EA001131B1 - 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

The invention relates to a method for determining a parameter selected from electrical conductivity and the relative volume of a component included in a composition containing many components. The invention is of particular interest for determining the relative volume of a component of the earth formation, for example, for determining the hydrocarbon content in a hydrocarbon-containing earth formation. The methods used so far for determining such content are based mainly on empirical models.

One such well-known method is described in the work of Electrical Conductivity in Oil Shale Sands, by Watsman M.N. and Smiths L.J.M., presented at the 42nd annual meeting in Houston on October 1-4, 1967 (materials 8PE 1863-A).

In this work, a method is proposed for determining a parameter selected from the electrical conductivity and the relative volume of the component included in the composition containing many components. The method consists in measuring the electrical conductivity of a given composition and choosing the relationship between the conductivity of the composition and the conductivity of this component.

The specified method uses a dependency, commonly called the Waxman-Smiths model:

С _о = С ../ Е * + ΒΟ,. / Ρ * where С _о - conductivity of a rock completely saturated with brine,

C, is the conductivity of the brine present in the reservoir,

P * - reservoir factor,

B is the equivalent conductivity of the sodium / clay exchange cations as a function of C ,,

Ο _ν is the cation exchange ability per unit pore volume.

The results obtained using this known method are not always accurate enough, probably due to the empirical nature of the Waxman-Smiths model, which determines the relationship between the conductivity of the earth and various other parameters.

The present invention solves the problem of creating a more accurate method of determining a parameter selected from the electrical conductivity and the relative volume of the component in the composition containing many components.

The proposed method consists in measuring the electrical conductivity of the composition, choosing the relationship between the electrical conductivity of the composition and a variety of composition parameters, including physical parameters characterizing the electrical conductivity and the relative volume of each component of the composition, all components being represented by physical parameters in the specified dependence, and determining the selected parameter from the specified dependence and measured conductivity of the composition.

It should be understood that electrical conductivity is understood as electrical conductivity per se or any value obtained on its basis, for example, electrical resistivity. In addition, the feature of the invention, namely, that all components are equally represented in the relationship, means that each component is represented in this relationship essentially the same with all other components.

The proposed method allows to obtain results that are more accurate. The selected dependence accurately takes into account the contributions of individual components to the conductivity of the composition. The dependence used in the proposed method is symmetrical for all components, i.e. no component is preferred over others. In addition, it was found that the proposed method provides the required accuracy at any threshold for the leakage of components. It should be understood that the degree of leakage of a component refers to the degree of constancy of the component in the composition. For example, the disappearance of component leakage means that the component is completely dispersed in the composition, and the complete leakage of the component indicates that the component is continuously dispersed in composition.

It is advisable that among the many composition parameters there should be at least one fitting parameter, each fitting parameter being determined by applying the indicated dependence to the data set obtained by measuring the electrical conductivity of at least one sample characteristic of the specified composition for different values of at least one of the parameters.

Preferably, the set of parameters includes an additional parameter, depending on the geometric configuration of the components in the composition.

An exact geometric representation with the help of the indicated additional component is achieved if the selected additional parameter is a function of many variables, each of which depends on the conductivity of one of the components and the mixing coefficient, while the mixing coefficients depend on the geometric configuration of the components in the composition.

It is advisable that the determination of the fitting parameter by applying the indicated dependence to the data set for the component is performed as an iterative process. By an iterative process is meant the repeated use of this dependence according to the minimization scheme. The minimization circuit is preferably applied to the incoherence between the measured electrical conductivities of the components and the electrical conductivities of the components determined from this relationship.

In the future, the principle of the invention will be described in more detail on a specific example of its implementation and comparative example.

Example.

Consider an isotropic system containing a significant amount of spherical inclusions in the form of an earth formation, which consists mainly of four components: non-conductive porous parent rock, non-conductive hydrocarbon fluid, conductive clay and conductive brine. The conductivity of the formation depends on the relative saturation with the brine of the pore space, and the hydrocarbon fluid is grouped with the parent rock, since they are both non-conductive. Thus, hydrocarbon and parent rock are introduced into the equation as the sum of their relative volumes. Effective conductivity _eff this earth formation is estimated by the expression (σ _3φ -σ ₀₎ (bo _eff + (1-b) σ ^{₀₎ _1 = Φ ^ (σ ^} -σ ₀₎ (0 + (1 ~ b) σ ₀ ) ^_1 where a _о is an additional parameter in the form of the conductivity tensor, k = 1 ... Ν, N is the number of components in the composition, and _e f is the conductivity tensor of the sample, and _k is the conductivity tensor of the component k, f _k is the relative component volume k, b - depolarization tensor (shape tensor). Preferably, the depolarization tensor is positive and has a single trace. In a preferred example, the depolarization tensor is 1/3 of the unit tensor.

The term σ ₀ means an additional parameter that can be considered as an additional primary medium into which the components were added until the primary medium was completely replaced by components, as a result of which no relative volume is associated with it. The presence of this primary medium allows the model to be symmetrical for all its components, i.e. none of the components of the rock, clay or brine - is preferred in the model. The dependence of σ ₀ on various parameters to be determined determines the seepage characteristics in the model. The setting σ ₀ = σ ^^ yields the well-known mean T-matrix approximation, which is also called the generalized Clausius-Mossotti equation. This model is characterized by a noticeable asymmetry between the brine component and other components, since only the brine will leak out, regardless of its relative volume. The choice of the consistent conductivity of the primary medium, σ0 = σ ^, leads to the well-known approximation of the coherent potential, which is also called the generalized Brugemann equation. This model is symmetrical for all components, but its disadvantage is that it requires unrealistically high percolation thresholds for each component.

In a preferred embodiment, the additional parameter σ0 is chosen as

Σ b. <s _to ; for k = 1,2,3 where 11 _k is the mixing coefficient tensor related to component k, and this tensor contains mixing coefficients representing geometric information about the spatial distribution of the components in the formation. These coefficients determine connectivity, i.e. the degree of seepage of the individual components. The coefficients do not have a negative sign and satisfy the following normalization condition:

Σ - for k = 1, 2, 3.

This normalization ratio ensures that the obtained effective conductivity σ ^ satisfies the HashinStrikman limits known to specialists.

In addition, a component having a relative volume tending to zero cannot leak, and therefore the corresponding connectivity parameter must be zero

11ш 11 _к , = 0; for φ _k => 0.

It is advisable to choose the mixing coefficient tensor as

Bk = Ak fk V *. (£ ^λ π Ф "ν") ' ¹ where k, η = 1 ... Ν, N is the number of components that make up the specified set of components,

X _to - leakage rate tensor related to component k, f _to - relative volume of component k,

Y _k - leakage rate related to component k.

It is advisable that at least one of the parameters 11 _k , X _k and V be a fitting parameter.

To test the invention, data were obtained from 27 core samples of shale sands presented in the above-mentioned publication 8PE. In this work, the С _о - СТ curves for core samples are given, ranging from almost pure sand (ρ _ν = 0.017 equiv / L) to extremely shale sand (ρ _ν = 1.47 equiv / L). All samples contained kaolinite, montmorillonite and illite separately or together. Typical petrophysical data for each sample are given in the attached table, in which Φ is the sample porosity, k is the sample permeability, and ρ _ν is the cation exchange capacity per unit pore volume of the sample. The conductivity of each sample in a fully saturated brine state was measured for 8-10 salinity of the brine. In addition, the concentration membrane potential was measured on the samples.

The parameters of this model were selected as follows:

(1) Brine

The relative volume of brine, f _s is determined from the porosity, amount of water associated with the clay and water saturation and conductivity brine _b (C = \ E is determined by the temperature and salinity of the brine. Two parameters percolation, X _s and V, are free parameters.

(2) Rock / hydrocarbon

The volume of hydrocarbons, _fs , is determined by the total porosity, the amount of water associated with clay and the hydrocarbon saturation of 1-8 _ν , and the volume of the parent rock, f _g , is calculated using the rule of sum and relative volumes. Both the rock and the hydrocarbon have a conductivity tending to zero. The leakage parameters, λ _Γ and X _bc , of both components are taken as unity. The mixing coefficient related to the rock / hydrocarbon, th _g / _s , follows from the condition

(3) Clay

Clay volume, f _s , and clay conductivity, and _s , are freely chosen parameters. The permeation rate, λο, is taken equal to zero, which corresponds to non-layered clays. It was found that the additional free parameter did not provide a significant improvement in the model suitable for the data set.

Measurements were made of C _o - C \ for excessive salinity, namely, salinity in the range of 1-300 g / l. The relative volume of brine fluctuated slightly for the entire salinity range for the sample taken. Therefore, the leakage parameter V in the experiment was taken equal to unity, as a result of which the leakage parameter _11b took a constant value, and the number of free parameters decreased to three.

For each sample, an adjustment was made to the curve С _о - С \ to minimize the relative incoherence, defined as

where C _about , _rac is the calculated conductivity of the samples completely saturated with brine,

With _about , _izm - the measured conductivity of the samples completely saturated with brine of the rock,

2- - summation of salinity.

The attached table shows the results of three adjustable parameters f _c , and _c and 11 _b and relative incoherence.

In addition, the table shows the incoherence between the membrane potential (^ _calculation ), determined by the proposed method, and the measured membrane potential (T _ISM )

The membrane potential is a particularly interesting value, since it is a direct non-destructive measure of the contribution of clay to the total conductivity, which was not used to determine the fitting parameters.

The following is a comparative example to more specifically illustrate the invention.

Comparative example.

As mentioned above, in the above publication 1, in addition to data for 27 core samples, an empirical model is proposed, which is generally referred to as the Waxman-Smiths model. To compare the proposed method with the Waxman-Smiths model, the relative incoherence between the measured conductivities and conductivities determined using the Waxman-Smiths model and the relative incoherence between the measured concentration membrane potentials and concentration membrane potentials determined using the Waxman-Smiths model were determined. These relative incoherences for all 27 samples are shown in the table. For the Waxman-Smiths model, the following well-known expression was used:

С _о = С _те / Г * + ВОЛ * at Г * = ф ^-т where т is a free parameter (also called a cementation index), О, - is determined from the measurements of the sample, as well as the porosity ф, and the standard A chart for calculating the effects of salinity and temperature on conductivity measurements.

From a comparison of the incoherence values obtained using the proposed method, and the incoherence values obtained using the Waxman-Smiths model, it is seen that the proposed method allows to obtain better results. In particular, the extremely low incoherence values for the concentration membrane potential, which are mainly constant over the entire 9 _ν range, indicate that the accuracy of the results obtained by the proposed method is much higher.

The proposed method can find application in determining the relative volume of brine or hydrocarbon in the earth formation, if there is logging data characterizing the conductivity of the formation. The method can be implemented, for example, as follows. An electrical conductivity logging of the earth formation is carried out using a logging tool lowered into a borehole in the earth formation. For an isotropic reservoir containing brine (index b), clay (index c) and non-conductive rock and hydrocarbon (g / g index), the rock and hydrocarbon are grouped together, since their conductivity tends to zero. The dependence ^σ ^ ~ ^σ ο _y, ~ ^σ ο ^ + 2σ ₀ ΓΓ * σ * + 2σ _{0 is} chosen, where Co “y ⁵ , bk 0k

Jk ⁼ ^ k <^ k Yk (Σλη φ _η ν _η ) ¹ in which σ ₀ is an additional parameter, k, η = 1 ... Ν, N is the number of components, σ ^ is the conductivity of the earth formation, σ _κ is the conductivity component k, f _k - the relative volume of component k,

11 _k is the mixing coefficient related to component k, / _k is the leakage coefficient related to component k, ν \. „Is the leakage rate relating to components k, η.

Each component has to four parameters: f _s σ ^ / k and ν ^ wherein vWF, σβ, σ ^ / ns measured directly. In addition, _s = 0 for dispersed clay. The 1st _kns and f _{v / ns} follow from the sum rule. It is necessary to determine the parameters σ,., Λ _Β , ν _Β and f _s . These parameters are determined by direct modeling on experimental data. _{σ,., λ Β, ν} Β remain unchanged throughout the geological formation, and f _and depended on _the depth. The experimental data for determining the parameter include logging measurements of the brine-containing zone, laboratory measurements of the reservoir resistivity coefficient (PCR) and experimental measurements of brine salinity. Log data from the brine-containing zone is used to correlate the local parameter φ _with the appropriate combinations of 1o§§ / 1oG known in the logging area. σ,., λ _Β , f _in and correlation, 1 _s with suitable combinations of 1o§§ / 1o§ can be used in hydrocarbon-containing formations. For well logging, the above dependence and the indicated parameters, the relative brine volume, and hence the relative hydrocarbon volume, are determined as a function of depth.

Petrophysical data options incoherence in the invention incoherence in the prototype Sample N F to [to] Ων [equiv4p] Us about _with [t8 / st] Bb V Δ ² _g “ ^s o Gd . Σ4 ² _{g s} one 0.239 659 0.017 0,0532 2.9581 0.2016 0.002 0.018 0.009 0,026 2 0.212 105 0,052 0.1822 1.3537 0.2038 0.002 0,035 0,061 0,099 3 0.231 397 0,052 0.1376 1,8607 0.2517 0.002 0.014 0,031 0,097 4 0, 080 1.34 0.26 0.1323 1,3325 0.1788 0.010 0.119 0,045 0.010 5 0, 154 55 0.2 0.3216 1,4851 0.3752 0.005 0,042 0.149 0.128 6 0.215 29th 0,095 0.3467 1,0193 0.1370 0.003 0,026 0.206 0.257 7 0.171 3.5 0,053 0.3779 0.7847 0,1200 0.008 0.016 0.312 0.446 8 0.171 7.66 0,053 0.3119 0.8994 0.1274 0.007 0.018 0.234 0.366 nine 0, 199 57 0,085 0.3935 1,0627 0.1613 0.007 0,025 0.276 0.351 10 0, 125 0,042 0.263 0.432 0.3113 0,0255 0,029 0,074 0.483 0.262 eleven 0.125 0,0106 0.253 0,4007 0.2590 0.0233 0,037 0,057 0.348 0, .203 12 0,110 1.86 0.28 0.5855 0.8601 0.1326 0.018 0.010 0.760 0, .542 thirteen 0,110 0.3 0.28 0.5998 1,0802 0.1286 0,020 0.016 0.868 0.589 14 0,110 2.08 0.28 0.5815 0.6025 0.1998 0,054 0,029 0.854 0.538 fifteen 0,092 0.128 0.41 0.509 1.4537 0,0402 0,027 0,025 0.917 0.449 sixteen 0.103 0.024 0.67 0.7202 1.4583 0,1103 0.010 0.013 1,263 0.529 17 0.140 0.575 0.33 0.7763 1,5783 0.0977 0,050 0.013 1,606 0.919 eighteen 0.259 3.78 0.59 0.7033 2.8964 0.1357 0.012 0.007 1,173 0.507 nineteen 0.259 17.1 0.59 0.6408 2,8227 0.1484 0.010 0.012 0.823 0.376

Petrophysical data options incoherence in invention prototype incoherence Sample N F to [TE] Ων [equiv / l] Os [t8 / st] Bb ^Sy ~ ^s $ Σ4 , Σδ ^! . twenty 0.259 44.8 0.59 0.5978 3,4771 0.2113 0.003 0,023 0.674 0.286 21 0.238 315 0.29 0.6984 1,3859 0.1812 0.009 0,031 0.632 0.546 22 0.225 1.92 0.72 0.7651 2,4172 0,0766 0.016 0.013 1,808 0.637 23 0.242 54.3 1,04 0.7306 4.0758 0.1165 0,022 0.011 1,640 0.490 24 0.216 0.546 0.81 0.7751 2.6418 0,0659 0,021 0.014 2.1-3 0.703 25 0, .187 0,0348 1.27 0.7995 3.4510 0,0726 0.005 0,040 0.490 0.369 26 0.229 1,53 1.47 0.7491 5.0425 0,0887 0,042 0,026 2, .155 0.470 27 0.209 0.263 1.48 0.7656 5,1455 0,0884 0.001 0,067 0.495 0.326

CLAIM

Claims (20)

1. The method of determining the parameter of a component in the composition of the earth formation, selected from the electrical conductivity and the relative volume of the component in the composition containing many components of the earth formation, which consists in drilling a well in the earth formation to obtain a core sample, measuring the conductivity of the composition using a logging tool , choose the relationship between the conductivity of the composition and many parameters of the composition, including the physical parameters characterizing the conductivity and relative volume each component of the composition, and all components are essentially equally represented by physical parameters in the specified dependence, and determine the selected parameter from the specified dependence and the measured conductivity of the composition, characterized in that an additional parameter is introduced into the specified dependence, which depends on the conductivity of one of the components and the mixing coefficient while the mixing coefficient depends on the geometric configuration of the components in the composition and determines the degree of seepage of the individual components. 2. The method according to claim 1, characterized in that the specified set of composition parameters includes at least one fitting parameter, which is determined by applying this dependence to a set of data obtained by measuring the conductivity of at least one sample, characteristic for the specified composition, for different values of at least one of these parameters. 3. The method according to claim 1 or 2, characterized in that the indicated dependence is chosen as (о _Э ф- © о) (b © _Э ф + (1-б) © о) ^_1 = Σφκ. (© κ- © ο ) (ok + (1-b) σ0) ^_1 Oo wherein an additional parameter is a conductivity tensor k = 1 ... Ν, N - the number of components in the composition, and _e p - conductivity tensor of the sample, О _к is the conductivity tensor of component k, φ _к is the relative volume of component k, Е is the depolarization tensor. 4. The method according to any one of claims 1 to 3, characterized in that said additional parameter is selected as ^σ ο = Σ ^Е к Ok where О _о represents an additional parameter in the form of a conductivity tensor characteristic of conductivity in three main directions, k = 1 ... Ν, N is the number of components in the composition, О _к - conductivity tensor of component k, E _to - mixing coefficient tensor related to component k. 5. The method according to any one of claims 1 to 4, characterized in that the mixing coefficients are selected so that their sum is essentially equal to one. 6. The method according to any one of claims 1 to 5, characterized in that the mixing coefficients do not have a negative value. 7. The method according to any one of claims 1 to 6, characterized in that each mixing coefficient is selected as a function of at least the relative volume of the component related to the specified mixing coefficient. 8. The method according to claim 7, characterized in that said function is a monotonically increasing function in the relative volume of the component related to the mixing coefficient. 9. The method according to claim 7 or 8, characterized in that the function is chosen so that the mixing coefficients tend to zero for vanishing relative volume of the component related to the mixing coefficient. 10. The method according to any one of claims 1 or 9, characterized in that each mixing coefficient is selected as Ek = Хк ф _к Ук (Х λ φ _η У _п ) - 'к, η = 1 ... Ν, N is the number of components making up the specified set of components, λ _1: is the leakage rate tensor related to component k, f _k is the relative volume of the component k, Y _{k> n} is the leakage rate related to the components k, η. 11. The method according to p. 10, characterized in that at least one of the parameters 1ι _1:. λ] <and V is a fitting parameter. 12. The method according to any one of claims 3 to 11, characterized in that the depolarization tensor has a positive value. 13. The method according to any one of claims 3-12, characterized in that the depolarization tensor has a single trace. 14. The method according to any one of claims 3 to 13, characterized in that the depolarization tensor is equal to 1/3 of the unit tensor. 15. The method according to any one of paragraphs. 1-14, characterized in that the determination of the fitting parameter by applying this dependence to the data set is performed as an iterative process. 16. The method according to clause 15, wherein the iterative process consists in the repeated use of this dependence in the minimization scheme. 17. The method according to clause 16, characterized in that the minimization circuit is applied to the mismatch between the measured electrical conductivities of these components and the electrical conductivities of the components determined using this relationship. 18. The method according to any one of paragraphs. 1-17, characterized in that the said composition is the earth layer. 19. The method according to p. 18, characterized in that the said earth formation contains at least one component of rock, brine, hydrocarbon fluid and clay. 20. The method according to claim 19, characterized in that the specified determined parameter is the relative volume of the hydrocarbon fluid or brine. Eurasian Patent Organization, EAPO Russia, Moscow, GSP 103621, M. Cherkassky per., 2/6