# Low Permeability Gas-Bearing Sandstone Reservoirs Characterization from Geophysical Well Logging Data: A Case Study of Pinghu Formation in KQT Region, East China Sea

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## Abstract

**:**

_{w}), irreducible water saturation (S

_{wirr}). Finally, two techniques, established based on the crossplots of mean value of apparent formation water resistivity (R

_{wam}) versus variance of apparent formation water resistivity (R

_{wav})—S

_{w}versus S

_{wirr}—were adopted to distinguish hydrocarbon-bearing formations from water saturated layers. Field applications in two different regions illustrated that the established methods and techniques were widely applicable. Computed petrophysical parameters matched well with core-derived results, and pore fluids were obviously identified. These methods were valuable in improving low permeability sandstone reservoirs characterization.

## 1. Introduction

_{c}) from NMR logging; several techniques have been raised in the last 12 years [20,43,47,50,51,52]. Volokitin and Looyestijn (2001) and Looyestijn (2001) proposed a linear scale function to transform the NMR T

_{2}distribution as a pseudo-P

_{c}curve to characterize formation pore structure [43,50]. This function was verified to be available in conventional formation with a high quality. However, in low permeability sandstone reservoirs, pore structure was overestimated [20]. Although Xiao et al. (2016) raised an alternative method to construct pseudo-P

_{c}curve form NMR logging based on formation classification, it had regional limitations [20]. In different regions or for different types of formation, the classification criteria were varied, meaning that it cannot be widely used.

## 2. Geological Setting

## 3. Reservoir Petrophysical Characteristics

## 4. Method of Pore Structure Characterization and Evaluation

#### 4.1. Formation Pore Structure

_{2}time and P

_{c}based on the piecewise function calibration (PFC) method [20]. By using the PFC method, NMR T

_{2}distributions were transformed as pseudo-P

_{c}curves. Then, low permeability sandstone reservoirs pore structure was characterized in Pinghu Formation.

#### 4.2. Theory of Characterizing Pore Structure Based on NMR Logging

_{2}relaxation time of a water-wettable rock is dominated by surface relaxation and bulk relaxation; diffusion relaxation can be ignored due to negligible contribution [57]:

_{2}is the surface relaxation rate; S is the pore surface area in μm

^{2}; V is the pore volume in μm

^{3}; subscript por stands for rock pore size; r

_{por}is the pore radius in micrometer; and F

_{s}is the pore shape geometric factor. Its value is constant once pore shape is assumed as regular.

_{c}is the capillary pressure in MPa; R

_{c}is the pore throat radius in μm.

_{2}relaxation time can be expressed:

_{c}value can be acquired from NMR logging. If we normalize NMR T

_{2}amplitudes and reversely accumulate them based on the principle displayed in Figure 8, a pseudo-P

_{c}curve can be constructed from NMR data.

#### 4.3. Constructing Pseudo-P_{c} Curves from NMR Logging Based on Formation Classification

_{c}curves from NMR logging reliable, the PFC method was used. This method covered several procedures:

_{2}distributions and MICP curves were collected as the basic dataset. In the Pinghu formation of KQT Region, 34 core samples were recovered.

_{2}distributions were also classified by using the same criterion. In this study, 34 core samples were classified into three types. The classification criteria are listed in Table 1.

_{2}spectra were processed by using the same criteria used to obtain three average NMR T

_{2}distributions. These three average NMR T

_{2}distributions are reversibly accumulated and normalized to extract NMR inverse accumulative curves (Figure 10).

_{2}relaxation time and P

_{c}is established for every type of core sample based on the principle illustrated in Equation (5). It should be noted that the used parameters in the transformation model were different in large pore throats and small pore throats for the same type of core sample. These transformation models were expressed as Equations (7) and (8).

_{l}and n

_{l}are the parameters involved to transform T

_{2}time as a P

_{c}in the large pore throat; C

_{s}and n

_{s}are the involved parameters to transform T

_{2}time as a P

_{c}value in the small pore throat.

_{c}curves from NMR data were established and displayed in Figure 12. Good power functions existed in two parts for every type of core sample. Once these models were extended into field applications, pseudo-P

_{c}curves can be consecutively synthesized, and they can be used to replace MICP curves to characterize formation pore structure.

## 5. Estimation of Reservoir Petrophysical Parameters

#### 5.1. Porosity Calculation

_{D}is the porosity calculated from density logging in fraction; φ

_{N}is the porosity calculated from neutron logging in fraction; φ

_{Dclay}is the porosity calculated from density logging in clay point in fraction; φ

_{Nclay}is the porosity calculated from neutron logging in clay point in fraction; ρ

_{b}is the bulk density, ρ

_{clay}is the bulk density in clay point; ρ

_{ma}and ρ

_{f}are the bulk density of rock matrix and pore fluid, respectively. The units are is g/cm

^{3}; CNL is the neutron logging value; and CNL

_{clay}is the neutron logging value in clay point; the unit is v/v.

_{D}, φ

_{N}, φ

_{Dclay}and φ

_{Nclay}, low permeability sandstone reservoir porosity was calculated based on the triangular chart:

_{ND}is the true formation porosity calculated from density and neutron logging in gas-bearing reservoirs.

#### 5.2. Permeability Calculation

_{c}curve was established (Figure 15). In this figure, the comprehensive physical property index was defined as the square root of the ratio of permeability and porosity ($\sqrt{\raisebox{1ex}{$K$}\!\left/ \!\raisebox{-1ex}{$\phi $}\right.}$). Compared with Figure 1, permeability calculation accuracy was improved greatly. Combining with Figure 12 and Figure 15, formation permeability can be calculated well after pore structure was first characterized in the intervals in which field NMR logging was acquired. The permeability prediction model based on R50 is expressed:

#### 5.3. Water saturation Evaluation

_{0}is the rock resistivity with fully water saturation; R

_{t}is the rock resistivity with hydrocarbon saturated; and R

_{w}is the formation water resistivity. The unit of the parameters is Ω.m. S

_{w}is the water saturation in v/v. F is the formation factor. I is the resistivity index, m is the cementation exponent, n is the saturation exponent, a and b are the coefficient that associated with lithology. a, b, m and n are collectively referred to as rock resistivity parameters.

#### 5.4. Optimization of Cementation Exponent

_{10}(φ) and log

_{10}(F) in a linear coordinate, the relationship between porosity and formation factor can be expressed by a quadratic function:

_{10}(φ) versus log

_{10}(F) should pass (0.0), the value of z was defined as 0.0.

#### 5.5. Extraction of Saturation Exponent Based on Formation Classification

#### 5.6. Estimation of Irreducible Water Saturation (S_{wirr})

_{wirr}) is an important parameter in evaluation of low permeability sandstone reservoirs and identification of pore fluids, because high S

_{wirr}is a key factor that causes contrast of low resistivity in such type of reservoirs [3]. Generally, S

_{wirr}is calculated from NMR logging by using a T

_{2cutoff}. However, since a reasonable T

_{2cutoff}cannot be consecutively acquired in a whole well, a fixed T

_{2cutoff}of 33 millisecond (ms) was always used [63]. In the Pinghu Formation, the experimental values of T

_{2cutoff}s were divergent (Figure 18). It was difficult to calculate S

_{wirr}based on the method related to the T

_{2cutoff}. To establish a model to calculate S

_{wirr}, relationships among S

_{wirr}with other formation parameters were analyzed. Finally, we found that S

_{wirr}was heavily associated with comprehensive physical property index (Figure 19). Hence, S

_{wirr}can be calculated once porosity and permeability were available, even if no NMR logging data were acquired.

## 6. Identification of Pore Fluids Based on Geophysical Well Logging

#### 6.1. Identifying Pore Fluids Based on Apparent Formation Water Resistivity

_{0}, R

_{w}and porosity is expressed in Equation (16). Combined with Equations (16) and (20) and after some transformation, a derivative equation can be written as

_{0}by R

_{t}in Equation (23), formation water resistivity can still be calculated. However, it was not true formation water resistivity. Thus, we named it as apparent formation water resistivity and defined it as R

_{wa}:

_{wa}is the apparent formation water resistivity in Ω.m.

_{wa}is equal to R

_{w}in water saturated layers, because measured R

_{t}was equal to R

_{0}. However, in hydrocarbon-bearing reservoirs, R

_{t}deviated from R

_{0}and its value varied due to the effects of many factors. These factors included porosity, content of saturated hydrocarbon, pore structures, and so on. Thus, the calculated R

_{wa}was not a fixed value in a whole interval, but rather, fluctuated around a certain value as a normal distribution. In hydrocarbon-bearing reservoirs, the distribution range of R

_{wa}was wide. On the contrary, R

_{wa}was narrowly distributed in water saturated layers. The distribution range was situated between these two in hydrocarbon and water formation (Figure 20a,c).

_{wa}distribution, we extracted two parameters: R

_{wa}mean value and R

_{wa}variance. These two parameters, respectively, represented the position and width of R

_{wa}distribution in an interval and are expressed as follows:

_{wam}is the mean value of apparent formation water resistivity, R

_{wav}is the variance of apparent formation water resistivity, R

_{wa}(i) is the i

^{th}R

_{wa}, and the unit of them is Ω.m. Amp(i) is the amplitude that corresponds to R

_{wa}(i), k is the number of calculated R

_{wa}in a whole interval.

_{wam}and R

_{wav}were, respectively, calculated. We found that the crossplot of these two parameters was very effective in distinguishing hydrocarbon-bearing reservoirs from water saturated layers (Figure 21). This figure indicated that hydrocarbon-bearing reservoirs always contain high R

_{wam}and R

_{wav}, whereas values of these two parameters were low in water saturated layers. Criteria of identifying pore fluids based on R

_{wam}and R

_{wav}are listed in Table 2.

#### 6.2. Identifying Pore Fluids Based on S_{w} and S_{wirr}

_{w}and S

_{wirr}, to identify pore fluids. In hydrocarbon-bearing reservoirs, hydrocarbon occupies the big pore space; irreducible water is adsorbed on the pore surface and occupies in the small pore space; and there was no movable water. Hence, S

_{wirr}was infinitely close to S

_{w}. On the contrary, besides irreducible water, abundant movable water was present in water saturated layers. Hence, we raised a parameter of free water saturation (S

_{wf}), which was defined as the difference of S

_{w}and S

_{wirr}, to characterize movable water content. We established a crossplot of S

_{w}versus S

_{wf}to indicate pore fluids (Figure 22). Based on this crossplot, we raised the criteria of identifying pore fluids and listed them in Table 2.

## 7. Field Applications

_{2}spectrum, which was acquired from Halliburton’s MRIL-Prime tool. In the fifth track, we compared constructed pseudo-P

_{c}curves (PC_DIST exhibited as variable density) and measured laboratory capillary pressure curves of core samples (red line). It should be noted that the exhibited pseudo-P

_{c}curves and experimental capillary pressures had been transformed from an air–mercury system to an oil–water system to make them much reasonable in reflecting in-suit formation pore structure. The transformation formula is expressed as Equation (27).

_{c})

_{w_o}and (P

_{c})

_{air_Hg}are, respectively, the capillary pressure in water–oil and air–mercury systems in MPa. σ

_{w_o}and σ

_{air_Hg}are the surface tension between two phases of fluids in water-oil and air-mercury systems in dyn/cm, respectively, whereas θ

_{w_o}and θ

_{air_Hg}are the contact angles between the two phases of fluids in (

^{O}).

_{c}curves and experimental results in laboratory indicated the reliability of characterizing pore structure by using synthesized P

_{c}curves. RC_DIST displayed in the sixth track was pore throat radius distribution extracted from the pseudo-P

_{c}curve. In the seventh and eighth tracks, we compared calculated porosity (PHIT) and permeability (PERM) with core-derived results. Meanwhile, median pore throat radius (R50) and maximal pore throat radius (RMAX), extracted from pseudo-P

_{c}curves, were compared with core-derived results in the ninth and tenth tracks. Good consistency between calculated parameters by using the proposed technique and core-derived results illustrated the value of raised methods. In the last track, we compared water saturation calculated by using the improved Archie’s equation (SWC) and irreducible water saturation (SWIRR). Combined with constructed P

_{c}curves, pore throat radius distribution and pore structure parameters, we can conclude that the intervals of ×187.00 to ×202.50 m and ×231.30 to ×248.60 m were high-quality formations with good pore structure and superior pore throat connectivity. Meanwhile, overlapping of SWC and SWIRR illustrated that the upper formation contained ultra-low water saturation, and no movable water existed. Hence, this interval was identified as hydrocarbon-bearing reservoirs. However, although the interval of ×231.30 to ×248.60 m contained relatively high resistivity and good pore structure, SWC and SWIRR curves were separated, and SWC was higher than 60.0%. This meant that the pore spaces contained plenty of movable water; it was considered as a pure water saturated layer. In these two intervals, R

_{wam}and R

_{wav}also indicated that the pore fluid of the upper layer was hydrocarbon, whereas the lower formation was water (Figure 24). These interpretation results were verified by DST data. The DST data, which were acquired from the interval of ×186.7 to ×202.4 m, indicated that approximated 338.5 bbl of oil and 22.87 × 10

^{4}m

^{3}of gas were produced per day with no water. However, in the interval of ×231.70 to ×244.00 m, approximately 48.15 m

^{3}of water was produced per day. This verified the reliability of the proposed methods. If we only observed resistivity curves, this interval was easily misjudged as a hydrocarbon-bearing reservoir.

## 8. Extensive Application

_{2}distribution as pseudo-P

_{c}curves for four types of formations. Good relations still exist for every type of formation. This ensures that formation pore structure can be characterized well. Afterwards, formation porosity, permeability, water saturation (S

_{w}) and irreducible water saturation (S

_{wirr}) can also be calculated.

_{wam}and R

_{wav}and S

_{w}versus S

_{wf}were raised and shown in Figure 26a,b, separately. High compliance demonstrated the superiority of the proposed method.

_{c}curves and pore throat radius distributions, an interval of ×455.3 to ×490.4 m was considered as high-quality formations, with the exception of some interbeds with high gamma rays. Based on the standards established in Figure 26a,b, this interval was identified as a hydrocarbon-bearing formation. This identification was verified by DST data acquired in the interval of ×462.0 to ×491.0 m, which showed that approximately 9.51 × 10

^{4}m

^{3}of gas was produced per day.

## 9. Conclusions

- Combined with NMR and capillary pressure theories, a method which can be used to transform NMR T
_{2}spectrum as pseudo-P_{c}curve was established. The method was named the piecewise function calibration method. It was used to quantitatively characterize low permeability sandstone reservoir pore structure and classify reservoirs into three categories in the Pinghu Formation. - The triangular chart of neutron and density was used to well calculate porosity. A model which uses median pore throat radius as an input parameter was introduced to estimate permeability from pseudo-P
_{c}curve. For the water saturation calculation, Archie’s equation was used, and the involved rock resistivity parameters were optimized. Field examples illustrated that the proposed methods are valuable in our target Pinghu Member. - Two techniques, used to identify pore fluids based on the crossplots of mean value of apparent formation water resistivity versus variance of apparent formation water resistivity; and water saturation versus irreducible water saturation, were raised. Field examples in two different regions illustrated that these techniques were valuable in indicating pore fluids. They can be widely used in low permeability sandstones with similar physical properties, whereas common methods would lose their role due to low resistivity contrast. Our raised methods and techniques can further improve complicated formation characterization and allow for high-quality reservoir predictions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Relationship between core-derived porosity (φ) and permeability (K) in the Pinghu Formation of KQT Region, East China Sea. Relationship between these two parameters are poor. This makes it impossible to accurately calculate permeability from porosity.

**Figure 2.**Relationship between porosity versus formation factor (

**a**) and water saturation versus resistivity index (

**b**) in the Pinghu Formation of KQT Region, East China Sea. Divergent relations among these parameters led to low water saturation calculation accuracy based on the traditional Archie equation.

**Figure 4.**Lithology identification based on thin slices analysis data of 134 core samples (

**a**), facies type (

**b**,

**c**) in Pinghu Formation of KQT Region, East China Sea.

**Figure 5.**Histograms of core-derived porosity (

**a**) and permeability (

**b**) in Pinghu Formation of KQT Region, East China Sea.

**Figure 6.**MICP and corresponding J function curves acquired from 34 core samples. These core samples were drilled from the Pinghu Formation in KQT Region, East China Sea. In this figure, P

_{c}represents mercury injection pressure in MPa and S

_{Hg}represents for mercury injection saturation under every mercury injection pressure in %. J function can be used to express the pore structure and formation type after the effect of physical properties of rock was removed. The shape and position of MICP and J function curves were reflected in rock pore structure. The MICP curve located in the bottom once rock pore structure was good, because mercury can be easily injected into the pore space under the same P

_{c}. On the contrary, MICP curve located in the top for rock contains poor pore structure.

**Figure 7.**Relationships between median pore throat radius (R50) versus permeability (

**a**) and maximal pore throat radius (R

_{max}) and permeability (

**b**). These two figures indicate that pore structure was the main factor that controlled permeability in the Pinghu Formation. With the increased of R50 and R

_{max}(reflecting formation pore structure), formation permeability increased.

**Figure 8.**Principle of constructing pseudo-P

_{c}curve from NMR data (

**a**) and comparison of synthesized pseudo-P

_{c}curve with laboratory measured MICP curve for a core sample (

**b**).

**Figure 9.**MICP curves of three types of core samples (

**a**–

**c**) and the average MICP curves (

**d**) in the Pinghu Formation. Each color in a-c represents a capillary pressure curve that belongs to different formation types. These figures indicated that the first type of formation was dominant in our target formation.

**Figure 10.**Inverse accumulative curves of three types of core samples (

**a**–

**c**) and the average inverse accumulative curves (

**d**) in the Pinghu Formation.

**Figure 11.**Crossplots of porosity versus permeability (

**a**) and porosity versus R50 (

**b**) for three types of core samples in Pinghu Formation.

**Figure 12.**Models of transforming NMR T

_{2}distribution as pseudo-P

_{c}curves based on PFC method.

**Figure 13.**Calculation of porosity based on triangular chart of neutron and bulk density (

**a**) and determination of clay point based on the crossplot of density and neutron logging (

**b**). The green area was the selected clay point.

**Figure 14.**MICP curve and pore throat radius distribution for a representative core sample. This figure illustrated that the highest frequency of pore throat radius statistical histogram corresponded to 50% mercury injection saturation. This indicated that R50 was the main factor that controlled rock permeability in the Pinghu Formation.

**Figure 15.**Crossplot of median pore throat radius (R50) and comprehensive physical property index for 34 core samples. Permeability could be precisely calculated after formation pore structure was first characterized.

**Figure 16.**Novel relationship between porosity and formation factor in low permeability sandstones in Pinghu Formation. This figure illustrated that the relationship between porosity versus formation factor was well expressed by using various cementation exponent, especially for rocks with porosity lower than 8.0%. If we directly used Archie’s equation, cementation exponent would be overestimated and water saturation should be underestimated.

**Figure 17.**Improved relationships between water saturation versus resistivity index in low permeability sandstones in the Pinghu Formation. This figure illustrated that saturation exponent is heavily affected by pore structure. From the first to third type of rocks (green dots, yellow triangles and gray diamonds, respectively), saturation exponents were gradually increasing due to pore structure declining.

**Figure 18.**Experimental NMR T

_{2cutoff}s of core samples in the Pinghu Formation. The measured T

_{2cutoff}s were not a fixed value; this resulted in the difficulty of the S

_{wirr}calculation.

**Figure 19.**Relationship between S

_{wirr}and comprehensive physical property index in low permeability sandstones in the Pinghu Formation. With the formation pore structure becoming better, the corresponding S

_{wirr}decreased.

**Figure 20.**Distributions of R

_{wa}in formation with different pore fluids. Based on the morphology of R

_{wa}distribution, pore fluids can be qualitatively identified. Hydrocarbon-bearing reservoirs contained wide R

_{wa}distribution (

**a**), R

_{wa}distribution of water saturated layers was narrow (

**b**). Hydrocarbon and water formation is situated between these two (

**c**).

**Figure 21.**Identification of pore fluids based on crossplot of mean value of apparent formation water resistivity (R

_{wm}) and variance of apparent formation water resistivity (R

_{wv}).

**Figure 22.**Identification of pore fluids based on crossplot of S

_{w}and movable water saturation (S

_{wf}) in the Pinghu Formation.

**Figure 23.**A field example of characterizing formation pore structure, calculating formation parameters and identifying pore fluids based on the proposed techniques in this study. By using our raised techniques, the upper layer was identified as a hydrocarbon-bearing formation, and the lower interval was a water saturated layer. If we only used resistivity curves, the lower formation would be misidentified.

**Figure 24.**Pore fluids identification results of two intervals in a well displayed in Figure 23.

**Figure 25.**Models of transforming NMR T

_{2}distribution as pseudo-P

_{c}curves based on PFC method in HG Formation of NB Region, East China Sea.

**Figure 26.**Crossplots of R

_{wam}versus R

_{wav}(

**a**) and S

_{w}versus S

_{wf}(

**b**) that used to identify pore fluids in HG Formation of NB Region, East China Sea.

**Figure 27.**A field example of characterizing formation pore structure, calculating formation parameters and identifying pore fluids in HG Formation of NB Region.

**Table 1.**Establishment of rocks classification criteria based on MICP curves and physical properties in the Pinghu Formation of KQT Region.

Rock Type | Porosity (%) | Permeability (mD) | Median Pore Throat Radius (μm) | Median Pressure (MPa) | Maximum Pore Throat Radius (μm) | R35 (μm) | Threshold Pressure (MPa) | MICP Curve Morphology |
---|---|---|---|---|---|---|---|---|

I | 11.3~16.4 | 15.4~402.0 | 1.02~14.57 | 0.05~0.72 | 9.51~33.78 | 2.82~19.69 | 0.02~0.08 | Demarcation of large and small pore throat is obvious |

II | 10.0~18.9 | 1.41~8.14 | 0.44~1.48 | 0.50~1.67 | 1.36~6.99 | 0.78~2.18 | 0.07~0.49 | Demarcation of large and small pore throat is obvious |

III | 7.9~10.0 | 0.16~0.44 | 0.11~0.48 | 1.53~6.79 | 0.49~1.45 | 0.22~0.73 | 0.25~1.67 | Demarcation of large and small pore throat isn’t obvious |

Pore Fluid | R_{wam} (Ω.m) | R_{wav} (Ω.m) | S_{w} (%) | S_{wf} (%) |
---|---|---|---|---|

Hydrocarbon-bearing formation | Greater than 0.80 | Greater than 0.05 | Less than 60.00 | Less than 27.00 |

Hydrocarbon and water formation | 0.69~0.80 | Lower than 0.05 | 60.00~70.50 | 27.00~60.00 |

Water saturated layer | Lower than 0.69 | Lower than 0.05 | Greater than 70.50 | Greater than 60.00 |

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## Share and Cite

**MDPI and ACS Style**

Gao, F.; Xiao, L.; Zhang, W.; Cui, W.; Zhang, Z.; Yang, E. Low Permeability Gas-Bearing Sandstone Reservoirs Characterization from Geophysical Well Logging Data: A Case Study of Pinghu Formation in KQT Region, East China Sea. *Processes* **2023**, *11*, 1030.
https://doi.org/10.3390/pr11041030

**AMA Style**

Gao F, Xiao L, Zhang W, Cui W, Zhang Z, Yang E. Low Permeability Gas-Bearing Sandstone Reservoirs Characterization from Geophysical Well Logging Data: A Case Study of Pinghu Formation in KQT Region, East China Sea. *Processes*. 2023; 11(4):1030.
https://doi.org/10.3390/pr11041030

**Chicago/Turabian Style**

Gao, Feiming, Liang Xiao, Wei Zhang, Weiping Cui, Zhiqiang Zhang, and Erheng Yang. 2023. "Low Permeability Gas-Bearing Sandstone Reservoirs Characterization from Geophysical Well Logging Data: A Case Study of Pinghu Formation in KQT Region, East China Sea" *Processes* 11, no. 4: 1030.
https://doi.org/10.3390/pr11041030