Process method for reducing high-moisture associated gas in oil sand development

Abstract

The invention relates to a process method for reducing high-moisture associated gas in oil sand development, which comprises the following steps: starting a circulating preheating working condition: returning fluid from an injection well and a production well to a casing gas pipeline after passing through a throttle valve, and separating a sand-containing solid phase, a liquid phase and a gas phase by starting a separator; the gas phase of the starting separator is divided into two paths and simultaneously enters a cooling unit consisting of a starting air cooler and a production air cooler to be cooled, and the cooled gas enters the production separator; under the normal production working condition, the starting separator and the starting air cooler are in an off-line state, and the high-moisture-content casing gas is subjected to decrement treatment through the production air cooler and the production separator; the high-moisture-content casing gas enters a production air cooler, and the cooling load of the production air cooler is regulated and controlled according to a cooling load regulation and control calculation formula; and after cooling, part of steam is condensed into a liquid state and enters a production separator to complete gas-liquid separation. According to the method, the heat exchange efficiency is improved, the gas volume of the sleeve is reduced to the maximum extent, condensate is recycled, and meanwhile the flowability of emulsion is not affected.

Description

Technical Field

[0001] This invention relates to a process for reducing associated gas volume in high-moisture oil sands development, belonging to the field of conventional oil and gas treatment technology. Background Technology

[0002] Steam-assisted gravity drainage (SAGD) is a commonly used and efficient technology in oil sands development and extra-heavy oil thermal recovery. SAGD development is usually divided into 2-3 stages: the circulation preheating stage, the SAGD normal production stage, and some oilfields reduce steam consumption in the later stages of production by injecting non-condensable gas.

[0003] In the early stages of production, a preheating phase is initiated. This involves injecting a large amount of 300°C saturated steam to preheat the reservoir, reducing crude oil viscosity, increasing its fluidity, and creating steam chambers. This process typically lasts 3-6 months, depending on the number of wells at the site. Approximately 50%-70% of the injected steam returns to the surface, undergoes simple processing by a separator, and is then transported to the central processing plant via the casing gas pipeline. Under these conditions, the gas passing through the casing gas pipeline is saturated steam.

[0004] After the reservoir is fully preheated, it enters the normal production (SAGD) stage. Steam is continuously injected into the reservoir to maintain its temperature and pressure, ensuring continuous crude oil flow. During this stage, most of the steam injected, along with the condensate and formation water, mixes with the crude oil to form an asphalt emulsion, which is then transported through pipelines to the central processing plant. Some light hydrocarbon components and gases such as CO2 enter the casing gas pipeline through the annulus structure of the production well. In the SAGD stage, the wellhead operating temperature is approximately 200℃-230℃, and the steam injection pressure is approximately 7100 kPa. Under design conditions, the downhole subcooling value is approximately 10℃-20℃, about 1%-2% of the produced water in the production well evaporates and enters the casing gas pipeline, the wellhead annulus temperature is approximately 170-205℃, and the pressure is 650-800 kPa. However, in actual production, the subcool value is usually adjusted to around 5°C to stabilize output, and may even drop to 0°C under extreme conditions. This means that the temperature of the water component in the emulsion is equal to the saturated steam temperature, and steam breakthrough may even occur. Therefore, the amount of produced water carried into the casing gas in gaseous form is much greater than the design value. According to production data, approximately 5%-12% of the produced water enters the casing gas pipeline, resulting in water vapor accounting for 86%-99% of the total volumetric flow rate of the casing gas.

[0005] Because the gas in the casing is acidic, the extremely high water content increases the volumetric flow rate, which not only requires increasing the pipe diameter but also easily causes corrosion of the pipes and equipment.

[0006] Current surface engineering designs typically address casing gas delivery volume and pipeline corrosion issues by increasing the diameter of the casing gas delivery pipe and raising the corrosion allowance value, without pre-treating the casing gas. However, due to the unstable gas delivery volume during SAGD well site operation, especially during start-up and preheating cycles, pipeline delivery capacity often limits the delivery volume per cycle of preheating, leading to extended preheating periods. Simultaneously, long-distance pipelines generate large amounts of condensate, posing significant operational challenges. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a process for reducing associated gas volume in oil sands development with high moisture content. This method can stably and efficiently pretreat high-temperature, high-humidity casing gas, achieving the effects of reducing water content and volumetric flow rate. For different subcooling values ​​at different stages of SAGD production, the cooling load is automatically adjusted to improve heat exchange efficiency, minimize casing gas volume, recover condensate, and without affecting emulsion fluidity. The treated casing gas exhibits a 70% reduction in water content and a 50%-70% reduction in volumetric flow rate.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A process for reducing associated gas emissions from high-moisture oil sands development includes: S1: Start-up cycle preheating condition: S11: The return fluid from the injection well and the production well (168-205℃, 680-2550kPa) is collected into the casing gas pipeline after passing through the throttle valve. The temperature of the casing gas pipeline after the valve is 170-175℃ and the pressure is 700kPa. After the start-up separator separates the sand-containing solid phase, liquid phase and gas phase, the sand-containing liquid is pumped into the asphalt emulsion delivery pipeline by the delivery pump, and the gas phase (saturated steam) enters the cooling unit. S12: The gas phase of the start-up separator is divided into two paths and simultaneously enters the cooling unit composed of the start-up air cooler and the production air cooler to be cooled to 150-165℃, releasing the latent heat in the gas. After cooling, the gas enters the production separator to separate the steam and condensate. The condensate enters the asphalt emulsion conveying pipeline, and the steam enters the associated gas conveying pipeline. S13: In the production separator, about 48-52% of the liquid is separated and pumped into the asphalt emulsion pipeline by the production separator delivery pump. The gas phase volume fraction is reduced by about 48%-52% and enters the casing gas delivery pipeline.

[0009] S2: Normal production SAGD operating condition: Under normal SAGD production conditions, the start-up separator and start-up air cooler are offline, and the high-humidity jacket gas is reduced in volume by passing through the production air cooler and production separator. S21: Each production well enters the main pipe manifold through the casing gas branch pipe from the annulus casing interface. The flow rate through the main pipe is monitored, and when the mass flow rate q... m The cooler is not started when the flow rate is ≤1 / 3 of the rated flow rate; when the mass flow rate q m When the flow rate is greater than 1 / 3 of the rated flow rate, adjust the cooling load. S22: The control system reads the bottom-hole temperature and pressure data of each well and calculates the subcool value; S23: Calculate the theoretical fluid flow rate based on the subcool values ​​of each well. ; S24: Calculate the flow meter readings on the manifold. and The ratio when / When the value is greater than 1.3, the system alarms and switches to manual adjustment of the cooling load; when / If ≤1.3, continue with the subsequent process; S25: High-humidity casing gas enters the production air cooler. The cooling load of the production air cooler is adjusted according to the cooling load control calculation formula to cool the casing gas to 155-160℃. S26: After cooling, some of the steam condenses into liquid and enters the production separator to complete gas-liquid separation. The gas phase is transported from the top into the gas pipeline, and the liquid phase is lifted by the production separator's conveying pump into the asphalt emulsion conveying pipeline.

[0010] In the aforementioned process for reducing associated gas volume in high-moisture oil sands development, preferably, under the circulating preheating condition, the cooling load distribution between the start-up air cooler and the production air cooler is: starting air cooler cooling load / production air cooler cooling load = 1-2, and both air cooler fans are frequency converter controlled, with adjustable cooling load.

[0011] In the aforementioned process for reducing associated gas emissions from high-moisture oil sands development, the subcool value is preferably calculated using the following formula:

[0012]

[0013] In the formula, T 0 represents the downhole temperature monitoring value. T s The saturated steam temperature under bottom hole pressure conditions. P 0 represents the bottom hole pressure monitoring value.

[0014] The aforementioned process for reducing associated gas emissions in high-moisture oil sands development is preferably... The calculation formula is as follows:

[0015] In the formula, The required cooling fluid volume is based on theoretical calculations. m 1- m i For injection well 1- i The mass flow rate of the injected steam, a 1- a i The evaporation coefficient (the evaporation coefficient is a fixed coefficient calculated based on the subcool value, which is divided into 4 levels, each with a different evaporation coefficient value), 1- i Number the injection well.

[0016] The aforementioned process for reducing associated gas emissions in high-moisture oil sands development is preferably... The calculation formula is as follows:

[0017] In the formula, The required cooling fluid volume is calculated based on monitoring data. This refers to the amount of gas injected into a single well. q 0 represents the gas monitoring flow rate in the casing of a single well. q ncg1 - q ncgi The amount of NCG injected into a single well. n This represents the total number of well pairs.

[0018] The aforementioned process for reducing associated gas emissions from high-moisture oil sands development, preferably, uses the following formula for calculating cooling load regulation:

[0019] In the formula, Q For cooling load, T 3 represents the inlet air temperature of the production cooler.

[0020] The aforementioned process for reducing associated gas consumption in high-moisture oil sands development preferably involves dividing the subcooling of a single well into four stages for cooling capacity control, as detailed below: When the subcool value of a single well is higher than 10℃, the evaporation coefficient a is taken as 0.01; when it is higher than 30℃, the subcool value monitor will alarm. When the subcool value of a single well is between 5 and 10℃, the evaporation coefficient a is taken as 0.02; When the subcool value of a single well is between 2 and 5℃, the evaporation coefficient a is taken as 0.08; When the subcool value of a single well is below 2℃, the evaporation coefficient a is taken as 0.10.

[0021] The present invention has the following advantages due to the adoption of the above technical solutions: 1. This invention addresses the characteristics of cyclic preheating and return of the gas phase during normal production in the SAGD production process by configuring different cooling and dehumidification equipment. This effectively reduces the volume of gas phase transport while avoiding the risk of condensate entering the emulsion pipeline due to excessive temperature drop, which could affect the fluidity of the asphalt emulsion.

[0022] 2. The circulating preheating of the present invention adopts a start-up cooler and a start-up separator, which can be reused offline at other well sites after production, reducing equipment and cooling waste.

[0023] 3. This invention calculates the subcool value based on measured values ​​such as steam injection, bottom hole pressure, and bottom hole temperature in a single well, taking into account the changes in single well production and injection volume during the production and development process, and has operational flexibility.

[0024] 4. This invention proposes a basis for adjusting the cooling capacity, which solves the problem of difficulty in adjusting the cooling load of air coolers. Attached Figure Description

[0025] Figure 1 SAGD High Moisture Content Casing Gas Reduction Flowchart - Cycle Start-up Phase Flowchart; Figure 2 Flowchart for reducing the amount of high-humidity casing gas in SAGD - Flowchart for the normal production SAGD stage; Figure 3 This is a control roadmap for the SAGD stage of normal production. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0027] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," "third," "fourth," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect.

[0028] For ease of description, spatial relative terms may be used in the text to describe the relationship of one element or feature relative to another element or feature as shown in the figure. These relative terms include, for example, "inside," "outside," "middle," "outer," "below," "above," etc. Such spatial relative terms are intended to include different orientations of the device in use or operation, other than those depicted in the figure.

[0029] Since the circulating preheating condition is typically the peak flow rate of the casing gas, the return fluid under this condition is saturated steam with almost no non-condensable gas components and a high pressure (2500 kPa, 230°C). Existing technologies only address the return fluid under the circulating preheating condition. Under the circulating preheating condition, the return fluid from the injection well and production well is reduced to 700 kPa and 170°C via a throttle valve before entering the start-up separator to complete gas-liquid separation. 36%-50% of the fluid forms a liquid phase, which is then pumped into the emulsion pipeline by a booster pump. The remaining gas phase enters the casing gas pipeline, thus achieving a balanced flow rate.

[0030] Under SAGD production conditions, no treatment is performed on the casing gas. For the dehumidification process of high-temperature and high-humidity gases, a low-temperature cooling method is generally used, in which a refrigerant exchanges heat with the humid gas to lower the temperature below the saturated steam temperature, thereby completing dehumidification and moisture recovery.

[0031] Existing casing gas treatment for oil sands has the following disadvantages: In existing oil sands development projects, the volume of casing gas generated under start-up circulation conditions is about 2-3 times that under SAGD conditions, requiring the design of larger pipe diameters to meet the requirements of start-up circulation conditions. However, due to the large fluctuations in steam injection volume from the initial to the later stages of start-up circulation, as well as the temperature, pressure, and return rate of the return fluid, the separation effect of the start-up separator often fails to meet design expectations. The actual casing gas volume exceeds the pipeline's transport capacity, which forces the well site to complete the start-up process in multiple batches, extending the production cycle.

[0032] Existing low-temperature cooling and dehumidification methods for oil sands development have the following drawbacks: 1. Due to the long distance between well sites and central processing plants, refrigerant cannot be supplied, requiring the use of air coolers for cooling. This necessitates a large floor space, and the cooling effect is directly related to ambient temperature, making it difficult to control. 2. The separated liquid after cooling needs to be pressurized and transported to the emulsion pipeline. Because the liquid temperature is low after cooling, mixing it can lower the temperature of the asphalt emulsion, affecting its fluidity. 3. The cooler outlet temperature is difficult to control, and the casing gas contains a large amount of acidic gas, causing corrosion to long-distance pipelines.

[0033] To address the aforementioned technical problems, this invention provides a process for reducing associated gas volume in oil sands development with high moisture content. This method can stably and efficiently pretreat high-temperature, high-humidity casing gas, achieving the effects of reducing water content and volumetric flow rate. It automatically adjusts the cooling load according to the subcooling value at different stages of SAGD production, thereby improving heat exchange efficiency, minimizing casing gas volume, recovering condensate, and without affecting emulsion fluidity. The treated casing gas exhibits a 70% reduction in water content and a 50%-70% reduction in volumetric flow rate.

[0034] like Figure 1 , 2 As shown in Figure 3, the process method for reducing associated gas consumption in high-moisture oil sands development involved in this invention includes the following steps: S1: Start-up cycle preheating condition: S11: The return fluid from the injection well and the production well (168-205℃, 680-2550kPa) is collected into the casing gas pipeline after passing through the throttle valve. The temperature of the casing gas pipeline after the valve is 170-175℃ and the pressure is 700kPa. After the start-up separator separates the sand-containing solid phase, liquid phase and gas phase, the sand-containing liquid is pumped into the asphalt emulsion delivery pipeline by the delivery pump, and the gas phase (saturated steam) enters the cooling unit. S12: The gas phase of the start-up separator is divided into two paths and simultaneously enters the cooling unit composed of the start-up air cooler and the production air cooler to be cooled to 150-165℃, releasing the latent heat in the gas. After cooling, the gas enters the production separator to separate the steam and condensate. The condensate enters the asphalt emulsion conveying pipeline, and the steam enters the associated gas conveying pipeline. S13: In the production separator, about 48-52% of the liquid is separated and pumped into the asphalt emulsion pipeline by the production separator delivery pump. The gas phase volume fraction is reduced by about 48%-52% and enters the casing gas delivery pipeline.

[0035] S2: Normal production SAGD operating condition: Under normal SAGD production conditions, the start-up separator and start-up air cooler are offline, and the high-humidity jacket gas is reduced in volume by passing through the production air cooler and production separator. S21: Each production well enters the main pipe manifold through the casing gas branch pipe from the annulus casing interface. The flow rate through the main pipe is monitored, and when the mass flow rate q... m The cooler is not started when the flow rate is ≤1 / 3 of the rated flow rate; when the mass flow rate q m When the flow rate is greater than 1 / 3 of the rated flow rate, adjust the cooling load. S22: The control system reads the temperature and pressure data at the bottom and top of each well and calculates the subcool value of the interface. S23: Calculate the theoretical fluid flow rate based on the subcool values ​​of each well. ; S24: Calculate the flow meter readings on the manifold. and The ratio when / When the value is greater than 1.3, the system alarms and switches to manual adjustment of the cooling load; when / If ≤1.3, continue with the subsequent process; S25: High-humidity casing gas enters the production air cooler. The cooling load of the production air cooler is adjusted according to the cooling load control calculation formula to cool the casing gas to 155-160℃. S26: After cooling, some of the steam condenses into liquid and enters the production separator to complete gas-liquid separation. The gas phase is transported from the top into the gas pipeline, and the liquid phase is lifted by the production separator's conveying pump into the asphalt emulsion conveying pipeline.

[0036] The technical solution of the present invention will be described in detail below with reference to specific examples.

[0037] Example 1 The oil sands development well site in the K region of North America contains 21 well pairs. The casing gas volume and moisture content under their start-up circulation conditions and normal production conditions are shown in Table 1.

[0038] Table 1

[0039] Using the method described in this invention, under startup cycle conditions with a cooling load of 34MW, the fluid temperature after cooling is 134℃, the maximum water carried by the gas phase after cooling is 225t / d CWE, and the gas volumetric flow rate of the casing is reduced by up to 85%. Under normal production SAGD conditions with a cooling load of 12-20MW, the fluid temperature after cooling is 160℃, the maximum water carried by the gas phase after cooling is 150t / d CWE, and the gas volumetric flow rate of the casing is reduced by up to 76%. After cooling, the diameter of the casing gas pipeline is reduced from 24” to 10”.

[0040] Example 2 The North American LW oil sands development well site, comprising 13 well pairs, shows the casing gas volume and moisture content under its circulation start-up and normal production conditions as shown in Table 2.

[0041] Table 2

[0042] Using the method described in this invention, under startup cycle conditions with a cooling load of 22MW, the fluid temperature after cooling is 170℃, the maximum water carried by the gas phase after cooling is 229t / d CWE, and the maximum reduction in the gas volumetric flow rate of the casing is 81%. Under normal production SAGD conditions with a cooling load of 7MW, the fluid temperature after cooling is 161℃, the maximum water carried by the gas phase after cooling is 213t / d CWE, and the maximum reduction in the gas volumetric flow rate of the casing is 69.9%. After cooling, the diameter of the casing gas pipeline is reduced from 20” to 12”.

[0043] Example 3 The North American LE area oil sands development well site, comprising 9 well pairs, shows the casing gas volume and moisture content under its circulation start-up and normal production conditions as shown in Table 3.

[0044] Table 3

[0045] Using the method described in this invention, under startup cycle conditions with a cooling load of 37MW, the fluid temperature after cooling is 170℃, the maximum water carried by the gas phase after cooling is 458t / d CWE, and the maximum reduction in the gas volumetric flow rate of the casing is 74%. Under normal production SAGD conditions with a cooling load of 12MW, the fluid temperature after cooling is 158℃, the maximum water carried by the gas phase after cooling is 141t / d CWE, and the maximum reduction in the gas volumetric flow rate of the casing is 64.6%. After cooling, the diameter of the casing gas pipeline is reduced from 16” to 10”.

[0046] Comparative example: The North American N-zone oil sands development well site, comprising 8 well pairs, shows the casing gas volume and moisture content under its circulation start-up and normal production conditions as shown in Table 4.

[0047] Table 4

[0048] The project did not treat the high-moisture casing gas. The casing gas outlet pipeline diameter was 22". Due to the return fluid volume during the cycle start-up phase being much greater than the design volume, the casing gas pipeline could not meet the transportation requirements. The number of well pairs started per cycle was reduced from the design value of 8 pairs to 5 pairs, and the start-up cycle was extended. During SAGD production, due to the large amount of condensate transported along the pipeline, which exceeded the capacity of the condensate drainage facilities in the original design pipeline, the operating parameters needed to be manually adjusted.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A process for reducing associated gas emissions in high-moisture oil sands development, characterized in that, include: Start-up cycle preheating condition: The return fluids from the injection well and the production well are collected into the casing gas pipeline after passing through the throttle valve. The sand-containing solid phase, liquid phase and gas phase are separated by the start-up separator. The sand-containing liquid is pumped into the asphalt emulsion delivery pipeline by the delivery pump, and the gas phase enters the cooling unit. The gas phase of the start-up separator is divided into two paths and simultaneously enters the cooling unit composed of the start-up air cooler and the production air cooler for cooling to release the latent heat in the gas. After cooling, the gas enters the production separator to separate the steam and condensate. The condensate enters the asphalt emulsion conveying pipeline, and the steam enters the associated gas conveying pipeline. Normal SAGD operating conditions during production: Under normal SAGD production conditions, the start-up separator and start-up air cooler are offline, and the high-humidity jacket gas is reduced in volume by passing through the production air cooler and production separator. Each production well enters the main pipe manifold through the casing gas branch pipe from the annulus casing interface. The flow rate through the main pipe is monitored, and when the mass flow rate q... m The cooler is not started when the flow rate is ≤1 / 3 of the rated flow rate; when the mass flow rate q m When the flow rate is greater than 1 / 3 of the rated flow rate, adjust the cooling load. The control system reads the bottom-hole temperature and pressure data of each well and calculates the subcool value on the interface. The theoretical flow rate of fluid was calculated based on the subcool values ​​of each well. ; Calculate the flow meter readings on the manifold. and The ratio when / When the value is greater than 1.3, the system alarms and switches to manual adjustment of the cooling load; when / If ≤1.3, continue with the subsequent process; High-humidity casing gas enters the production air cooler, and the cooling load of the production air cooler is adjusted according to the cooling load control calculation formula to cool the casing gas to 155-160℃. After cooling, some of the steam condenses into liquid and enters the production separator to complete gas-liquid separation. The gas phase is transported from the top into the gas pipeline, while the liquid phase is lifted by the production separator's delivery pump into the asphalt emulsion delivery pipeline.

2. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 1, characterized in that, Under the cyclic preheating condition, the cooling load distribution between the start-up air cooler and the production air cooler is: cooling load of the start-up air cooler / cooling load of the production air cooler = 1-2. Both air cooler fans are frequency converter controlled, and the cooling load is adjustable.

3. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 2, characterized in that, The formula for calculating the subcool value is as follows: In the formula, T 0 represents the downhole temperature monitoring value. T s The saturated steam temperature under bottom hole pressure conditions. P 0 represents the bottom hole pressure monitoring value.

4. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 3, characterized in that, The calculation formula is as follows: In the formula, The required cooling fluid volume is based on theoretical calculations. m 1- m i For injection well 1- i The mass flow rate of the injected steam, a 1- a i The evaporation coefficient is 1- i Number the injection well.

5. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 4, characterized in that, The calculation formula is as follows: In the formula, The required cooling fluid volume is calculated based on monitoring data. This refers to the amount of gas injected into a single well. q 0 represents the gas monitoring flow rate in the casing of a single well. q ncg1 - q ncgi The amount of NCG injected into a single well. n This represents the total number of well pairs.

6. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 5, characterized in that, The formula for calculating cooling load regulation is as follows: In the formula, Q For cooling load, T 3 represents the inlet air temperature of the production cooler.

7. The process for reducing associated gas emissions in high-moisture oil sands development according to claim 6, characterized in that: The cooling capacity of a single-well subcooler is controlled in four levels, as detailed below: When the subcool value of a single well is higher than 10℃, the evaporation coefficient a is taken as 0.01; when it is higher than 30℃, the subcool value monitor will alarm. When the subcool value of a single well is between 5 and 10℃, the evaporation coefficient a is taken as 0.02; When the subcool value of a single well is between 2 and 5℃, the evaporation coefficient a is taken as 0.08; When the subcool value of a single well is below 2℃, the evaporation coefficient a is taken as 0.10.

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