OA10507A - Determining a parameter of a component in a composition - Google Patents

Abstract

1. A method of determining a parameter in a composition of an earth formation selected from the electrical conductivity and the volume fraction of a component in a composition comprising a plurality of components of an earth formation, the method comprising: - drilling a borehole in an earth formation to obtain a core sample to be tested; - measuring the electrical conductivity of the composition by a logging instrument; - selecting a relationship between the electrical conductivity of the composition and a plurality of composition parameters including, for each component, physical parameters representing the electrical conductivity and the volume fraction of the component, the components being substantially equally represented in said relationship by means of said physical parameters; and - determining said selected parameter from said relationship and the measured conductivity of the composition, characterized in that an auxiliary parameter is introduced in said relationship, depending on the conductivity of one of said components and a mixing coefficient, whereby the mixing coefficients depend on the geometrical configuration of the components in the composition and determine the amount of percolation of the individual components. 2. The method of claim 1, wherein said plurality of composition parameters includes at least one fitting parameter, and wherein each fitting parameter is determined by applying said relationship to a data set obtained by measuring the electrical conductivity of at least one sample representative for said composition for various magnitudes of at least one of said parameters. 3. The method of claim 1 or 2, wherein said relationship is selected to be (σeff-σ0) (Lσeff + (1-L) σ0)<-1> = Σφk(σk-σ0) (Lσk+ (1-L) σ0)<-1> wherein σ0 represents the auxiliary parameter in the form of a conductivity tensor, k = 1 ... N, N being the number components, σeff represents the conductivity tensor of the sample, σk represents the conductivity tensor of component k, φk represents the volume fraction of component k, L represents a depolarisation tensor. 4. The method of any of claims 1-3, wherein said auxiliary parameter is selected to be σ0 = Σ hk.σk; wherein σ0 represents the auxiliary parameter in the form of a conductivity tensor representative for the conductivity in the three principal directions, k = 1 ... N, N being the number of components, σk represents the conductivity tensor of component k, hk represents the mixing coefficient tensor pertaining to component k. 5. The method of any one of claims 1-4, wherein said mixing coefficients are selected so that the sum of the mixing coefficients substantially equals unity. 6. The method of any of claims 1-5, wherein said mixing coefficients are non-negative. 7. The method of any of claims 1-6, wherein each mixing coefficient is selected to be a function of at least the volume fraction of the component pertaining to said mixing coefficient. 8. The method of claim 7, wherein said function is a monotonous increasing function in the volume fraction of the component pertaining to the mixing coefficient. 9. The method of claim 7 or 8, wherein said function is selected so that the mixing coefficient vanishes for vanishing volume fraction of the component pertaining to the mixing coefficient. 10. The method of any of claims 1-9, wherein each mixing coefficient is selected as hk = λk φ kvk (Σλn φn vn)<-1> wherein k,n = 1... N, N being the number components in said plurality of components, λk represents a percolation rate tensor pertaining to component k, φk represents the volume fraction of component k, vk,n represents a percolation exponent pertaining to component k, n. 11. The method of claim 10, wherein at least one of hk λk and v forms a fitting parameter. 12. The method of any of claims 3-11, wherein the depolarisation tensor is positive. 13. The method of any of claims 3-12, wherein the depolarisation tensor has unit trace. 14. The method of any of claims 3-13, wherein the depolarisation tensor equals 1/3 times the unit tensor. 15. The method of any of claims 1-14, wherein the step of determining each fitting parameter by applying said relationship to the data set is carried out through an iterative process. 16. The method of claim 15, wherein the iterative process includes repeatedly applying said relationship in a minimisation scheme. 17. The method of claim 16, wherein the minimisation scheme is applied to a mismatch between the measured electrical conductivities of said components and the electrical conductivities of the components as determined through said relationship. 18. The method of any of claims 1-17, wherein said composition includes an earth formation. 19. The method of claim 18, wherein said earth formation includes at least one of rock, brine, hydrocarbon fluid and clay. 20. The method of claim 19, wherein said parameter which is determined forms the volume fraction of one of the hydrocarbon fluid and the brine.

Description

010507 1

.TS $Q2S

DETERMINING A PARAMETER OF ACOMPONENT IN A COMPOSITION

The présent invention relates to a method ofdetermining a parameter selected from the electricalconductivity and the volume fraction of a component in acomposition comprising a plurality of components. The 5 invention is of particular interest for determining the volume fraction of a component of an earth formation, forexample to détermine the hydrocarbon-content of ahydrocarbon bearing earth formation. Various knownmethods of determining such content hâve been applied 10 until now, which known methods are generally based on empirical models.

One such known method is described in "Electricalconductivities in oil-bearing shaly sands", Waxman M.H.and Smits SPE paper 1863-A presented at 42nd Ann. 15 Fall Meeting, Houston, October 1-4, 1967.

This publication discloses a method of determining aparameter selected from the electrical conductivity andthe volume fraction of a component in a compositioncomprising a plurality of components, wherein the 20 electrical conductivity of the composition is measured, and a relationship between the conductivity of thecomposition and the conductivity of a component isselected.

This known method uses the following relationship 25 which is generally referred to as the Waxman-Smits model:

Co = Cw / F* + BQV / F* where Co = conductivity of fully brine saturated rock

Cw = conductivity of brine présent in the formation 2 010507 F* = a formation factor B = équivalent conductance of sodium clay-exchangecations as a function of Cw

Qv = cation exchange capacity per unit pore volume.The results achieved with this known method are notalways sufficiently accurate, probably because of theempirical nature of the Waxman-Smits model which providesa relationship between the earth conductivity and thevarious other parameters.

It is an object of the invention to provide a moreaccurate method of determining a parameter selected fromthe electrical conductivity and the volume fraction of acomponent in a composition comprising a plurality ofcomponents.

The method according to the invention theretocomprises : measuring the electrical conductivity of thecomposition; selecting a relationship between the electricalconductivity of the composition and a plurality ofcomposition parameters including, for each component,physical parameters representing the electricalconductivity and the volume fraction of the component,the components being substantially equally represented insaid relationship by means of said physical parameters;and determining said selected parameter from saidrelationship and the measured conductivity of thecomposition.

It is to be understood that by the electricalconductivity is meant the electrical conductivity itselfor any quantity derived therefrom, such as the electricalresistivity. Furthermore, the feature that the componentsare substantially equally represented in the relationshipimplies that each component is represented in the 010507 relationship in substantially the same way as any otherof the components.

With the method according to the invention it isachieved that results of increased accuracy are provided.The selected relationship takes accurately account of theindividual contributions of the components to theconductivity of the composition. The relationship appliedin the method according to the invention is symmetricalin the components, i.e. no component is favoured overanother component. Moreover, it was found that the methodaccording to the invention provides the desired accuracyfor any percolation threshold of the components. In thisrespect it is to be understood that the amount ofpercolation of a component refers to the degree ofcontinuity of the component in the composition. Forexample, vanishing percolation of a component impliesthat the component is fully dispersed in the composition,and full percolation of a component implies that thecomponent is continuous throughout the composition.

Advantageously said plurality of compositionparameters includes at least one fitting parameter, andwherein each fitting parameter is determined by applyingsaid relationship to a data set obtained by measuring theelectrical conductivity of at least one sample représentative for said composition for various magnitudes of at least one of said parameters.

Preferably said plurality of parameters includes anauxiliary parameter depending on the geometricalconfiguration of the components in the composition.

Accurate geometrical représentation by the auxiliarycomponent is achieved if said auxiliary parameter isselected so as to be a function of a plurality ofvariables, each variable depending on the conductivity ofone of said components and a mixing coefficient, whereby 010507 4 the mixing coefficients dépend on the geometrical configuration of the components in the composition.

Advantageously the step of determining each fittingparameter by applying said relationship to the data setof the component is carried out through an itérativeprocess. Suitably the itérative process includesrepeatedly applying said relationship in a minimisationscheme. The minimisation scheme is preferably applied toan incohérence between the measured electrical conductivities of said components and the electricalconductivities of the components as determined throughsaid relationship.

The invention will be described hereinafter in moredetail and by way of the following example andcomparative example.

Example

Consider an isotropie system with essential sphericalinclusions in the form of an earth formation whichessentially consists of four components: non-conductingporous rock matrix, non-conducting hydrocarbon fluid,conducting clay, and conducting brine. The conductivityof the formation dépends on the fractional brinesaturation of the pore space, and the hydrocarbon fluidcomponent is grouped with the rock matrix, both beingnon-conducting. Thus, the hydrocarbon component and therock matrix component only enter the équations with thesum of their volume fractions. The effective conductivityaeff of this earth formation is evaluated through theexpression (oeff - σ0) . (Laeff + (I-Duq)-1 = Σ <t>k (ak - σ0) . (Lck + (1-L)σθ)_1 wherein σθ represents the auxiliary parameter in theform of a conductivity tensor 5 010507 k = 1 ... N, N being the number of componentsaeff represents the conductivity tensor of the sampleay represents the conductivity tensor of component kφ^ represents the volume fraction of component kL represents the depolarisation tensor (shapetensor)

Preferably the depolarisation tensor is positive andhas unit trace. In an attractive embodiment thedepolarisation tensor equals 1/3 times the unit tensor.

The term gq dénotés an auxiliary parameter which canbe thought of as being an additional host medium intowhich components are added until the host medium has beencompletely replaced by the components so that no volumefraction is associated with the host medium. Theexistence of the host medium enables the model to besymmetrical in ail its constituents: none of thecomponents rock, clay or brine in the model is favouredover any of the other components. The dependence of gq onvarious parameters, yet to be determined, governs thepercolation behaviour of the model. Setting gq = Gkr£neleads to the known Average T-matrix Approximation, alsoreferred to as the generalised Clausius-Mossottiéquation. This model has a clear asymmetry between thebrine component and the other components since only thebrine component will percolate, irrespective of itsvolume fraction. Selecting a self-consistent host mediumconductivity, Gq = Geff, ieads to the known CohérentPotential Approximation, also referred to as thegeneralised Bruggeman équation. This model is symmetricalin ail components but has the drawback of requiringunrealistically high percolation thresholds for eachcomponent.

In a suitable embodiment, the auxiliary parameter Gqis selected as follows: 6 010507 σθ = Σ hjç ajç ; for k = 1, 2, 3 wherein hjç represents the mixing coefficient tensorpertaining to component k, which tensor contains mixingcoefficients representing geometrical information on thespatial distribution of the components in the formation.These coefficients détermine the connectivity, i.e. theamount of percolation of the individual components. Thecoefficients are non-negative and fulfil the normalisation condition·. Σ h]ç = 1; for k = 1, 2, 3

The normalisation relation ensures that the result'ingeffective conductivity ceff satisfies the Hashin -Shtrikman bounds, which are well known to those skilledin the art.

Furthermore, a component with a vanishingly small volumefraction can not percolate, hence the correspondingconnectivity parameter should vanish: lim hjç = 0; for => o

Suitably the mixing coefficient tensor is selected to be hk = λνΦι<-νν ( ΥΧ-.ό^ν~) 1 ru - - T J». ^ ». — x x i x i ix wherein k,n = 1 ... N, N being the number ofcomponents in said plurality of components λ}ς represents the percolation rate tensor pertainingto component k represents the volume fraction of component kv represents the percolation exponent pertaining to component k 010507 7

Suitably at least one of h^, and v forms a fittingparameter. A data set on 27 shaly-sand core samples has beenused to test the invention, which data set is describedin the above indicated SPE paper. This publicationprovides Co - Cw curves on the core samples ranging fromalmost clean sand (Qv = 0.017 eq/1) to extremely shalysand (Qv = 1.47 eq/1). The samples contained Kaolinite,Montmorillonite and Illite, either in combination orseparately in each sample. The characteristic petrophysical data of each sample are listed in theappended Table, in which φ dénotés the porosity of thesample, κ dénotés the permeability of the sample, and Qvdénotés the cation exchange capacity per unit pore volumeof the sample. The conductivity of each sample in fullybrine saturated condition was measured for eight to tensalinities of the brine. Furthermore, concentrationmembrane potential measurements were made of the samples.

The parameters in this model were selected asfoiiows: 1) Brine;

The volume fraction of brine, φ]~,, is determined by theporosity, the amount of clay-bound water, and the watersaturation Sw. The brine conductivity cj-, (=CW) isdetermined by the brine salinity and the brine température. The two percolation parameters, and v, S-y-ο "Ftcici ο υό m ,ο t ν'n -ι~ ·_» <_* J- «-Λ. L l IC» U- C»» A» ü? · 2) Rock / Hydrocarbon;

The volume of hydrocarbons, φ^, is determined by thetotal porosity, the amount of clay-bound water, and thehydrocarbon saturation 1 Sw, while the volume of the rockmatrix, φΓ, is calculated using the sum rule and thevolume fractions. Both the rock and the hydrocarbon hâvevanishing conductivity. The percolation parameters λΓ andÀhc of both components was set at value 1. The mixing 8 010507 coefficient pertaining to rock/hydrocarbon hr/hc followsfrom the condition Σ hk = 1. 3) Clay;

The volume of clay Φε and the clay conductivity σε are 5 free fitting parameters. The percolation rate Àc was set ata value 0, which is a suitable choice for non-laminatedclays. It furthermore appeared that an additional freeparameter did not give a significant improvement of themodel fit to the data set. 10 The Co - Cw measurements were made for an extreme salinity range, namely a brine salinity between 1 - 300g/l. For a given sample the brine volume fraction varied onlyslightly over the whole salinity range. In view thereof thepercolation parameter v was set equal to unity in the test, thereby 15 reducing the percolation parameter hb to a constant, andreducing the number of free parameters to three.

For each sample, a fit to the Co - Cw curve was made byminimising the relative incohérence defined as: 20 Σ Δ2 Co - Cw = Σ salinities wherein

Co' calc-Co, meas 2Co, meas

Co cale = ^e calculated conductivity of the fully brinesaturated rock samples;

Co meas = the measured conductivity of the fully brinesaturated rock samples; Σ = summation over the salinities.

The results for the three fitting parameters Φε, σαand hb, and the relative incohérence are given in theappended Table. 25 010507

Furthermore, the Table gives the incohérence betweenthe membrane potential (Tcaïc) determined by the method ofthe invention and the measured membrane potential (Tmeas) : T'calc - Tmeas Σ δ2μρ = Σ (-------------------------) 2

Tmeas

The membrane potential is a particularly interestingquantity for being a direct, non-destructive, measure of theclay contribution to the overall conductivity, which has notbeen used to détermine the fitting parameters.

To illustrate the invention more specifically,reference is made to the following comparative example.Comparative example

As stated above Ref. 1 discloses, apart from the data set on the 27core samples, furthermore an empirical model which is generallyreferred to as the Waxman-Smits model. To compare the methodaccording to the invention with the Waxman-Smits model, therelative incohérence between the measured conductivities and theconductivities found from the Waxman-Smits model, and therelative incohérence between the measured concentrationmembrane potentials and the concentration membrane potentialsfound from the Waxman-Smits model, were determined. Theserelative incohérences for ail 27 samples are listed in the Table. Inapplying the Waxman-Smits model, use has been made of the wellknown expression :

Co = Cw / F* + BQV ! F*with F* = φ-m 010507 10 where m is a free parameter (also referred to as thecementation exponent), Qv is determined from samplemeasurements, just as the porosity φ, and the standard B-chart has been used to calculate the salinity and 5 température effects on the conductivity measurements.

From a comparison between the incohérence values found by using the method according to the invention, andthe incohérence values found by using the Waxman-Smitsmodel, it is clear that the method according to the 10 invention provides improved results. Especially the extremely low incohérence values for the concentrationmembrane potential, which values are moreover fairlyconstant over the entire Qv range, indicates that themethod according to the invention provides results of 15 increased accuracy.

The method according to the invention can suitably be applied to détermine the volume fraction of brine orhydrocarbon in an earth formation, whereby a well-logrepresenting the electrical conductivity of the formation 20 is provided. Such application can, for example, be carried out in the following manner. The well-log of theelectrical conductivity of the earth formation is madeusing a logging tool lowered in a borehole formed in theearth formation. For an isotropie formation with 25 components brine (subscript B), clay (subscript C), and non-conducting rock + hydrocarbon (subscript R/HC) therock and the hydrocarbon are groupcd tegether because oftheir vanishing conductivities. The selected relationshipthen is: aeff_(To 3 CTk “ σο ----------- = X <j)k. ------- CTeff + 2 σο k=l ak + 2σο 30 wherein 11 010507 σΟ - Σ hkQk hk = ^k(t)kVk ( Σληφηνη) 1 in which σο represents the auxiliary parameter k, η = 1 ... N, N being the number components creff represents the conductivity of the earth formation ajç represents the conductivity of component k φ^ represents the volume fraction of component k hy represents the mixing coefficient pertaining to component k;

Xr represents the percolation coefficient pertaining tocomponent k vk,n represents the percolation exponent pertaining tocomponent k, n

Each component k has four parameters: φ^, σ^, λ^·, andv^, of which φβ, σΒ and are directly measured.

Furthermore, Xq = 0 for dispersed clay. From the sumrules h^/HQ and φβ/βο follow. Parameters which are yet tobe determined are σς, λβ, νβ and φ^. These parameters aredetermined through forward modelling on experimentaldata. Gç, λβ ancj νβ are invariable over the geologicalformation , while φΒ will be depth dépendent. Theexperimental data for the parameter détermination consistof well-log measurements from a brine containing zone,laboratory Formation Resistivity Factor (FRF)measurements and brine saturation experiments. The loginformation from the brine containing zone is used tocorrelate the local parameter φς to suitable logs/logcombinations, as is known to those skilled in the art ofwell logging. σ^, λβ and φβ and the corrélation of çq tosuitable logs/log combinations can be used in hydrocarbonbearing formations. From the well-log, the aboverelationship and the indicated parameters, the volume 010507 12 faction of brine and thus also the volume fraction ofhydrocarbon is determined as a function of depth. 13 010507

.6408 2.8227 0.1484 0.010 0.012 0.823 0.376 14 010507

Claims (19)

1. 010507 15 TS 6028 PCT NEW CLAIM

   1. A method of determining a"parameter selected from theelectrical conductivity and the volume fraction of acomponent in a composition comprising a plurality ofcomponents of an earth formation, the method comprising: measuring the electrical conductivity of thecomposition; selecting a relationship between the electricalconductivity of the composition and a plurality ofcomposition parameters including, for each component,physical parameters representing the electricalconductivity and the volume fraction of the component,the components being substantially equally represented insaid relationship by means of said physical parameters;and determining said selected parameter from saidrelationship and the measured conductivity of thecomposition, characterized in that said plurality ofparameters includes an auxiliary parameter being selectedas a function of a plurality of variables, each variabledepending on the conductivity of one of said componentsand a mixing coefficient, whereby the mixing coefficientsdépend on the qeometrical configuration of the componentsin the composition and détermine the araount ofpercolation of the individual components.
2. 2. The method of claim 1, wherein said plurality ofcomposition parameters includes at least one fittingparameter, and wherein each fitting parameter isdetermined by applying said relationship to a data setobtained by measuring the electrical conductivity of at MCS13/TS6028P2 010507 16 least one sample représentative for said composition forvarions magnitudes of at least one of said parameters.
3. 3. The method of claim 1 or 2, wherein said relationshipis selected to be I 5 (CTeff _ σθ) · (Lcreff (I-L)Gq) = Σ φ]ζ (^k "" (k®k (1-L)σθ)"1 wherein σθ represents the auxiliary parameter in theform of a conductivity tensor k = 1 ... N, N being the number components10 aeff represents the conductivity tensor of the sample σ]ς represents the conductivity tensor ofcomponent k φ]ς· represents the volume fraction of component k15 L represents a depolarisation tensor
4. 4. The method of any of daims 1-3, wherein saidauxiliary parameter is selected to be σ0 = Σ hkak wherein σθ represents the auxiliary parameter in the20 form of a conductivity tensor représentative for the conductivity in the three principal directions; k = 1 ... N, N being the number of components;σ^ represents the conductivity tensor of componentk; 2b hjç represents the mixing coefficient tensor pertaining to component k.
5. 5. The method of any one of daims 1-4, wherein saidmixing coefficients are selected so that the sum of themixing coefficients substantially equals unity.
6. 6. The method of any of daims 1-5, wherein said mixing coefficients are non-negative.
7. 7. The method of any of daims 1-6, wherein each mixingcoefficient is selected to be a function of at least the 010507 17 10 15 20 25 volume fraction of the component pertaining to saidmixing coefficient.
8. 8. The method of claim 7, wherein said function is amonotonous increasing function in the volume fraction ofthe component pertaining to the mixing coefficient.
9. 9. The method of claim 7 or 8, wherein said function isselected so that the mixing coefficient vanishes forvanishing volume fraction of the component pertaining tothe mixing coefficient.
10. 10. The method of any of daims 1-9, wherein each mixingcoefficient is selected as = ^^kvk ( Σληφηνη) 1 wherein k,n = 1 ... N, N being the number componentsin said plurality of components λ]ς represents a percolation rate tensor pertaining tocomponent k φ]ς represents the volume fraction of component kvk,n represents a percolation exponent pertaining tocomponent k,n.
11. 11. The method of claim 10, wherein at least one of h^,λ]ς and v forms a fitting parameter.
12. 12. The method of any of daims 3-11, wherein thedepolarisation tensor is positive.
13. 13. The method of any of daims 3-12, wherein thedepolarisation tensor has unit trace. T"· V·» Λ *** Λ +“ Λ ·£ «"« VI «t F X ÜC LUCS UiiUUl O X. CXXXJ^ depolarisation tensor equals 1/3 times the unit tensor.
14. 15. The method of any of daims 1-14, wherein the step ofdetermining each fitting parameter by applying saidrelationship to the data set is carried out through anitérative process.
15. 16. The method of claim 15, wherein the itérative processincludes repeatedly applying said relationship in aminimisation scheme. 30 010507 10 - 18 -
16. 17. The method of daim 16, wherein the minimisationscheme is applied to a mismatch between the measuredelectrical conductivities of said components and theelectrical conductivities of the components as determinedthrough said relationship.
17. 18. The method of any of daims 1-17, wherein saidcomposition indudes an earth formation.
18. 19. The method of daim 18, wherein said earth formationindudes at least one of rock, brine, hydrocarbon fluidand clay.
19. 20. The method of daim 19, wherein said parameter whichis determined forms the volume fraction of one of thehydrocarbon fluid and the brine. MCS13/TS6028PC