RO118781B1 - Method of determining a parameter of a physical model - Google Patents

Abstract

The invention relates to a method of determining a parameter of a physical model representing the electrical behaviour of a composition. The method comprises defining said model by a relationship between at least one electrical property of the composition, a plurality of physical variables of said parameters, and measuring the first electical property of the composition. A sample which is representative for said composition is selected and a second electrical property of the sample is measured for various magnitudes of at least one of said physical variables. An incoherence function is selected, defining a difference between the measured electrical properties and electical properties as calculated from said relationship, said incoherence function being such that independent measurements are wheighted in dependence of their accuracy. The said parameter is determined by minimizing the incoherence function. The first and the second property can be one and the same.

Description

The present invention relates to a method for determining a parameter in a physical system representing the electrical behavior of a composition. The method can be applied in the geological data sheets of drilling, where the objective is to determine the amount of fluid, such as water, salt solution and hydrocarbon, in the soil formation of interest, if the fluid can be economically exploited; In the state of the art, physical drilling models are generally applied to the geological drilling datasheets. According to the results of the geological data sheets and the physical model, the content of the component of the earth formation is determined.

A well-known method for determining the parameters of such a physical model is described in the Electrical Conductivities in the clay-bearing oil sands, Waxman Μ. H. and Smits L. J. M., SPE paper 1863-Presented at the 42nd Annual Fall Meeting, Houston, October 1-4,1967.

This publication refers to a method of determining a parameter of a physical model representing the electrical behavior of the earth formation, consisting of defining the model by the relationship between the electrical conductivity of the formation, a plurality of physical variables of the formation and the parameter, selecting a samples which is representative for the said formation and the measurement of the conductivity of the sample for various magnitudes and physical variables, and the determination of the said parameter by applying the selected relation to the measurement of the conductivity of the sample.

In this known method, the model that refers in particular to the Waxman-Smits model is defined by the relation:

where:

C _t = conductivity of the partially saturated salt solution formation represented by the sample; C _w = conductivity of the salt solution present in the formation;

S _w = water saturation in the pore space (0 ... 1) which is equal to 1-S ₀ where S indicates _a hydrocarbon saturation;

B - the equivalent conductance of the sodium cations changed clay according to C _w and temperature; Q _v cation exchange capacity on the volume of pore units;

G * = the formation factor of the formation represented by the sample; G * is represented as:

G * = <P ' ^m ' S _w ⁿ 'where:

Φ = porous space in the formation;

parameter to be determined, in the form of the cementing exponent; n * = parameter to be determined, in the form of the saturation exponent;

The parameters m * and '\ n * characterize the response of the earth's conductivity to the change of physical variables such as Φ and in the known method, these parameters are determined by a mutually independent path, that is:

- by using conductivity measurements in a non-carbon bearing area in the soil formation or with conductivity measurements in the laboratory on a lot of saturated salt solution samples; m * can be determined from the relation between log (C _t ¹ ) and log (0) or log (C _w C _t ' ¹ ) and log (0>), respectively; and

- by using conductivity measurements in the laboratory on a lot of samples with partially saturated brine, n * can be determined by the relation between:

RO 118781 Β1 l ° g (4)

The results obtained with this known method are not sufficiently accurate, probably due to the parameters determined in a non-optimal manner.

US-A-4398151 discloses a method of ensuring the correct electrical grades of clay sand formations, penetrated by drilling wells, using workplace measurements in well drilling, to determine the capacity of cation change on the volume of the unit 55 pores. .

US-A-4338664 describes a method for interpreting carat measurements, made in the wellbore, to evaluate the formation of the earth, in this method, a number of output parameters is determined from a number of carat measurements made in the borehole. probe by solving the set of response equations, where each response equation 60 refers to a single parameter measured at the output parameters. The incoherence function is derived from the deviations between the values calculated by the measured parameters and the measured values, where the deviations are multiplied by weighting factors.

The object of the invention provides an improved method of determining a parameter of the physical model representing the electrical behavior of the composition. 65

The method according to the invention consists of:

- defining said model through a relation between at least one electrical property of the composition, a lot of physical variables of the composition and the said parameter;

- measuring a lot of electrical properties including a first electrical property of the composition; 70

- selecting an incoherence function, defining a difference between the measured electrical properties and the electrical properties determined by the said relation, the incoherence function being such that the measured values are weighted according to accuracy; and

- determining said parameter by minimizing said incoherence function, characterized in that the set of electrical properties includes a second electrical property 75 of the sample which is representative for said composition; the method also includes choosing a sample and measuring the second electrical property of the sample for various quantities, of at least one of the physical variables.

By minimizing the incoherence function, each parameter is determined such that all experimental data, both from the in situ measurements of the composition and from the 80 laboratory measurements on the representative sample for the composition, are taken into account in a weighted manner. . For example, if the composition forms an earth formation, the exact measurements of the geological data sheet for drilling are considered according to the incoherence, with less weight than the measurements of the exact sample. It was realized that the parameters are determined with exact increasing results in the physical model, and the applications 85 have, therefore, an increased accuracy.

The step of determining said parameter, by minimizing said incoherence function, is appropriate to include an iterative process.

It is advantageous for a lot of parameters to be determined simultaneously by minimizing said incoherence function, each parameter being represented in said relation. 90

It is appropriate that the incoherence function can be selected so that independent measurements of equal true accuracy are equally represented.

Moreover, the incoherence function is preferably monotonically increasing, with the deviation between the measured electrical properties and the calculated electrical properties.

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For example, the incoherence function may be of the form:

Ι ^ -τκγ where:

/ = 1 ... N, N being the number of physical measurements,

X, represents the measured electrical property,

Yj represents the calculated electric property,

G and H represent the functions of the electric property (H (X)> 0)

F represents a function with \ / X * 0 (F (X)> F (0)), ^ represents the weight assigned to the physical measurement (w ^ O).

The functions F, G and H can be selected as follows: FfX> / Xf, aeR, a> 0 G (X) = X ?, B&R, β * 0 H (X) = 1 or H (X) = G ( X).

Another suitable form of the incoherence function is:

where:

/ = 1 ... N, N being the number of physical measurements,

Xi represents the measured electrical property,

Yi represents the calculated electrical property, w, represents the weight attributed to the physical measurement (w ^ O).

Moreover, the incoherence function can be of the form:

where:

/ = 1 ... N, N being the number of physical measurements,

X, represents the measured electrical property,

Y, represents the calculated electric property,

Wj represents the weight assigned to the physical measurement (Wj> 0).

In a practical embodiment of the invention, at least one electrical property of the composition has been defined in said relationship and the second electrical property of the sample has been measured; these are selected according to the conductivity, resistivity and membrane potential.

Moreover, it is appropriate to select the first electrical property of the composition according to conductivity and resistivity.

The composition may include, for example, a fluid and then the pattern forms a saturated pattern for the fluid in the composition.

Applying the invention in the core technique to drilling wells, said composition contains an earth formation, and the model forms a saturated model, to select a salt solution and a liquid hydrocarbon contained in the formation.

In selecting said relationship, it is preferable to include in the electrical conductivity of the composition and a plurality of composition parameters, including, for each component of the composition, the physical parameters representing the electrical conductivity and the volumetric fraction of the component, the components being equally represented in said relationship , by means of said physical parameters.

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The model used in the application of the invention may be the Waxman-Smits model, the Archie model, the Poupon-Leveaux model, the Simandoux model, the Dual-Water model of Clavier-CoatesDumanoir, or the actual average model of Spalburg. 145

Said relationship is selected so as to include the electrical conductivity of the composition and a plurality of composition parameters, the physical parameters representing the electrical conductivity and the volumetric fraction of the component, said relationship being such that the components are represented in said relationship by means of said physical parameters. It is understood that each of the components is represented in the relationship in the same way as any other 150 components.

For example, the relationship can be selected as:

(o _el) - aJ · (Lo _e „+ (1- L) σ ₀ / '= Σ Φ, (a _k - oj. (Lo _k + (1-L) σ ₀ ) ¹

155 where σ ₀ represents an auxiliary parameter in the form of the conductivity tensor;

k = 1 ... N, N being the number of components;

o _e "represents the tensile conductivity of the sample;

o _k represents the tensor of conductivity of component k;

<P _k represents the volume fraction of component / c, 160

L represents the depolarization tensor (the form tensor);

It is advantageous for the selected auxiliary parameter to be:

165 where h _k represents the tensor of the mixing coefficient that is related to component k.

It is preferable that each mixing coefficient be selected as follows:

h _k = A _k <t> _k v (Σλ _η Φ _η ν) ¹ where: 170 k, n = 1 ... N, N being the number of components in the set of components;

Ă _k represents the flow rate tensor in relation to component k;

Φ _κ represents the volume fraction of component k;

v _kn represents the leakage exponent in relation to component k, n.

The invention will be described further, in an embodiment, in more detail. 175

It is considered a set of measurements made on the formation of earth consisting of rock, salt solution, clay and hydrocarbons. Measurements include:

A) core data on a water carrier range in the formation, data containing mainly conductivity and porosity measurements under known conditions S _w (= 1), and T;

B) core data on an interval in the said formation likely to be carrying 180 hydrocarbons, which data mainly contain conductivity and porosity measurements under known conditions T; and

C) laboratory data on the core files representative of said formation, data containing conductivity, porosity, and Q _v measurements under controlled conditions C ", T.

Then, from the laboratory data, the correlation between porosity and providing Q _v information along the core data can be made. As a saturated model, the Waxman-Smits model will be used, which refers to the description of the method in the prior art, in other words:

190

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For the data mentioned in points A) and C), an incoherence function P (m *, n *) is defined by the following relation:

(K _t -c _Q y “(K _tJ -c, y mi K / Ί K where:

/ = 1 ... N, N = total number of independent measurements related to A); Wj = the weight attributed to the measured conductivity of the rock;

C _ti = a i-measured conductivity of the rock whose values depend on m *. n *; K _ti = take measured conductivity of the rock;

j = M = total number of independent measurements related to C);

Wj = the weight assigned to the measured conductivity of the rock;

C _tj = ja measured conductivity of the rock, whose values depend on m *, n *;

K _tj - ja measured conductivity of the rock;

m * = determined parameter, in the form of the cementing exponent; n * = determined parameter, in the form of the saturation exponent;

The weight is chosen in proportion to the inverse of the accuracy variations of the measurements. The values m *, n * are determined by minimizing P (m *, n *) using a multidimensional down simplex method, which is a well-known iterative mathematical method from the prior art.

The resulting values for m * and n * can then be used in the Waxman-Smits model to solve for S _w data related to B), thus ensuring water saturation (also from hydrocarbon saturation) in the soil formation.

Claims (17)

claims 1. Method of determining a parameter in a physical system representing the electrical behavior of a composition, method consisting of: - defining said model through a relation between at least one electrical property of the composition, a lot of physical variables of the composition and the said parameter; - measuring a lot of electrical properties including a first electrical property of the composition; - selecting an incoherence function defining a difference between the measured electrical properties and the electrical properties determined by the said relation, the incoherence function being such that the measured values are weighted according to accuracy; and - determining the said parameter by minimizing said incoherence function, characterized in that the set of electrical properties includes a second electrical property of the sample which is representative for said composition, and that the method further contains the choice of a sample and the measurement of the second electrical property of the sample for different magnitudes, of at least one of the physical variables. Method according to claim 1, characterized in that the step of determining said parameter by minimizing the incoherence function includes an iterative process. Method according to claim 1 or 2, characterized in that a plurality of said parameters is determined simultaneously, by minimizing the incoherence function, each parameter being represented in said relation. Method according to any one of claims 1 ... 3, characterized in that said incoherence function is selected such that independent measurements of equal accuracy are equally represented. RO 118781 Β1 5. Method according to any one of claims 1 ... 4, characterized in that 240 at least one electrical property of the composition must define in the said relation and the second electrical property, measured, of the sample, according to the conductivity, resistivity and the membrane potential. . Method according to any one of claims 1 ... 5, characterized in that the first measured electrical property of the composition is selected according to the conductivity and 245 resistivity. Method according to any one of claims 1 ... 6, characterized in that said composition includes a fluid, and the model forms a saturated model for the fluid in the composition. 8. The method according to claim 7, characterized in that said composition 250 contains an earth formation, and the model forms a saturated model, for a selection of salt solution and liquid hydrocarbon, contained in the formation. Method according to any one of claims 1 ... 8, characterized in that said relationship is selected to include the electrical conductivity of the composition and a plurality of composition parameters including, for each component, in the composition, the physical parameters 255 representing the electrical conductivity and the volumetric fraction of the component, the so-called relation being such that the components are equally represented in the said relation, by means of the said physical parameters. Method according to claim 9, characterized in that the relationship is selected as follows: 260 (a _ef r ^ o). (Lo _e „+ (1- L) σ ₀ ) ¹ = Σ <t> _k (a _k - oj. (At _k + (1-L) σ ₀ ) ' ¹ where σ ₀ represents an auxiliary parameter in the form of the conductivity tensor ; k = 1 ... N, A / being the number of components; a _eff represents the tensile conductivity of the sample; 265 o _k represents the tensor of conductivity of component k; Φ _κ represents the volume fraction of component Ic, L represents the depolarization tensor. Method according to any one of claims 1 ... 8, characterized in that said model forms one of the Waxman-Smits model, the Archie model, the Poupon-270 Leveaux model, the Simandoux model, the Dual-Water model of Clavier-Coates-Dumanoir. and Spalburg's actual average model. Method according to any one of claims 1 ..11, characterized in that the step of determining said parameter, by minimizing said incoherence function, is done by minimizing the algorithm. 275 Method according to any one of claims 1 ... 12, characterized in that said function is monotonically increasing, depending on the deviation between the measured electrical properties and the calculated electrical properties. 14. Method according to any one of claims 1 ... 13, characterized in that the incoherence function is of the form: 280 G (JQ-G (r,.) // (%,) 285 where: i- N being the number of physical measurements, X, represents the measured electrical property, Y represents the calculated electric property, RO 118781 Β1 G and H represent the functions of the electric property (H (Xi)> 0) F represents a function with t / X / O (F (X)> F (0)), ^ represents the weight assigned to the physical measurement (w,> O). Method according to claim 14, characterized in that: F (X) = lXf ^I , asR, a> 0 G (X) = XP, βεΗβϊΟ H (X) = 1 or H (X) = G (X) Method according to any one of claims 1 ... 13, characterized in that said incoherence function is of the form: where: i = 1 ... N, N being the number of physical measurements, Xi represents the measured electrical property, Yi represents the calculated electrical property, ^ represents the weight attributed to the physical measurement (w ^ O). The method according to any one of claims 1 ... 13, wherein said incoherence function is of the form: