Prediction of high-quality reservoirs using the reservoir fluid mobility attribute computed from seismic data

Journal Pre-proof Prediction of high-quality reservoirs using the reservoir fluid mobility attribute computed from seismic data Yijiang Zhang, Xiaotao Wen, Lian Jiang, Jie Liu, Jixin Yang, Songming Liu PII:

S0920-4105(20)30102-9

DOI:

https://doi.org/10.1016/j.petrol.2020.107007

Reference:

PETROL 107007

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 30 July 2019 Revised Date:

24 January 2020

Accepted Date: 27 January 2020

Please cite this article as: Zhang, Y., Wen, X., Jiang, L., Liu, J., Yang, J., Liu, S., Prediction of highquality reservoirs using the reservoir fluid mobility attribute computed from seismic data, Journal of Petroleum Science and Engineering (2020), doi: https://doi.org/10.1016/j.petrol.2020.107007. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.

Prediction of High-Quality Reservoirs using the Reservoir Fluid Mobility Attribute Computed from Seismic Data Yijiang Zhanga,b , Xiaotao Wena,b *, Lian Jiangc , Jie Liud , Jixin Yanga,b , Songming Liu a,b a b c d

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu, Sichuan 610059, China College of Geophysics, Chengdu University of Technology, Chengdu, Sichuan 610059, China Department of Earth and Atmospheric Sciences, University of Houston, Houston, Texas, USA Shenzhen Branch of CNOOC Ltd., Shenzhen, Guangdong 518054, China

ABSTRACT The reservoir fluid mobility, which can reflect the pore connectivity, is an important seismic attribute in reservoir development. The current method to obtain reservoir fluid mobility is based on rock physical experiments. However, the current method can only obtain the reservoir fluid mobility at the well location, rather than for a large range within the exploration area. To accurately extract the reservoir fluid mobility of a large portion of an exploration area, we propose a new method of calculating the reservoir fluid mobility using seismic data. First, the algorithm obtains the approximate reservoir fluid mobility by substituting the reflection coefficient of the dominant frequency content at the low-frequency end of the seismic data for its instantaneous spectrum. Then, the synchrosqueezing generalized S-transform and the LucyRichardson algorithm (SSGST-LR) are used to calculate the instantaneous spectrum of the reservoir fluid mobility. Rearrangement of the generalized S-transform’s results can improve the temporal and spatial resolutions of the time-frequency transform. Moreover, the interference between the different frequency signals can be eliminated more effectively by the LucyRichardson algorithm. Finally, by performing fluid replacement in the well, we demonstrate the

influence of fluid type on fluid mobility. We used synthetic data and real data to verify the superiority of our method. This example shows that our proposed method can accurately extract the reservoir fluid mobility and predict the distribution of high-quality reservoirs in an exploration area.

Keywords: Time-frequency analysis, High resolution, Synchrosqueezing generalized Stransform and the Lucy-Richardson algorithm, Reservoir fluid mobility, Reservoir prediction.

1 INTRODUCTION High-quality reservoir prediction provides important guidance for the development and deployment of oilfields. The reservoir fluid mobility extracted from low-frequency seismic information has an excellent ability to image reservoirs. Silin et al. (2004, 2006) derived a propagation equation for low-frequency reflection in saturated porous medium in an asymptotic model based on the basic fluid flow theory. They determined that the frequency component of the reflection coefficient is proportional to the square root of the product of the fluid mobility, the fluid density, and the seismic signal frequency of the reservoir. Korneev et al. (2004) estimated the frequency-dependent reflection coefficient using the low-frequency component of the seismic data to predict the oil production rate of reservoirs. Since then, Goloshubin et al. (2006) formally introduced the concept of the low-frequency imaging attribute and proved the relationship between this attribute and oil production. In addition, he has used the imaging attribute to predict the oil-water contact and the oil production rate.

According to the theory of low-frequency asymptotic analysis, Goloshubin et al. (2008) used both fluid flow and scattering effects to prove that the seismic imaging attribute is strongly dependent on the frequency distribution of the seismic data, which is proportional to the fluid mobility. Then, they used it to estimate the reservoir’s permeability. Although the imaging attribute and the reservoir fluid mobility attribute both contain information on the reservoir’s physical properties and fluid mobility, the reservoir fluid mobility more directly reflects the permeability and the fluid viscosity and more accurately reflects the fluid mobility of the reservoir. Dai et al. (2010) determined the fluid mobility from seismic data and used this attribute to satisfactorily predict the properties of a reservoir. Cai (2012) carried out a systematic study of the relationships between the imaging attribute and the fluid mobility attribute and the permeability and the oil production rate. In addition, he also attempted to validate his prediction of the oil production rate by directly using the low-frequency components of seismic signals, well log data and testing data. Chen et al. (2012) used the generalized S-transform to calculate the reservoir fluid mobility and proposed a theoretical method for determining the optimal frequency based on the theory of lowfrequency asymptotic analysis. Chen et al. (2013) tried to identify gas-saturated rocks by integrating low-frequency shadow theory and the fluid mobility attributes, which greatly reduced the non-uniqueness and the uncertainty of the fluid identification. Ren et al. (2013) estimated fluid mobility from the frequency-dependent azimuthal amplitude-versus-offset (AVO), which demonstrated the importance of the frequency attributes in fluid mobility studies. Han et al. (2013) proposed the high-resolution inversion spectral decomposition method, which is a spectral

decomposition method with a high resolution. In this method, the spectral decomposition is described as a geophysical inversion problem, and a regularization condition is added to make it meet the sparse constraint condition. The
 norm regularization algorithm is used to solve this problem, and the multi-solution of the time-frequency analysis is reduced by this method. The implementation steps are as follows. The seismic data is projected onto the frequency-division wavelet database using a sparse inversion algorithm, and then, the results are rearranged to obtain a sparse time-frequency spectrum. Zhang et al. (2015) proposed a method for calculating fluid mobility based on this method, which improves the imaging resolution of the reservoir fluid mobility. The time-frequency characteristics of the seismic data play an important role in hydrocarbon detection (Zhang et al., 2016). In addition, the time-frequency analysis method is an effective means of estimating seismic frequency properties. Therefore, it is a good choice for estimating the fluid mobility of a reservoir using time-frequency analysis methods. At present, reservoir fluid mobility is most commonly obtained using the time-frequency analysis method on the low-frequency components of the seismic information. However, the existing timefrequency analysis method has a limited resolution, making it difficult to accurately extract the thin reservoir fluid mobility. Therefore, this study focuses on improving the resolution of reservoir fluid mobility. The synchrosqueezing transform (SST) was introduced by Daubechies and Maes (1996). It is a reassignment technique used to produce a sharpened time-frequency representation of a signal with modulated oscillations (Mousavi and Langston, 2017). Subsequently, several improved

synchrosqueezing transform methods have been widely used in geophysical exploration. Liu et al. (2018) applied the synchrosqueezed curvelet transform (SSCT) to ground roll attenuation. Based on the SST, Daubechies et al. (2011) introduced the synchrosqueezed wavelet transform, which is a combination of wavelet analysis and the reallocation method and has a higher time-frequency resolution than the wavelet transform (WT). In contrast to the WT and the synchrosqueezed wavelet transform, the result of the S-transform (ST) is an intuitive time-frequency spectrum, not a time-scale spectrum. Furthermore, the ST can display the high-frequency, low-amplitude components of a signal better. Thus, Huang et al. (2015) proposed the synchrosqueezing Stransform (SSST). Gao et al. (2003) determined that the ST does not work well for seismic data analysis since its basic wavelet is not appropriate. By deriving the ST, Gao et al. (2003) obtained the generalized S-transform (GST), which is more suitable for processing non-stationary signals. However, due to the limitations of the uncertainty principle, the resolution of the GST is not good enough. As a non-linear time-frequency analysis method, the Wigner-Ville distribution (WVD) eliminates the limitations of the uncertainty principle and achieves a high-resolution timefrequency aggregation. However, it produces cross-term interference when the signals have multifrequency components. Lu et al. (2009, 2013) developed the deconvolutive short-time Fourier transform (DSTFT), which applies the Lucy-Richardson algorithm to the STFT spectrum, and thus, it improves the efficiency of the spectral decomposition and decreases the cross-term interferences. Zhu et al. (2015) used the DSTFT to obtain the common frequency section and improved the effect of thin reservoir recognition. Zhang et al. (2017) presented the deconvolutive

generalized S-transform (DGST), which can distinguish different frequency signals better and is more flexible than the DSTFT. The purpose of this study was to predict high-quality reservoirs based on differences in reservoir fluid mobility. Using Silin et al.’s (2006) low-frequency asymptotic analysis theory, we constructed a reservoir fluid mobility calculation method based on the synchrosqueezing generalized S-transform and the Lucy-Richardson algorithm. The remainder of this paper is organized as follows. In Section 2, the method for calculating the reservoir fluid mobility is described. We combine the DGST with the SST to obtain the synchrosqueezing generalized Stransform and the Lucy-Richardson algorithm. In Section 3, the features of the GST, the SST and the synchrosqueezing generalized S-transform and the Lucy-Richardson algorithm are compared using real seismic data. In Section 4, the model test is used to validate the proposed method. In Section 5, the method is applied to a case study to distinguish high-quality reservoirs and relatively tight reservoirs when the reservoirs contain the same type of fluid and to determine the location of the reservoirs. Finally, the Gassmann fluid replacement equation is used to replace the different types of fluids in the well, and the influence of the fluid type on fluid mobility is discussed.

2

Calculation of Reservoir Fluid Mobility Based on the SSGST-LR Method

2.1 Calculation of Reservoir Fluid Mobility Silin et al. (2006) presented a low-frequency asymptotic formula for the reflection of seismic plane p-waves from a fluid-saturated porous medium at a given angular frequency:

R =  +  (1 + ) κ ⁄ ,

(1)

where  and  are the dimensionless real coefficients related to the mechanical properties (e.g., densities, porosities, elastic coefficients) of the fluid and the rock, respectively. i is an imaginary unit, κ is the reservoir’s permeability,  is the bulk density of the reservoir fluid-rock system, ω is the angular frequency, and η is the fluid viscosity. The derivation of ω is accomplished using the following equation: 





=   (1 + ) κ ⁄ .

(2)

Based on Silin et al.’s (2006) theory, Goloshubin et al. (2006) introduced the concept of the imaging attribute,

A(x, y) =

( ) 

~

"( )

.



(3) Equation (3) states that when the frequency  is in the low-frequency domain, the first derivative of the reflection amplitude is proportional to the first derivative of the reflection coefficient. This provides a theoretical basis for us to replace the reflection coefficient R() with the instantaneous 

spectral amplitude S() at frequency  in a real application. If ∁=   (1 + )  ⁄, the above equation can be expressed as '

A(x, y) ≈ ∁&( , (4) where ∁ is a complex function of the porous rock parameters, which can be obtained from well data (Goloshubin, 2006).

Goloshubin et al. (2008) further used the fluid flow and the scattering effects to derive a frequency-dependent seismic attribute, which is proportional to fluid mobility. Then, they applied it to the analysis of reservoir fluid mobility. This attribute has been widely used in recent years and has yielded good results in practical applications. Assuming that the fluid mobility of the *

reservoir is F = , based on Equation (4), the following formula is obtained: (

+=

 ( )  [ ] . 

∁,

(5) Because the reservoir fluid mobility is in the form of a parabolic function, the coefficient ∁ can be obtained from a parabolic fit (Chen, 2012). When an exploration field lacks well data, ∁ can also be set as a constant based on a qualitative analysis of the fluid types of the reservoir. Equation (5) indicates that the reservoir fluid mobility is proportional to the square of the firstorder derivative of the reflectivity divided from the frequency. After the time-frequency decomposition of the seismic signals is performed, the instantaneous spectrum amplitude or the energy can accurately describe the seismic reflection amplitude or the energy of the frequency. Therefore, in practice, the instantaneous spectral amplitude a() can be used to replace the reflection coefficient R() at frequency  when calculating reservoir fluid mobility (Chen et al., 2012). The reservoir fluid mobility can be expressed as  ( ) 

+ = ∁, 1



 3()  ] . 

2 ≈ ∁, [

(6) Compared with other wavelet-based and S-transform time-frequency methods, the SSGST-LR has

higher imaging and inter-signal interference elimination abilities. Thus, in this paper, we use the SSGST-LR to calculate the instantaneous spectral amplitude a(). Finally, by substituting a() into Equation (6), we obtain the value of the reservoir fluid mobility. 2.2 Synchrosqueezing Generalized S-transform and Lucy-Richardson Algorithm The SSGST-LR can be divided into two steps: (1) squeeze and rearrange the GST outcome, and (2) perform a 2D deconvolution operation between the synchrosqueezing generalized S spectrum and the Wigner-Ville distribution of the window function. This method is described briefly below. First, the GST of signal x(t) must be calculated using the following equation: >

5678 (9, :) = ;?> <(=)

@|B|C √E

F

GH, I,C (JGK), ,

F ?LEBM N= O > 0, R > 0.

(7)

O and R are the scaling parameters of the GST. When the two parameters of the generalized Stransform are adjusted, when λ is fixed, the smaller p is, the larger the analysis window of the generalized S transform is; and when p is fixed, the smaller λ is, the larger the analysis window is. Compared with λ, the effect of adjusting p on the analysis window is more drastic. Therefore, in practical applications, we need to adjust these two parameters flexibly according to the scale of the actual seismic data decomposition, so that the resolution of the seismic data can reach the analysis scale required. By setting δ(:) = λ|:|U , in which δ is a scale factor that determines the time width of the window function, Equation (7) can be written as

GST(δ, :, τ) =

Z, (JGK), > Y ? , F ?LEB(M?[) F ?LEB[ N=. ;?> <(=) √E F

(8)

By setting ψ(=) =



√E

J,

F ? , F LEM , in which ψ is an appropriately chosen wavelet, Equation (8) can

be expressed as >

GST(δ, :, τ) = δF ?LEB[ ;?> <(=)ψ[δ(= − 9)]N=,

(9)

where ψ(=) is the complex conjugate of ψ(=). According to Parseval's theorem, Equation (9) can be written in the frequency domain as follows:

GST(δ, :, τ) =



E

> ` (δ? _)F L[a N_ , F ?LEB[ ;?> <^(_)ψ

(10)

` (_) is the where _ is the angular frequency; <^(_) is the Fourier transform of signal x(t); and ψ complex conjugate of the Fourier transform of ψ(=). By considering a single harmonic signal

<^(_) = bc[d(_ − 2c: ) + d(_ + 2c: )]. (11) And substituting Equation (11) into Equation (10), we can get

` ∗ (2cδ? : ). GST(δ, :, τ) =  F ?LE(B?Bg )[ ψ f

(12) The instantaneous frequency :i is estimated by deriving the spectrum of the generalized Stransform: j

jk

` [2c(λ|:|?U ): .. GST(:, τ) = − cb(: − : )F ?LE(B?Bg )[ ψ

(13)

jl"m(B,k) :i(:, τ) = : + [ 2c567(:, τ).? jk .

(14) 



By superimposing the spectrum of the interval [:n −  :o , :n +  :o ] near any centre frequency :n

and placing the superimposed value at the centre frequency, we obtain the synchrosqueezing generalized S-transform (SSGST), which greatly improves the frequency resolution of the generalized S-transform. The SSGST is expressed as

665678 (:n , 9) = (:o? ) ∑Br:|Bt (Bu,[)?Bt |vBu/ |5678 ( τ ,f )|:' ∆:' ,

(15)

where :' is the discrete frequency of the GST; ∆:' = :' − :'? ; and :n and Δ:n are the midfrequency and the squeezing frequency bands, respectively. ∆:n = :n − :n?. Now, the spectrum of the SSGST is obtained as

6yz{8 (:n , 9) = |665678 (:n , 9)|.

(16)

The spectrum of the SSGST can be expressed using the following 2D convolution: >

>

6yz{8 = ;?> ;?> WVD (9, ) × WVD8 (= − 9, : − )N9N, (17) where ‚ƒ8 is the WVD of the original signal x(t), and WVD„ is the WVD of the Gaussian window h(u). Because the window function h(u) is known, its WVD„ can be calculated from it. The WVD of signal x(t) is expressed as ‰>

[

[

‚ƒ8 (=, :) = ;?> < ‡= + ˆ < ∗ (= − )F ?ŠEBM N9. (18) According to the above formula, the WVD is non-linear, and there will be cross-term interferences in the operation, which makes it difficult to distinguish whether the frequency components are actually within the distribution. In the SSGST-LR, an iterative 2D deconvolution, e.g., the Lucy-Richardson algorithm, is applied to the SSGST spectrogram to improve the time-frequency resolution. The Lucy-Richardson

algorithm can be expressed as

8? (‹ + 1) = 8? (‹)( ∗

"Œ Ž ⨂ŒG (')

),

(19)

where ‹ + 1 is the current iteration number; ∗ and ⨂ are the correlation and convolution operators, respectively;  is the WVD of the Gaussian window; and 68 is the SSGST spectrum of the original signal. By deconvoluting the SSGST spectrum, the deconvolution results, which are similar to its time-frequency resolution, can effectively suppress the generation of cross-term interferences in the WVD and improve the accuracy of signal recognition.

3

Numerical Simulation of Synthetic Cases

3.1 Time-Frequency Analysis of Real Seismic Data To verify the validity of the time-frequency transform method, we extracted the 20 Hz singlefrequency sections of the same actual seismic section using the GST, the SST, and the SSGST-LR (Figure 1). Figure 1(a) shows the seismic section. By comparing the single-frequency sections obtained using the different time-frequency analysis methods, we conclude that the resolution of the GST single-frequency section shown in Figure 1(b) is limited. The resolution of the singlefrequency section of the SST shown in Figure 1(c) is better than that of the GST, but the continuity of the strata in the transverse direction is poor and the intervals are not clear enough. The compression coefficient is l. The SSGST-LR single-frequency section (Figure 1(d)) has a better vertical resolution and lateral continuity, which provides more detailed information for later seismic interpretation and analysis. It is worth noting that a wide-band signal will be compressed into a narrow-band signal by the synchrosqueeze transform. In the field of geophysics, although the synchrosqueeze transform can improve the time-frequency resolution, it will reduce the frequency bandwidth of the seismic signal to some extent. Therefore, the problem of maintaining the frequency bandwidth of the seismic signal as much as possible should be considered when using the synchrosqueeze transform. The application of synchrosqueeze

transform to seismic data is reasonable only when the frequency band of the seismic signal is not over-compressed. In practical applications, the compression coefficient should not be too small. Otherwise, the bandwidth of the seismic signal will be seriously compressed, resulting in poor lateral continuity of the frequency attribute seismic section.

Figure 1. Seismic section and 20 Hz single-frequency sections of the different time-frequency analysis methods. (a) The seismic section; (b) the single frequency section of the GST (O=50, R=0.3); (c) the single frequency section of the SST (l=1/8); and (d) the single frequency section of the SSGST-LR (O=30, R=0.3, l=1/8, n=25).

3.2 Reservoir Fluid Mobility Calculation of Synthetic Post-Stack Seismic Data In addition, we designed a geological model (Figure 2(a)) to verify and compare the fluid mobility calculated by the GST and the SSGST-LR. A similar model was proposed by Chen (2012) to simulate an anticlinal formation hosting a gas-bearing permeable reservoir. However, in this study, the single gas-bearing reservoir was replaced by a thinly interbedded reservoir to compare the fluid mobility resolution of the GST and SSGST-LR methods. Within the model, the target strata are indicated by yellow arrows, the gas-bearing reservoir is shown in red (indicated by yellow arrows), and the other zone is the dry layer. The simulation section shown in Figure 2(b) is based on the viscous-diffusive wave equation, which is an acoustic wave equation that

uses viscosity and fluid dispersivity measurements (Goloshubin et al., 2002; Korneev et al., 2004). The wave equation simulates the frequency-dependent character of a fluid-bearing reservoir very well. The mobility section calculated using the GST (Figure 2(c)) shows an anomalous area in the horizon containing the gas-bearing layer of the reservoir. In contrast, the same anomalous area appears in the model calculated using the SSGST-LR (Figure 2(d)), but it is divided into two layers, which correspond to thin, gas-bearing inter-beds.

Figure 2. Fluid mobility analysis of synthetic seismic data for a permeable, two-layer, gas-bearing reservoir model. (a) Permeable, two-layer, gas-bearing reservoir model (gas-bearing layers are indicated by yellow arrows); (b) synthetic seismic profile of the model; (c) fluid mobility section of the model calculated using the GST(an anomalous area is indicated by a yellow arrow, O=50, R=0.3); and (d) fluid mobility section of the model calculated using the SSGST-LR (two anomalous layers are indicated by two yellow arrows, O=30, R=0.3, l=1/8, n=25).

4

Field-Data Example

The study area is in the central-southern part of the Dongsha massif in China where numerous

reef reservoirs have developed in structural highs. One giant oil field has been discovered in this area. This field is the first offshore giant reef oil field located in the northern-western part of the study area. Figure 3 shows a seismic section of the study area intersecting a known well. Figure 4 is the amplitude spectrum of the seismic section, which has a dominant frequency of at least 40 Hz. In order to demonstrate that our time-frequency transform method improves the temporal and spatial resolutions of the time-frequency transform, which is conducive to a more accurate extraction of the reservoir fluid mobility, we compared the time-frequency spectrum of a synthetic trace obtained using different time-frequency transform methods. Figure 5 (a) shows the P-wave, the density well logs, and a synthetic trace (the blue curve). Figure 5 (b) shows the GST time-frequency spectrum of the synthetic trace. Figure 5 (c) shows the SST time-frequency spectrum of the synthetic trace. Figure 5 (d) shows the SSGST-LR time-frequency spectrum of the synthetic trace. Note that the resolution of the time-frequency spectrum of the SST and the SSGST-LR at 1285 ms is better than that of the GST. In addition, the time-frequency spectrum of the SSGST-LR has a better recognition ability than that of the SST within the thin layers (as indicated by the black arrow). Based on these analysis, we concluded that the SSGST-LR algorithm can be used to characterize the time-frequency distribution of the thin layers in seismic data, making it more suitable for extracting reservoir fluid mobility. Figure 5 6 shows the 40 Hz single-frequency section of the seismic section obtained using the SSGST-LR. The well log data indicate that the reservoir has a uniform oil-water contact and is driven by bottom water. The

target formation is the Miocene carbonate stratum. Figure 7 is the well log interpretation of well W1, the daily oil production of an initial test of this well is 356m3 . In Figure 7, the first row is the porosity, the second row is the resistivity, and the third and fourth rows show the distribution of the high-quality reservoirs and the relatively tight reservoirs. All of the fluids in the reservoirs are oil, and all of the reservoirs are composed of limestone with an average porosity of 21.13% and an average permeability of 651×10-3 µm2 . The pink areas in Figure 7 indicate the high-quality reservoirs with an average porosity of 20%-30%, which are the main producing intervals in the study area. The light blue areas in Figure 7 indicate the relatively tight reservoirs with an average porosity of 10%-20%. Compared with the highquality reservoirs, the relatively tight reservoirs are tighter and have a lower porosity. The well log interpretation shows multiple high-quality reservoirs and relatively tight reservoirs from top to bottom. Figure 8 shows the section’s acoustic impedance inversion result. It can be seen from the figure that there are several relatively low-impedance layers in the study area. For comparison purposes, we calculated the reservoir fluid mobility sections based on the GST (Figure 9) and the SSGSTLR (Figure 10). The reservoir fluid mobility section calculated based on the GST shows only one thick anomaly ( black ellipse in Figure 9), which cannot be used to distinguish the high-quality reservoirs and the relatively tight reservoirs. However, in the reservoir fluid mobility section calculated using the SSGST-LR, the high-quality reservoirs and the relatively tight reservoirs can be clearly discerned (Figure 10). Note that the high fluid mobility corresponds to the high

porosity reservoirs and the low fluid mobility corresponds to the relatively low porosity reservoirs, which is more consistent with the section acoustic impedance inversion result and corresponds to the geological and sedimentary background of the study area. Because the overall sedimentary environment of carbonate reefs is stable, the sea level experienced several smallscale rises and falls during this period, and thus, a number of reservoirs with high porosity and low porosity were formed. In conclusion, the reservoir fluid mobility section calculated using the SSGST-LR can more accurately predict the high-quality reservoirs than conventional methods.

Figure 3. Seismic section (the oil-bearing reservoir is indicated by the black ellipse).

Figure 4. Amplitude spectrum of the seismic section.

Figure 5. Time-frequency spectrum of the synthetic seismic trace using different methods. (a) The well logs and synthetic trace; (b) the GST (O=50, R=0.3); (c) the SST (l=1/8); and (d) the SSGST-LR (O=30, R=0.3, l=1/8, n=25).

Figure 6. Forty hertz single-frequency section of the seismic section.

Figure 7. Results of the well-logging interpretation for well W1 within the study area. The results show multiple high-quality reservoirs and relatively tight reservoirs.

Figure 8. The section’s acoustic impedance inversion result.

Figure 9. Reservoir fluid mobility section based on the GST (the black ellipse indicates the position of the oil-bearing interval, O=50, R=0.3).

Figure 10. Reservoir fluid mobility section based on the SSGST-LR (O=30, R=0.3, l=1/8, n=25).

5

Discussion The practical application shows that the acoustic impedance and the reservoir fluid mobility can be used to determine the location of the reservoir, and the reservoir fluid mobility more accurately distinguishes the high-quality reservoirs and the non-high-quality reservoirs, which provides a favorable basis for the next development deployment in the oilfield. In addition to porosity, fluid types also affect fluid mobility. Next, the influence of the fluid types on fluid mobility is discussed. We use the Gassmann equation to replace the fluid in the well in the study area with 100% oil-saturated, 50% oil-saturated, and 100% water-saturated fluids. After fluid replacement, the P-wave, the S-wave, and the density curve of the well are different. As the water saturation increases, the values of the P-wave and the density curve increase, while the changes in the S-wave are small. We used the well curve after the fluid replacement to make a new synthetic trace and analyzed the fluid mobility of the synthetic trace. Figure 11 shows the comparison between the original well curve and the 100% oil-saturated well curve and the fluid mobility of the synthetic trace. Figure 12 shows the comparison between the original well curve and the 50% oil-saturated well curve and the fluid mobility of the synthetic trace.

Figure 13 shows the comparison between the original well curve and the 100% water-saturated well curve and the fluid mobility of the synthetic trace. In these figures, the red well curve is the original well curve, and the blue well curve is the well curve after fluid replacement. By comparing different fluid types with the same porosity, we found that as the water saturation increases, the fluid viscosity coefficient of the fluid becomes decreases and the value of the fluid mobility increases. It should be noted that a difference in fluid mobility exists in the case of a large difference of fluid types. In addition, the complex geological structure in the actual exploration area also affects the identification of the reservoir fluid mobility of the fluid types.

Figure 11. The original well curve vs. the 100% oil-saturated well curve (left) and the fluid mobility of the synthetic trace

(right).

Figure 12. The original well curve vs. the 50% oil-saturated well curve (left) and the fluid mobility of the synthetic trace

(right).

Figure 13. The original well curve vs. the 100% water-saturated well curve (left) and the fluid mobility of the synthetic trace (right).

6

Conclusions

We developed a high-resolution reservoir fluid mobility calculation method using the SSGST-LR. By adopting the reallocation method, the SSGST-LR reallocates the coefficients of the generalized S-transform, resulting in higher temporal and spatial resolutions and energy aggregation. The synchrosqueezing generalized S-transform spectrum is substituted into the Lucy-Richardson algorithm to further eliminate the

interference between the different frequency signals. The numerical simulation results and real-data examples demonstrate that the calculation of the reservoir fluid mobility based on the SSGST-LR provides a more precise estimation of the fluid mobility, which is good for determining the location of high-quality reservoirs. In addition, the influence of the fluid type on fluid mobility is illustrated by the Gassmann fluid replacement. As the water saturation increases, the fluid mobility increases, which provides a basis for identifying reservoir fluid types based on fluid mobility.

Acknowledgements This study was financially supported by the National Science Foundation of China (Grant No. 41774142), the National Key S&T Special Projects of China (Grant No. 2016ZX05026001-005), and the Excellent Innovation Team Project of the CDUT (Grant No. KYTD201403). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Data and materials availability The data associated with this research is available and can be obtained by contacting the corresponding author.

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Highlights (1) The synchrosqueezing generalized S-transform spectrum is proposed to improve the temporal and spatial resolutions of time-frequency transform. (2) The synchrosqueezing generalized S-transform and the Lucy-Richardson algorithm are introduced into the calculation of the reservoir fluid mobility to improve the accuracy of reservoir prediction. (3) The Gassmann fluid replacement equation is used to replace the different fluid types in the well, and the influence of the fluid types on fluid mobility is discussed.

Author Contribution Statement Term

Definition Ideas; formulation or evolution of overarching research goals and Conceptualization aims Methodology Development or design of methodology; creation of models Programming, software development; designing computer programs; implementation of the computer code and supporting Software algorithms; testing of existing code components Verification, whether as a part of the activity or separate, of the overall replication/ reproducibility of results/experiments and other Validation research outputs Application of statistical, mathematical, computational, or other Formal analysis formal techniques to analyze or synthesize study data Conducting a research and investigation process, specifically Investigation performing the experiments, or data/evidence collection Provision of study materials, reagents, materials, patients, laboratory samples, animals, instrumentation, computing resources, or other Resources analysis tools Management activities to annotate (produce metadata), scrub data and maintain research data (including software code, where it is necessary for interpreting the data itself) for initial use and later Data Curation reuse Preparation, creation and/or presentation of the published work, Writing - Original specifically writing the initial draft (including substantive Draft translation) Preparation, creation and/or presentation of the published work by Writing - Review & those from the original research group, specifically critical review, Editing commentary or revision – including pre-or postpublication stages Preparation, creation and/or presentation of the published work, Visualization specifically visualization/ data presentation Oversight and leadership responsibility for the research activity planning and execution, including mentorship external to the core Supervision team Management and coordination responsibility for the research Project administration activity planning and execution Acquisition of the financial support for the project leading to this Funding acquisition publication Yijiang Zhang: Methodology, Software, Writing- Original draft preparation. Xiaotao Wen: Conceptualization. Lian Jiang: Writing- Reviewing and Editing. Jie Liu: Data curation. Jixin Yang: Validation. Songming Liu: Investigation.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: