Bài báo SPE (IPTC 18132 MS)

Therefore, our discussion will berestricted to relative permeability data are derived from laboratory experiments.The main challenge in the derivation process is how to obtain a reliable

Oil -Water Relative Permeability Data for Reservoir Simulation Input, Part-I: Systematic Quality Assessment and Consistency Evaluation

Ammar Agnia and Hossein Ali Algdamsi, Schlumberger; Mohamed Idrees Al Mossawy, Universiti Teknologi PETRONAS

Copyright 2014, International Petroleum Technology Conference

This paper was prepared for presentation at the International Petroleum Technology Conference held in Kuala Lumpur, Malaysia, 10 –12 December 2014 This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s) Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s) The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited Permission to reproduce in print is restricted

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Abstract

The relative permeability concept has been used extensively in reservoir engineering As numericalreservoir simulation has become more popular as a tool for reservoir development, the role of relativepermeability data became even more evident and important Its key use is to control the advancement andmobility of different fluids simultaneously coexisting in the porous media, and hence controlling therecovery of the fluids However, deriving a reliable relative permeability data set remained a majorchallenge In reservoir engineering, this challenge has been present for many decades and might be so inthe foreseeable future Another challenge is to have a data set which is internally consistent and does nothinder the simulation performance Optimistically, with the significant literature accumulated over theyears in deriving and using relative permeability, some techniques can be extracted for data quality check,control and assurance This paper covers the limitations of the conventional methods used for calculatingrelative permeability from displacement experiments It also compiles all contemporary techniques in asystematic workflow for quality assessment and consistency evaluation The workflow has been demon-strated with different synthetic and field examples This paper will provide a reference for reservoirengineers who have an interest in investigating, checking the quality, and preparing relative permeabilitydata set usable for reservoir simulation process

Introduction

Special core analysis (SCAL) is the hub of the evaluation and management of hydrocarbon reservoirs.Relative permeability is one the main constituent of the SCAL which importance is widely recognized forthe prediction of oil recovery during displacement by water As any other piece of data, high quality andreliable relative permeability data set can reduce uncertainty in dynamic reservoir modelling and provide

a sound foundation for reservoir engineering studies Conversely, ppoor quality data can result in lost timedue to rework and additional studies, inadequate development plans, and inefficient investment

Relative permeability curves can be generated from different sources such as mathematical models andexperimental methods However, experimental methods are more desirable for two reasons First, theyproduce specific relative permeability relationships for specific reservoirs Second, it is best available

approach to resemble the flooding process in the field provided that the experiments performed onrepresentative core samples and fluids from the reservoir under study Therefore, our discussion will berestricted to relative permeability data are derived from laboratory experiments.

The main challenge in the derivation process is how to obtain a reliable relative permeability data set.The term reliable will often be used in referring to relative permeability data set with is a good probabilitythat the defined relationships are representative of the reservoir and inherently repeatable Judgmentregarding reliability will be made according to analysis of results that are judged to have been obtainedusing valid laboratory procedures When the term valid is used in referring to laboratory measurements

it will mean that none of the procedures used during the test are inconsistent with obtaining reliable resultsfor the sample tested For instance, the use of an extracted core plug with altered wettability other thanthe reservoir one would generally mean that the results are invalid The source of unreliability may beattributed to the following reasons:

● The derived relative permeability data set are usually prone to excremental artefacts

● The state of the experiment does not fit the model’s assumptions used to derive the relativepermeability data sets In another word, the methods of calculating relative permeabilities fromdata obtained from displacement experiments don’t describe all physical effects encountered in theexperiment

● The dependence of relative permeability on wide range of variables and conditions (Fluidsaturations, Saturation history, initial saturations values, wettability, pore geometry, overburdenstress, clay and fines content, temperature, interfacial tension and viscosity, and displacement rate)(Dandekar 2013)

● The uncertainty involved in all stages of deriving the relative permeability (Grimstad et al 1997).The validation process can be portrayed as a systematic correction of the inherent errors of theexperiments and the derivation techniques, in a way that the true characteristics of the relative permea-bility are preserved An example is the systematic approach in assessing the validity of extracted relativepermeability profile from experimental result and assuring the reliable and representative portion of thedata was utilized to produce the relative permeability characteristics and guarantee the consistency andquality of revealed end -point

There are many techniques disseminated in the literature for checking the quality of relative ability Those techniques are compiled to enable the reader of performing data quality assessment andconsistency evaluation The quality check scheme followed within this paper starts with preliminary checkfor the quality of the experiment, relative permeability, and data sets provided to simulators Beforestarting it will be good to start the discussion with a brief review of the relative permeability concept andthe methods used to measure it in the laboratory

perme-Overview

Water Oil Relative Permeability

The relative permeability is a macroscopic property that is defined through extensions of Darcy’s law tomultiphase flow (Grimstad et al 1997) It is defined as the ratio of the effective permeability of a specificfluid to reference permeability The reference permeability can be any of the following (Qadeer, Brigham,and Castanier 2002):

1 Absolute permeability to one of the phases

2 Klinkenberg corrected gas permeability

3 Non-wetting phase effective permeability at irreducible wetting phase saturation

4 Wetting phase effective permeability at irreducible non-wetting phase saturation

The choice of the reference permeability is not critical in itself However, it is very important to that

it is stated and consistently applied (Qadeer, Brigham, and Castanier 2002, Glover 2002)

Relative permeability data should be obtained by experiments that best model the type of displacementthat is thought to dominate reservoir flow performance (Fanchi 2006) A number of laboratory measure-ment techniques for deriving the relative permeability are described in the literature Generally, threemethods exist to measure relative permeability: steady-state (Osoba et al 1951), unsteady displacement

relative permeability is measured directly; whereas it is indirect measurement in the unsteady-state andcentrifuge methods (Mohanty and Miller 1991) The steady-state method has an advantage of simplecalculations, and disadvantage of tedious long procedure The unsteady-state method takes less time butrequires more complicated calculations (Al-Mossawy and Demiral 2011) The centrifuge method is fairlyquick but gives the relative permeability of the displaced phase only (Mohanty and Miller 1991) Each ofthese methods will be discussed briefly in the following sections

Steady-state Coreflood

Steady-state experiment is run with simultaneous flow of two phases, both wetting and non-wetting, atdifferent flow rates The flow rate of one phase is increased while the other is decreased gradually At eachrate change, the pressure drop and the saturations are closely monitored Equilibrium, i.e steady-statecondition, is established within the system once the pressure drop across the core and the saturations arenot changing with time At that point, effective and relative permeabilities for individual phases arecomputed using the pressure drop, flow rates, length and cross sectional area of the core, and viscosities

of fluids into Darcy’s law (Bennion and Thomas 1991) The saturations of the phases are varied bychanging the ratio of the flow rates of the fluids Thus the relative permeability curves can be determinedover a representative range of saturations (Qadeer, Brigham, and Castanier 2002) In general, between fiveand ten stages are usually needed to establish relative permeability curves The test does not necessarilydepict reservoir fluid displacement mechanism where one fluid displaces the other, since the test is nottruly a displacement test but rather an equilibrium flow test However, its virtue is that rate effectsassociated with viscous instabilities are eliminated Capillary pressure forces are usually ignored but theexperiment can be designed in such way the end effects are eliminated (Bennion and Thomas 1991) Thedata obtained by steady-state method is at least as believable as the plausible model on which they arebased (Darcy’s law), especially if convincing measures are taken to minimize the capillary end effects

A major difficulty is the determination of saturation at each stage There are different methods that areused for in-situ determination of fluid saturation in cores such as measurement of electric capacitance,nuclear magnetic resonance, neutron scattering, X-ray absorption, gamma-ray absorption, volumetricbalance, and weighing the sample techniques (Honarpour, Koederitz, and Herbert 1986) However, theproblem is the identification of a single value to represent average saturation over the whole core plug ateach equilibrium stage There is also uncertainty as to whether the fluid distributions are representative

of the displacement process Saturations measurements such as weighing the sample will interrupt flowand can cause problems of capillary contact with the sample end pieces (Heaviside and Black 1983) Animportant advantage of the method is that it is possible to define relative permeability across a bordersaturation range, even for systems having favourable mobility ratios Although the technique allowsflooding with hundreds of pore volumes of water, relative permeability still may not be measured at lowoil saturations in high permeability and intermediate wettability rocks The steady-state method has also

an advantage of simple calculations, but a disadvantage of tedious long procedure where days or weeksare often required to achieve equilibrium for each saturation point (Bennion and Thomas 1991)

The main advantages of the steady-state technique are:

1 Relative permeability data are calculated over the full saturation range

2 Simple calculations

The disadvantages are:

1 There is also uncertainty as to whether the fluid distributions are representative of the displacementprocess (Heaviside and Black, 1983)

2 It does not necessarily depict reservoir fluid displacement mechanism where one fluid displacesthe other

3 The experiments are time consuming and thus expensive

Unsteady-state Coreflood

In unsteady-state method, only one of the phases is injected into the core to displace the other The theory

is based on Buckley-Leverett Equation (Buckley and Leverett 1942) as a process model The idea is tomonitor the pressure differential across the core and production history of controlled multiphase displace-ment experiment, and then to back-calculate the relative permeability values with analytical methods.Different approaches have been developed to determine relative permeability data from the unsteady-statedisplacement (Johnson, Bossler, and Naumann 1959,Jones and Roszelle 1978,Mitlin et al 1998,Toth et

effects The cumulative production data also are processed to provide a basis for calculating averagesaturation levels to be associated with the relative permeability values The method is preferred to thesteady-state for its rapidness and, to some extent, it can depict reservoir fluid displacement mechanismwhere one fluid displaces the other However, it is more susceptible to end effects, rate-dependentinstability effects, and potential non-equilibrium between displacing and displaced fluids (Bennion andThomas 1991) Nevertheless, the unsteady-state methods, comparatively speaking, supply the wanted dataquickly with reduced expense

Other models also have been presented based on the initial and final stages of the flow process (Corey

The main advantages of the unsteady-state method are:

1 Appropriate “shock-front” development

2 Ability to flow at appropriate reservoir flow rates

3 Relatively fast (and therefore relatively inexpensive)

4 Relatively low throughput (less prone to fines migration)

The main disadvantages are:

1 Inlet and outlet boundary effects, especially at low rates which invalidate Buckley-Leverett theory

2 Relatively complex interpretation

Centrifuge Oil Relative Permeability Tests

The method is based on the concept of rotating a core at various angular velocities to initiate forceddrainage or imbibition process For every rotational speed, the fluid production is collected in a pipette andmeasured at equilibrium The average saturation derived from the effluent production volume With thedriving force remaining constant, the relative permeability of the displaced phase is directly proportional

to the oil production rate The production is measured as function of the drainage time then relativepermeability is produced by differentiation of the data according to the algorithm devised by (Hagoort

1980) The model interpret the centrifuge experiment as a gravity drainage process based on the followingmajor assumptions: capillary effects are negligible, the invading fluid mobility is much larger than thedisplaced fluid mobility, and the acceleration along the sample is uniform There are several types ofcentrifuge experiments: single-speed, multi-speed, constantly-accelerating and constant flow rate centri-fuge techniques (Bauget et al 2012)

A major advantage of the test is that large pressure differentials can be created across the core plugwithout creating an unstable displacement The higher pressure differentials imposed by centrifuge results

in relative permeability data over an extended saturation range, i.e to lower oil saturations The design ofexperiments requires a balance between the Brownell-Katz (or Bond) number criteria and retention due

to a capillary end effect (Hirasaki, Rohan, and Dudley 1995) Hagoort’s analytical calculation from asingle-speed experiment underestimates the relative permeability maximum due to the time needed by thecentrifuge to reach the selected speed (Bauget et al 2012) It also overestimates the final liquid saturationsince capillary end effects are not taken into account (Bauget et al 2012) Notable limitations of thetechnique are; values of water relative permeability cannot be defined from a single-speed displacement

of oil by water, disability of using live oil, and fines migration in cores with high content of illite For amulti-speed experiment, the relative permeability determination requires history matching with a numer-ical simulator (Bauget et al 2012)

Which technique?

The choice of measuring technique for relative permeability can be a challenging task For example, each

of the above mentioned techniques is claimed to yield residual oil saturation and relative permeability.Experimental artefacts and neglected physical phenomena could invalidate the classical interpretationtheory and often make the interpretation of special core analysis experiment highly unreliable Forinstance, the capillary end effect is present during the laboratory water flood which cannot be squeezedaway, except at extremely high rates or after excessively long flooding times, resulting in artificially highresidual oil saturations Thus, the capillary pressure is interfering with a relative permeability measure-ment in the steady-state or unsteady-state apparatus Conversely, it’s possible to say that relativepermeability effects interfere with a capillary pressure measurement in the centrifuge The centrifuge does,

on the other hand, yield the true value of residual oil saturation The choice of test method should be madewith due regard for reservoir saturation history, rock and fluid properties (Glover 2002) In addition,laboratory measurements of relative permeability should be representative of flow behavior in thereservoir For example, centrifuge experiments are often used in studies where gravity drainage isidentified as the dominant recovery mechanism (Edwards et al 1998) The unsteady-state method is moreoften used because it is substantially quicker In some cases the steady-state method is needed to fullydefine the curves ranges However, this can lead to difficulties if data from the different methods is not

in agreement (Heaviside and Black 1983) Integrating the results from different types of tests can be ofgreat help in recognizing which parts of each data set are reliable and which are invalid The unsteady statetest provides reliable results within the mid saturation range and the experiment artefacts start to show up

at high saturation range Therefore the centrifuge results will be used as supplementary of the unsteadystate results Numerical simulations of laboratory experiments should be an essential element to reconcilethe experimental results Numerical simulations can be also used in the experimental design stage, and forquality control on contractor interpretation of experimental data In summary, thorough understanding ofprocedures and conditions used to obtain the results and the strengths and weaknesses of each test theexperimental results can be reconciled

Quality check of experiment

Laboratory measurements are prone to experimental and physical erroneous effects that can propagate tothe derivation of relative permeability, hence making it unreliable Therefore, flooding experiments should

be designed in such way such that eliminate or minimize these effects on measurements For example, endeffects are generally reduced by using high viscous pressure gradients and equilibration times are chosensufficiently long to reduce “after-flow” effects due to low relative permeability (Kokkedee et al 1996,

become unstable and trigger fines migration A combination of proper experimental design such as

flooding at high rate, using longer cores (composite core), using capillary mixing sections numericalsimulation of the experimental data is required The use of numerical simulation to aid proper interpre-tation of laboratory experiments proved to be an efficient tool to minimize the impact of the experimentalartefacts on the results and conclusions of the study Reducing the experimental artefacts is notstraightforward Therefore, the laboratory tests should be conducted ideally under conditions where thelaboratory values for the key flow parameters match the field values (Mohanty and Miller 1991) A simpleway of presenting the flow phenomena that depend on these parameters in a very complex manner is thescaling group concept in which key flow parameters interrelated and can be expressed by a different set

of dimensionless numbers that defines the critical ranges of these parameters Relative permeability in turndepends on the pore structure, wettability and flooding conditions, which can be represented by a set ofdimensionless groups (Mohanty 2002) Following this procedure, one could resolve inconsistenciesobserved between different experimental techniques and procedures The flooding condition can berepresented by a set of dimensionless groups including capillary number, bond number and heterogeneityindex(Mohanty and Miller 1991)

Flow rate

Rapoport and Leas scaling group (Rapoport and Leas 1953) has often been used to select the rate of water

flood required for stabilized flow The term “stabilized flow” refers to flow where the shape of the front

does not change with time The effect of capillary pressure in core floods is to spread the front, but at thesame time there is a wave sharpening effect because of the convex-upward shape of the fractional flowcurve These two effects tend to balance and make the wave approach an asymptotic limit or stabilizedflow It is not obvious that a stabilized flow region exists in all the different wettability situations As anexample, if the objective is to find rate-independent residual oil saturation, a stabilized flow region may

be one of the rate selection criteria (Haugen 1990, Chen and Wood 2001, Skauge, Thorsen, and Sylte

2001, Rapoport 1955) The Rapoport and Leas scaling group is defined as:

Eq.1

Where: L core length, v the interstitial velocity and ␮w water viscosity

Experimentally, a critical value could be found beyond which a flood is stabilized This is done inpractice by plotting oil recovery at breakthrough versus Lv␮w as in Fig.1 The value at which recoverybecomes independent of the scaling coefficient gives the critical value (Kyte and Rapoport 1958) reported

that Lv␮ w ⬎1 (cm2/min.cp) resulted in a minimal end effect However, questions can raises that whether:

1 Conducting the flooding experiments at field rate is more representative, and

2 Conducting the experiments at higher rate would lead to de-saturation of S ?

Figure 1—Relation between oil recovery at breakthrough and scaling coefficient ( Rapoport and Leas 1953 )

It is important when designing displacement

ex-periments for measurements of relative permeability

to consider the following points:

1 A high pressure gradient will be required to

minimize capillary pressure end effects

Lv␮ w ⬎1.

2 The pressure gradient, however, should be

small compared to the total operating

pres-sure so that the incompressible fluid assumption is valid

3 the core should be homogeneous;

4 The driving force and fluid properties are held constant

Capillary number

The key flow parameter that controls the final fluid saturation is the capillary number N c which defined

as a ratio of viscous to capillary (interfacial tension) forces (Fulcher, Ertekin, and Stahl 1985) andgenerally have the form (Masalmeh 2012) of:

Eq.2

Where: u is Darcy’s velocity, ␮ is the viscosity of the displacing phase, ␴ is the interfacial tension, ␪

is the contact angle and ␸ is the porosity in fraction

In general, the actual flow within the reservoir is driven by viscous or gravitational forces However,capillary forces are usually present and may dominate Within pore scale the flow paths are determined

by the capillary forces (Chandler et al 1982) If viscous forces are increased, they may becomecomparable to the capillary forces at the pore scale which may alter the flow paths and thus the relativepermeability (Maas 2011) This change in flow dynamics can be reflected as a capillary numberdependence of the relative permeability This dependence can play an important role in flow processeswhich may not applicable to the field situation, and therefore should be avoided in laboratory experiments,

if proper and reliable basic reservoir data are to be obtained (Boom et al 1995, Masalmeh 2012,Maas

2011)

The capillary end effect can be represented by a dimensionless flow parameter, N c endwhich is the ratio

of a characteristic capillary pressure to the viscous pressure drop across the core, and can be approximated

Eq.3

Where: ␴ is the interfacial tension, ␮o is oil viscosity, L core length, ␸ is the porosity in fraction, and

K is the absolute permeability.

This parameter has a critical value range in which it affects the relative permeability derived by

analytical techniques For example, in water-wet for N c end⬎0.1, both oil and water permeability decrease

as N c end increases however, when N c end⬍ 0.1 it does not affect relative permeability (Mohanty and Miller

mixed-wet media and their typical ranges in the field and in the laboratory

Where:⌬␳ is the density difference between the displacing and displaced phase, g is the Acceleration due to gravity and K is the absolute permeability.

If the driving force for displacement is gravity (as in centrifuge experiments) its dominance can bechecked with the Bond number De-saturation effects can cause changes in capillary pressure and relativepermeability at high flow rate and/or low interfacial tension that (usually) do not occur under normal fieldconditions To avoid these effects, the critical Bond number (ratio between gravitational and capillaryforces) should be checked (Skauge, Thorsen, and Aarra 1997) concluded with experiments that centrifugeexperiments can be clearly influenced by Bond number variations Furthermore, oil relative permeabilityincreases with centrifugal speed for all classes of permeability they tested They showed that theremaining oil saturation vary with Bond number Critical Bond number values at which a speed insensitiverelative permeability can be obtained is in the order of 10-5 This Bond number requirement implies anupper limit for the centrifugal acceleration

Instability number

One of the conditions for the onset of instability during two phase immiscible displacement is that the

mobility ratio is higher than 1 (M ⫽ k rw ␮o /k ro ␮w⬎1) An unstable displacement leads to prematurebreakthrough and a longer period of two-phase flow at the outlet (Mohanty and Miller 1991) At present,

no techniques are available, which allow the interpretation of unstable data (Maas 2011) Therefore, inlaboratory experiments, this situation is undesirable In one dimensional laboratory experiments, espe-cially for light oil, there is less potential for fingers to grow In case that there is a potential for frontinstability, the experiment can be designed such that the rates are increased in steps where the high rate

is only applied at the end if capillary end effect is still present The effects of fingering and capillaritycannot be suppressed simultaneously At low rates, fingering is small, but the capillary end effect is high

On the other hand, at high rates, fingering is large, but the capillary end effect is low (McPhee and Arthur

1994) For the critical ranges of instability number the reader is referred to (Mohanty and Miller 1991)

Figure 2—In situ saturation profiles at rate 2 ft/day ( Chen and Wood 2001 )

techniques (Trewin and Morrison 1993) In-situ saturation profiles can also be used as observed data tovalidate the process of numerical simulation.

Experiment’s report

The main entrance to any successful quality check is a coherent and transparent experiment’s reporthighlighting any experimental difficulties encountered and indicates the most reliable data Engineersshould ensure that provision of this information is part of the contract

Relative permeability result quality checks

Identifying reliable special core analysis results

The first challenge is to differentiate those laboratory results which are considered reliable representative

of the reservoir from those which are clearly invalid or highly questionable SCAL flow parameters, likecapillary pressure, relative permeability and residual oil saturation depend strongly on the wetting state ofthe rock material being investigated Therefore, for the determination of a set of representative SCAL data,the wettability state of the core sample in the laboratory should approach as close as possible thewettability state of the reservoir Water-oil results are more likely to be unreliable due to factors associatedwith wettability Wettability can be altered as the result of:

1 The drilling mud used during the coring operation,

2 When and how the core was preserved and

3 The procedures and conditions used in making measurements in the laboratory

Understanding the history of the core material used in the special core analysis program, includingcoring fluid, preservation techniques and laboratory procedures used SCAL data obtained on plug which

is taken with such care from the reservoir, that ideally all the properties including wettability areconserved at the surface should be representative Key considerations for include

1 the drilling mud used to obtain the core material,

2 the timing and method of core preservation,

3 the laboratory handling of the core, i.e cleaning, drying, etc.,

4 the type of test conducted, steady or unsteady state, waterflood, centrifuge, etc.,

5 The fluids used and fluid properties, test conditions, i.e pressure, temperature, pressure tial, flooding rate, etc

differen-Figure 3—In situ saturation profiles at rate 39 ft/day ( Chen and Wood 2001 )

Extraction of valid water-oil relative permeability data

Conventionally, SCAL laboratory data are interpreted analytically In the interpretation, the effect ofcapillary pressure in a relative permeability experiment might be fully ignored In reality, both capillarypressure and relative permeability affect flow behaviour in any laboratory experiment accordinglylaboratory data invariably needs to be refined prior to use in a reservoir simulation model or in handcalculations due to the following:

1 First, it is sometimes necessary to disregard one portion of curves due to a particular weakness ofthe measurement technique An example of this is the unreliability of the high water saturationportion of unsteady state relative permeability results conducted at low rates on some samples

2 Second, it is often necessary to extend the laboratory results beyond the saturation range covered

in the test

The review should summarize the amount of valid data of the various types for the field in questionconsequently it is often appropriate to classify the results of the review and divided into groups such as:

● Data considered to be valid for further use

● Data of questionable validity, but which may be required if there is inadequate clearly valid data,

● Data which is clearly invalid or highly questionable

Integrating the results from different types of tests and recognizing which parts of each data set arereliable and which are invalid Thorough understanding of procedures and conditions used to obtain theresults and the strengths and weaknesses of each special core analysis data set As it’s known that theunsteady state test provides reliable results within the mid saturation range and the experiment artefactsstart to show up at high saturation range Therefore the centrifuge results will be used as supplementary

of the unsteady state results Residual oil saturation S or is very important characteristic in defining the

relative permeability curves Centrifuge experiment may not achieve the true value of S or , in this case S or

from post imbibition capillary pressure curve may be utilized which is not the subject of this paperNumerical simulations of laboratory experiments should be key element in Especially the use ofdifferent experimental techniques in combination with numerical simulations, aimed to history-match thedifferent experimental data sets with a single set of capillary pressure and relative permeability curves,allows us to effectively combine the strengths of the various techniques, whilst at the same timeconsistently taking account of all artefacts Moreover, numerical simulations can be used in the experi-mental design stage, and for quality control on contractor interpretation of experimental data

Water Oil relative permeability consistency check

Below are the consistency checks that can be applied to the crude relative permeability (Stiles 2013,

1 There should be agreement between k ro values at intermediate water saturations from validwaterflood tests and centrifuge oil relative permeability tests Results from the waterflood shouldgenerally be given greater weighting over intermediate water saturations where they do not agree

with results from the centrifuge k ro test

2 Values of residual oil saturation at the end of the various tests (on the same rock type) should beordered as follows, with the residual oil saturation decreasing from top to bottom:

● Reservoir conditions waterflood,

● Centrifuge k ro test,

● Centrifuge P c test

3 The k - value at the end of an unsteady-state waterflood should be less than the k

-measured at the conclusion of a centrifuge

test

4 The resulted relative permeability curve

from an unsteady-state waterflood, when

plotted on a logarithmic scale, should be

concave downward A curve which is

con-cave upward may be the result of

● Invalid (high) values of k rwat low water saturations due to lack of capillary Equilibrium at thestart of the waterflood

● Excessive flattening of the k rw curve at high water saturations may be due to plugging bymobile fines

5 Corey exponents (N o and N w) determined from the final curves (determined by plotting k ro and k rw

versus normalized water saturation on a log-log scale) should be consistent with wettabilitymeasurements Guidelines on Corey exponents for various wettability’s are shown in Table-2

(Stiles 2013):

6 Low k rw end-point values may be the result of progressive plugging of the core by mobile fines

during the flood (A k rw curve which decreases at high water saturation may be the result ofplugging at the end of the flood.)

7 Endpoint value approaching or exceeding 1 may be the result of the wettability of the core havingbeen altered to oil-wet by an inappropriate coring fluid, i.e oil-base mud

8 Very high k rw end-point can also be the result of not desaturation samples adequately prior to

flooding (High k rw end-pointvalues are more acceptable where they are measured at low residual oilsaturations)

General characteristics of water-oil relative permeability curves

The general characteristics expected in relative permeability are as follows (Stiles 2013, McPhee 2007,

Glover 2002):

1 As the water saturation is increased in the core two curves are defined; an oil relative permeability

curve (k ro ) and a water relative permeability curve (k rw) For homogeneous plugs the curves are

smooth and monotonic (The k ro curve is ever decreasing and the k rwis ever increasing) The final

oil saturation at the end of the test is referred to as the residual oil saturation S or

2 k rw at S or which is referred to as the “k rw end-point” This value is often used as an indication of thewettability of the rock/fluid system As with residual oil saturation, care must be exercised in using

k rw end-point, as its value can be severely understated if the flooding of the sample did not proceed

as far as it might due to laboratory considerations Should the value of Sor be too high due to

premature ending of the flood, the k rw end-point will be too low

3 Another important characteristic of the results is the saturation at which values of k rw and k roareEqual, i.e the saturation at which they cross This saturation can be used in comparing sets of

curves It can also be used in conjunction with the k rw end-pointand the connate water saturation as

a measure of wettability

4 Relative permeability should be plotted on a logarithmic scale such a plot is useful in constructing

a smooth k ro curve at low water saturations where little data are often available from laboratorymeasurements due to efficient displacement in the core Such a curve is also very useful in judging

the validity of the data assessing the values of k roat low oil saturations and judging whether or not

the k ro curve should be extended to even lower oil saturations

5 Valid relative permeability data often produce a straight line on a log–log plot when the relative

Table 2—Relative permeability characteristics vs wettability ( Stiles

2013 ) Wettability N o N w k rw end-point

Strongly Water-Wet 2 to 3 4 to 6 0.1 to 0.4 Mixed Wettability 3 to 5 2 to 4 0.5 to 0.9

permeability data are plotted versus normalized saturations It is a valuable tool, not only ininterpolating and extrapolating relative permeability curves, but also in assessing the validity oflaboratory data.

6 Display the results with values of k ro and k rwplotted on both a linear and a logarithmic scale Bothcurves should be smooth and concave upward when plotted on the linear scale and smooth andconcave downward on the logarithmic scale Where portions of the curves do not conform to theseshapes it is a sign that distortion has taken place

Assessing the validity of relative permeability data

1 Review laboratory procedures to identify any potential shortcoming which could have produceddistortions in the reported results which should consider answering the following question:

● Were special efforts made to preserve natural wettability?

● Was the test conducted on individual or composite cores?

● Was reservoir oil or refined oil used?

● Was the test conducted at room or reservoir conditions?

● What test procedure was used: steady-state, unsteady-state or centrifuge?

● At what rate was the core flooded?

● What was the pressure differential at the end of the flood?

● Was special attention given to “scaling” the waterflood?

● Was the flooding rate increased (“bumped”) at the end of the flood?

● If so what was the effect on S or and on k rw?

● Is there any evidence of “plugging” during the flood?

Valid relative permeability data often produce a straight line on a log-log plot when the relativepermeability data are plotted versus normalized saturation for and oil oil-water system, deviationfrom linearity could be due to measurement artefact such as:

● Flood front Instability:

y Problem only with unsteady-state method

y Relative permeability to water too high during early portion of flood

y Problem with mixed-wet rocks mitigated by reducing flooding rate and use of composite core

● Distortion of oil relative permeability curve by “Tail” of capillary pressure curve:

y Early termination of waterflood leads to Sor is too high

y Need to revise relative permeability to oil upward and extend

y Mitigate by flooding at higher rate and use composite core

● Capillary End Effect:

y Relative permeability to oil and water too low if capillary effects not minimised

y problem with water-wet and mixed-wet steady state and unsteady state

y Mitigate by flooding at higher rate” laboratory result scaling”

Odeh’s technique for reducing the rate effect on oil and water relative permeabilities

relative permeability values which causes distortions in the dynamic displacement measurements, asshownFig.4 They observed that, at high oil saturations, the relative permeability curves measured at highflow rates are more or less independent of the flow rate They also observed that a plot of the ratio ofrelative permeability to oil and the oil flow rate versus the average water saturation forms a straight line

at high oil saturations They assumed that, in this region, the oil relative permeabilities are not affected

by the capillary end effect (Qadeer, Brigham, and Castanier 2002) The steps are as follows:

1 Calculate the relative permeability’s to oil and water by the relative by analytical methods fromdynamic displacement data obtained from coreflood experiment

2 Plot and versus The average water saturation,

3 The plots and versus The average water saturation, normally show straight-line segments

at low water saturation ranges for relatively high flow rates as shown in Fig.5 Determine if astraight line segment exists in areas of the plot corresponding to high average oil saturations, and

if it does, extend the straight line segment to the end of the plotted data, otherwise draw a tangent

to the smooth curve from a beginning point of the plot as shown in Fig.6 This may present adifficulty because the contruction of a tangent is subject to personal judgment This is a drawback

The (K ro)cor values represent relative permeability with effect of displacement rate essentiallyremoved

5 Plot (k ) , values vs water saturation at the effluent end S as shown in Fig 7

Figure 4 —Calculated k roat different rates ( Odeh and Dotson 1985 )

Jess Stiles’ technique

(Stiles 2013) utilized Corey correlation in its interpretative form to quality check the relative permeabilityobtained from analytical methods after experiments The approach can be summarised as follows:

1 Identify the reliable portions of the reported results

2 Define relative permeability characteristics from analysis of those results

3 Refine unreliable results using these characteristics

The analysis method is based on the assumption that oil and water relative permeability relationshipscan generally be defined using the following Equations:

Figure 5—Correction procedure of k ro( Odeh and Dotson 1985 )

Figure 6 —Correction procedure of k ro( Odeh and Dotson 1985 )

S on: normalized oil saturation, fraction

S wn: normalized water saturation, fraction

S wi: initial or connate water saturation, fraction

S or : the true residual oil saturation, fraction

N o: Corey exponent for the oil curve, dimensionless

N w : Corey exponent for the water curve, dimensionless

k rw end-point ⫽ k rw at true residual oil saturation which will sometimes be denoted with k rw=, fraction

k ro at S wi⫽ 1.0

All relative permeability values are expressed as a fraction of the base permeability which, for thesediscussions, is the effective oil permeability measured at connate water saturation at the start of thelaboratory test

The above Equations are valuable diagnostic tool, not only in interpolating and extrapolating relativepermeability curves, but also in assessing the validity of laboratory data It is to be emphasised thatchanges in Corey exponents are accompanied by changes in other relative permeability characteristics, i.e

initial water saturation, residual oil saturation and k rw end-point A qualitative and quantitative evaluation of

water-oil relative permeability could help on establishing k rw end-point , S or , N w and N o The tics” defined above are be used together in the following way to define oil and water relative permeability.The following steps demonstrate the application of this method on data from the North Sea:

“characteris-Figure 7—Corrected k ro( Odeh and Dotson 1985 )

1 Display the results with values of k ro and k rwplotted on both a linear and a logarithmic scale Bothcurves should be smooth and concave upward when plotted on the linear scale and smooth andconcave downward on the logarithmic scale Where portions of the curves do not conform to theseshapes it is a sign that distortion has taken place.Fig.8andFig.9below this indicate that there aresome distortions in the reported results.

2 The first step in Stiles’ technique is to estimate the true residual oil saturation iteratively from

analysis of the k ro curve versus normalized oil saturation the saturation range using differentassumed values of true residual oil saturation as shown in Fig.10 The various relationships

between k ro and S onare plotted on a log-log plot, and the assumed value that produces the beststraight line through reliable data is used as an approximation of true residual oil saturation

3 Using the estimated value of true residual oil saturation an estimate k rw end-point is made from

analysis of the k rw data versus normalized water saturation S wnon a log-log plot and extending the

trend through the more reliable data to the point where S Equals unity, i.e where S Equals true

Figure 8 —Visual check of relative permeability curves on linear scale

Figure 9 —Visual check of relative permeability curves on logarithmic scale