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ACS Omega
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ACS Omega
2470-1343
American Chemical Society

10.1021/acsomega.4c02279
Article
Calculation of Porosity and CO2 Content in CO2-Bearing Gas Formations Based on Density and Neutron Logging Forward and Inverse Methods
https://orcid.org/0000-0001-7329-3412
Zhang Hengrong *†
Tan Wei †
Hu Desheng †
Hu Xiangyang †
https://orcid.org/0000-0003-4619-0236
Sun Jianmeng ‡
Yang Dong †
† CNOOC Limited, Zhanjiang 524057, China
‡ China University of Petroleum (East China), Qingdao 266580, China
* Email: zhanghr@cnooc.com.cn.
23 08 2024
10 09 2024
9 36 3767837686
08 03 2024
01 07 2024
21 06 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

When the gas reservoir contains CO2, the logging response tends to be complex. When calculating porosity with neutron and density curves, the accuracy of porosity calculation is reduced due to the uncertainty of fluid parameters, which in turn affects the evaluation of CO2 content. It increases the uncertainty of reserve evaluation. In this paper, a forward modeling model of density logging is established based on the equivalent volume model, and the method of neutron logging is formed by putting forward the nonlinear formula of the reciprocal of the comprehensive deceleration length. The key parameters and their variation rules of neutron logging and density logging forward modeling under different temperature and pressure conditions are obtained by experimental means and Monte Carlo method, respectively. The variation law of the influence of different CO2 content on neutron logging and density logging curves is simulated. The research shows that with the increase of CO2 content, the neutron logging value of gas reservoir decreases, while the density logging value increases, and the greater the porosity of gas reservoir, the more obvious this change trend is. Compared with CH4, CO2 has a more significant impact on the excavation effect of neutron logging. On this basis, combined with the conductivity model of the study area, the porosity and CO2 content of CO2 bearing gas reservoir are solved by the least-square method. The practice shows that the relative error of porosity calculation is within ±4% and the error of CO2 content calculation is within ±10%, which proves the reliability of this method.

China National Offshore Oil Corporation 10.13039/501100003764 CNOOC-KJ 135 ZDXM 38 ZJ 01 ZJ document-id-old-9ao4c02279
document-id-new-14ao4c02279
ccc-price
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pmc1 Introduction

The Yinggehai Basin contains huge amount of natural gas resources, but nonhydrocarbon gases, mainly CO2, are widely distributed with complex patterns,1−4 which is one of the important constraints to the exploration and development of gas fields in the western South China Sea. When the gas reservoir contains CO2, there is a large impact on the response characteristics of logging curves such as density and neutron. It reduces the accuracy of reservoir porosity calculations, which in turn affects the evaluation of reservoir parameters such as saturation and poses a great risk for reservoir studies. By analyzing the characteristics of logging data, some relatively effective methods for CO2 gas formation identification were developed by previous authors,5−8 on the basis of which the study of CO2 gas formation reservoir logging evaluation was carried out. Shenglin et al.9,10 proposed an optimization algorithm to solve for the porosity and pore component content of CO2-bearing reservoirs, which involves numerous model parameters and is difficult to obtain accurately due to the idea that all logging curve response values are linearly weighted according to different volume components, resulting in inconvenience and low accuracy in practical application. Di et al.11,12 who used neutrons to predict CO2 content using long source distance count rate values, gas average hydrogen content index, which is based on mathematical and statistical ideas for model building and lacks certain theoretical derivation. Jun et al.13 solved the problem of calculating the porosity of a gas formation with a single CO2 content using a volumetric physical model combined with the Alchian formula, but the proposed formation component model is too idealized and does not take into account the large variation in subsurface CO2 content. In conclusion, none of the above methods discusses how CO2 content variation affects density and neutron logging curves in terms of logging principles, and the resulting methods for calculating porosity and component content of CO2-bearing gas formations lack certain petrophysical theoretical models to support them. To address the problems, we build a density logging orthorectified model based on the equivalent volume model, and form the neutron logging orthorectified model by studying the inverse calculation model of the migration length of the formation to neutrons. The key parameters of the model are obtained by means of experiments and mathematical statistics, and then the forward simulation of CO2 content variation on the response characteristics of gas formation density and neutron logging is carried out. On this basis, the joint solution of porosity and CO2 content is carried out in combination with the conductive model of the study area in order to form a set of forward and inverse methods for density and neutron logging of high-temperature and high-pressure CO2-bearing gas formations.

2 CO2-Bearing Gas Formation Density, Neutron Logging Forward Methods

2.1 Density Logging Forward Model

The principle of density logging is to use the Compton effect to detect the electron density index of the formation, and the bulk density of most minerals in the formation has an approximately linear relationship with their electron density index. Therefore, the volumetric model is a very effective equivalent model used to characterize density logging.14 For sand mudstone formations, the formation can usually be equated as consisting of a rock skeleton, mud, and pore fluids. Among them, the pore fluids include formation water, CH4, and CO2. based on the content of each component of the formation, an equivalent formation volume model can be developed as in Figure 1.

Figure 1 Equivalent volume model of formation.

According to the linear weighting principle, the density logging value of the formation can be expressed as eq 1.1

where DEN is the density logging value, g/cm3; ρi is the density of various skeletal minerals, g/cm3; Ci is the volume ratio of various skeletal minerals, fractional; φe is the effective porosity, fractional; ρw is the density of formation water, g/cm3; ρCH4 is the density of methane, g/cm3; ρCO2 is the density of carbon dioxide, g/cm3; SCH4 is the saturation of methane, fractional; SCO2 is the saturation of carbon dioxide, fractional; Vsh is the mud content, fractional; ρsh is the density of mud, g/cm3.

Among the above parameters, the skeletal mineral types, proportions and respective densities can be obtained through experiments such as X-diffraction of rock chips or cores; the lithology of the study area is sandstone with quartz as the main component, and its density is taken as 2.65 g/cm3; the mud content Vsh can be calculated from the natural gamma curve; the density of mudstone can be read from the density log of pure mudstone section (the density of mudstone in the study area is generally 2.64 g/cm3); and the density of formation water is usually taken as 1.0 g/cm3. It is generally believed that the amount of variation in density of the solid and liquid components mentioned above with changes in formation temperature and pressure is small and negligible. However, the densities of the gas components CH4 and CO2 in the pore space are more sensitive to changes in temperature and pressure. The density variation patterns of the two gas components of CH4 and CO2 experimentally measured under different formation temperatures and pressures are given in Figure 2.15,16

Figure 2 Density variation of CH4 and CO2 at different temperatures and pressures values.

Based on the data in Figure 2, the equations for calculating the CH4 and CO2 densities under different temperature and pressure conditions were obtained by binary regression fitting as eqs 2 and 3.2

3

The formation temperature of the main target section in the study area is about 175 °C and the formation pressure is about 65 MPa, corresponding to two gas densities of CH4 and CO2 calculated by the above equation as 0.213 and 0.672 g/cm3, respectively.

2.2 Thermal Neutron Logging Orthorectification Model

Neutron logging detects the deceleration capacity of the formation for neutrons, which varies for different materials in the formation. According to the two-group diffusion theory,17 the count rates of the two probes near and far from the thermal neutron logging are shown in eq 4.4

where, φ(r) is the neutron flux, r is the source distance (r1 < r2), cm; Lf is the deceleration length of fast neutrons, cm; Lt is the diffusion length of fast neutrons, cm.

The sum of the deceleration length and the diffusion length of the formation for fast neutrons is usually defined as the migration length. Therefore, the migration length of the formation can be used to calculate the count ratio of the neutron instrument, which is then scaled to obtain the neutron logging value. Since neutron logging is essentially a study of the collision and transport of fast neutrons with matter in the space state, the state migration equations are complex and difficult to solve, so the migration lengths of different substances are usually obtained using Monte Carlo simulation methods.18−20 As shown in Figure 3, the migration length of pure gas is simulated by using a sphere model with a radius of 1–300 cm, a pulsed neutron source located at the center of the sphere, and an interval of 1 cm between different spheres, and the migration length of different substances is calculated by recording the surface flux of each sphere according to Fermi’s age theorem.

Figure 3 Calculation model of neutron migration length.

For the solid skeleton and formation water, the migration length variation under different temperature and pressure conditions is negligible. However, for the gases in the pore space, changes in temperature and pressure conditions will lead to changes in their concentrations, which in turn will have a large impact on the migration lengths. Figure 4 shows the migration lengths of methane and carbon dioxide at different temperatures and pressures from Monte Carlo simulations.

Figure 4 Migration length variation of CH4 and CO2 at different temperatures and pressures values.

As can be seen from Figure 4, the migration lengths of both methane and carbon dioxide decrease with increasing pressure when the temperature is kept constant, while the migration lengths of both increase with increasing temperature when the pressure is kept constant. This is due to the effect of temperature and pressure on the concentration (i.e., density) of the gases, which leads to the change of their migration lengths. That is, the greater the concentration of the gas the smaller the migration length and, conversely, the greater it is. And the migration length of methane is more sensitive to changes in temperature and pressure than that of carbon dioxide. This is due to the fact that methane contains the element hydrogen, which contributes most to neutron deceleration, and its ability to decelerate neutrons gradually increases with increasing concentration, while carbon dioxide does not contain hydrogen and has a weaker ability to decelerate neutrons itself, so this variation pattern is relatively insignificant.21 The migration lengths of CH4 and CO2 can be obtained by fitting the data in Figure 4 as a function of temperature and pressure, respectively, as shown in eqs 5 and 6.5

6

The migration lengths of some stratigraphically common minerals under temperature and pressure conditions (175 °C, 65 MPa) in the study area, as determined from Monte Carlo simulation methods, are given in Table 1.

Table 1 Migration Length of Common Substances in Formation

matter	chemical formula	migration length Ls (cm)	inverse of migration length ξ (cm–1)	
quartz	SiO2	30.54	0.033	
calcium carbonate	CaCO3	25.54	0.039	
water	H2O	6.92	0.145	
methane	CH4	23.51	0.043	
carbon dioxide	CO2	72.45	0.014	

Since each component of the formation has a different deceleration capacity for fast neutrons, it is necessary to characterize the deceleration capacity of the formation for fast neutrons using the integrated migration length. And according to eq 4, it can be seen that there is a better linear relationship between the inverse of the migration length and the count ratio of neutron logging compared to the migration length. The inverse of the migration length of the material in the formation pore can be formed by a linearly weighted combination of each fluid component of the pore in proportion to its respective volume.22 Therefore, the expression for the inverse of the migration length of CO2-bearing gas formations in the study area for fast neutrons can be defined as eq 7.7

ξw, ξCH4, ξCO2, ξm are the inverse of the migration lengths of formation water, methane, carbon dioxide, and skeleton, cm–1, respectively. is the mud indicator parameter, satisfying eq 8.8

After determining the integrated migration length of the stratum, the Monte Carlo simulation calculation method is used to establish its relationship with the counting ratio. A Monte Carlo neutron calculation model is shown in Figure 5, which consists of a pulsed neutron source and two He-3 neutron detectors. The detector source distances are 29 and 58 cm, respectively. Both detector diameters are 7 cm; near and far detector lengths are 7 and 15 cm, respectively. The detector and source are ideally shielded in the middle. The borehole diameter is 8.5 in standard borehole conditions. And the F4 card is used to record the density, neutron detector flux.

Figure 5 Monte Carlo neutron calculation model.

Based on the simulation results, the count ratio of compensated neutron logging instruments in the study area satisfies eq 9.9

The relationship (10), obtained by scaling the EcoScope series of Schlumberger’s follow-on neutron logging instruments in a standard well at the University of Houston, USA, allows the calculation of neutron logging response values corresponding to different count ratios.10

2.3 Forward Simulation of CO2 Effect on Density, Neutron Logging

Based on the response eqs 1 and 10 for density and neutron logging, a simulation study of the effect of CO2 content on the response characteristics of formation neutron and density logging can be performed. According to the porosity distribution of the gas formation in the study area, Figure 6 shows the pattern of density and neutron curve with increasing CH4 and CO2 content when the porosity of the formation is 10, 15, 20 and 25%, respectively. Among them, Figure 4a shows the gradual increase of CH4 saturation in the formation from 0% (pure water layer) to 100%; while Figure 4b shows the gradual replacement of CH4 in the pores of the pure gas layer by CO2. Table 2 shows the amount of variation of density and neutron logging values with CH4 and CO2 content for the two processes mentioned above.

Figure 6 Relationship between characteristics of neutron and density logging and variation of CH4 and CO2 content in gas reservoir under different porosity conditions.

Table 2 Statistics on the Amount of Variation of Density and Neutron Logging Values with CH4 and CO2 Content under Different Porosity Conditionsa

porosity (%)	CH4 replacement water process	CO2 replacement of CH4 process	
density logging values (g/cm3)	neutron logging values (%)	density logging values (g/cm3)	neutron logging values (%)	
DEN1 (Sw = 100%)	DEN2 (SCH4 = 70%)	Δ1	CNL1 (Sw = 100%)	CNL2 (SCH4 = 70%)	Δ2	DEN3 (SCO2 = 70%)	Δ3	CNL3 (SCO2 = 70%)	Δ4	
10	2.461	2.373	–0.088	8.763	1.378	–7.385	2.401	0.028	–0.113	–1.491	
15	2.379	2.247	–0.132	14.084	1.930	–12.155	2.289	0.042	–0.114	–2.044	
20	2.296	2.120	–0.176	19.931	2.420	–17.510	2.176	0.056	–0.134	–2.555	
25	2.214	1.994	–0.220	25.790	2.858	–22.932	2.064	0.070	–0.166	–3.024	
a Note: DEN1, DEN2 and DEN3 are the formation density logs for pure water, CH4-containing saturation of 70% and CO2-containing saturation of 70%, respectively. CNL1, CNL2 and CNL3 are the neutron logging values at pure water content, 70% saturation with CH4 and 70% saturation with CO2, respectively. Δ1 is the amount of change in CH4-bearing saturation of 70% relative to the density log value of the pure water-bearing formation. Δ2 is the amount of change in CH4-containing saturation of 70% relative to the neutron log value of the pure water-bearing formation. Δ3 is the amount of change in the density logging value of a formation containing 70% CO2 saturation relative to a formation containing 70% CH4 saturation. Δ4 is the amount of change in the neutron logging value of a formation containing 70% CO2 saturation relative to a formation containing 70% CH4 saturation.

From Figure 4a, it can be seen that when the formation is gradually filled with CH4 from the pure water layer, the density and neutron logging values of the formation under different porosity conditions both show a decreasing trend. Among them, the corresponding reduction in density logs under the above-mentioned different porosity conditions can be up to 0.088–0.220 g/cm3, while the corresponding reduction in neutron logs can be up to 7.385–22.932%, and the larger the porosity of the reservoir, the more obvious the above changes are. This is due to the fact that on the one hand, part of the water (movable fraction) in the formation pore space is replaced by CH4 gas and the average pore fluid density decreases; on the other hand, CH4 gas is much less capable of slowing down fast neutrons than formation water,17 and even its migration length is greater than that of formation skeletons such as quartz for a given formation condition (Table 1), which leads to a corresponding decrease in neutron porosity logging values.

And as can be seen from Figure 4b: As CO2 gradually replaces CH4 in the pore space, the neutron logging is further decreasing (up to 1.491–3.024 pu), while the density logging starts to increase (up to 0.028–0.070 g/cm3), and also shows that the larger the porosity of the reservoir the more obvious the above changes. This is due to the fact that nonhydrocarbon CO2 gas is less capable of slowing down neutrons (longer migration length) compared to CH4, so the neutron logging response value is lower; at the same time, the density of CO2 is greater than that of CH4 under formation temperature and pressure conditions, which leads to an increase in the density logging value. It can be seen that after the gas formation contains CO2, the neutron logging value decreases and the density logging value increases compared with the pure CH4 gas formation. At this time, if the conventional neutron-density rendezvous method (volumetric model) is used to calculate the porosity of the gas formation, the results will be smaller than those of the pure CH4-containing gas formation, which will affect the accuracy of saturation evaluation. To accurately calculate the porosity of CO2-bearing gas formations, the gas component content in the pore space needs to be clarified. Therefore, porosity, CH4 saturation and CO2 saturation are all key parameters for reservoir evaluation of CO2-bearing gas formation logs.

3 Joint Inversion Method of Porosity and CO2 Content

The above analysis clarified the existence of a clear variation pattern of density and neutron curves after the CH4 gas formation contains CO2, which provides a research basis for the accurate calculation of porosity and CO2 content. For density logging, the response equation satisfies eq 1. Therefore, the response equation for density logging of the formation in the study area satisfies eq 11:11

The equation is a quadratic equation about φe, Sw, SCH4, and SCO2. And for neutron logging, a quadratic multiple equation about φe, Sw, SCH4, and SCO2 is also obtained by combining eqs 7 to 10. Since its form is too complicated, eq 12 is used as the form instead:12

Also based on the Archie conductivity theory,23 the relationship between reservoir porosity and water content saturation can be obtained. The expression is eq 13:13

where Rt is the in situ formation resistivity, Ω·m, obtained from resistivity logging measurements. a, b, m, and n are rock electrical parameters, and the measured values under the temperature and pressure conditions of the formation in the study area are a = 1.0, m = 1.68, b = 1.0, and n = 1.59. Rw is the formation water resistivity, Ω·m, which is taken as 0.130 Ω·m according to the regional mineralization analysis; Rsh is the mudstone resistivity, Ω·m, which is generally 3 Ω·m in the study area.

And because the formation pore space is fully saturated, there14

Combining eqs 11 to 14, a quadratic multiple equation system consisting of four equations about φe, Sw, SCH4, and SCO2 is formed. The nonlinear inversion method can be used to find the set of model parameters that make the target equation reach minimum value,24,25 and set the target equation as15

Wd is the data weight, di is the logging response obtained from simulation, dm is the logging response obtained from measurement, and is the damping factor. x is the petrophysical model parameter vector, which can be expressed as16

The logging response d obtained from the simulation can be expressed as17

That is, the logging response d is the neutron logging, density logging and resistivity logging values, respectively. With the multidimensional joint inversion principle described above, in the inversion, it is first necessary to determine the initial values of the model (according to the reservoir characteristics of the study area, respectively, to satisfy the conditions,0.1 ≤ φe ≤ 0.25, 0 ≤ Sw ≤ 1, 0 ≤ SCH4 ≤ 1. Then the simulated response values including neutron logging, density logging and resistivity logging obtained by the forward method (eqs 11 to 14) established in the previous section are compared with the actual measured logging curves, and the corresponding model parameters are output when certain iteration termination conditions are satisfied, so as to obtain the optimal solutions for porosity, CH4 saturation and CO2 saturation of the gas formation.

4 Application Examples

Figure 7 shows the calculated results of the X-7 well in the deeper part of the study area. This well is located in the Yinggehai Basin of the South China Sea, approximately 130 km from Haikou City. The target formation of this well is H1 V gas group with a burial depth of 3800–4150 m. The porosity of the regional gas formation is mainly distributed from 9 to 14% and the permeability is 0.1–20 mD, which is a typical low-porosity and low-permeability reservoir. The well logging program includes natural gamma, deep to shallow resistivity, compensated neutron and compensated density, etc. Which is provided by the Ecoscope instrument of Schlumberger Company. Meanwhile, abundant well wall cores were obtained. According to the regional empirical formula, the temperature of the target formation of this well is about 175 °C and the pressure is about 65 MPa. The key parameters of gas density and deceleration length under the formation conditions of this well are obtained according to Figures 2 and 4, respectively, and the porosity and CO2 component content of this well are calculated according to the inversion method of this paper. The resistivity of the layers from 3967 to 3987 m (layers 1–6 explained in the figure) and 3996–4006.5 m (layers 7–10) is high (greater than the lower limit of regional gas resistivity of 10 Ω·m), and the envelope of neutron and density curves is obvious, which is a typical gas-bearing layer feature; while the resistivity of the layers from 4006.5–4012 m (layer 11) is significantly lower, and the envelope area of density and neutron The resistivity of layer 4006.5–4012 m (layer 11) is obviously reduced, and the density and neutron envelope area is narrowed, indicating that the gas-bearing properties become worse, which is the characteristic of gas-bearing water layer. The eighth channel of the figure shows the comparison between the porosity calculated by the conventional neutron-density rendezvous method (black solid line) and the method of this paper (red solid line) and the porosity of core analysis; the ninth channel shows the CO2 saturation (red solid line) and the gas-bearing saturation (blue solid line) calculated by the method of this paper, and the difference between the latter and the former is the hydrocarbon saturation (methane dominated); the tenth channel shows the ratio between the calculated CO2 saturation and the gas-bearing saturation, i.e., the CO2 content (pink curve). From the figure, it can be seen that (i) for the interpreted gas formation, the resistivity of the 3996–4006.5 m section is comparable or slightly higher than that of the 3967–3987 m section with the same lithology, but the corresponding neutron logging values are lower and the density logging values are larger, i.e., the density and neutron curves are shifted to the right in the figure, revealing that it is seriously affected by CO2; (ii) the CO2 content calculated using the method of this paper The results show that the overall CO2 content of 3996–4006.5 m is high (77.5–94.9%, average 82.3%), while the layer section of 3967–3987 m is lower (3.7–43.6%, average 18.6%), and the results are in good agreement with the results of sampling analysis at 3974.5, 3978.4 and 4001.4 m, respectively. The porosity calculated by the method of this paper is less different from the porosity calculated by the conventional neutron-density rendezvous method in the lower part of the layer with low CO2 content (3967–3987 m) and in the bottom part of the layer with gas and water (4006.5–4012 m), and it is in good agreement with the results of core analysis, while in the lower part of the layer with high CO2 content (3996–4006.5 m) the results of the conventional neutron-density rendezvous method are in good agreement with the results of core analysis. In the lower part of the high CO2 content layer (3996–4006.5 m), the results of the conventional neutron-density rendezvous method are small compared with the core analysis porosity, and the results of this paper are in better agreement. From the previous simulation results, we can see that this is due to the influence of CO2, the neutron curve of the gas layer is small and the density curve is large, so the porosity calculated by using the two rendezvous method will be smaller than the real value, while the upper high CH4 gas layer and the bottom gas-bearing water layer have less influence due to the lower CO2 content, so the calculation results of the two methods are in better agreement.

Figure 7 Calculation results of well X-7.

Table 1 lists the statistics of the error in the calculation of porosity and CO2 content for the 11 interpreted substrata (10 gas formations and 1 gas-bearing water formation) in this well section. The results show that the absolute errors of CO2 content calculation in this well range from −9.8 to 4.2%, and the overall absolute error is within ±10%, with an average of −2.4%. As for the porosity calculation, the relative errors of porosity calculated by the conventional neutron-density rendezvous method are from −6.2 to −2.3%, with an average of −3.7%, in the section of gas formation containing high CH4 (layers 1–6), excluding layer 2 due to the limited resolution of thin-layer logging data, while the relative errors of porosity calculated by the method in this paper are from −3.5 to 1.6%, with an average of −1.2%. The average relative errors of the two methods in the gas- and water-bearing section (layer 11) are −3.0 and −2.2%, respectively. In the section of high CO2-bearing gas layer (layer 7–10), excluding layer 9 due to the limited resolution of thin logging data, the relative error of porosity calculated by conventional neutron-density rendezvous method is −14.1 ∼ −12.8%, with an average of −13.4%; while the relative error of porosity calculated by the method in this paper is 1.5–1.9%, with an average of 1.7%. It can be seen that the method in this paper can accurately calculate the CO2 content of the reservoir, and the porosity calculation accuracy of the two methods is basically comparable when the reservoir is a gas-bearing water layer; while along with the increase of CO2 content, the conventional neutron-density rendezvous method has a larger error (overall small) in the calculation of porosity, while the method in this paper has a higher accuracy in the calculation of porosity because it considers the influence of CO2 on the density and neutron curve (Table 3).

Table 3 Statistics of Errors in Porosity and CO2 Content Calculation of Well X-7a

no.	depth (m)	con.	RT (Ω·m)	DEN (g/cm3)	CNL (%)	core porosity (%)	CO2 contain from sampling (%)	porosity (%)	CO2 contain (%)	
calculation result	relative error	calculation result	absolute error	
1	2	σ1	σ2	
1	3967.5–3972.4	gas layer	12.5	2.41	9.6	12.9	 	12.5	13.0	–3.0	0.8	23.8	 	
2	3972.4–3973.1	gas layer	14.2	2.42	10.6	10.3	 	10.8	11.0	4.9	6.8	11.6	 	
3	3973.1–3976.2	gas layer	20.3	2.39	8.0	13.8	15.9	12.9	13.3	–6.2	–3.5	20.1	4.2	
4	3977.2–3981.4	gas layer	22.7	2.37	8.3	13.7	9.9	13.2	13.3	–3.6	–2.9	8.3	–1.6	
5	3981.4–3982.7	gas layer	21.5	2.44	8.4	12.9	 	12.6	13.1	–2.3	1.6	22.1	 	
6	3982.7–3986.9	gas layer	17.0	2.37	9.5	14.6	 	14.1	14.3	–3.5	–2.1	7.3	 	
7	3996.1–3998.2	gas layer	20.1	2.41	6.7	13.7	 	12.0	13.9	–12.8	1.5	86.4	 	
8	3998.2–3998.9	gas layer	8.6	2.44	9.1	 	 	10.3	12.4	 	 	79.7	 	
9	3998.9–3999.5	gas layer	8.5	2.42	8.7	15.1	 	12.6	13.9	–16.6	–8.1	91.9	 	
10	4000.1–4006.5	gas layer	22.7	2.42	6.6	13.5	95.1	11.6	13.7	–14.1	1.9	85.3	–9.8	
11	4006.5–4012.0	gas-bearing water layer	7.2	2.44	11.7	13.4	 	13.0	13.1	–3.0	–2.2	27.5	 	
a Note: 1 and 2 adopt the porosity calculation results of neutron-density rendezvous method and this paper’s method, respectively; σ1 and σ2 adopt the errors of the two methods to calculate porosity compared with core values, respectively.

Figure 8 shows the calculation results of the Y-9 well of the study area. This well is located in the Yinggehai Basin of the South China Sea, approximately 134 km from Haikou City. The target layer of this well is T29, with a burial depth of 2110–2560 m. The porosity of the regional gas reservoir is mainly distributed at 16–24%, and the permeability is 12–130 mD. It belongs to a typical medium to medium high porosity and medium to medium high permeability reservoir. The temperature of the target layer in this well is about 129 °C, and the pressure is about 45 MPa. The logging data of this well is provided by the Ecoscope instrument of Schlumberger Company. The gas layer is 2144–2164 m, and samples were taken at 2145 m and 2162m, respectively. The CO2 content was tested to be 91.8 and 90.6%, indicating a high CO2 gas layer. From the figure, it can be seen that the CO2 content calculated by the method in this article is 91.6 and 96.2%, respectively, with an absolute error of −0.2 to 5.6%, which is in good agreement with the sampling results. Similar to Example 1, the porosity calculated by this method in the gas interval is significantly larger than that calculated by the conventional neutron density intersection method (with an average absolute value of about 2.3%), and is more consistent with the wall center analysis values (except for the 18th layer due to thin layer logging resolution, the relative error of porosity in other layers is −2.6 to 3.3%).

Figure 8 Calculation results of well Y-9.

This fully demonstrates that the method proposed in this article has good applicability under different temperature and pressure conditions and different formation porosity conditions in the study area.

5 Result & Discussion

1. A density logging forward modeling model is established based on the equivalent volume model; and a neutron logging forward modeling method is formed by combining the integrated migration length inverse model with the Monte Carlo method to obtain key parameters. The simulation study of CO2-bearing gas formation shows that the density logging value increases and the neutron logging value decreases as the CO2 content increases, and the larger the porosity of the gas formation, the more obvious the trend is.

2. Based on the density and neutron logging response equations, combined with the Indonesian conductivity equation, a joint inversion method for porosity and gas component content of CO2-bearing gas formations is formed. By calculating the actual well logging data, the prediction error of CO2 content is within ±10%, and the relative error of porosity calculation of CO2-bearing gas formations is within ±4% compared with the conventional method, which makes up for the latter’s deficiency of not considering the influence of logging response parameters of CO2 gas.

3. The joint inversion method proposed in this paper involves numerous parameters (density of CO2, CH4, neutron migration length, rock-electric parameters, etc.) in its derivation process under the formation temperature and pressure conditions and kept relatively constant, but in different gas reservoirs, the temperature and pressure and other conditions vary greatly, and the effects of their variations on the equation coefficients should be fully considered.

The authors declare no competing financial interest.

Acknowledgments

This paper is supported by the scientific and technological project of CNOOC (China) Co., Ltd. “Research on key technologies for producing 20 million cubic meters of oil in the west of South China Sea” (CNOOC-KJ 135 ZDXM 38 ZJ 01 ZJ).
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