CN106324688A - Reservoir irreducible water saturation determining method and device - Google Patents

Abstract

The present invention provides a method and device for determining the irreducible water saturation of a reservoir, wherein the method includes: constructing an exponential hyperbolic sine function, performing a Laplace transform on the exponential hyperbolic sine function to obtain an asymptotic step function; according to the The specified value condition satisfied by the asymptotic step function, obtain the unknown parameters in the exponential hyperbolic sine function, update the constructed exponential hyperbolic sine function according to the obtained unknown parameters; Integral transformation is performed on the NMR echo data to determine the irreducible water saturation of the reservoir. This application does not need to invert the NMR echo data first to obtain the T2 spectrum through inverse Laplace transform, which can avoid the uncertainty brought by the inversion. _In the case of low signal-to-noise ratio of the NMR echo data, Accurate reservoir irreducible water saturation can be obtained.

Description

Method and device for determining irreducible water saturation of reservoir

technical field

The invention relates to the technical field of well logging data processing in petroleum exploration, in particular to a method and device for determining the irreducible water saturation of a reservoir.

Background technique

NMR logging is currently the only logging method that can distinguish mobile fluid from bound fluid in the formation, and has unique advantages that other logging methods do not have. Whether the calculation of reservoir irreducible water saturation is accurate or not directly affects the accuracy of reservoir oil and gas evaluation, the rationality of reserve calculation and the reliability of productivity prediction, and it also directly affects the later test and completion plan. Therefore, it is of great significance to study an accurate determination method of irreducible water saturation in reservoirs.

At present, the method of determining the irreducible water saturation by nuclear magnetic resonance logging is mainly to perform inverse Laplace transform _on the NMR echo data, invert to obtain the T2 spectrum, and then use the T2 cut _- off value to obtain the irreducible water saturation. However, the inversion of NMR echo data is a serious ill-conditioned problem, and small disturbances in the measurement data will have a great impact _on the inversion results, resulting in great uncertainty in the inverted T2 spectrum, thus _The error of reservoir irreducible water saturation calculated according to T2 spectrum increases. Therefore, in the prior art, for nuclear magnetic resonance echo data with a low signal-to-noise ratio, the calculation accuracy of irreducible water saturation in the reservoir cannot meet the needs of field applications in oilfields.

Contents of the invention

This application provides a method and device for determining the irreducible water saturation of a reservoir, which is used to solve the problem in the prior art that the T2 spectrum is obtained by inverting the NMR echo data through inverse Laplace transform, and the T2 spectrum is obtained by using the T2 _{cut -} off value. The irreducible water saturation method has inaccurate inversion results, and the T ₂ spectrum obtained by inversion has great uncertainty, which leads to the problem of large error in the calculated irreducible water saturation of the reservoir.

In order to solve the above technical problems, a technical solution of the present invention is to provide a method for determining the irreducible water saturation of a reservoir, including:

Construct exponential hyperbolic sine function, do Laplace transform to described exponential hyperbolic sine function, obtain the asymptotic step function of T2 domain _;

According to the specified value condition satisfied by the progressive step function, obtain unknown parameters in the exponential hyperbolic sine function, and update the constructed exponential hyperbolic sine function according to the obtained unknown parameters;

According to the updated exponential hyperbolic sine function, the collected nuclear magnetic resonance echo data is integrally transformed to determine the irreducible water saturation of the reservoir.

Another technical solution of the present invention is to provide a device for determining the irreducible water saturation of a reservoir, including:

a data acquisition unit, configured to acquire nuclear magnetic resonance echo data;

A construction unit for constructing an exponential hyperbolic sine function, performing a Laplace transform on the exponential hyperbolic sine function to obtain an asymptotic step function of the T2 domain _;

The unknown parameter obtaining unit is used to obtain the unknown parameters in the exponential hyperbolic sine function according to the specific value conditions satisfied by the progressive step function, and update the constructed exponential hyperbolic sine function according to the obtained unknown parameters;

The reservoir irreducible water saturation determination unit performs integral transformation on the collected nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function to determine the reservoir irreducible water saturation.

The method and device for determining the irreducible water saturation of the reservoir provided by the present invention perform Laplace transformation on the constructed exponential hyperbolic sine function to obtain an asymptotic step function, and determine the exponential hyperbolic according to the specific value conditions satisfied by the asymptotic step function For the unknown parameters of the sine function, according to the determined exponential hyperbolic sine function, the original NMR echo data is directly integrated and transformed to determine the irreducible water saturation of the reservoir, without having to go through the inverse Laplace transform first. T ₂ spectrum, thus avoiding the uncertainty brought by the inversion. Therefore, this method can still obtain accurate reservoir irreducible water saturation even when the signal-to-noise ratio of NMR echo data is very low.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

Fig. 1 is a flowchart of a method for determining irreducible water saturation of a reservoir according to an embodiment of the present invention;

Fig. ₂ shows the reservoir T2 distribution model (solid line) and the corresponding progressive step function (dotted line);

Fig. 3 A and Fig. 3 B are the lateral relaxation time T distribution model schematic diagrams of the simulation _two kinds of reservoirs of the embodiment of the present invention;

4A and 4B are schematic diagrams of NMR echo data without noise and NMR echo data with noise added according to an embodiment of the present invention;

Figure 5A and Figure 5B are the exponential hyperbolic sine function and asymptotic step function when T _C =33ms of the embodiment of the present invention;

Fig. 6 is a structural diagram of a device for determining irreducible water saturation of a reservoir according to an embodiment of the present invention.

detailed description

In order to make the technical features and effects of the present invention more obvious, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings. The present invention can also be described or implemented in other different specific examples. The equivalent transformations done within all belong to the protection category of the present invention.

In the description of this specification, descriptions referring to the terms "one embodiment", "a specific embodiment", "some embodiments", "for example", "examples", "specific examples", or "some examples" etc. mean It means that a specific feature, structure, material or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. The sequence of steps involved in each embodiment is used to schematically illustrate the implementation of the present invention, and the sequence of steps therein is not limited and can be appropriately adjusted as required.

As used herein, "comprising", "comprising", "having", "comprising" and so on are all open terms, meaning including but not limited to.

As shown in Figure 1, Figure 1 is a flow chart of a method for determining reservoir bound water saturation according to an embodiment of the present invention. The problem of large error in the calculation result of water saturation. Specifically, including:

Step 101: Construct an exponential hyperbolic sine function, and perform a Laplace transform _on the exponential hyperbolic sine function to obtain an asymptotic step function in the T2 domain.

The progressive step function described in the present application is similar to the unit step function, and the difference is that the transition section of the progressive step function is an increasing function, and the function value is gradually increased from 0 to 1, as shown by the dotted line in Figure 2, The unit step function is a jump transition, and the function value jumps directly from 0 to 1.

Step 102: Calculate unknown parameters in the exponential hyperbolic sine function according to the specific value condition satisfied by the progressive step function.

After the unknown parameters are obtained, the constructed exponential hyperbolic sine function is updated according to the obtained unknown parameters, that is, the obtained unknown parameters are substituted into the constructed exponential hyperbolic sine function to obtain the updated exponential hyperbolic sine function.

Specific value conditions such as the 0-point function value, the infinite function value, the cut-off point function value, etc. of the asymptotic step function.

Step 103: Carry out integral transformation on the collected nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function to determine the irreducible water saturation of the reservoir.

During specific implementation, the irreducible water saturation is calculated by the following formula:

${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; it</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; it</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, S _wi is the irreducible water saturation, t _E is the echo interval, i is the ith echo, it _E is the time, k(it _E , T _C ) is the value of the exponential hyperbolic sine function corresponding to it _E , T _C is the cut-off value of NMR T ₂ spectrum, which can be determined through core experiments, and is a known quantity, G(it _E ) is the NMR echo data collected when it _E , and N is the number of echoes.

In detail, the exponential hyperbolic sine function formula constructed in the above step 101 is:

k(t, T _C ) = λe ^-βt sh(at) (2)

Among them, k(t, T _C ) is a function of time t, λ, β, a are unknown parameters, and t is time in time domain.

The asymptotic step function formula of the T2 domain obtained after performing Laplace transform on formula ( ₂ ) is:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Wherein, K(T ₂ , T _C ) is a function of T ₂ , and T ₂ is the NMR transverse relaxation time.

The exponential hyperbolic sine function k(t, T _C ) described in this application exists for any t>0, and the asymptotic step function K(T ₂ , T _C ) exists for any T ₂ >0, and K(T ₂ , The value range of T _C ) is [0,1), and it increases monotonously within the domain. Specific value conditions (including extreme value and special value conditions) satisfied by the asymptotic step function include: and Wherein, n is the function value of the asymptotic step function at the cutoff value T _C , m is the slope of the asymptotic step function at the cutoff value T _C , and n and m are set values, which can be set according to experience.

During specific implementation, according to the nature of the asymptotic step function, usually, the function value of the asymptotic step function is 0.5 when the cut _- off value T is set, that is The slope m of the asymptotic step function at the cut-off value T _C should not be set too large. The larger m is, the steeper the asymptotic step function will be, and the obtained reservoir irreducible water saturation will be more affected by noise. After testing, preferably, m When the value is 0.3, the effect is better. At this time, the calculated unknown parameters are:

in,

Further, in order to understand the impact of noise on the calculation of irreducible water saturation of the reservoir, the variance of irreducible water saturation is calculated by the following formula:

${{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; \&lsqb;</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; it</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, σ _S is the standard deviation of bound water saturation, σ _e is the standard deviation of noise, t _E is the echo interval, i is the ith echo, it _E is time, k(it _E ,T _C ) is it _E is the corresponding exponential hyperbolic sine function value, and N is the number of echoes.

Further, because the actually collected nuclear magnetic resonance echo data is affected by noise, in order to verify the credibility of the calculation results, the irreducible water saturation is calculated repeatedly, and the average value of the calculation results is calculated to obtain the final Bound water saturation.

In order to illustrate the technical solution of the present application more clearly, the derivation process of the exponential hyperbolic sine transformation method to obtain the irreducible water saturation formula (1) of the reservoir is described in detail below:

The echo data measured by NMR logging can be expressed by the following formula:

$\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; dT</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, G(t) is the collected NMR echo data, T ₂ is the NMR transverse relaxation time, the unit is s, f(T ₂ ) is the interval porosity of pores whose NMR relaxation time is T ₂ , the unit is pu, e(t) is noise.

As shown in Figure 2, the abscissa is the transverse relaxation time T ₂ , the ordinate is the interval porosity f(T ₂ ), the porosity corresponding to T ₂ >T _C is the movable water part, and the porosity corresponding to T ₂ <T _C Porosity is the bound water fraction. Calculate the saturation of movable water by the following formula:

$\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; dT</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Among them, A is the movable water saturation, the area of the oblique line in Figure 2; K(T ₂ , T _C ) is the asymptotic step function, shown by the dotted line in Figure 2.

According to (6), the irreducible water saturation of the reservoir can be obtained as: S _wi ＝1-A (7)

Let the laplace inverse transformation function of the asymptotic step function be k(t, T _C ), then K(T ₂ , T _C ) can be expressed as:

$\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Substituting formula (8) into formula (6), the following formula can be obtained:

$\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; \&equiv;</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; \&infin;</span>}}\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Among them, I{G(t)} means to perform integral transformation on G(t), discretize formula (9), and formula (1) can be obtained by combining formula (7).

Further, an experimental example is used below to illustrate that the irreducible water saturation method provided by the present application is more accurate than the irreducible water saturation determined by the prior art.

₁ ) Simulate _two distribution models of reservoir NMR transverse relaxation time T2, as shown in Figure 3A and Figure 3B, Figure 3A is a T2 distribution unimodal model, Figure 3B is a _T2 distribution bimodal model, the total porosity Both are 20pu. The abscissa is T ₂ (unit is s), and the ordinate is porosity (unit is pu). The T ₂ distribution preselects 128 components and the minimum and maximum values are 10 ^-4 s and 10 s, respectively.

₂ ) Forward modeling of the _two reservoir lateral relaxation time T2 distribution models in Figure 3A and Figure 3B, to obtain the NMR echo data shown in Figure 4A and Figure 4B, Figure 4A is derived from the T2 distribution unimodal model in Figure 3A Figure 4B is obtained from the forward modeling of the T ₂ distribution bimodal model in Figure 3B, including the NMR echo data without noise and the NMR echo data with noise added, and the echo interval is 0.2ms. The number of waves is 2000. The abscissa is time (in s), and the ordinate is porosity (in pu).

The specific acquisition process of the NMR echo data in Fig. 4A and Fig. 4B is as follows _: the NMR echo data is obtained by forward modeling of the NMR transverse relaxation time T2 distribution model simulated in Fig. 3A and Fig. 3B, and the NMR echo data is obtained at this time The wave data is noise-free, and then noise with a noise standard deviation of 2.0pu is added to the obtained NMR echo data to obtain the NMR echo data with noise added in Fig. 4A and Fig. 4B.

3) Setting the cut _- off value TC of the T2 distribution model shown in Figure 3A and Figure 3B to be _33ms , the images of the exponential hyperbolic sine function and progressive step function obtained according to the method of the present application are as shown in Figure 5A and Figure 5B, Figure 5A is the exponential hyperbolic sine function in the time domain, and Figure 5B is the corresponding function in the _T2 domain obtained from the exponential hyperbolic sine function through Laplace transform.

4) Calculate the irreducible water saturation according to the exponential hyperbolic sine function shown in FIG. 5A and the echo data shown in FIGS. 4A and 4B (technical solution of the present application). The irreducible water saturation (true value in this embodiment) is calculated according to the asymptotic step function shown in FIG. 5B and f(T ₂ ) shown in FIGS. 3A and 3B . The irreducible water saturation is calculated according to the progressive step function shown in Fig. 5B and f(T ₂ ) obtained from the inversion of the echo data shown in Figs. 4A and 4B (the prior art solution). In order to verify the credibility of the results, the experimental data was repeated 50 times to obtain the comparison results shown in the following table:

Among them, σ _e is the noise standard deviation, TRUE is the true value of bound water saturation, ESHT is the calculation result of the exponential hyperbolic sine transform method (the technical solution of this application), ILT is the calculation result of the existing method (the prior art solution), μ is the mean value of irreducible water saturation obtained from 50 processing results, σ is the standard deviation of 50 processing results, and rmse is the root mean square error of 50 processing results.

It can be seen from the comparison table that the results obtained by the method for determining the irreducible water saturation according to the embodiment of the present invention are closer to the true value of the irreducible water saturation than the results obtained by the existing method, and the standard deviation and root mean square error are smaller, which shows that The method of the invention is more accurate in determining the irreducible water saturation of the reservoir compared with the existing method, and can be applied to the NMR echo data with low signal-to-noise ratio to determine the irreducible water saturation of the reservoir.

As shown in FIG. 6 , FIG. 6 is a structural diagram of an apparatus for determining irreducible water saturation of a reservoir according to an embodiment of the present invention. The device can run on smart terminals, such as mobile phones, tablet computers, etc., through logic circuits, or realize the functions of various components by software in the form of functional modules, and run on the smart terminals. Specifically, the device includes:

The data collection unit 601 is configured to collect nuclear magnetic resonance echo data.

The construction unit 602 is configured to construct an exponential hyperbolic sine function, and perform a Laplace transform _on the exponential hyperbolic sine function to obtain an asymptotic step function in the T2 domain.

The unknown parameter obtaining unit 603 is used to obtain the unknown parameters in the exponential hyperbolic sine function according to the specific value conditions satisfied by the progressive step function, and update the constructed exponential hyperbolic sine function according to the obtained unknown parameters .

Reservoir irreducible water saturation determining unit 604 performs integral transformation on the collected nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function to determine reservoir irreducible water saturation.

In a specific embodiment, the irreducible water saturation determination unit 604 calculates the irreducible water saturation by the following formula:

Among them, S _wi is the irreducible water saturation, t _E is the echo interval, i is the ith echo, it _E is the time, k(it _E , T _C ) is the value of the exponential hyperbolic sine function corresponding to it _E , T _C is the NMR T ₂ spectrum cut-off value, G(it _E ) is the NMR echo data collected at it _E , and N is the number of echoes.

In detail, the formula of the exponential hyperbolic sine function constructed by the construction unit 602 is: k(t, T _C )= ^λe-βt sh(at), wherein, k(t, T _C ) is the exponential hyperbolic sine function , λ, β, a are unknown parameters, t is the time in the time domain, and T _C is the cut-off value of NMR T ₂ spectrum.

The asymptotic step function formula is: s=1/T ₂ , T ₂ is the nuclear magnetic resonance transverse relaxation time.

The exponential hyperbolic sine function k(t, T _C ) described in this application exists for any t>0, and the asymptotic step function K(T ₂ , T _C ) exists for any T ₂ >0, and K(T ₂ , The value range of T _C ) is [0,1), and it increases monotonously within the domain. The specific value conditions (including extreme value and special value conditions) satisfied by the asymptotic step function are: and Among them, n and m are set values.

In a specific embodiment, when n=0.5 and m=0.3, the unknown parameters calculated by the unknown parameter calculating unit 603 are respectively:

in,

The device for determining the irreducible water saturation of the reservoir provided by the present invention performs Laplace transform on the constructed exponential hyperbolic sine function to obtain an asymptotic step function, and determines the exponential hyperbolic sine function according to the specific value condition satisfied by the asymptotic step function According to the unknown parameters of the exponential hyperbolic sine function, the original nuclear magnetic resonance echo data is directly integrated and transformed to determine the irreducible water saturation of the reservoir, without first inverting the Laplace transform to obtain T ₂ Spectrum, thus avoiding the uncertainty brought by the inversion. Therefore, in the case of low signal-to-noise ratio of NMR echo data, this method can still obtain good evaluation results of irreducible water saturation of reservoirs.

Those skilled in the art should understand that the embodiments of the present invention may be provided as methods, systems, or computer program products. Accordingly, the present invention can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

The above description is only used to illustrate the technical solution of the present application, and anyone skilled in the art can modify and change the above embodiments without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention should be determined by the scope of the claims.

Claims (10)

1. A method for reservoir irreducible water saturation determination, comprising:

constructing an exponential hyperbolic sine function, and performing Laplace transform on the exponential hyperbolic sine function to obtain T₂A progressive step function of the domain;

according to a specific value condition met by the progressive step function, solving unknown parameters in the exponential hyperbolic sine function, and updating the constructed exponential hyperbolic sine function according to the solved unknown parameters;

and performing integral transformation on the acquired nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function to determine the saturation of the reservoir bound water.

2. The method of reservoir irreducible water saturation determination of claim 1, wherein said exponential hyperbolic function formula is: k (T, T)_C)＝λe^-βtsh (α T), where k (T, T)_C) Is an exponential hyperbolic sine function, lambda, β and α are unknown parameters, T is time domain time, and T is_CIs nuclear magnetic resonance T₂A spectral cutoff value;

the progressive step function formula is as follows:s＝1/T₂，T₂the nmr transverse relaxation time.

3. The reservoir irreducible water saturation determination method of claim 2, wherein said particular value condition is:andwherein n and m are set values.

4. The method of reservoir irreducible water saturation determination of any one of claims 1 to 3, wherein performing an integral transformation of the acquired nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function, the determining reservoir irreducible water saturation comprising: reservoir irreducible water saturation is found according to the following formula,

$S_{wi}=1-t_E\underset{i=0}{\overset{N}{\&Sigma;}}k({\mathrm{it}}_E,T_C)G\left({\mathrm{it}}_E\right);$

wherein S is_wiFor reservoir irreducible water saturation, t_EFor the echo interval, i is the ith echo, it_EIs time, k (it)_E,T_C) Is it_ETime-corresponding exponential hyperbolic sine function value, T_CIs nuclear magnetic resonance T₂Spectral cutoff value, G (it)_E) Is it_EAnd N is the number of echoes.

5. The reservoir irreducible water saturation determination method as set forth in claim 3, wherein n is 0.5 and m is 0.3, and the unknown parameters are calculated as:

wherein,

6. a reservoir irreducible water saturation determination apparatus, comprising:

the data acquisition unit is used for acquiring nuclear magnetic resonance echo data;

a construction unit for constructing an exponential hyperbolic sine function, and performing Laplace transform on the exponential hyperbolic sine function to obtain T₂A progressive step function of the domain;

an unknown parameter calculating unit, configured to calculate an unknown parameter in the exponential hyperbolic sine function according to a specific value condition that the progressive step function satisfies, and update the constructed exponential hyperbolic sine function according to the calculated unknown parameter;

and the reservoir irreducible water saturation determining unit is used for performing integral transformation on the acquired nuclear magnetic resonance echo data according to the updated exponential hyperbolic sine function to determine the reservoir irreducible water saturation.

7. The reservoir irreducible water saturation determination apparatus of claim 6, wherein said construction unit constructs an exponential hyperbolic sine function formula as: k (T, T)_C)＝λe^-βtsh (α T), where k (T, T)_C) Is an exponential hyperbolic sine function, lambda, β and α are unknown parameters, T is time domain time, and T is_CIs nuclear magnetic resonance T₂A spectral cutoff value;

the progressive step function formula is as follows:s＝1/T₂，T₂the nmr transverse relaxation time.

8. The reservoir irreducible water saturation determination apparatus of claim 7, wherein said particular value condition is:andwherein, the values of n and m are set values.

9. Reservoir irreducible water saturation determination apparatus as claimed in any one of claims 6 to 8, wherein said reservoir irreducible water saturation determination unit is specifically adapted to find the reservoir irreducible water saturation according to the following formula,

$S_{wi}=1-t_E\underset{i=0}{\overset{N}{\&Sigma;}}k({\mathrm{it}}_E,T_C)G\left({\mathrm{it}}_E\right);$

wherein S is_wiFor reservoir irreducible water saturation, t_EFor the echo interval, i is the ith echo, it_EIs time, k (it)_E,T_C) Is it_ETime-corresponding exponential hyperbolic sine function value, T_CIs nuclear magnetic resonance T₂Spectral cutoff value, G (it)_E) Is it_EAnd N is the number of echoes.

10. The reservoir irreducible water saturation determination apparatus as claimed in claim 9, wherein n is 0.5 and m is 0.3, and the unknown parameters calculated by the unknown parameter calculating unit are respectively:

wherein,