Volume fracturing compressibility characterization method

Abstract

The invention discloses a volume fracturing compressibility characterization method which comprises the following steps: measuring the horizontal ground stress of each well, calculating a stress difference coefficient D, observing the natural fracture development degree K of a well position reservoir, obtaining the elastic modulus and Poisson's ratio distribution of a reservoir section, and calculating the brittleness index B of reservoir rock according to the elastic modulus and Poisson's ratio distribution. And finally, calculating a compressibility index F according to the three parameters, and selecting a regional reservoir with the highest F value as a target dessert region for volume fracturing transformation. According to the method, the problem that the compressibility of the reservoir cannot be accurately described only by using the brittleness index in an existing reservoir compressibility characterization method is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field exploration and development methods, and in particular relates to a method for characterizing the compressibility of volume fracturing. Background Art

[0002] Volume fracturing is the main technical means for transforming difficult-to-use reservoirs such as shale oil and tight gas, and compressibility is a property that reflects whether shale oil, tight gas and other reservoirs can be effectively transformed into complex fracture networks through volume fracturing. At present, in the field of petroleum industry, compressibility is mainly characterized by the brittleness index of reservoir rocks. Under other similar conditions, the higher the brittleness index, the more complex the fracture system after fracturing. However, in addition to the brittleness index, the main factors controlling the complexity of fractures also include horizontal geostress and the degree of development of natural fractures. When the difference between the maximum horizontal geostress and the minimum horizontal geostress is smaller, the main fracture characteristics of hydraulic fractures are less obvious, and it is easier to form branch fractures; when the natural fractures are more developed, it is easier to form a complex fracture network in which hydraulic fractures and natural fractures communicate with each other. If the reservoir only has a high brittleness index, but the horizontal stress difference is large and the natural fractures are not developed, it is also difficult to form a complex fracture network. Summary of the invention

[0003] The purpose of the present invention is to provide a method for characterizing the compressibility of volume fracturing, which solves the problem that the existing method for characterizing the compressibility of reservoirs cannot accurately describe the compressibility of reservoirs by only using the brittleness index.

[0004] The technical solution adopted by the present invention is: a volume fracturing compressibility characterization method, which measures the horizontal ground stress of each well, calculates the stress difference coefficient D, and then obtains the degree of natural fracture development K of the reservoir at the observed well location, and then obtains the elastic modulus and Poisson's ratio distribution of the reservoir section. The reservoir rock brittleness index B is calculated from the elastic modulus and Poisson's ratio distribution, and finally the compressibility index F is calculated based on the above three parameters, and the regional reservoir with the highest F value is selected as the target sweet spot area for volume fracturing transformation.

[0005] The technical solution adopted by the present invention is also characterized in that:

[0006] Furthermore, the method for characterizing the compressibility of volume fracturing is specifically implemented in the following steps:

[0007] Step 1: Use rock mechanics acoustic emission experiments to obtain the horizontal geostress of each well in the block, and calculate the horizontal geostress difference coefficient D of the reservoir section of each well;

[0008] Step 2, according to the observation results of natural fractures in the oil layer core of the block, the development degree K of natural fractures in the reservoir at the observation well position is obtained;

[0009] Step 3, using the longitudinal and transverse wave velocities of the reservoir section measured by the well logging curve, according to the dynamic measurement method of elastic modulus and Poisson's ratio, obtain the elastic modulus and Poisson's ratio distribution of the reservoir section, and then calculate the reservoir rock brittleness index B based on the elastic modulus and Poisson's ratio;

[0010] Step 4, calculating the compressibility index F of the reservoir section according to the horizontal stress difference coefficient D, the degree of natural fracture development K and the reservoir rock brittleness index B obtained in steps 1, 2 and 3. The larger the value of the compressibility index F, the easier it is for the reservoir volume fracturing to form a complex fracture network;

[0011] Step 5: According to the compressibility index F distribution of the entire block, the reservoir in the area with the highest F value is selected as the target sweet spot area for volume fracturing transformation.

[0012] Furthermore, in step 1, each exploration well is drilled and cored, and the maximum horizontal geostress σH and the minimum horizontal geostress σh of each well are obtained by indoor rock mechanics experiments.

[0013] Furthermore, the stress difference coefficient D in step 1 is calculated according to formula (1):

[0014]

[0015] Among them, σH is the maximum horizontal geostress and σh is the minimum horizontal geostress.

[0016] Furthermore, the natural fracture development degree K in step 2 is specifically the average number of natural fractures developed per meter of oil layer length.

[0017] Furthermore, the reservoir rock brittleness index in step 3 is calculated by formula (2):

[0018]

[0019] Where E is the elastic modulus and v is Poisson's ratio.

[0020] Furthermore, the compressibility index F in step 4 is calculated according to formula (3):

[0021] F=a1×(1-D)+a2×K+a3×B (3)

[0022] Wherein, D is the stress difference coefficient, K is the degree of natural fracture development, and B is the reservoir rock brittleness index; the value of a1 is determined according to the size of σH-σh. If σH-σh≤5, a1 is 0.25; if 5<σH-σh≤10, a1 is 0.14; if σH-σh>10, a1 is 0.08; the value of a2 is determined according to the size of K. If K≤0.6, a2 is 0.5; if 0.6<K≤1.0, a2 is 0.62; if K>1.0, a2 is 0.7; the value of a3 is determined according to the size of B. If B≤0.35, a3 is 0.12; if 0.35<B≤0.5, a3 is 0.25; if B>0.5, a3 is 0.38.

[0023] The beneficial effects of the present invention are:

[0024] The present invention provides a method for characterizing the compressibility of volume fracturing, which solves the problem that the existing reservoir compressibility characterization method can not accurately describe the reservoir compressibility by only using the brittleness index. When the difference between the maximum horizontal ground stress and the minimum horizontal ground stress is smaller, the main fracture characteristics of the hydraulic fracture are less obvious, and it is easier to form branch fractures; when the natural fractures are more developed, it is easier to form a complex fracture network in which the hydraulic fractures and the natural fractures communicate with each other. If the reservoir only has a high brittleness index, but a large horizontal stress difference and undeveloped natural fractures, it is also difficult to form a complex fracture network. The method of the present invention adopts three parameters, which can more accurately characterize the reservoir compressibility. The method is easy to operate, highly reliable, simple and intuitive, and provides important guidance and basis for the optimization of sweet spots in block fracturing transformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a flow chart of the method. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the present invention clearer and more understandable, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings.

[0027] The present invention discloses a method for characterizing the compressibility of volume fracturing. The method measures the horizontal geostress of each well, calculates the stress difference coefficient D, observes the degree of development K of natural fractures in the reservoir at the well site, obtains the elastic modulus and Poisson's ratio distribution of the reservoir section, calculates the reservoir rock brittleness index B from the elastic modulus and Poisson's ratio distribution, and finally calculates the compressibility index F based on the above three parameters, and selects the regional reservoir with the highest F value as the target sweet spot area for volume fracturing transformation.

[0028] like Figure 1 As shown, the specific implementation steps are as follows:

[0029] Step 1: Use rock mechanics acoustic emission experiments to obtain the horizontal geostress of each well in the block. Drill and coring are performed on each exploration well. Use indoor rock mechanics experiments to obtain the maximum horizontal geostress σH and minimum horizontal geostress σh of each well. Calculate the horizontal geostress difference coefficient D of the reservoir section of each well to obtain the distribution of the stress difference coefficient in the block. The stress difference coefficient D is calculated according to formula (1):

[0030]

[0031] Among them, σH is the maximum horizontal ground stress, σh is the minimum horizontal ground stress;

[0032] Step 2: According to the observation results of natural fractures in the core of the oil layer in the block, the degree of development K of natural fractures in the reservoir at the observation well location is obtained. The degree of development K of natural fractures is specifically the number of natural fractures developed per meter of oil layer length on average, and the distribution of the degree of development K of natural fractures in the reservoir in the whole block is obtained accordingly;

[0033] Step 3: Using the P-wave and S-wave velocities of the reservoir section measured by the logging curve, the elastic modulus and Poisson's ratio distribution of the reservoir section are obtained according to the dynamic measurement method of the elastic modulus and Poisson's ratio, and then the reservoir rock brittleness index B is calculated based on the elastic modulus and Poisson's ratio. The reservoir rock brittleness index is calculated by formula (2):

[0034]

[0035] Where E is the elastic modulus and v is Poisson's ratio;

[0036] Step 4: Calculate the compressibility index F of the reservoir section according to the horizontal stress difference coefficient D, the degree of natural fracture development K and the reservoir rock brittleness index B obtained in steps 1, 2 and 3. The larger the value of the compressibility index F, the easier it is for the reservoir volume fracturing to form a complex fracture network. The compressibility index F is calculated according to formula (3):

[0037] F=a1×(1-D)+a2×K+a3×B (3)

[0038] Wherein, D is the stress difference coefficient, K is the degree of natural fracture development, and B is the reservoir rock brittleness index; the value of a1 is determined according to the size of σH-σh. If σH-σh≤5, a1 is 0.25; if 5<σH-σh≤10, a1 is 0.14; if σH-σh>10, a1 is 0.08; the value of a2 is determined according to the size of K. If K≤0.6, a2 is 0.5; if 0.6<K≤1.0, a2 is 0.62; if K>1.0, a2 is 0.7; the value of a3 is determined according to the size of B. If B≤0.35, a3 is 0.12; if 0.35<B≤0.5, a3 is 0.25; if B>0.5, a3 is 0.38;

[0039] Step 5: According to the distribution of the compressibility index F of the entire block, select the regional reservoir with the highest F value as the target sweet spot for volume fracturing transformation.

[0040] In order to make the purpose, technical solution and key points of the present invention clearer, the specific implementation of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0041] Example 1

[0042] Characterization method of volume fracturing compressibility:

[0043] Step 1: In order to find the sweet spot of reservoir volume fracturing in a shale oil reservoir, five vertical wells were deployed at different positions in the plane of the entire block as evaluation wells. The well numbers of these five wells are X-1, X-2, X-3, X-4, and X-5. After drilling to the target layer, these vertical wells were cored, and the maximum horizontal geostress σH and minimum horizontal geostress σh of each well were obtained by indoor rock mechanics acoustic emission experiments. Then, according to the calculation formula of geostress difference coefficient The in-situ stress difference coefficient D of the reservoir section of each well was calculated, as shown in Table 1;

[0044] Step 2: Observe the natural fractures of the oil layer cores taken from each evaluation well drilled in the block, and calculate the number of natural fractures per meter of oil layer length to obtain the natural fracture development degree K of the reservoir at each evaluation well location, as shown in Table 1;

[0045] Step 3: Using the P-wave and S-wave velocities measured by the well logging curve, the elastic modulus and Poisson's ratio distribution of the reservoir section are calculated according to the dynamic measurement method of elastic modulus and Poisson's ratio, and then the brittleness index formula defined by the elastic modulus and Poisson's ratio is used. The brittleness index of each well was obtained, as shown in Table 1;

[0046] Step 4: Using the compressibility index F characterization formula F=a1×(1-D)+a2×K+a3×B, calculate the compressibility index F of each evaluation well in the block;

[0047] Among them, D is the stress difference coefficient, obtained by step 1; K is the degree of natural fracture development, obtained by step 2; B is the reservoir rock brittleness index, obtained by step 3; a1, a2, and a3 are weight coefficients. Since the horizontal biaxial stress difference σH-σh of each well is less than 5, a1 is taken as 0.25; the degree of natural fracture development K is less than 0.6, so a2 is taken as 0.5; the interval of brittleness index B is between 0.35 and 0.5, so a3 is taken as 0.25; from the above parameters, the compressibility index F of each well can be obtained as F=0.25×(1-D)+0.5×K+0.25×B, and the specific calculated values ​​are shown in Table 1; the larger the value of compressibility index F, the easier it is for the reservoir volume fracturing in the area where the well is located to form a complex fracture network;

[0048] Step 5: By comparing the compressibility indexes F of the five evaluation wells, it is found that the compressibility index of the X-4 well is the largest, and the area where the well is located is preferably selected as the target sweet spot for volume fracturing stimulation.

[0049] Table 1 Compressibility index calculation parameters list

[0050]

[0051] Example 2

[0052] Step 1: A tight oil reservoir needs to be developed by horizontal well volume fracturing. In order to find the sweet spot, four vertical wells are deployed in the block plane as exploration wells. The numbers of these four exploration wells are N-1, N-2, N-3, and N-4 respectively. Each exploration well is drilled and cored. The maximum horizontal geostress σH and the minimum horizontal geostress σh of each well are obtained by indoor rock mechanics experiments. According to the calculation formula of the geostress difference coefficient The in-situ stress difference coefficient D of the reservoir section of each well was calculated, as shown in Table 2;

[0053] Step 2: Observe the natural fractures of the cores of the four exploration wells, calculate the number of natural fractures per meter of oil layer length, and obtain the degree of natural fracture development K of the reservoir at each evaluation well location, as shown in Table 2;

[0054] Step 3: Using the P-wave and S-wave velocities measured by the well logging curve, the elastic modulus and Poisson's ratio distribution of the reservoir section are calculated according to the dynamic measurement method of elastic modulus and Poisson's ratio, and then the brittleness index formula defined by the elastic modulus and Poisson's ratio is used. The brittleness index of each well was obtained, as shown in Table 2;

[0055] Step 4: Use the characterization formula of compressibility index F, F=a1×(1-D)+a2×K+a3×B, to calculate the compressibility index F of each exploration well in the block; wherein, D is the stress difference coefficient, obtained by step 1; K is the degree of natural fracture development, obtained by step 2; B is the reservoir rock brittleness index, obtained by step 3; a1, a2, and a3 are weight coefficients. Since the value range of the horizontal biaxial stress difference σH-σh of each well is between 5 and 10, a1 is 0.14; the range of the degree of natural fracture development K is between 0.6 and 1.0, a2 is 0.62; the value of the brittleness index B is less than 0.35, a3 is 0.12; from the above parameters, the compressibility index of each well can be obtained as F=0.14×(1-D)+0.62×K+0.12×B, and the specific calculated values ​​are shown in Table 2;

[0056] Step 5: By comparing the compressibility indexes F of the four exploration wells, it is found that the compressibility index of the N-4 well is the largest, and the area where the well is located is preferably selected as the target sweet spot for volume fracturing transformation.

[0057] Table 2 Compressibility index calculation parameters list

[0058]

[0059] Example 3

[0060] Characterization method of volume fracturing compressibility:

[0061] Step 1: A shale gas reservoir needs to be developed by horizontal well volume fracturing. In order to find the sweet spot, four vertical wells are deployed on the block plane as skeleton wells. The four skeleton wells are numbered G-1, G-2, G-3, and G-4 respectively. Each skeleton well is drilled and cored, and the maximum horizontal geostress σH and minimum horizontal geostress σh of each well are obtained by indoor rock mechanics experiments. According to the calculation formula of the geostress difference coefficient The in-situ stress difference coefficient D of the reservoir section of each well was calculated, as shown in Table 3;

[0062] Step 2: Observe the natural fractures of the cores of the four skeleton wells, calculate the number of natural fractures per meter of oil layer length, and obtain the degree of natural fracture development K of the reservoir at each evaluation well location, as shown in Table 3;

[0063] Step 3: Using the P-wave and S-wave velocities measured by the well logging curve, the elastic modulus and Poisson's ratio distribution of the reservoir section are calculated according to the dynamic measurement method of elastic modulus and Poisson's ratio, and then the brittleness index formula defined by the elastic modulus and Poisson's ratio is used. The brittleness index of each well was obtained, as shown in Table 3;

[0064] Step 4: Use the characterization formula of compressibility index F, F=a1×(1-D)+a2×K+a3×B, to calculate the compressibility index F of each skeleton well in the block; wherein, D is the stress difference coefficient, obtained by step 1; K is the degree of natural fracture development, obtained by step 2; B is the reservoir rock brittleness index, obtained by step 3; a1, a2, and a3 are weight coefficients. Since the values ​​of the horizontal biaxial stress difference σH-σh of each well are all greater than 10, a1 is taken as 0.08; the values ​​of the degree of natural fracture development K are all greater than 1, a2 is taken as 0.7; the values ​​of the brittleness index B are all greater than 0.5, a3 is taken as 0.38; from the above parameters, the compressibility index F of each well can be obtained as F=0.08×(1-D)+0.7×K+0.38×B, and the specific calculated values ​​are shown in Table 3;

[0065] Step 5: By comparing the compressibility indexes F of the four shale gas skeleton wells, it is found that the compressibility index of the G-2 well is the largest, and the area where the well is located is preferably selected as the target sweet spot for volume fracturing transformation.

[0066] Table 3 Compressibility index calculation parameters list

[0067]

[0068] Example 4

[0069] Characterization method of volume fracturing compressibility:

[0070] Step 1: A tight oil reservoir needs to be developed by horizontal well volume fracturing. In order to find the sweet spot, four vertical wells are deployed in the block plane as evaluation wells. The numbers of these four exploration wells are Q-1, Q-2, Q-3, and Q-4. Each evaluation well is drilled and cored. The maximum horizontal geostress σH and the minimum horizontal geostress σh of each well are obtained by indoor rock mechanics experiments. According to the calculation formula of the geostress difference coefficient The in-situ stress difference coefficient D of the reservoir section of each well was calculated, as shown in Table 4;

[0071] Step 2: Observe the natural fractures of the cores of the four evaluation wells, calculate the number of natural fractures per meter of oil layer length, and obtain the degree of natural fracture development K of the reservoir at each evaluation well location, as shown in Table 4;

[0072] Step 3: Using the P-wave and S-wave velocities measured by the well logging curve, the elastic modulus and Poisson's ratio distribution of the reservoir section are calculated according to the dynamic measurement method of elastic modulus and Poisson's ratio, and then the brittleness index formula defined by the elastic modulus and Poisson's ratio is used. The brittleness index of each well was obtained, as shown in Table 4;

[0073] Step 4: Use the characterization formula of compressibility index F, F=a1×(1-D)+a2×K+a3×B, to calculate the compressibility index F of each evaluation well in the block; wherein, D is the stress difference coefficient, obtained by step 1; K is the degree of natural fracture development, obtained by step 2; B is the reservoir rock brittleness index, obtained by step 3; a1, a2, and a3 are weight coefficients. Since the value of the horizontal biaxial stress difference σH-σh of each well ranges from 5 to 10, a1 is 0.14; the range of the degree of natural fracture development K is between 0.6 and 1.0, a2 is 0.62; the value of the brittleness index B is less than 0.35, a3 is 0.12; from the above parameters, the compressibility index of each well can be obtained as F=0.14×(1-D)+0.62×K+0.12×B, and the specific calculated values ​​are shown in Table 4;

[0074] Step 5: By comparing the compressibility indexes F of the four evaluation wells, it is found that the compressibility index of the Q-4 well is the largest, and the area where the well is located is preferably selected as the target sweet spot for volume fracturing transformation.

[0075] Table 4 Compressibility index calculation parameters list

[0076]

[0077] Comparative Example 1

[0078] Step 1: In order to find the sweet spot of reservoir volume fracturing in a shale oil reservoir, five vertical wells were deployed at different positions in the plane of the entire block as evaluation wells. The well numbers of these five wells are Y-1, Y-2, Y-3, Y-4, and Y-5. After drilling, these vertical wells were logged. The elastic modulus and Poisson's ratio distribution of the reservoir section were calculated based on the dynamic measurement method of elastic modulus and Poisson's ratio using the longitudinal and transverse wave velocities measured by the logging curves. Then, according to the brittleness index formula defined by the elastic modulus and Poisson's ratio, the elastic modulus and Poisson's ratio of the reservoir section were calculated. The brittleness index of each well was obtained, as shown in Table 5;

[0079] Step 2: The brittleness index of the evaluation wells of the shale oil reservoir is directly used as the evaluation basis of the compressibility; by comparing the brittleness index B of the five evaluation wells, it is found that the brittleness index of the Y-1 well is the largest, and the location of the well is preferably selected as the target sweet spot for volume fracturing transformation;

[0080] Table 5 Compressibility index calculation parameters list

[0081]

[0082] Comparative verification analysis:

[0083] In Example 1, the compressibility index F proposed in the present invention is used to optimize the target sweet spot area of ​​volume fracturing transformation. By comparing the compressibility index F, the compressibility index of the X-4 well is the largest, and the location area of ​​the well is preferably the sweet spot area; from the actual effect of the mine, the oil production of the X-4 well after implementation is the highest, as shown in Table 6, which confirms the correctness of the technical method of the present invention.

[0084] Table 6 Comparison of the effects of the method of the present invention and the conventional method

[0085]

[0086]

[0087] In Comparative Example 1, the conventional method used in the early stage was used to optimize the sweet spot based on the brittleness index. After comparison, it was considered that the brittleness index of the Y-1 well was the largest, and the area where the well was located was selected as the target sweet spot for volume fracturing transformation. However, the actual implementation result was that the Y-4 well had the highest production, indicating that the method of optimizing the sweet spot based on the brittleness index was less accurate.

[0088] After comparison, it is believed that the technical method proposed in the present invention is more accurate and reliable, and has a stronger guiding role in the actual mine field.

Claims

1. A method for characterizing volume fracturing compressibility, characterized in that: By measuring the horizontal ground stress of each well and calculating the stress difference coefficient D, the degree of natural fracture development K of the reservoir at the observed well location is obtained, and then the elastic modulus and Poisson's ratio distribution of the reservoir section are obtained. The reservoir rock brittleness index B is calculated from the elastic modulus and Poisson's ratio distribution. Finally, the compressibility index F is calculated based on the above three parameters, and the regional reservoir with the highest F value is selected as the target sweet spot for volume fracturing transformation.

2. The method for characterizing the compressibility of volume fracturing according to claim 1, characterized in that: Please follow the steps below to implement: Step 1: Use rock mechanics acoustic emission experiments to obtain the horizontal geostress of each well in the block, and calculate the horizontal geostress difference coefficient D of the reservoir section of each well; Step 2, according to the observation results of natural fractures in the oil layer core of the block, the development degree K of natural fractures in the reservoir at the observation well position is obtained; Step 3, using the longitudinal and transverse wave velocities of the reservoir section measured by the well logging curve, according to the dynamic measurement method of elastic modulus and Poisson's ratio, obtain the elastic modulus and Poisson's ratio distribution of the reservoir section, and then calculate the reservoir rock brittleness index B based on the elastic modulus and Poisson's ratio; Step 4, calculating the compressibility index F of the reservoir section according to the horizontal stress difference coefficient D, the degree of natural fracture development K and the reservoir rock brittleness index B obtained in steps 1, 2 and 3. The larger the value of the compressibility index F, the easier it is for the reservoir volume fracturing to form a complex fracture network; Step 5: According to the compressibility index F distribution of the entire block, the reservoir in the area with the highest F value is selected as the target sweet spot for volume fracturing transformation.

3. The method for characterizing the compressibility of volume fracturing according to claim 2, characterized in that: In step 1, each exploration well is drilled and cored, and the maximum horizontal geostress σH and the minimum horizontal geostress σh of each well are obtained by indoor rock mechanics experiments.

4. The method for characterizing volume fracturing compressibility according to claim 3, characterized in that: The stress difference coefficient D in step 1 is calculated according to formula (1): Among them, σH is the maximum horizontal geostress and σh is the minimum horizontal geostress.

5. The method for characterizing the compressibility of volume fracturing according to claim 2, characterized in that: The degree of development K of natural fractures in step 2 is specifically the average number of natural fractures developed per meter of oil layer length.

6. The method for characterizing the compressibility of volume fracturing according to claim 2, characterized in that: In step 3, the reservoir rock brittleness index B is calculated by formula (2): Where E is the elastic modulus and v is Poisson's ratio.

7. The method for characterizing volume fracturing compressibility according to claim 2, characterized in that: The compressibility index F in step 4 is calculated according to formula (3): F=a1×(1-D)+a2×K+a3×B (3) Wherein, D is the stress difference coefficient, K is the degree of natural fracture development, and B is the reservoir rock brittleness index; the value of a1 is determined according to the size of σH-σh. If σH-σh≤5, a1 is 0.25; if 5<σH-σh≤10, a1 is 0.14; if σH-σh>10, a1 is 0.08; the value of a2 is determined according to the size of K. If K≤0.6, a2 is 0.5; if 0.6<K≤1.0, a2 is 0.62; if K>1.0, a2 is 0.7; the value of a3 is determined according to the size of B. If B≤0.35, a3 is 0.12; if 0.35<B≤0.5, a3 is 0.25; if B>0.5, a3 is 0.38.

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