverable reserves water cut
Introduction Why Measure? Production profiles and ultimate recovery determined by: 1. static reservoir description volumetrics reservoir architecture 2. dynamics of multiphase flow relative permeabilities capillary pressure
Outline 1. Introduction 2. Basic Concepts 3. Overview of Test Methods 4. Interpretation
Basic Concepts General Expression for Fluid Flow Developed by Darcy in 1856. where: q = the rate of fluid flow (ml/s) A = cross-sectional area (cm2) µ = viscosity of the flowing fluid (cp) P = pressure drop across the sample (atm) L = length core (cm) q K = constant of proportionality - absolute permeability (Darcies) KA P L K is a constant when: the flow is laminar and Newtonian the fluid does not interact with the rock the rock is completely saturated and fluid is continuous.
Basic Concepts Relative Permeability is defined by setting up the Darcy Equation individually for each phase i that flows through the pore space: q i ( Kkri ) A i P L i where: qi = flow rate of phase i µi = viscosity of phase i Pi = pressure drop within phase i A = cross-sectional area L = length core Kkri = total permeability of phase i
Primary Drainage k ro,k rw... Measured primary drainage k ro (or k rg ) k rw is normalised k r usually referenced to K abs brine 1.00 0.90 0.80 krw kro (or krg) Note: imbibition k r and secondary drainage k r is referenced to k e at S wi Relative Permeability, k r 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Water Oil 0 0.25 0.5 0.75 1 Relative permeability, kr 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.000 0.200 0.400 0.600 0.800 1.000 Sw (PV) Water Saturation,S w
Outline 1. Introduction 2. Basic Concepts 3. Overview of Test Methods 4. Interpretation
Unsteady state Overview of Test Methods The basic methods used to measure relative permeability are: Steady state Centrifuge
Overview of Test Methods: USS USS (also termed as displacement or dynamic method) Displacing phase injected into a core at initial conditions Injection Rate Selection Either carried out at constant pressure drop or constant flowrate Constant pressure drop sometime used in gas floods due to difficulties in maintaining constant flowrate with compressible gases Constant flow rate normally used in oil or water floods Pressure drop across the core measured Produced fluids of both phases monitored Bump floods are normally carried out end of initial displacement to produce further oil
Overview of Test Methods: USS 1 250 0.9 0.8 200 Water Production (PV) 0.7 0.6 0.5 0.4 0.3 0.2 Measured Breakthrough Pressure (psi) 150 100 50 Main Flood 0.1 Bumped Flood 0 0 5 10 15 20 25 30 35 40 45 50 0 0 5 10 15 20 25 30 35 40 45 50 Oil Injection (PV) Oil Injection (PV)
Overview of Test Methods: USS Advantages Relatively quick to perform Reproduces correct pore level displacement mechanisms Break-through recovery Post break-through data and end-point recovery Disadvantages Rel perm data only collected in 2 phase flow region Complex interpretation procedures to calculate rel perm (JBN, CFS) Capillary pressure effects can distort recovery and pressure drop data High flowrates required to reduce capillary effects High flowrates may not be supported by critical velocity issues True residual oil is not always reached
Steady State method Overview of Test Methods: SS Simultaneous injection of 2 phases at a fixed ratio (fractional flow) of known individual flow rate System is allowed to reach steady state a given fractional flow. Steady state achieved when the injected fractional flow equals the effluent fractional flow (saturation constant) and pressure drop across the core remains constant Relative permeability calculated directly from the Darcy equation Assumes that the capillary pressure between phases is zero, i.e. Pw = Po Pressure drop across the core is used to calculate the relative permeabilities of the two phases f w 1 k 1 k ro rw. w. o
SS Imbibition Relative Permeability k ro,k rw... Imbibition in this case as the wetting phase (brine) is increasing 1.00 S/S krw (fw 5%, 10%, 20%, 50%, 70%, 90% and 100%) 0.80 S/S kro (fw 5%, 10%, 20%, 50%, 70%, 90% and 100%) Relative Permeability 0.60 0.40 0.20 0.00 0.00 0.20 0.40 0.60 0.80 1.00 Brine Saturation, PV
Overview of Test Methods: SS Advantages Data is easy to interpret Large saturation range of the relative permeability curve (if not the complete range) can be measured Process controlled by fractional flow equation Disadvantages Relatively long time to achieve SS at each fw f (1 to 2 days or weeks at extremes ) Uncertainty as to whether fluid displacement is truly representative of the reservoir process. Possible fines mobilisation due to large volume throughputs Application of Darcy s s Law is only valid if the saturation in the core is uniform
Overview of Test Methods: Centrifuge Centrifuge method Centrifuge permits gravity displacement (under centrifugal forces) to be the major force for displacement Negates viscous and capillary forces for optimal conditions to be applied
Overview of Test Methods: Centrifuge Advantages Gravity stable displacement, not affected by high mobility ratios (no viscous fingering) Flood not controlled by capillary forces (Capillary end effects may be lower than by flooding) Automated data capture Allows early data acquisition, hence early curve definition Provides large data set for wider curve definition Performed with attention to bond number (N B ) - to ensure not overly de-saturated Produced valid data at true endpoint saturations where Rel Perms are small (<0.0001) Disadvantages Only a single relative permeability is measured (displaced phase) Uncontrolled imbibition at Swi compared to SS and USS as the sample is bathed in the displacing fluid at start High pressure and temperature conditions are difficult to realise Tests using gas, oil, water are confined to the drainage mode (i.e. increasing saturation) Samples may be altered by high forces applied, esp. poorly consolidated. Calls for proper encapsulation before testing.
Outline 1. Introduction 2. Basic Concepts 3. Overview of Test Methods 4. Interpretation
Interpretation Key link of laboratory data (S, ΔP) to reservoir engineering data (Kr, Pc) JBN analysis of USS data Corey exponent representation Core Flood Simulation
Interpretation JBN analysis method is based on Buckley-Leverett theory and is used to analyse USS data to calculate relative permeabilities. The method calculates the relative permeability of each phase at the outlet end of the core. 2 phase range only ie from breakthrough to end point. It is only valid for tests carried out using immiscible, incompressible fluids in homegenous media with stable flood front with negilible capillary pressure In most cases capillary effects are present and using this method in such circumstance can lead to: Apparent low Kr data (suppressed mobility of phases) Artifically early breakthrough Apparent high ROS
Interpretation Corey exponent representation is often used to model oil and water relative permeability functions. 1. Water wet 1. Sor ~30% +; no = 2 to 3; kro 0.6 to 0.8 2. Swi ~10% +; nw = 4 to 6; krw 0.1 to 0.4 2. Oil Wet Water and oil exchange places 3. Intermediate Wet Sor, Swi ~20%; no, nw 3 to 5; kro, krw ~0.5 k rw kro k k rw, or ro, wi Sw S wi 1 S wi S 1 S w S 1 S wi S or or or n w n o
Interpretation Simulation is used as a validation tool for both USS and SS tests Can account for the effects of capillary pressure to derive relative permeabilities that are free from artifacts that are generated in the laboratory. Simulated production and pressure drop data is compared to measured data and relative permeability data is iteratively adjusted until a good match to measured data is obtained. Simulated saturation profiles can also be used to refine the solution further Limitations to CFS is validity of measured Pc function and the correct Pc function should be used (ie imbibition or drainage)
Core Flood Simulation: Production and Pressure data 30 Water Recovery (ml) measured water recovery 25 simulated water recovery 20 15 10 5 7 - - 20 40 60 80 100 120 Production data Time (hours) Pressure Difference (atm) 6 5 4 3 2 Measured Simulated data Pressure drop data 1 0 0 20 40 60 80 100 120 140 Time (hours)
Gas Displacing Water Flood: Simulated Kr data Relative Permeability 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Simulated data: curves corrected for effects of capillary pressure Measured data: Low Kr due to end effects 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Gas Saturation
END