1) Highly conductive fractures

Highly conductive fractures consist of mostly open structural fractures, columnar joints, and dissolution fractures. The direction or orientation of these fractures depends on the regional tectonic stress field, and pores and cavities are developed in as bead strings along fracture faces. In an FMI imaging chart, they show black sine curves or narrow stripes with multigroup characteristics and long extensions (Figure 6.3a, Table 6.1).

2) High-resistivity fractures

These fractures refer to early structural fractures and columnar joints, which are closed or filled with high-resistivity materials. In an imaging chart, they show white sine curves or narrow stripes with multigroup characteristics and long extensions (see Figure 6.3b, Table 6.1).

3) Microfractures

This group comprises blast fractures, contraction fractures, and weathering fractures with a limited extension, as well as structural fractures that are locally filled or closed. They serve primarily as connections between pores in the reservoir. In an FMI imaging chart, microfractures show black irregular lines or narrow stripes with a short extension, without any typical sine-curve or group characteristics. Therefore, these fractures usually do not fit the sine-curve theory (see Figure 6.3c, Table 6.1).

4) Drilling-induced fractures

These fractures are non-natural fractures generated during drilling and related to crustal stress. The fracture orientation follows the direction of the maximum horizontal principal stress. In the imaging chart, they show feathered or chevron-shaped black symmetrical curves (180 degrees) appearing along the sidewall with single-group characteristics and a long extension (see Figure 6.3d, Table 6.1).

1) Fracture identification based on lithological constraints and identification

Different types of major fractures are developed in different lithologies. Structural fractures and dissolution fractures are developed in all lithologies; contraction fractures occur mainly in effusive volcanic rocks; blast fractures occur in explosive volcanic rocks and near volcanic conduit facies; and sutured fractures occur in the hot base surge subfacies of explosive facies. Therefore, lithological constraints for fracture identification are established through lithological identification.

2) Identification of natural fractures through image logging

Natural fractures can be ultimately identified according to petrogenetic differences and the response characteristics of image logging and by determining the differences between natural fractures and geological features (e.g., layer interfaces, fault planes, shale stripes, bedding planes, rhyolitic structures, and hydraulic fractures):

1. Layer interface. This refers to the interface between two sets of formations. In an image logging chart, layer interfaces are marked by a group of nearly parallel conductivity anomalies. Compared with fractures, layer interfaces have the characteristic of uniform, continuous, and integral distribution, and they do not intersect each other. Usually there is a color transition between layer interfaces and formations (Figure 6.4a).

2. Shale stripes. Unlike fractures, the high conductivity anomalies of shale stripes are generally parallel, regular, and have clear boundaries. Even after severe tectonic deformation, the change in their widths will not be significant (Figure 6.4b).

3. Beddings. Beddings appear in groups within a certain range. In general, low-angle beddings are parallel to each other and demonstrate extremely good regularity between lines (Figure 6.4c).

4. Faults. There is displacement in the formations at both sides of fault plane, but there is no displacement in the fracture system (Figure 6.4d).

5. Rhyolitic structure. In an image logging chart, rhyolitic structures are deformed sine curve in shape with a visible disturbance trace, but the line is smooth. The long axis of elongated vesicles is aligned with the direction of magmatic flow (Figure 6.4e).

6. Perlitic structure. As the name implies, this is a unique structure for perlite and is marked by arcuate or concentric cracks; these cracks divide acidic volcanic glass into many small balls. In imaging logs, perlitic structure shows dark-colored, arcuate, or concentric lines under a high-resistivity background. Therefore, it can be easily distinguished from fracture zones (Figure 6.4f).

7. Heavy mud hydraulic fractures. These are the hydraulic fractures caused by the imbalance between drilling fluid and structural stress, resembling stress-release fractures, and generally developed in two to four groups (Figure 6.4g).

8. Scratches of drilling tools. These scratches are caused by the friction between drilling tools and the well sidewall, without sine-curve characteristics in the imaging chart, and their cutting depth is shallow (Figure 6.4h).

3) Classified pickup of natural fractures and induced fractures

On the basis of a clear understanding of the differences between natural fractures/induced fractures and other similar geological features, natural fractures and induced fractures are picked up in the classification process using special image logging interpretation software and the human-machine interaction approach. This lays the foundation for fracture parameter calculation and the evaluation of fracture development, fracture effectiveness, and fracture orientation.

1) Dual laterolog

A dual laterolog provides resistivity curves that reflect undisturbed formations and fracture-invaded zones.

In deep and shallow laterolog resistivity curves, open fractures result in a decrease in resistivity values and a difference between the deep and shallow laterolog resistivity values. Thus, high-angle fractures (dip angle > 75 degrees) have a positive separation (i.e., RLLD > RLLS (recorded laterolog shallow)), low-angle fractures (< 60 degrees) have a negative separation, and oblique fractures (60 ~ 75 degrees) have a small separation or no separation (see Table 6.2) [5,6].

In volcanic reservoirs, high-angle structural fractures are predominant. In dual laterolog curves, fracture-bearing intervals are characterized by decreased resistivity value, and positive separation between deep and shallow laterologs. Figure 6.5 is a crossplot of the surface porosity of fractures in cored intervals, which shows a difference between deep and shallow laterolog resistivity values [(RLLD−RLLS)/RLLD] in the XX gas field. This figure shows that the more developed the fractures (the greater the surface porosity), the smaller the RLLD, and the larger the RLLD−RLLS values. This implies that high-angle fractures are responsible for the decrease in resistivity and the increase in positive separation between deep and shallow laterolog resistivity values.

2) Acoustic log

There is no response for high-angle fractures in P-wave interval transit time curves. Instead, the response increases in low-angle fracture and network fracture intervals, and even “jumping cyclic waves” occur in these intervals. At the same time, fractures cause an increase in the acoustic travel time of S waves and Stoneley waves but a decrease in their amplitude. The amount of change is greater than that of P waves [5,7], and the velocity ratio (Δt_s/Δt_c) of P wave to S wave increases (see Table 6.2).

Figure 6.6 is the crossplot of surface porosity of fractures in the cored interval and the P-S ratio of acoustic travel time in the XX gas field. This figure demonstrates that the P-S ratio of acoustic travel time increases as the surface porosity of fractures increases, but it is affected by fluid properties.

3) Compensated density and compensated neutron logs

A compensated density log reflects the total porosity in rocks, whereas a neutron log detects the hydrogen content in formations. Fractured intervals have reduced density and increased neutron log values, but natural gas causes a decrease in both density and neutron values (see Table 6.2). Under identical conditions, therefore, the level of fracture development is determined with the direction of relative change in density and neutron log values [5,7].

4) Gamma spectrometry log

Fluid is more active in fractures than in matrix pores, which facilitates abnormal uranium enrichment and intensifies the radioactivity in formations [5,7]. The degree of fracture development can be determined by analyzing the uranium enrichment characteristics (see Table 6.2).

5) Caliper log

In dual- (or multiple-) caliper log curves, well radius enlargement and ROP change occur when the caliper detects an open fracture. The more developed the fracture, the more significant the caliper response. Therefore, an asymmetrical hole enlargement is the primary basis for fracture identification in dual-caliper (or multiple-caliper) log curves (see Table 6.2).

1) High-angle fractures

In conventional log curves, high-angle fractures commonly have a smooth box shape and are characterized also by moderate amplitude values and a large separation of deep and shallow laterologs, small interval transit time, high density, and significant neutron log values.

The brecciated lava reservoir interval in 3705 to 3744 m of Well XX8 is a typical example (Figure 6.7). Core description and imaging log identification information indicate that this interval has the characteristics of abundant vesicles and dissolution pores, good matrix properties, and its fractures are mostly high-angle structural fractures. Its conventional log curve shows a smooth box shape. Its average value of deep and shallow laterolog resistivity is 38 Ω·m and 21 Ω·m, respectively. The acoustic transit time is 71 μs/ft on average, with neutron porosity of 14% on average and rock density 2.32 g/cm³ on average. As the gas test in the studied interval shows, its natural production rate of natural gas is up to 23 × 10⁴ m³/d, its producing pressure differential is 8 MPa, and no water is produced. A short-period production testing for 30 days shows that the gas production rate was maintained at 15 × 10⁴ m³/d, the water production rate increased from 6.3 m³/d to 98 m³/d, and the water-gas ratio stabilized at 6.6 to 6.8 m³/10⁴ m³, implying that the water from the lower water zone has risen up into the gas zone along high-angle fractures.

2) Low-angle fracture

Low-angle fractures have a bayonet shape in conventional log curves, with low amplitudes in resistivity curves, a large negative separation between deep and shallow laterologs, large interval transit time, small density, and large neutron values.

The tuff-bearing volcanic brecciated reservoir in 3863 to 3866 m of Well XX5 is a typical example (Figure 6.8). Core description and imaging log interpretation indicate that a group of low-angle fractures (3 ~ 4) is developed in this interval. Conventional log curves show a bayonet shape. Their average values of deep and shallow laterolog resistivity are 44 Ω·m and 50 Ω·m, respectively, which are lower than those of the surrounding rocks. A negative separation is also observed. Their interval transit time is 64 μs/ft on average, and their neutron porosity has an average of 5%, which is slightly higher than that of the surrounding rocks. Their rock density has an average of 2.58 g/cm³, which is slightly lower than that of the surrounding rocks.

3) Network (netlike) fractures

These are formed by intercrossing fractures with various occurrence patterns, indicating a high degree of fracture development. In conventional log curves, the intervals with network fractures have serrated and box shapes and a low-amplitude resistivity curve. Whether deep and shallow laterologs show positive or negative separation depends on the occurrence of dominant fractures. Their interval transit time is long, neutron porosity is high, and the density is small.

The brecciated lava reservoir interval in 4108 to 4122 m of Well XX9 is a typical example (Figure 6.9). The imaging log indicates that this interval is rich in predominantly high-angle network fractures. Conventional log curves are serrated or box shaped. Their average value of deep and shallow laterolog resistivity is 230 Ω·m and 95 Ω·m, respectively, and a positive separation is observed. Their interval transit time has an average of 65 μs/ft, and their neutron porosity is 4% on average—higher than that of the surrounding rocks. Their rock density is 2.52 g/cm³ on average—lower than that of the surrounding rocks. As shown by the gas test in this interval, the natural production rate of natural gas is 0.33 10⁴ m³/d, and the water production rate is up to 5.96 m³/d.

4) Stress-release fractures

Stress-release fractures are developed mainly in tight intervals where tectonic stress is not easily released. In conventional log curves, they have a smooth box shape. They are characterized by a high amplitude resistivity curve, a small positive separation or no separation in deep and shallow laterolog resistivity, a short interval transit time, low neutron porosity, and high rock density values.

The dacite formation in 3980 to 3985 m of Well XX401 is a typical example (Figure 6.10). The imaging log indicates that this interval has abundant 180-degree symmetrical stress-release fractures. Its conventional log curve has a smooth bell shape. The average value of deep and shallow laterolog resistivity is 1452 Ω·m and 1244 Ω·m, respectively, and a small positive separation is observed, albeit larger than that of the surrounding rocks. Their interval transit time has an average of 52 μs/ft, and their neutron porosity is 3% on average—lower than that of the surrounding rocks. Their average rock density is 2.57 g/cm³—higher than that of the surrounding rocks.

1) Calculation methods

The calculation methods commonly used are as follows:

1. Secondary porosity method. In reservoirs dominated by high-angle fractures, the variation of interval transit time is small, whereas the rock density and neutron porosity are high. An indicator function that reflects the degree of high-angle fracture development is thus established:

$\mathrm{FPR}2={\mathit{\varphi }}_{\mathrm{ND}}-{\mathit{\varphi }}_{\mathrm{S}}$

  (6.2.1)

Where

ϕ_ND — neutron and density crossplot porosity (%);

ϕ_S — acoustic porosity (%).

2. Apparent pore structure index method. Fractures improve the flow pathways and electric conduction paths in reservoirs, and they cause the pore structure index to decrease. An indicator function that reflects the degree of overall fracture development is thus established:

${\mathrm{m}}^{*}=\left(\log \mathit{Rw}-\log \mathit{Rt}\right)/\log \mathit{\varphi }$

  (6.2.2)

Where

Rw — formation water resistivity (Ω·m);

Rt — original formation resistivity (Ω·m);

ϕ — matrix porosity (%).

3. Deep and shallow laterolog amplitude difference method. High-angle fractures cause an increase in the positive separation between deep and shallow laterolog resistivity. An indicator function that reflects high-angle fracture development degree is thus established:

$\mathrm{FLPL}=\left(\mathrm{RLLD}-\mathrm{RLLS}\right)/\mathrm{RLLD}$

  (6.2.3)

Where

RLLD — deep laterolog resistivity (Ω·m);

RLLS — shallow laterolog resistivity (Ω·m).

4. Uranium anomaly index method. Fractures provide the migration pathway for various fluids, which become more active than in the matrix. Formations with abundant fractures have higher enrichment of radioactive uranium. A fracture identification indicator function based on gamma spectrometry is established:

$\mathrm{FPU}=U/\mathit{Th}$

  (6.2.4)

Where

U — gamma spectrometry uranium curve (ppm);

Th — gamma spectrometry thorium curve (ppm).

5. Fracture probability function method. A comprehensive method of fracture probability function is established based on the preceding methods. This method will further amplify the log response of fractures and improve the congruence rate of fracture identification. The fracture probability function calculation formula is

$\mathit{FIDX}=\frac{W1\cdot \mathit{XFPR}2+W2\cdot {\displaystyle X_m}+W3\cdot \mathit{XFPU}+W4\cdot \mathit{XFLPL}}{W1+W2+W3+W4}$

  (6.2.5)

Where

XFPR2 — the normalized curve of FPR2;

Xm — the normalized curve of m*;

XFPU — the normalized curve of FPU;

XFLPL — the normalized curve of FLPL;

W1–W4—the weighted coefficients for XFPR2, Xm, XFPU, and XFLPL.

6. Fracture development exponential function method. To reduce artificial errors, a fracture development exponential function curve that semiquantitatively evaluates fracture development is further established:

$\mathrm{FID}2=\mathrm{AFD}2·\mathrm{FPR}2/{\mathrm{m}}^{*}$

  (6.2.6)

Where

AFD2—adjusting parameter, which is 100 herein.

2) Calculation results

A fracture indicative curve is established using the previously described methods. The relationship between the indicative curve and fracture parameters of FMI imaging logs is then determined. The adaptability of each method is analyzed here.

Calculation of fracture indicative curve using conventional logs

Secondary porosity (FPR2), the apparent pore structure index (m*), deep and shallow laterolog amplitude difference (FLPL), uranium anomaly index (FPU), fracture probability function (FIDX), and fracture development index (FID2) are calculated based on conventional logs using the preceding methods. Traces 8 to 13 in Figure 6.11 show that FPR2, m*, FIDX, and FID2 are generally consistent with the fracture development characteristics determined through image logging, and the correlation between FPU, FLPL, and imaging log interpretation results is poor. This implies a poor applicability or adaptability of the deep and shallow laterolog amplitude difference method and the uranium anomaly index method to the identification of fractures in volcanic reservoirs.

Applicability and adaptability

The applicability and adaptability of each method is analyzed by establishing the relationship between indicative curves and imaging log fracture parameters.

Based on calculated fracture indicative curves and the expression between each calculated curve and fracture parameters of the FMI imaging log, the adaptability of individual evaluation methods is analyzed.

In Well XX14, the thickness of volcanic rocks is approximately 400 m. Rhyolite, rhyolitic brecciated lava, rhyolitic tuffaceous lava, and rhyolitic volcanic breccia are encountered during drilling. Lithofacies include effusive facies, explosive facies, volcanic conduit facies, extrusive facies, and volcanic sedimentary facies. Therefore, this well can be regarded as highly representative of various lithologies. The calculation result of Well XX14 and analysis (Figure 6.12, Table 6.3) shows the following:

Table 6.3

Table of Adaptability Analysis of the Calculation Methods of Fracture Indicative Curves by Conventional Logs

Method	Analysis of Relationship with Fracture Hydrodynamic Width via Imaging Logs		Correlated Thickness	Lithology	Lithofacies
	Expressions	Rt
Secondary porosity method	y = 0.01ln(x) + 0.013	0.62	400 m	Rhyolite, breccia lava, tuffaceous lava, volcanic breccia	Effusive facies, explosive facies, volcanic conduit facies, extrusive facies
Pore structure index method	y = 0.22ln(x) + 3.193	0.62
Deep and shallow laterolog difference	y = 0.04ln(x) + 0.385	0.1
Uranium anomaly index method	y = 0.012ln(x) + 0.223	0.02
Fracture probability function method	y = 0.105ln(x) + 0.316	0.71
Fracture development index method	y = 0.703x0.346	0.73

1. The volcanic secondary porosity method. FPR2 increases with fracture development and correlates fairly well with the hydrodynamic width of fractures determined via imaging logs (Figure 6.12c), showing a good applicability and adaptability for this method.

2. The apparent pore structure index method. m* decreases with the degree of fracture development and correlates fairly well with the hydrodynamic width of fractures determined via imaging logs (Figure 6.12d), also indicating a good applicability of this method.

3. The deep and shallow laterolog difference method. FLPL increases with high-angle fracture development and correlates poorly with the hydrodynamic width of fractures determined on the basis imaging logs (Figure 6.12e); this method is highly affected by the variation of lithology, induced fractures, and fluid type, indicating poor applicability.

4. The uranium anomaly index method. FPU increases with fracture development and correlates poorly with fracture hydrodynamic width determined via FMI imaging logs (Figure 6.12f); this method is highly affected by the variation of lithology and sedimentary environment and thus is of poor applicability.

5. The fracture probability function method. FIDX increases with fracture development and correlates fairly well with fracture hydrodynamic width determined via imaging logs (Figure 6.12a); it shows somewhat improved results compared with single methods and offers good applicability and adaptability.

6. The fracture development index method. FID2 increases with fracture development and correlates fairly well with the fracture hydrodynamic width determined from imaging logs (Figure 6.12b); it has been improved somehow compared with single methods and offers good adaptability.

Among these six evaluation techniques, the methods based on deep and shallow laterolog difference and uranium anomaly index are shown to have a poor applicability or adaptability due to the impact of such factors as lithological change, induced fractures and fluid type variation; they are mainly suitable for qualitative analysis of volcanic reservoirs with stable lithology and significant difference of fluid activity. The other four methods offer a good applicability and adaptability and can be used to semiquantitatively evaluate the degree of fracture development.

3) Parameter characteristics of fracture indicative curve in volcanic rocks

In the XX gas field, the calculation results of several wells have been statistically analyzed, and the results can be summarized as follows (Table 6.4): secondary porosity (FPR2) is between 0.009% to 0.082% with an average value of 0.048%, which means that the secondary action in volcanic reservoirs is not strong; the apparent pore structure index m* ranges between 1.2 to 3.8 with an average value of 2.3; the fracture probability function (FIDX) ranges between 0.32 to 0.97 with an average value of 0.67; and the fracture development index (FID2) ranges between 0.3 to 5 with an average value of 2.5.

In this study, fracture density (FVDC) refers to the linear density, which is defined as the number of fractures per unit length (1 m) of the sidewall (unit: 1/m). Fracture density parameters are generally calculated from the fracture pickup in the acoustic or electric imaging chart. Other methods for fracture density calculation carry various degrees of uncertainty [9].

Fracture length (FVTL) is defined as the total fracture length per unit area (m²) of the sidewall (unit: m/m² or 1/m). It is statistically determined by special software based on fracture identification.

2) Fracture width

Fracture width refers to the opening width of a fracture along the normal direction. It can be determined by acoustic/electric imaging and conventional logs.

The calculation method based on FMI imaging logs

Fracture width is generally smaller than the resolution of microresistivity image logging, which cannot be read directly. Instead, it has to be calculated indirectly on the basis of fracture color representation in the imaging log chart [10], and it is calculated using the following formula:

$\epsilon =a{\displaystyle {\mathit{AR}}_{\mathit{xo}}^{1-b}}{\displaystyle R_m^b}$

  (6.3.1)

Where

ɛ — width of a single fracture (mm);

a, b — constants related to instruments, wherein b is close to zero;

A — the area of conductivity anomaly (mm²) caused by fracture;

R_xo, R_m — resistivity values of invaded zone and drilling fluid (Ω·m).

The width of fractures is different in a different part of the reservoir. Fracture width can be determined by one of the two methods according to the result of point-by-point calculation:

1. The average fracture width (FVA), which is defined as the average value of all the fracture trajectory widths per unit well interval (1 m)

2. The average hydrodynamic width of the fracture (FVAH), which is defined as the cube and extraction of cubic root of fracture trajectory widths per unit well interval (1 m), which can be regarded as a fitting for the fracture hydrodynamic effect

The calculation method based on conventional logs

Before acoustic or electric imaging log was invented, Sibbit and colleagues provided a method for fracture width calculation with a dual laterolog resistivity curve [6]. This technique first requires the judgment of fracture occurrence, followed by the following parameter calculations, respectively:

$\mathrm{High}‐\mathrm{angle}\mathrm{fractures}:\epsilon =2.50\times {\displaystyle {10}^3}\times \left({\displaystyle C_s}-{\displaystyle C_d}\right)/{\displaystyle C_m}$

  (6.3.2)

$\mathrm{Low}‐\mathrm{angle}\mathrm{fractures}:\epsilon =8.33\times {\displaystyle {10}^2}\times \left({\displaystyle C_d}-{\displaystyle C_b}\right)/{\displaystyle C_m}$

  (6.3.3)

Network fractures: first determine the width of high-angle and low-angle fractures, respectively, and then sum them up,

Where

ɛ — fracture width (μm);

C_d, C_s, C_m — conductivity values of deep laterolog, shallow laterolog and mud (mS/m);

C_b— matrix conductivity (mS/m) can be read from tight intervals near the interpreted layer.

3) Fracture porosity

Fracture porosity is calculated with an acoustic/electric imaging log and a conventional dual laterolog:

1. The calculation method based on the FMI imaging log. For FMI imaging logs, fracture porosity (FVPA) is defined as the apparent opening area of fractures per unit area of coverage in imaging chart (unit: cm²/cm²), calculated using the following formula:

$\mathrm{FVPA}=\mathrm{FVA}·\mathrm{FVTL}\times 400/\left(\mathrm{\pi }·{\mathrm{CAL}}^2\right)$

  (6.3.4)

Where

FVPA — fracture porosity (cm²/cm²);

FVA — average fracture width (cm);

FVTL — fracture length (m);

CAL — well radius (cm).

2. The calculation method based on conventional logs. Fracture porosity is calculated with a dual laterolog curve using the following formulae:

$\mathrm{Water}\mathrm{layer}:{\mathit{\varphi }}_{\mathrm{f}}=\sqrt[{\displaystyle m_{\mathrm{f}}}]{\left({\displaystyle C_s}/{\displaystyle K_{\mathrm{r}}}-{\displaystyle C_d}\right)/\left({\displaystyle C_m}-{\displaystyle C_{\mathrm{w}}}\right)}$

  (6.3.5)

$\mathrm{Oil}/\mathrm{gas}\mathrm{layer}:{\mathit{\varphi }}_{\mathrm{f}}=\sqrt[{\displaystyle m_{\mathrm{f}}}]{\left({\displaystyle C_s}/{\displaystyle K_{\mathrm{r}}}-{\displaystyle C_d}\right)/{\displaystyle C_m}}$

  (6.3.6)

Where

ϕ_f— fracture porosity (fraction);

C_w— formation water conductivity (mS/m);

m_f— fracture pore structure index, which is related to width variations and the bending of a fracture, typical range 1 to 1.3;

K_r— fracture’s influence coefficient on shallow laterolog resistivity, which is related to fracture occurrence and development degree; typical range 1.1 to 1.3; values of 1.3 to 1.5 for reservoirs with poor fracture development.

4) Fracture permeability

Fracture permeability is divided into two types. The first type, referred to as intrinsic fracture permeability, only takes into account the conductivity of fracture for fluid flow, ignoring the condition of surrounding rocks. It is mainly affected by the fracture surface, the fluid flowing direction, and the intrinsic characteristics of fractures. Its typical expression is

${\displaystyle K_{\mathit{if}}}=\frac{1}{12}\left({\displaystyle {cos}^2}\alpha {\displaystyle \sum _{i=1}^{{\displaystyle N_{\alpha }}}{\displaystyle d_i^2}}+{\displaystyle {cos}^2}\beta {\displaystyle \sum _{i=1}^{{\displaystyle N_{\beta }}}{\displaystyle d_i^2}}+\cdots \right)$

  (6.3.7)

For the second type, known as fracture permeability of fractured reservoirs, the fracture and its surrounding rocks are treated as a whole hydrodynamic unit. This permeability is related to the degree of fracture development and the connection between fracture and matrix pores, calculated using the following formula:

${\displaystyle K_{\mathrm{f}}}={\displaystyle K_{\mathit{if}}}\times {\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}$

  (6.3.8)

Based on fracture occurrences and their combination types, the fracture permeability is calculated based the following three models:

$\left\{\begin{array}{l}\mathrm{Single}\mathrm{group}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=8.5\times {\displaystyle {10}^{-4}}{\displaystyle d^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}\\ \mathrm{Multigroup}\mathrm{vertical}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=4.24\times {\displaystyle {10}^{-4}}{\displaystyle d^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}\\ \mathrm{Netlike}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=5.66\times {\displaystyle {10}^{-4}}{\displaystyle d^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}\end{array}\right.$

  (6.3.9)

Where

K_if, K_f — the intrinsic permeability of fractures, fracture permeability (mD);

d_i, d — width of the i-th fracture, average fracture width (μm);

α, β — the angle of a fracture and fluid flowing direction (°);

n_α, n_β — number of fractures in fracture group that form α and β angles with the fluid flowing direction (fractures);

ϕ_f — fracture porosity (fraction).

The calculation result of Formula 6.3.9 represents the sidewall fracture permeability [10], where the radial extension characteristics and bending degree of the fracture are not reflected. To better reflect the reservoir fracture permeability, Formula 6.3.9 is improved as follows:

$\left\{\begin{array}{l}\mathrm{Single}‐\mathrm{group}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=8.5\times {\displaystyle {10}^{-4}}{\displaystyle {\mathit{Rd}}^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}/{\displaystyle m_{\mathrm{f}}}\\ \mathrm{Multigroup}\mathrm{vertical}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=4.24\times {\displaystyle {10}^{-4}}{\displaystyle {\mathit{Rd}}^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}/{\displaystyle m_{\mathrm{f}}}\\ \mathrm{Netlike}\mathrm{fractures}:{\displaystyle K_{\mathrm{f}}}=5.66\times {\displaystyle {10}^{-4}}{\displaystyle {\mathit{Rd}}^2}{\displaystyle {\mathit{\varphi }}_{\mathrm{f}}}/{\displaystyle m_{\mathrm{f}}}\end{array}\right.$

  (6.3.10)

Where

R — fracture radial extension coefficient.

When a the radial extension of a fracture is greater than 2 to 3 m, the fracture is approximately of infinite extension (R = 1); when its extension is 0.5 to 2 m, it is of medium extension (R = 0.8); when its extension is 0.3 to 0.5 m, it is of shallow extension (R = 0.4); and when its extension is less than 0.3 m, it is of extremely shallow extension (R = 0);

The m_f value refers to the structural characteristics index of the fracture, which reflects the fracture width and the degree of bending. For wide fractures, m_f = 1.0; for narrow fractures, m_f = 1.3. The greater the m_f value, the less a fracture contributes to permeability.

1) The fundamental principle

At a certain angle between the direction of particle vibration caused by the S wave and the fracture strike, the so-called S-wave splitting will occur—that is, the incident S wave splits into a fast S wave and a slow S wave, which have particles parallel and perpendicular to the fracture strike, respectively, vibrating and propagating upward along the borehole axis and traveling at different velocities. In fractured volcanic formations, therefore, the S-wave velocity of the dipole sonic imaging (DSI) log generally shows obvious azimuthal anisotropy. The S-wave anisotropy of the formation is measured by the orthogonal dipole technique. Stress-release fractures, other fractures, and faults are identified, and their strikes are evaluated tentatively by parameters such as energy-percentage anisotropy (OffEne), acoustic travel time anisotropy (SLOANI), and time-based anisotropy (TIMANI).

2) The evaluation method

Figure 6.20 is an example of fracture effectiveness evaluation through the integrated use of DSI anisotropy and the FMI imaging chart. In the left chart, the third trace shows the velocity and energy-percentage anisotropy of fast and slow S waves; the fourth trace shows the azimuth and error of fast and slow S waves. This chart demonstrates that this reservoir section has very strong anisotropy and a wide range of variation in fast S-wave azimuth, implying that the phenomenon causing such anisotropy has multiple distribution azimuths. In the FMI imaging log chart, the anisotropy is caused by multiple high-angle fractures of different azimuths, and both the width and extension range of fractures are quite large, suggesting that these are effective fractures. The right chart shows just the opposite. The fractures shown in the FMI imaging log chart have a small width with limited extension, thus being ineffective fractures. The anisotropic characteristics shown in the DSI log are inconspicuous.

Many factors affect rock anisotropy, including variations in lithology, directivity and changes in rock texture and porous structure, and lineation and distribution of rock constituents. On the basis of acoustic anisotropic analysis and other log data, therefore, the uncertainty of evaluation can be reduced through an integrative interpretation of fracture effectiveness.

1) Definition of core coordinates

As shown in Figure 6.22, a standard XYZ coordinate system is established as follows: first, mark a line through the center of a circle, which is the cross section of the core column; this line is parallel with a group of fractures, and it is defined as the x-axis (the virtual north direction); second, drawing a line along the length of the core as the z-axis. Then, extract a minicore 25 mm in diameter along the direction of the marked line (x-axis), and establish a corresponding coordinate system xyz in this tiny core. Therefore, the corresponding relationship between these two coordinate systems is

$\left\{\begin{array}{l}X=-z\\ Y=y\\ Z=x\end{array}\right.$

  (6.3.11)

The occurrence of the fracture face within the XYZ coordinate system is known. The geographic coordinates of the tiny core sample can also be determined through measurements. The fracture occurrences data within the geographic coordinate system can be determined using this coordinate conversion formula.

2) Measuring the direction of magnetization of minicore sample

The magnetism that volcanic rocks obtained during a rock’s cooling moment is called the characteristic remanence (ChRM), which records the direction of the geomagnetic field when the rock was formed. The direction of the geomagnetic field when the volcanic rocks were formed can be determined by measuring the direction of their characteristic remanence. Once the characteristic remanence has been formed, it may decrease due to viscous demagnetization, or it may increase due to viscous remanence (VRM, which refers to the new intensity of magnetization continuously obtained below the Curie temperature). The ultimate direction of viscous remanence (which accounts for approximately 50% of the natural remanence) is consistent with the direction of the present geomagnetic field. Therefore, the direction of the present geomagnetic field (i.e., the present geographic direction) can be determined on the rock specimen through measurement of the direction of viscous remanence [14,15].

Viscous remanence can be erased under low-temperature demagnetizing conditions. Thermal demagnetization can be carried out at 12 temperature levels (i.e., 100° C, 150° C, 200° C, 250° C, 300° C, 350° C, 400° C, 450° C, 500° C, 530° C, 550° C, and 570° C). Each of the low-temperature components obtained through step-by-step thermal demagnetization below 300° C represents the direction of later viscous remanence, while each of the high-temperature components obtained above 300°C represents the direction of characteristic remanence. Figure 6.23 shows the demagnetization analysis of a core sample from the depth of 3100 m in Well XXSG2. Its natural remanent magnetization is 306 mA/m, which shows a uniform decrease from the demagnetization intensity of NRM –250° C to 70% of natural remanent magnetization, indicating approximately a viscous remanence demagnetization vector of NE 30 degrees. Beyond 300° C, as the demagnetization temperature rises, the remanent magnetization decreases gradually until it reaches 570° C when the remanent magnetization attenuates to 0.3 mA/m, indicating that the overall demagnetization direction of characteristic remanence remains at approximately NW 317 degrees with a dip angle of 61 degrees. This indicates that the direction of the magnetic field was NW 317 degrees when the volcanic rock was formed, whereas the direction of the present geomagnetic field is NE 30 degrees and the fracture direction is aligned largely toward the NE.

1) Coherence calculation method

The calculation method for seismic coherence is simple, using the following formula to calculate the correlation coefficient on the basis of the number of traces, the dip angle, and the time window of the given data volume:

$R\left(t,{\displaystyle {\mathit{\varphi }}_{max}}\right)=\frac{{\displaystyle \sum _{L=t-N/2}^{L=t+N/2}{\displaystyle T_L}{\displaystyle T_{L+\mathit{\varphi }}^{\prime }}}}{{\displaystyle \sum _{L=t-N/2}^{L=t+N/2}{\displaystyle T_L^2}{\displaystyle {T^{\prime }}_{L+\mathit{\varphi }max}^2}}}$

  (6.4.1)

Where

R — coherence coefficient, which is a function of the time of seismic trace and the dip angle between two seismic traces;

t — time;

φ — dip angle, which is affected by azimuth and is not easily to be determined;

T, T′— seismic trace data pair.

The number of coherent traces involved in the calculation includes linear 3-trace, orthogonal 3-trace, orthogonal 5-trace, and orthogonal 9-trace. A greater number of traces will lead to a greater averaging effect. Multitrace coherence is used mainly to highlight major faults. In contrast, fewer coherent traces lead to a smaller averaging effect. Coherence of fewer traces is suitable for identifying minor faults or fracture zones. Selection of the coherent time window typically depends on the apparent period t of reflection waves in the seismic profile. Its value is usually in the range of t/2 to 3 t/2.

2) Prediction of fracture distribution using coherence analysis technique

Figure 6.32 shows the T580-line migration profile, coherence profile, and T713-line coherence profile of the XX gas field. It demonstrates that the location in the migration profile with an event offset shows poor-coherence stripes in the coherence profile, whereas the location with good event continuity shows good coherence in the coherence profile. The area near Well XX602 with good coherency shows white stripes in the coherence profile, where fractures or faults are undeveloped, and the gas test confirms dry layers; the area near Well XX1 with poor coherency shows black irregular stripes in the coherence profile, where fractures or faults are developed, and the gas test shows commercial gas layers. This confirms that the coherence analysis technique can be used to identify fractured zones. However, the coherent data anomaly caused by lithological changes or poor data quality must be identified.

1) Instantaneous amplitude (A)

Instantaneous amplitude reflects the energy level of seismic reflection waves. The presence of pores, cavities, and fractures in reservoirs causes a decrease in reservoir velocity, reflection coefficient, and amplitude and energy of the reflection waves. Figure 6.34 demonstrates the presence of a low-amplitude areas in the southwest of Well Blocks XXS4 to XXS2-1, the east of Well XXS101, and the southeast of Well XXS2, which are in agreement with the poor-coherence area in the coherence analysis and the strong absorption area in the absorption coefficient analysis.

2) Instantaneous phase (Q)

The instantaneous phase reflects the continuity of seismic reflection waveforms. In terms of seismicity, minor faults and zones of pores, cavities, and fractures are characterized by event offsets, chaos, discontinuities, the increased number of event, and so on. In Figure 6.35, the areas of the chaotic instantaneous phase are mainly located in regions near Wells XXS4 to XXS2-1, Wells XXS to XXS2-25, west of Well XXS101, and near Well XXWS3. This is slightly different from the coherence areas and strong absorption areas.

3) Instantaneous frequency (F)

A rapid change in seismic wave frequency is related to factors such as stratigraphic pinch-outs and oil-gas-water interfaces. The presence of fractures in reservoirs causes the reservoir reflection coefficient sequence to change, which also results in abrupt changes in the instantaneous frequency, which is mainly reflected by the decrease of the instantaneous frequency. In Figure 6.36, areas of relatively low instantaneous frequency are mainly located in regions near Wells XXS1-1 to XXS2-7, north of Well XXS4, east of Well XXS101, and south of Wells XXS2-25 to XXS201. These correspond well with the poor-coherence areas and strong absorption areas.

1) Methods for calculating absorption coefficient

Under low-frequency conditions, when the seismic wave propagates in viscoelastic media, the absorption coefficient can be expressed with the following formula:

$\alpha \approx \frac{1}{2}\frac{{\eta }^{\prime }{\displaystyle {\omega }^2}\sqrt{\mathit{\rho }}}{{\displaystyle {\left(\lambda +2\mu \right)}^{3/2}}}=\frac{1}{2}\frac{{\eta }^{\prime }{\displaystyle {\omega }^2}\sqrt{\mathit{\rho }}}{{\displaystyle {\left(\kappa +4/3\mu \right)}^{3/2}}}$

  (6.4.2)

Where

α — absorption coefficient;

η′— viscosity coefficient of viscoelastic media;

ω — circular frequency (Hz);

ρ — rock density (g/cm³);

κ — elastic modulus of rocks (N/m²);

λ, μ — lame coefficient.

The absorption coefficient is related to the rock density, elastic modulus, viscosity coefficient, and the seismic wave’s frequency. Assuming that c is a constant in viscosity coefficient η′ = c/ω and that P-wave velocity ν is used in place of the elastic coefficient, then the absorption coefficient can be simplified as follows:

${\displaystyle {\alpha }_e}\approx \frac{c}{2}\frac{1}{\mathit{\rho }{\displaystyle {\nu }^3}}$

  (6.4.3)

Therefore, the effective absorption coefficient is inversely related to the cube of wave velocity. In other words, the sensitivity of the absorption coefficient in reflecting seismic anomalies far exceeds that of velocity, thus making it feasible to use the absorption analysis technique to predict fractures.

2) Prediction of fractures using absorption coefficient analysis method

There are two types of absorption coefficients: absolute absorption coefficient and relative absorption coefficient. Relative absorption coefficient refers to the absolute absorption coefficient divided by the background absorption coefficient, which highlights seismic energy absorption anomaly areas to better reflect the heterogeneity of geological bodies and as such is widely used to predict fractures.

Figure 6.37 is the planar distribution diagram of the absorption coefficient on the top surface of YC3I in Well Block XXS2-1, in which strong absorption areas are located mainly near Wells XXS2-6 to XXS2-1 and XXS2-17 to XXWS3; favorable reservoirs proven by drilling are mostly located in areas marked by high absorption coefficient values. This implies that the absorption coefficient method is suitable for predicting fractures in volcanic reservoirs.

1) VVA technique

The VVA technique identifies fractures with the characteristics of reflection wave velocity that changes with the incident azimuth. As shown in Figure 6.41, the P-wave velocity of the HTI medium is [26,27]

${\displaystyle V_{p0}}\left(i,\mathit{\varphi }\right)=\alpha \left[1+{\displaystyle {\delta }^{\left(\nu \right)}}{\displaystyle {sin}^2}{\displaystyle i{\cos }^2}\mathit{\varphi }+\left({\displaystyle {\epsilon }^{\left(\nu \right)}}-{\displaystyle {\delta }^{\left(\nu \right)}}\right){\displaystyle {sin}^4}{\displaystyle i{\cos }^4}\mathit{\varphi }\right]$

  (6.4.4)

Where

i — incident angle;

α — p-wave velocity during vertical incidence;

δ^(v), ε^(v)— Thomsen parameters of the HTI medium;

ϕ — azimuth, which is the angle between the ray plane (i.e., the source-receiver azimuth) and the HTI medium’s axis of symmetry.

From Formula 6.4.4, for horizontal fractures, ϕ = 90 degrees and V_p0 = α, where the V_p0 value is the maximum.

For vertical fractures,

$\varphi =0°\mathrm{and}{\displaystyle V_{p0}}=\alpha \left(1+{\displaystyle {\delta }^{\left(\nu \right)}}{\displaystyle {sin}^2}{\displaystyle i{\cos }^{2}i}+{\displaystyle {\epsilon }^{\left(\nu \right)}}{\displaystyle {sin}^{4}i}\right)$

where the V_p0 value is the minimum; and the azimuth and velocity between them range between these two values.

When directional vertical fractures are present in the formation, the velocity along different azimuths will show an ellipse: the velocity is the maximum when it propagates along the fracture strike. The velocity is the minimum when the propagation is perpendicular to the fracture strike. Mallick, Craft, and colleagues believe that the long axis direction of the azimuthal ellipse represents the fracture strike and the ellipticity represents the fracture density.

2) AVA technique

AVA refers to the change of amplitude with azimuth. The AVA technique identifies fractures based on the characteristics of reflection amplitude that change with incident azimuth. Rüger provided a P-wave reflection coefficient formula for HTI media [26,27]:

$\begin{array}{l}{\displaystyle R_p}\left(i,\mathit{\varphi }\right)=\frac{1}{2}\frac{\Delta Z}{\overline{Z}}+\frac{1}{2}\left\{\frac{\Delta \mathit{\alpha }}{\overline{\alpha }}-{\displaystyle {\left(\frac{2\overline{\beta }}{\overline{\alpha }}\right)}^2}\frac{\Delta G}{\overline{G}}+\left[\mathrm{\Delta }{\displaystyle {\delta }^{\left(\nu \right)}}+2{\displaystyle {\left(\frac{2\overline{\beta }}{\overline{\alpha }}\right)}^2}\Delta \mathit{\gamma }\right]{\displaystyle {cos}^2}\mathit{\varphi }\right\}{\displaystyle {sin}^2}i\\ +\frac{1}{2}\left[\frac{\Delta \mathit{\alpha }}{\overline{\alpha }}+\mathrm{\Delta }{\displaystyle {\mathit{\epsilon }}^{\left(\nu \right)}}{\displaystyle {cos}^4}\mathit{\varphi }+\mathrm{\Delta }{\displaystyle {\mathit{\epsilon }}^{\left(\nu \right)}}{\displaystyle {sin}^2}\mathit{\varphi }{\displaystyle {cos}^2}\mathit{\varphi }\right]{\displaystyle {sin}^{2}i}{\displaystyle {tan}^{2}i}\end{array}$

  (6.4.5)

From the preceding discussion, it can be concluded that the P-wave reflection coefficient of the HTI medium is related not only to the P-wave velocity, S-wave velocity, shear modulus, and Thomsen anisotropy parameters δ and ɛ, but also to the incident azimuth and incident angle. Rüger believes that for a large fixed incident angle, the change of the HTI medium’s P-wave reflection coefficient with incident azimuth shows elliptical characteristics, the ellipticity being proportional to fracture density, and the long axis azimuth of the ellipse representing the fracture azimuth [26,27].

3) FVA technique

The seismic scattering theory for fractured reservoirs suggests that the seismic wave’s high-frequency attenuation caused by fractures results in the anisotropy of the seismic reflection frequency. The FVA technique detects fractures by the azimuthal anisotropy of 3D P-wave frequency attributes. Like VVA and AVA, the long axis direction of the ellipse of frequency changes with the azimuth and represents the fracture strike, and the ellipticity represents the anisotropic intensity of the frequency, which is related to the density of open fractures.

The frequency attributes related to attenuation mainly include the following: (1) the maximum amplitude frequency (i.e., the frequency corresponding to the maximum amplitude) is related to the fluid—the greater the seismic wave attenuation, the lower the frequency; (2) the frequency corresponding to 85% of seismic energy (i.e., the corresponding frequency when the energy in the analysis time window reaches 85% of total energy; Figure 6.42) is related to fluid properties—the greater the seismic wave attenuation, the smaller the frequency value; and (3) the frequency attenuation gradient refers to the intensity of frequency attenuation within unit distance (or time) and reflects the absorption of P-wave propagation by the strata—the stronger the strata’s absorption, the greater the gradient value.

1) Forward modeling

Forward modeling is an important approach for building petrophysical models and analyzing the seismic anisotropic response characteristics of the models, which is the basis for predicting fractures with prestack seismic data.

HTI media are formed in volcanic reservoirs where vertical fractures are developed, and five independent elastic coefficients are needed to describe the anisotropic characteristics. Random anisotropic media will be formed by stratum inclination caused by tectonic movement, and 21 elastic coefficients are needed to describe the anisotropy. On the basis of the fractured reservoir geological model and elastic media model, and using rock P-wave velocity, S-wave velocity, and density parameters, the prestack forward model is built to calculate the elastic tensor and anisotropy-equivalent Thomsen indices, to calibrate the response of prestack seismic reflection along individual azimuths, and to determine the relationship between seismic reflection amplitude and fractures. The calculation results provide seismic responses to fractures at near-borehole seismic traces, including prestack amplitude variation with offset (AVO) characteristics, prestack AVO characteristics of individual azimuths, and the changes in AVO characteristics with azimuth influenced by fractures.

Figure 6.43 shows the results of prestack forward modeling for Well XX5 at different incident angles. The designed fracture direction is true north, where the azimuth is 0 degrees toward the true east direction. The first trace in the diagram is the gamma curve. The second trace shows synthetic traces and seismic records. For the third trace, the upper section simulates how the reflection amplitude of volcanic reservoirs changes with the changing incident angle with different azimuths, and the lower section is the amplitude ellipse simulated by reflection amplitudes of individual azimuths at different incident angles. Figure 6.43 demonstrates the following:

1. When the incident angle is small, it is equivalent to the vertical incidence of seismic waves, where the reflection amplitude of various azimuths has no difference; the larger the incident angle, the bigger the difference. Therefore, prestack fracture detection requires data acquired using large incident angles (i.e., large offsets).

2. With a fixed azimuth, the amplitude of the reflection wave is the maximum when it is perpendicular to the fracture direction (an incident angle of 0 degrees), decreases as the incident angle increases, and becomes the minimum when it is parallel to the fracture direction (90 degrees).

3. The difference between reflection amplitudes at various azimuths increases with the incident angle, and likewise the ellipticity of reflection amplitudes increases with the incident angle. When the incident angle is ≤ 3 degrees, the ellipticity is 1. At an incident angle of 12 degrees, the ellipticity is 1.006. When the incident angle reaches 24 degrees, the ellipticity is 1.026. At an incident angle of 27 degrees, the ellipticity is 1.033.

The incident angle in the target layer of the field survey system in the XX gas field is between 2 degrees and 13.5 degrees, without significant azimuthal differences. The requirements of prestack fracture detection in processing must be ensured as much as possible.

2) Prestack subazimuth processing of fractures

Prestack subazimuth processing of fractures is an important part of prestack fracture detection. The processing procedure is as follows.

Subazimuth processing

Subazimuth processing is the most important step in prestack fracture detection. It is affected by uneven azimuth distribution, survey system offset, and the raw data interval times. On the basis of the actual situation in the XX gas field, the azimuth division scheme is determined by the method of azimuth division with unequal spacing (Table 6.6). At the same time, the range of offset is restricted at 200 to 1600 m, for the following reasons: (1) near-offset data come from near-vertical incident seismic waves and cannot reflect the azimuthal AVO characteristics of the fracture media; (2) the azimuth distribution or seismic data volume offsets are uneven, with unequal azimuth being used for division and uniformization processing being performed in bins; and (3) the bin cover times cannot be too large because some bins will have to take a detour far away, but the cover times should not be too small either because the stack quality will deteriorate. It is generally appropriate to use the cover times of 25.

Table 6.6

Azimuth Division Table

Range of azimuth/(degrees)	0 ~ 41.4	41.4 ~ 68	68 ~ 90	90 ~ 112.3	112.3 ~ 138.6	138.6 ~ 180
Average azimuth/(degrees)	20.7	54.7	79	101.2	125.5	159.3

Figure 6.44 is the processed profile of different attributes at different azimuths, and the results of subazimuth processing show that the structures have a normal shape, and the signal-to-noise ratio (SNR) and resolution satisfy the fracture detection requirements.

3) Prestack fracture prediction methods

Method selection

The application of various methods on the volcanic rock reservoirs of the XX gas field within the 0 to 20 ms time window range produced four types of distribution maps of anisotropic intensities (Figure 6.45). Among these, the warm tones indicate a strong anisotropic intensity and highly developed vertical fractures, and cold tones indicate a weak anisotropic intensity and less developed vertical fractures. The correlation analysis of fracture characteristics of the drilled target layer (Table 6.7) indicates that among the four attributes, the “quantile frequency of seismic energy” offers the highest congruence rate of up to 80%, and the remaining three methods are relatively poor, with a congruence rate of 60%. Therefore, the “quantile frequency of prestack seismic energy” attribute is selected for predicting fracture development characteristics of volcanic reservoirs.

Table 6.7

Table of Matching Information on Fracture Development in the Upper Interval of Cycle I in Volcanic Rocks of the XX Gas Field within a 0- to 20-ms Time Window

Well Name	Fracture Density/(Fractures/M)	Quantile Frequency of Seismic Energy	Attenuation Gradient	Dominant Frequency	Amplitude
601	4.5	Match	Unmatch	Unmatch	Unmatch
XX1	1.9	Match	Unmatch	Match	Unmatch
XX6	4.45	Match	Match	Match	Match
XX5	0	Match	Match	Match	Match
XX502	3.7	Fair match	Match	Unmatch	Match

Fracture prediction

On the basis of prestack subazimuth processing of seismic data and the changes in quantile frequency of seismic energy with azimuth, the volcanic rock fracture development and orientation in target layers are predicted horizontally.

Figure 6.46 shows the following results of fracture prediction in the research area. Figure 6.46a illustrates the magnitude of ellipticity of the azimuthal ellipse for the “quantile frequency of seismic energy” attribute, where warm tones indicate a large ellipticity and a high fracture density, and cold tones depict a small ellipticity and a low fracture density. Figure 6.46b shows the result of directional rose-diagram statistics within the elliptical space of the same attribute. This result indicates the azimuth of fractures, and the size of the statistical grid is 100 m × 100 m. In this figure, the fault trends represented by black polygons are predominantly NNW and secondarily NNE; fractures are mostly developed to the left of faults along the NNW direction, and the fracture direction is mostly EW and NNW.

4) Analysis of controlling factors

The major controlling factors in prestack fracture prediction include the following.

1) The relationship between fracture index RTC and wave impedance

The dual laterolog resistivity is fairly sensitive to fractures. On the basis of crossplot analysis of wave impedance versus deep and shallow laterolog resistivity values (Figure 6.47), the conversion formula fitting wave impedance to resistivity is obtained:

$\mathit{RLLD}=0.043{\displaystyle e^{0.0006\mathrm{Im}}}$

  (6.4.6)

The formula converting deep laterolog to shallow laterolog is obtained through statistics:

$\mathit{RLLS}=-3.853\times {\displaystyle {10}^{-5}}{\displaystyle {\mathit{RLLD}}^2}+0.916\mathit{RLLD}+4.234$

  (6.4.7)

The formula converting deep/shallow laterolog to fracture index RTC is as follows:

$\mathit{RTC}=\left(2.589\mathit{RLLD}-1.589\mathit{RLLS}\right)/\mathit{RLLS}$

  (6.4.8)

Where

RLLD, RLLS — deep laterolog resistivity, shallow laterolog resistivity, (Ω·m);

Im — wave impedance [(g/cm³) · (m/s)];

RTC — fracture index; the larger the RTC value, the more developed the high-angle structural fractures.

2) The relationship between fracture development index FID2 and wave impedance

The degree of fracture development is positively correlated with the fracture development index but inversely correlated with wave impedance. Correlation analysis (Figure 6.48) indicates that there is a negative linear relationship between fracture development index FID2 and wave impedance:

$\mathit{FID}2=7.82-0.0004\mathrm{Im}$

  (6.4.9)

Where

FID2 — fracture development index;

Im — wave impedance [(g/cm³) (m/s)].

1) RTC inversion

This inversion is performed in three steps: (1) the previously mentioned expressions are used to convert relative wave impedance data volume obtained through sparse-spike inversion into deep and shallow laterolog resistivity data volume; (2) a geological model is built by interpolating deep and shallow laterolog resistivity curves, followed by frequency band compensation performed on the model to correct its low-frequency and high-frequency components, and finally absolute deep and shallow laterolog resistivity inversion data volumes are generated; and (3) RTC data volumes are ultimately obtained through conversion in accordance with the relationship between deep/shallow laterologs and RTC.

2) FID2 inversion

This inversion is performed in the following steps using the so-called double inversion approach (Figure 6.49): (1) an apparent acoustic curve is established by the statistical relationship between the fracture development index (FID2) and acoustic wave; (2) reservoir horizon calibration and wavelet extraction occur; (3) the inversion model is constructed; (4) the pseudo-impedance volume derived from the characteristic parameters of fractures is obtained through constrained inversion of the model; and (5) fracture development index 3D data volume is obtained through constrained inversion of the characteristic parameter curve for the fractures.

1) Method of poststack seismic attribute analysis

1. Coherence analysis. This is a sophisticated attribute analysis technique. It predicts fractures based on the dissimilarity between adjacent seismic traces. Its advantages include easy extraction of attributes and simple operation. However, it is strongly affected by factors such as lithological boundaries and faults, with strong ambiguity.

2. Margin-detection technique. This method predicts fractures through image analysis, which is visual, intuitive, and suitable for detecting large faults. For fracture prediction, however, the boundaries tend to be fuzzy, of low definition, and easily affected by faults, lithological boundaries, and so on.

3. Three-instantaneous-attribute method. This method detects fractures directly with P-wave dynamical information (amplitude, frequency, phase), which is simple, direct, and reliable. However, this method is significantly affected by internal structure and fluid type in volcanic rocks, also resulting in strong ambiguity.

4. Absorption coefficient method. This method predicts fractures based on the principle that fractures will intensify the seismic wave absorptive attenuation. Its advantages include high sensitivity and a good prediction result. However, it is strongly affected by the gas-bearing nature of formations and is also influenced by many other factors such as porous structures, fluid flow, and local saturation effect, also leading to strong ambiguity.

5. Stress analysis. This method predicts fracture distribution by calculating the strain generated during tectonic activities using the kinematic tectonic reconstruction method. It has a reliable theoretical basis and offers a good prediction result. However, the tectonic reconstruction process is complicated, thus the prediction result is affected by factors such as formation thickness, lithology, and structural history, resulting in some uncertainty.

The method of poststack seismic attribute analysis requires high-quality poststack 3D seismic data.

2) Prestack seismic prediction methods

These methods predict fracture distribution by the “quantile frequency of seismic energy” attribute based on fracture anisotropy. Their advantages include the ability to reduce ambiguity through subazimuth processing. However, subazimuth processing needs a huge data volume and a long cycle time, and it requires the data volumes acquired via wide azimuth and processed via subazimuth. At the same time, the prediction result is easily affected by other anisotropic media (such as mudstone) in the formation.

3) Fracture parameter inversion method

The spatial distribution of characteristic parameters of fractures is predicted using seismic inversion techniques, which are simple to implement and offer a high well-point congruence rate. However, their prediction effectiveness depends on the level of correlation between fracture parameters and seismic information, leading to a high degree of prediction uncertainty. They are also strongly affected by the thickness and distribution pattern of sedimentary rocks, leading to further increase in uncertainty. The fracture parameter inversion methods require high-quality 3D seismic data.