Determination of gas saturation radial profile from multi-frequency NMR data

(54) Title: DETERMINATION OF RADIAL PROFILE OF (57) Summary: GAS SATURATION FROM MULTIPLE FREQUENCY NMR DATA (30) Unionist Priority: 3/22/2007 us 11 / 689,887 (73) Holder (s): Baker Hughes Incorporated (72) Inventor (s): Sheng Fang, Songhua Chen (74) Attorney (s): Dannemann, Siemsen, Bigler &

Ipanema Moreira (86) International Order: pct US2008057459 de

19/03/2008 (87) International Publication: wo 2008 / H5969de

25/09/2008

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Descriptive Report of the Invention Patent for DETERMINATION OF RADIAL PROFILE OF GAS SATURATION FROM

MULTIPLE FREQUENCY NMR DATA.

Background of the Invention

1. Field of the Invention

The present invention relates to the use of nuclear magnetic resonance (NMR) imaging techniques, and in particular, the use of multiple frequencies for the determination of radial gas saturation profiles.

2. Description of the Related Art

Several instruments applying Nuclear Magnetic Resonance (NMR) imaging technology are useful for measuring certain petrophysical properties of earth formations. NMR well filing instruments typically include a magnet for polarizing cores to earth formation in the vicinity of a well. Polarization typically occurs over a static magnetic field; at least one antenna is used to transmit pulses of radio frequency (RF) energy in the formations, which manipulate rotations for the desired measurements. The magnitude of the RF energy emitted by the processing cores and the rate at which changes in magnitude are related to certain petrophysical properties of interest in earth formations.

A typical modality of an NMR filing instrument for the characterization of geological deposits includes a lateral or centralized NMR filing instrument. Typically, the instrument operates using a gradient magnetic field and multiple frequencies f. An example of such an instrument is MR Explorer^SM provided by Baker Hughes, Incorporated of Houston, Texas (referred to as MREX Instrument, the filing instrument or simply as an instrument).

There are several main operational parameters in the NMR well archiving. These parameters should be optimized for the efficient operation of an NMR well filing instrument.

Such parameters include a filing speed (speed of movement of the instrument along the well), the average energy and peak energy supplied to the instrument and transmitted as RF pulses, and the signal-to-noise ratio (SNR). Other parameters of interest include the vertical resolution of the instrument and the radial depth of investigation of the measurements made by the instrument within the formations surrounding the well.

The physical parameters of particular interest to well operators are the fractioned volume of the pore spaces in the earth formations (porosity), the texture of the stone and the connectivity of the pore spaces, and the nature of fluids contained in the pore spaces. Typical earth formations containing oil contain water and hydrocarbons; some pores can be filled with water and others with hydrocarbons. Since hydrocarbons generally have different NMR relaxation properties than water, several NMR relaxometry techniques have been developed to qualitatively determine the nature of the fluids present in certain earth formations.

One method, for example, allows discrimination between gas and oil, and light oil and water. This method includes performing spin-echo NMR experiments using two different waiting times, T_w. The waiting time T_w is the delay between individual CarrPurcell-Meiboon-Gill (CPMG) spin echo measurement sequences. See S. Meiboom et al., Rev. of Sei. Instr. v. 29, p. 6881 (1958). Another technique, described in US patent No. 5,498,960, issued to Vinegar et al, uses two different inter-echo spacing times, T_and, for CPMG sequences measured in a gradient magnetic field. Typically, the inter-echo spacing time T_and is the time between the new phase of the radio frequency energy (RF) pulses applied to the filing instrument's antenna to create a new phase of the nuclei that are influenced by NMR research. The new phase of RF pulses results in spin echoes whose amplitude is measured. Gas, oil and water generally have different automatic diffusion capabilities, and these differences will be reflected in the differences in apparent cross-linking time T₂ calculated for an earth formation between the CPMG sequences measured using values ​​other than the inter-echo spacing time T_and. The technique described in the '960 patent by Vinegar et al. for discriminating the types of fluids in pore spaces of earth formations, typically uses two inter-echo spacing time values ​​T_and.

In addition to the acquisitions of multiple times of inter-echo spacing T_and and multiple waiting times T_w, the use of multiple frequencies f in NMR measurements improves aspects of training assessment. State-of-the-art NMR filing instruments have a depth of investigation (DOI), (interchangeably referred to as radial depth) less than about 12.7 cm (5 inches) deep within a formation. In this way, the sensitive volume is typically leveled or invaded by the mud filtrate. The difference in the depth of the investigation associated with different frequencies makes it possible to study the variation of the invasion within the scope of the NMR sensitive volumes, such variation can be better observed for the gas reservoir, since the gas mobility is greater among all types of reservoir fluid. By processing frequency data separately, it is possible to observe the variation in gas saturation if it occurs. However, since the scope of the NMR-sensitive volume is limited to just a few centimeters, the variation in limited zone saturation is limited, and the consistency of the results processed with individual frequency data can be compromised for high-noise data.

The invasion can be seen as a process of replacing mobile formation fluids with mud filtrates introduced by drilling a well. For a well having water-based drilling mud, the hydrocarbon saturation becomes less in the invaded area due to the invasion of the water-based mud filtrate. For a well having an oil-based drilling size, the hydrocarbon saturation in the invaded zone can be increased from the native oil saturation (such as the case where mobile water exists) or relatively unchanged. Gas saturation, S_g, is always reduced or intact in the invaded area when using drilling mud which is one of water based and oil based. In order to compensate for the variation possibilities, it is necessary to use all the frequency data in the processing simultaneously.

Therefore, what is needed are techniques for data processing for multiple frequencies, where processing techniques provide a determination of a radial gas saturation profile.

Brief Summary of the Invention

A method for determining fluid saturation in a formation at a plurality of radial depths near a well is described, the method including: obtaining multiple frequency nuclear magnetic resonance (NMR) response data for the formation; and data processing to simultaneously determine fluid saturation at each radial depth.

Also described is a computer program product including machine-readable instructions stored on machine-readable media, instructions for determining fluid saturation in a formation at a plurality of radial depths near a well by: obtaining data multiple-frequency nuclear magnetic resonance (NMR) response for formation; and data processing to simultaneously determine fluid saturation at each radial depth.

Brief Description of Drawings

Referring now to the drawings in which similar elements receive similar numbers in the various figures;

Figure 1 shows the aspects of an NMR filing instrument in a well;

Figure 2 shows a radial profile where the invasion exists within a gas tank;

Figure 3 presents aspects of a procedure for the termination of gas saturation in different radial positions;

Figure 4 illustrates the variation in water and gas saturation determined at six different frequencies;

Figure 5 illustrates the variation of the water relaxation time spectrum T2 for six different frequencies;

Figure 6 illustrates a user interface illustrating the aspects of the results of Simultaneous Inversion of Multiple Echo Sequences (SIMET) considering an invasion process;

Figure 7 provides a comparison of gas saturation for different noise models and at different frequencies against the true model;

Figure 8 illustrates a user interface illustrating aspects of SIMET results without considering the invasion process;

Figure 9 provides a comparison of the total porosities for different noise models before and after considering the invasion process;

Figure 10 illustrates the aspects of the SIMET results considering the invasion process for a model without invasion;

Figure 11 illustrates the aspects of the SIMET results considering the invasion process for a model without invasion. The oil phase is considered in SIMET;

Figure 12 also presents the SIMET results considering the invasion process for a model without invasion, where the oil phase is considered in SIMET and the water-based mud is considered;

Figure 13 illustrates the SIMET results considering the invasion process for a model without the invasion, and where the oil phase is considered in SIMET and the oil-based sludge is considered;

Figure 14 illustrates the SIMET results considering the invasion process, where the relaxation time spectrum T₂, porosities, and saturations are all for the lowest frequency f;

Figure 15 illustrates the water porosity results of processing individual frequency data for five different noise models: e

Figure 16 shows gas porosity results from processing individual frequency data using five different noise models.

Detailed Description of the Invention

The multi-frequency NMR echo sequences contain responses originating from fluids in the pores of underground formations. Different response data can be performed for different radial positions, within distances as short as a few centimeters. The distribution of relaxation time for fluids within the pores may be different due, at least in part, to an invasion process. The difference is particularly noticeable in the data from a gas well. Techniques for determining fluid saturation from different frequency data are described here. The techniques improve sensitivity in detecting small variations of invasion by simultaneously processing all frequency data together and combining physical restrictions.

Figure 1 illustrates a well filing device disposed in a well 22 penetrating the earth formations 23, 24, 26, 28 for measurements of properties of the earth formations 23, 24, 26, 28. The well 22 in figure 1 it is typically filled with a fluid 34 known in the art as drilling mud. A sensitive volume generally illustrated at 58 and having a cylindrical shape or a fraction of a substantially cylindrical shape, is arranged in one of the earth formations, illustrated by 26. The sensitive volume 58 is a predetermined part of the earth formations 26 in which measurements of Nuclear magnetic resonance (NMR) are performed, as will be explained further.

NMR instruments suitable for use in accordance with the teachings here include, MREX® by Baker Hughes, Incorporated of Houston, Texas, in addition to MRIL® of Halliburton Corporation, of Houston, Texas. MREX® generally includes a side antenna and a gradient magnetic field for the formation of fluid assessment and analysis measurements in almost any well environment regardless of well size, well deviation, or well conductivity. The side design mitigates the driving effects of drilling mud on the quality of NMR data. MREX® generally uses static or pulsed radio frequency magnetic fields to perform spinecho magnetic resonance measurements in the well. The basic principle of MREX® measurement is the use of a static magnetic field to polarize protons in the formation fluids. Those skilled in the art will recognize that these instruments, and other aspects of NMR instruments, as discussed here or that may be compatible, are illustrative and not limiting.

In typical embodiments, the sensitive volume 58 includes materials such as those found inside a well 22 including a mixture of liquids including water, salt water, drilling fluid, minerals, clay, mud, oil and fluids and formation that are native to formations 23, 24, 26, 28 or introduced in them. NMR measurements can be used to determine a variety of forming properties and other aspects of interest.

It is recognized that certain fluids such as drilling mud may be of interest or have particular problems when taking measurements. In general, the drilling mud is considered to include several components. For example, drilling mud includes base fluid (typically fresh water or brine, or oil or synthetic fluids), additives and solid particles.

As used here, the term mud fluid generally refers to all of the mud (the paste that contains the solid particles and the liquid). The solid particles are blocked by the porous formation and form a thin layer on the well wall (which is known as mud cake) and the base fluid, together with the additives that can be mixed are filtered through the mud cake and invade the formation , when the difference between the pressure of the well and the formation is greater than the capillary pressure of the mud cake. Thus, the fluid that invades is often known as a mud filtrate. In addition, the term fluid generally refers to liquid hydrocarbon, gas, water and mud filtrate, gas condensate and other fluids as is known to those skilled in the art.

Turning again to figure 1, a string of filing instruments 32, typically including an NMR apparatus, is typically lowered into well 22 by means of a cable 30. The cable 30 can be wound and unwound from a winch or drum 48. Instrument string 32 can be electrically connected to surface equipment 54 by an electrically insulated conductor (not shown separately in figure 1) that forms part of cable 30. Surface equipment 54 may include a portion of a telemetry system 38 for communicating control signals and data to instrument string 32 and computer 40. The computer may also include a data recorder 52 to record measurements made by the apparatus and transmitted to surface equipment 54. Typically, the computer includes a variety of input / output devices and other support devices to improve the operation of the device and estimates made using it.

An NMR probe 42 can be included in instrument string 32. The configuration of an NMR measurement tool can be centralized or decentralized. Illustrated in figure 1 is an example of an NMR tool centered within well 22 by means of an upper centralizer 56 and a lower centralizer 57 attached to the instrument string 32 in axially spaced locations. Centralizers 56, 57 can be of the types known in the art, such as bowsprings.

The circuit assembly for the operation of the NMR probe 42 can be located inside a cartridge of electronic parts of NMR 44. The circuit assembly can be connected to the probe of NMR 42 through a connector 50. The probe of NMR 42 is typically located within a protective housing 43 which is designed to exclude drilling mud 34 from inside probe 42. The function of probe 42 will be explained later.

Other well filing sensors (not shown separately for the sake of clarity of illustration in figure 1) can form part of the instrument string 32. As illustrated in figure 1, an additional archiving sensor 47 can be located above the electronic parts cartridge NMR 44. Other filing sensors, as shown in 41 and 46, can be located inside or below the lower centralizer 57. Parts of the electronic NMR parts can be located inside the electronic part cartridges that form part of other archiving sensors. The locations of other sensors 41, 46, 47 illustrated in figure 1 are a matter of convenience for the system designer and are merely illustrative.

Other aspects of the illustrative modality of the NMR probe 42 are provided in US Patent No. 5,712,566, entitled Nuclear Magnetic Resonance Apparatus and Method, issued on January 27, 1998 to Taicher et al., And incorporated herein by reference in its entirety . Another non-limiting example is described in US Patent No. 4,710,713 also issued to Taicher et al., And incorporated by reference here in its entirety. It should be recognized that these modalities of the NMR instruments are illustrative only, and do not limit the teachings here.

Instrument string 32 is used to perform NMR measurements and collect NMR response data from inside the well 22.

The techniques described here provide a method for simultaneous determination of gas saturations at different radial depths in formation 26 near well 22 from NMR measurement data that includes measurements taken at different frequencies. In general, a modality of the technique requires the processing of measurement data using SIMET (Simultaneous Inversion of Multiple Echo Sequences) without considering the variation of S gas saturation_g different frequency data; removal of all non-mobile fluids; removing fluid in addition to gas and filtering mud for a three-phase case (even if the effect of the fluid is typically small); calculation of a geometric mean relaxation time T2 for gas; inversion of partial porosities corresponding to the relaxation time compartments T₂ for the mobile fluid and a single or several around the geometric mean of T gas relaxation time₂ (where a monotonous constraint on S gas saturation_g at different depths is used in the inversion algorithm); and calculation of S gas saturations_g at different radial depths and sending the results.

Multi-frequency NMR data contains proton responses at different radial positions, RP_X, also referred to as radial depth. Consider the example provided in figure 2. In figure 2, well 22 is illustrated with the NMR probe 42 disposed in it. A series of radial positions RPi, RP₂..... RPn θ illustrated as concentrically surrounding well 22. Each radial position RP_X it occupies part of the surrounding formation 26, and represents a depth of investigation (DOI). Well 22 passes through a gas deposition 60. Part of the gas deposition 60 undergoes invasion, which is presented as an invasion zone 29. Also as shown in figure 2, the sensitive volume 58 includes gas deposition areas 60, and the invasion zone 29 of the gas deposition 60.

Although the sensitive volume 58 is presented as cylindrical or circular, this is not always the case. That is, the technique is not completely limited to cylindrical or a part of the cylindrical shape. For example, the shape can be elliptical, or it can have another shape. The format typically includes a series of non-overlapping wraps (that is, radial depths) associated with different frequencies. For example, the sensitive volume 58 of the MREX® instrument is not strictly circular. The sensitive volume does not need to be the same width as the ring (thinner on the sides so that it looks like a crescent). Briefly, the sensitive volume 58 can include a variety of shapes and other geometric properties.

NMR data from well 22 typically includes complex data. For example, high frequency NMR signals may be affected more by invaded mud filtrate than deeper low frequency reading signals. Therefore, it can be considered that the saturation of gas S_gderived from the high frequency data will not be higher than the S gas saturation estimates_g determined from lower frequency data. An algorithm that takes all frequency data into account simultaneously can advantageously use that consideration.

A technique for determining gas saturation at different radial positions RP_X is provided here. This technique recognizes that the gas is generally displaced by the mud filtrate (water or oil). Additionally, this technique recognizes that while the oil (or water) within the formation can also be at least slightly displaced by water (or oil) in the mud filtrate, the response to this change is negligible and, therefore, is not considered.

Referring now to Figure 3, an illustrative algorithm 100 for determining a radial profile for saturation of gas S_g from NMR data is provided. In a first step 110, response data from multi-frequency NMR echo sequences is obtained. In a second step 120, a non-mobile fluid component in the gas deposit 60 is determined and then removed from the data. The precise determination of the non-mobile fluid component is provided as a result of SIMET processing. SIMET is used to derive spectra for different fluids considering that the deposition of gas 60 has a generally similar appearance for each radial position RP_X. Although those skilled in the art may recognize that consideration could cause some errors in a final solution, the spectra for non-mobile fluids are adequately accurate for removal from total responses. In addition, it is possible to determine non-mobile fluids by processing single frequency data (using less data) to avoid such consideration. The porosity for the mobile fluid and gas is also obtained in the second step 120 (or additional use) by SIMET processing. In a third step 130, the response of the non-mobile fluid (and fluid in addition to the mud and gas filtrate) is removed.

In a third stage 130, for a case of three phases (that is, multiple phases), a third fluid in the formation (a fluid in addition to the mud and gas filtrate) is also considered to have a minor effect due to displacement by the filtrate of mud. After the response of the interference fluids (i.e., the third fluid) is removed from the response data, the remaining response in the response data is associated with the moving sludge filtrate and the gas.

After SIMET processing, if present, non-mobile fluids and the third fluid in addition to the mobile fluid and gas can be removed. The geometric mean relaxation time T2 for the mobile mud filtrate (T₂mf) and gas (T_2g) are calculated from the SIMET results. In addition the total porosity (φ ™) for the filtered sludge and gas fluid is obtained. Since the gas has a well-defined spectrum, a single T_2g or several compartments around it are used. For the mobile mud filtered fluid, a single geometric average relaxation time for the mobile mud filtered fluid, T_{2 m}f, or several compartments around the geometric mean relaxation time T₂ they cannot provide flexibility in the description of the spectrum. Usually the compartments that represent the moving part of the filtered mud fluid are all used. If the properties of the filtered mud fluid are known, such as diffusion D and the reasons for the longitudinal relaxation time T1 through the transverse relaxation time T₂ for fluid and gas, the response function, A^jj (t) for each compartment can be represented by equation (1):

Tw^J __t_ (yG^JT &lt;&gt;^J)²Df a! = HI, Qe f^2l)and ¹² G) rj where i represents ιτη, m₂, ..., m_M, or g, whichever corresponds to the fluid compartments and the gas compartment; j represents different sequences of acquisition of a specific waiting time T_w, inter-echo spacing T_and and applied field gradient G; f represents m or g of fluid or gas (respectively) that can be identified from the representation of i; HI represents a hydrogen index; D represents the diffusion capacity; R represents the ratio of T1 to T_2l and γ represents the geomagnetic ratio of hydrogen.

Once the response function, A \ (t) has been determined, the echo sequences are grouped by the gradient values ​​(G) in an ascending order and represented as jk (k = 1, 2, ..., N) , where N represents a number of frequencies. Partial porosities for the mobile mud filtrate and single gas component are represented as P^kj. Accordingly, residual instrument responses after removing responses from non-mobile fluids can be calculated according to equation (2):

<img file="BRPI0809121A2_D0002.tif" />

(2)·

Since the porosity P^k can reasonably be considered to be a constant in different radial positions, RP_X, equation (3) applies:

k ^M kp^k + Εώ- yp^k

<img file="BRPI0809121A2_D0003.tif" />

(3) where φ, ην represents the total porosity for the mobile sludge filtrate and gas obtained from the SIMET results without considering invasion 29 and M represents the number of compartments for the mobile sludge filtrate. When the invasion process exists, the total porosity &lt;j&gt;_mv it is less than it should be due to the effects of a lower hydrogen index. Thus, a correction term Δφ (&gt; 0) is introduced and inverted here to obtain better accuracy. By replacing equation (3) with equation (2) and applying the correction term Δφ, equation (4) is obtained:

<img file="BRPI0809121A2_D0004.tif" />

(4)

Using the vector and matrix annotation, equation 4 can be written as equation (5):

_THE* p * = d^THE (5) where

<img file="BRPI0809121A2_D0005.tif" />

<img file="BRPI0809121A2_D0006.tif" />

<img file="BRPI0809121A2_D0007.tif" />

<img file="BRPI0809121A2_D0008.tif" />

<img file="BRPI0809121A2_D0009.tif" />

(7);

d^k =

-A -φ g mv (8).

Based on the invasion logic, the partial porosities P^kcorresponding to all the sludge filtrate compartments for different frequencies f satisfy the relation provided in equation (9):

<td>pl &lt;P² &lt;</td><td> ..&lt;_PN</td>

<td>ml ml</td><td>ml</td>

<td>pl &lt;p² &lt;</td><td>- &lt;P^N</td>

<td>m2 m2</td><td>m2</td>

<td>P¹ &lt;P²</td><td>&lt;.. &lt;pⁿ</td>

<td>mM mM</td><td>mM</td>

(9).

In order to implement the logic of equation (9) in algorithm 100, an incremented annotation for the partial porosities P^kj is given as equation (10):

= r ml + ΔΡ ml ml ml

P¹ + ΔΡ¹ + ΔΡ²ml ml ml p^N = p^[ _ + ΔΡ¹ + AP² + ml ml ml ml

AP

Ml ml (10).

The same annotations can be applied to P^km2-. P^kmM · For all f frequencies, strangers can now be represented by the column vector provided in equation (11).

ΔΡ¹ ... ΔΡ ^^-1 ΔΡ¹ ··· ΔΡ ^ F .. / J ΔΡ¹ rA rA ηΰ. ηΰ ηΰ mM mM mM J (11)

Note that all elements in the vector p are non-negative. Non-negative restrictions can be easily implemented in inversion. The right side of equation (11) is the combination of all data that are calculated based on equation (8), for all frequencies f. A typical arrangement is provided in equation (12).

(Μ i

mv

Α²· Φ)^T ··· (M -A^N φ)^Tg ^Vmv J_N g ™ '1 -' 2 and a corresponding matrix is ​​provided in equation (13):

A = where g ml m2 mM (12);

(13);

g ^J2 i ²gj

B = ml

<td></td><td>-J¹</td><td></td>

<td>ml</td><td>g</td><td></td>

<td>^j2 THE ²</td><td>THE -THE ²</td><td>THE ²</td>

<td>ml</td><td>g</td><td>ml</td>

<td>Theⁿ</td><td>-Theⁿ</td><td>Theⁿ</td>

<td>ml</td><td>g</td><td>ml</td>

N, 1 = 1.2, ... M.

(14);

(15).

THE^N-THE^N ml

Everything that results in a final equation to be solved, which is provided as equation (16):

₅ Ap = d where p&gt; 0.

Note that the size of matrix A is NEt_Otaix (N.M + 1), where NEt_Otai represents a total number of echoes for all echo sequences.

After obtaining the solution by combining the mobile fluid porosity (φ, ην) θ the total porosity (&lt;j&gt;_t) from SI MET, gas saturations in different radial positions RP_X can be calculated by equation (17).

S * = 8

1 I ρ. + ··· + ρ .. + Σ (Λρ, tn2 mM yjm \

Ap^l + · M2 (17).

Φ_ί+ Αφ where k = 1,2, ..., N.

In a fourth step 140, a geometric mean for the relaxation time T₂ is calculated for gas. Normally, the spectrum associated with the gas is very accurate and can be represented by a single geometric mean, while the spectrum for the filtered fluid of moving mud (water or oil) is more complicated. In this case, the spectrum for the filtered mobile mud fluid is typically represented by all relaxation time compartments T₂. One compartment (up to several compartments around the geometric mean for relaxation time T₂ of the filtered sludge fluid can be used. Geometric means for relaxation time T₂ they are calculated from the SIMET results in the second step 120, after the removal of the non-mobile fluid and the third fluid. In a fifth step 150, the calculation of the partial porosities corresponding to the compartments for different frequency data and a correction term for the porosity of mobile fluid is determined by a linear inversion. The calculation of partial porosities is restricted by aspects of the invasion. In a sixth step 160, gas saturations for different frequency data are then calculated from partial porosities and a corresponding porosity correction term. It is natural for those skilled in the art that the steps for removing non-mobile fluids and the third fluid in addition to the mud and gas filtrate are optional. All can be included in the inversion described above.

In order to validate the algorithm 100, two cases are presented. A first case considers a two-phase model with a profile gradually changed to S gas saturation_g. A second case involves processing a two-phase model that has no intrusion. Responses are calculated for a typical acquisition sequence (where response data is provided by twenty-four echo sequences using six frequencies).

For each case, five different noises (each noise having 100 levels) were added to the synthetic data. The levels and noise were based on the noise characteristics of actual measurements. The first four noise models were pure random noises of zero, half, once, or twice the standard deviation of the corresponding echo sequence. The latest noise model uses noise channel data. In both cases, the water and gas diffusion capacities were realized as 5.2E-9 m²/ if 70.0E-9 m²/s. The reasons for Ti relaxation time over T relaxation time₂ for water and gas it was 2 and 1, respectively. The relaxation time compartment position T₂ for gas it was 3 seconds and the hydrogen index was 1 for water and 0.5 for gas. The total porosity used was 25.7 pu in both cases.

In the case involving invasion, the saturation of S gas_g ranged from about 32% to 43% (see figure 4). The water relaxation time spectrum T₂ correlated at different frequencies (equivalent to different radial positions RP_X) is illustrated in figure 5. Figure 6 presents a user interface illustrating the results of the SIMET inversion where consideration is given to the varied gas saturation S_g and water saturation S_w. In figure 7, the average gas saturation^Sg for 100 levels of five different noise models it is compared with the true values ​​provided. As illustrated, gas saturation S_g for different radial positions RP_X can be determined within the error of about 5% for all five noise models. SIMET results (without considering the invasion process) are illustrated in figure 8.

Two observations can be derived from figure 8: one is that the saturation of gas S_g (about 25%) is less than one of the true values ​​(32% to 43%) for different frequencies; the other is that the total porosity is greater than a pu less than a true one. The comparison of total porosities with and without considering the invasion process is illustrated in figure 9. With the consideration of the invasion process, the total porosity can be improved to an accuracy of 1 pu.

In the case where no invasion occurs, saturation of S gas_g it is unchanged and maintained at 30% in all radial positions. All other parameters are the same as those used in case 1. The purpose of testing this case is to see if the inversion creates some artifacts. Figure 10 illustrates the results. It is observed that the consistent invasion cannot be identified within an accuracy of about 5% based on the gas saturation S_g for different frequencies noun—_x. Noise does not cause some variations in the gas saturation determined S_g. However, the variation is less where the noise is less. and can be controlled by various processing techniques. An example of such a technique is the averaging of noise data during data processing.

To further assess the stability of algorithm 100, the oil phase is added in the inversion. The results are illustrated in figure 11. Figure 11 illustrates that only a slight difference can be seen. Figures 12 and 13 illustrate two additional examples that include the oil spectrum in the model, but processed with water-based mud or oil-based mud considered, respectively. Again, algorithm 100 does not create an artificial gas invasion profile.

By processing data from a well 22 to a gas well, the invaded zone 29 with varying gas saturations S_g can be identified and the total porosity estimate can be improved. Figure 14 illustrates such an example. To reduce the effects of noise, the data was stacked using RA = 16 (number of average data points). It is recommended that data be stacked before using algorithm 100.

Processing the individual frequency data separately, the gas saturation S_g at different depths can be obtained. However, the accuracy of the gas saturation determined S_g it typically depends on data quality and the proper selection of acquisition sequences. The porosities of water and gas determined in five different noise models are illustrated in figures 15 and 16. These models are for PoroPerm and MREX gas acquisitions. From these two figures, it is observed that the results of noise-free data (noise model 1) clearly illustrate the relationship of relative variation between solutions at different frequencies, but the noise in the data destroys the relationship. In other words, the results of processing different frequency data separately can be distorted, even for the relative relationship. Increasing the average level can be useful.

An invasion of mud filtrate in a gas well can cause S gas saturation_g vary at different depths where the investigation is carried out. This variation can sometimes be seen in multi-frequency NMR acquisitions. Without considering this effect in the simultaneous inversion, the total porosity and saturation of gas S_gwould have some guidelines. By considering the invasion process in the simultaneous invasion, the saturation of gas S_g at varying depths of investigation it can be well determined and the total porosity can be improved to obtain better precision.

Supporting the teachings presented here, several components of analysis including at least one of a digital system and an analog system, the system having components such as a processor, storage media, memory, input, output, communications link (wired, without wire, optical or other), user interfaces, software programs, signal processors (digital or analog) and other components (such as resistors, capacitors, inductors and others) can provide the operation and analysis of the device and the methods described here. It is considered that these teachings can be implemented in conjunction with a set of executable instructions per computer stored in a computer readable medium, comprising ROM, RAM, CD ROM, flash or any other computer readable medium, known or not, that when executed causes a computer to implement the method of the present invention. These instructions can provide equipment operation, control, data collection and analysis and other functions deemed relevant by a system designer, owner, user or other personnel.

In addition, several other components can be included and requested to provide aspects of the teachings presented here. For example, at least one sample line, sample storage, sample chamber, sample exhaust, pump, piston, power supply (for example, at least one of a generator, a remote supply and a battery), supply of vacuum, pressure supply, cooling unit or supply (ie, cooling), heating component, driving force (such as translation force, propulsion force or a rotating force), magnet, electromagnet, sensor, electrode, transmitter, receiver, transceiver, controller, optical drive, electrical drive and electromechanical drive can be included in support of several aspects discussed here.

Still further, the teachings presented here may be suitable for use in conjunction with other techniques known in the art. For example, it is considered that the teachings presented here can be combined or compatible with at least other methodologies or phenomena involving nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), seismic waves, acoustic waves, mineralogy, gravitation, conductivity, resistivity , permissiveness, permeability, ionization radiation and non-ionization radiation in addition to other technologies and phenomena.

Those skilled in the art will recognize that the various components or technologies may provide certain beneficial or necessary features or characteristics. Accordingly, these functions or features, as may be necessary to support the appended claims and their variations, are recognized as being inherently included as a part of the teachings presented here and a part of the described invention.

While the invention has been described with reference to the illustrative modalities, it will be understood by those skilled in the art that various changes can be made and their equivalences can be replaced by elements without departing from the scope of the invention. In addition, many modifications can be made to adapt a particular instrument, situation or material to the teachings of the invention without departing from its essential scope. Therefore, it is intended that the invention is not limited to the particular mode described as the best mode contemplated for carrying out that invention, but that the invention includes all modalities that are within the scope of the appended claims.