CN104680009B - A kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing - Google Patents

A kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing Download PDF

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CN104680009B
CN104680009B CN201510075248.9A CN201510075248A CN104680009B CN 104680009 B CN104680009 B CN 104680009B CN 201510075248 A CN201510075248 A CN 201510075248A CN 104680009 B CN104680009 B CN 104680009B
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vertical shaft
refuse landfill
unit
permeability
flow
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CN104680009A (en
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刘磊
薛强
曾刚
王平
陈亿军
马骏
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Wuhan Institute of Rock and Soil Mechanics of CAS
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Wuhan Institute of Rock and Soil Mechanics of CAS
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Abstract

The invention discloses a kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing, comprise the following steps:Determine the basic parameter of vertical shaft place reservoir area;Determine the permeability and gas production rate of reservoir area junk-heap body;The flow value of different pumping intensity, punching segment length and the corresponding single vertical shaft of permeability is calculated with the first Optimization Design Method;According to data on flows storehouse, with the second Optimization Design Method, the optimum well spacing of multiple vertical shafts, punching segment length and pumping intensity are determined;Construction of Silo is carried out, and multiple vertical shafts is run by optimum pumping intensity.The method turns to target with the maximum of vertical shaft collecting amount, carry out the prediction of multiple vertical shaft collecting amounts, provide the optimization scheme of multiple vertical shaft synthetic operations, by distribution and the running status of optimum suction well, enhance control and collection of the vertical shaft to biogas in landfill yard reservoir area, the collection efficiency of collection system is effectively increased, the Operating ettectiveness to improve category sludge gas generation engineering provides technical support.

Description

A kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing
Technical field
The present invention relates to refuse landfill pollution prevention technical field, more particularly to a kind of refuse landfill is distributed with vertical shaft And running optimizatin method for designing.
Background technology
Refuse landfill gas gathering system generally can be divided into two big class of horizontal trachea collection system and vertical shaft collection system. At present, the refuse landfill gas well collection system of domestic operation exploitation, mostly with《House refuse Sanitary Landfill Technology specification》 (CJJ17-2004) it is foundation, it is stipulated that landfill gas guide facility preferably adopts vertical shaft (pipe), transverse tube (ditch) or anyhow may also be employed Connected guide facility.Specify that the gabion that vertical shaft can adopt perforation placed in the middle preferably matches somebody with somebody stone with level outside perforated pipe in the setting of vertical shaft The filling of the shape things such as material, the well spacing of vertical shaft are usually arranged as 45~50m, and do not make related description for vertical shaft arranges depth etc.. When landfill depth adopts active inducing QI more than 20m, transverse tube is preferably set.The method is risen for garbage category sludge gas security control Arrived certain preventive and therapeutic effect, but biogas collection and control effect it is unsatisfactory, usual collection efficiency is only 25~40%.Together When, there is bigger difference in the constituent of different geographical house refuse, cause each not phase of biogas occuring regularity in landfill yard reservoir area Together, the internal structure of Design of Waste Landfill Site construction and the environmental condition of location there is also larger diversity, further The uncertainty of biogas output is exacerbated, while also resulting in the uncertainty of vertical shaft capture range and operation intensity.
In vertical shaft design of the prior art, there is the angle from shaft structure, it is proposed that many designs, By the technological means cemented the well using sleeve, the weight of grit in the deadweight and sleeve by sleeve itself, it is to avoid rubbish is filled out Bury a gas guide well and the problems such as deformation, damage occur, efficiently solve the problems, such as the silting of gas, it is ensured that the smooth guide of gas And sealing problem.But the method only unilaterally changes the setting of vertical shaft, does not propose the distribution scheme of gas well, for rubbish is filled out The collection efficiency for burying field entirety gas well does not make effectively assessment.Further, from the angle of Engineering technical parameters, analyze and take out The concrete influence factor of gas well pumping efficiency, the design and optimization to extraction well play certain promotion, but, to engineering skill The consideration of art parameter is not comprehensive, does not analyze heap body permeability in landfill yard reservoir area, gas deliverability, vertical shaft punching section and pumping strong The impacts of the parameter to extraction well pumping efficiency such as degree, do not propose reasonably to optimize handss to the integral layout of refuse landfill vertical shaft Section.Therefore, in prior art, in the case that in each refuse landfill in each department, biogas occuring regularity diversity is larger, also do not have A kind of vertical shaft design can be obtained.
The content of the invention
The present invention is distributed and running optimizatin method for designing by providing a kind of refuse landfill vertical shaft, solves existing skill In art, vertical shaft design fails to propose rational optimization means to refuse landfill vertical shaft integral layout, in each rubbish in each department In the case that in landfill yard, biogas occuring regularity diversity is larger, it is impossible to obtain the technical problem for preferably collecting efficiency, realize The reasonably optimizing of refuse landfill vertical shaft integral layout, the vertical shaft that the vertical shaft Optimization Design is designed, in different regions In the case that biogas occuring regularity diversity is larger in different refuse landfills, can obtain.
A kind of refuse landfill that the present invention is provided is distributed with vertical shaft and running optimizatin method for designing, is comprised the following steps:
S1:Determine the basic parameter of vertical shaft place reservoir area;
S2:Determine the permeability and gas production rate of the reservoir area junk-heap body;
S3:According to the basic parameter, permeability and gas production rate, with the first Optimization Design Method, calculate single described The gas pressure value of vertical shaft, meanwhile, calculate different pumping intensity, punching segment length and the permeability corresponding single described The flow value of vertical shaft, and set up data on flows storehouse;
S4:According to the data on flows storehouse, with the second Optimization Design Method, determine between the optimum well of the plurality of vertical shaft Away from, punching segment length and pumping intensity;
S5:Landfill yard Construction of Silo is carried out according to the optimum well spacing of the plurality of vertical shaft and punching segment length, according to institute The pumping intensity for stating optimum runs the plurality of vertical shaft.
Preferably, the basic parameter of reservoir area described in step S1 is provided with warehouse-in by the junk data filled out by reservoir area Material determines;The basic parameter includes:The reservoir area depth, garbage loading embeading age.
Preferably, the permeability in step S2 determines that by exhaustive test gas production rate is supervised by gas pressure Determination is tested in test.
Preferably, first Optimization Design Method in step S3 includes:
According to permeability and gas production rate, gas pressure value is determined with methane migration equation of continuity;The biogas is moved Moving equation of continuity is:Wherein, p is gas pressure;Permeabilities of the k for junk-heap body;ε For constant;μ is mixed gas kinematic coefficient of viscosity;QgFor gas production rate;
The excursion of flow in single vertical shaft running is determined with single vertical shaft flow rate calculation formula;Wherein, institute Stating single vertical shaft flow rate calculation formula is:QwFor vertical shaft flow, unit m3/h;μ is mixing The gas motion coefficient of viscosity, unit are Pas;RwFor vertical shaft radius, unit m;P be the gas pressure, unit Pa;PwTo take out Gas intensity level, unit are Pa;H is punching segment length, unit m;RiFor the vertical shaft radius of influence, unit m;
The corresponding gas pressure p is calculated with the methane migration equation of continuity;By calculated institute State gas pressure p, set different permeability k value, punching length value h and pumping intensity level Pw, with the single vertical shaft Flow rate calculation formula calculates corresponding vertical shaft flow value Qw
Preferably, second Optimization Design Method in step S4 is:With the permeability value, punching segment length Value, pumping intensity level and vertical shaft flow value are optimization input variable, are rationally made with well spaced relationship formula, well spacing with vertical shaft flow It is constraints with scale relationships formula, vertical shaft discharge relation formula, target is turned to vertical shaft flow summation maximum, obtains the plurality of Vertical shaft optimum well spacing simultaneously under service condition, punching segment length and it is evacuated intensity;
Wherein, the vertical shaft flow with well spaced relationship is:Q'wErect for multiple Individual well gas flow under the conditions of well pumping simultaneously, unit m3/h;μ be mixed gas kinematic coefficient of viscosity, unit Pas;L is Well spacing, unit m;RwFor vertical shaft radius, unit m;P be the gas pressure, unit Pa;PwTo be evacuated intensity, unit Pa;H is Punching segment length, unit m;
The well spacing reasonable function scale relationships formula is:Wherein, H be reservoir area depth, unit For m;
The vertical shaft discharge relation formula is:Wherein, QgFor the aerogenesis of vertical shaft overlay area Amount, unit m3/h;Q′wjFor the flow of jth mouth vertical shaft, unit m3/h;N is vertical shaft quantity summation;QMAXFor vertical shaft flow summation, Unit m3/h。
The technical scheme provided in the embodiment of the present application, at least has the following technical effect that:
It is distributed by above-mentioned vertical shaft and running optimizatin method for designing, asks for obtaining pumping intensity level, the well spacing of optimum Value and the length value that punches, save design time.Multiple vertical shaft running optimizatin designs can be according to specific landfill yard reservoir area work Condition is designed, and engineer applied has more preferable adaptability and motility.Multiple vertical shaft running optimizatin designs are based on collection efficiency What principle of optimality was carried out, vertical shaft is realized by controlling pumping intensity, well spacing, punching length and collect the maximization of efficiency, keep away The excessive construction delay for being evacuated and causing is exempted from, has simplified technique and ensure that the continuous service of vertical shaft collection.The optimization design side Method not only solves vertical shaft and collects that gas efficiency is low, the chaotic problem of vertical shaft distribution arrangement, and also a saving a large amount of manpowers, thing Power, financial resources.The Optimization Design is used in the different refuse landfills of different regions, the vertical shaft designed can be managed The collection efficiency thought, significantly improves garbage category sludge gas collection efficiency, increased the economic benefit of marsh gas power generation engineering, very The good demand for having adapted to garbage category sludge gas generating.
Description of the drawings
Vertical shaft distribution and the flow chart of running optimizatin method for designing that Fig. 1 is provided for the application.
The shaft structure schematic diagram that Fig. 2 is provided for the embodiment of the present application.
The vertical shaft well spacing distribution schematic diagram that Fig. 3 is provided for the embodiment of the present application.
The landfill area plane graph that Fig. 4 is provided for the embodiment of the present application.
Specific embodiment
Referring to accompanying drawing 1, a kind of refuse landfill that the embodiment of the present application is provided is distributed with vertical shaft and running optimizatin design side Method, comprises the following steps:
S1:Determine the basic parameter of vertical shaft place reservoir area.
S2:Determine the permeability and gas production rate of reservoir area junk-heap body.
S3:According to basic parameter, permeability and gas production rate, with the first Optimization Design Method, the single vertical shaft is calculated Gas pressure value, meanwhile, calculate the streams of different pumping intensity, punching segment length and the corresponding single vertical shaft of permeability Value, and set up data on flows storehouse.
S4:According to data on flows storehouse, with the second Optimization Design Method, the optimum well spacing of multiple vertical shafts, punching section are determined Length and pumping intensity.
S5:Landfill yard Construction of Silo is carried out according to the optimum well spacing of multiple vertical shafts and punching segment length, according to optimum Pumping intensity runs multiple vertical shafts, and the collecting methane amount to multiple vertical shafts is monitored, and verifies the optimization method for carrying The effectiveness of high biogas collecting amount.
Further, in the step S1 junk data and warehouse-in data filled out by reservoir area by the basic parameter of reservoir area determines; Basic parameter includes:Reservoir area depth, garbage loading embeading age.Permeability in step S2 determines that by exhaustive test gas production rate leads to Cross gas pressure monitoring test to determine.
Further, the first Optimization Design Method in step S3 includes:According to permeability and gas production rate, move with biogas Move equation of continuity and determine gas pressure value;Methane migration equation of continuity is:Wherein, p For gas pressure;Permeabilities of the k for junk-heap body;ε is constant;μ is mixed gas kinematic coefficient of viscosity;QgFor gas production rate.
The excursion of flow in single vertical shaft running is determined with single vertical shaft flow rate calculation formula;Wherein,Wherein, QwFor vertical shaft flow, unit m3/h;μ be mixed gas kinematic coefficient of viscosity, unit For Pas;RwFor vertical shaft radius, unit m;P be the gas pressure value, unit Pa;PwTo be evacuated intensity level, unit is Pa;h For segment length of punching, unit m;RiFor the vertical shaft radius of influence, unit m.
Corresponding gas pressure p is calculated with methane migration equation of continuity;By set different permeability k value, Punching length value h and pumping intensity level Pw, corresponding vertical shaft flow value Q is calculated with single vertical shaft flow rate calculation formulaw, Then by all permeability k value, punching length value h and pumping intensity level PwWith corresponding vertical shaft flow value QwSet up after statistics Data on flows storehouse.
Further, the second Optimization Design Method in step S4 is:With permeability value, punching length value, pumping intensity Value and vertical shaft flow value are optimization input variable, with vertical shaft flow and well spaced relationship formula, well spacing reasonable function scale relationships Formula, vertical shaft discharge relation formula are constraints, turn to target with vertical shaft flow summation maximum, obtain multiple vertical shafts and run bar simultaneously Optimum well spacing, punching segment length and pumping intensity under part;Wherein, can be by the permeability k value in multiple vertical shafts, punching segment length Angle value h and pumping intensity level PwWith corresponding vertical shaft flow value QwStatistics forms the data on flows storehouse of multiple vertical shafts.
Wherein, vertical shaft flow with well spaced relationship is:Q'wIt is same for multiple vertical shafts When pumping under the conditions of individual well gas flow, unit m3/h;μ be mixed gas kinematic coefficient of viscosity, unit Pas;L is between well Away from unit m;RwFor vertical shaft radius, unit m;P be the gas pressure value, unit Pa;PwTo be evacuated intensity level, unit Pa;H is Punching segment length, unit m.
The well spacing reasonable function scale relationships formula is:Wherein, H be reservoir area depth, unit For m.
The vertical shaft discharge relation formula is:Wherein, QgFor the aerogenesis of vertical shaft overlay area Amount, unit m3/h;Q′wjFor the flow of jth mouth vertical shaft, unit m3/h;N is vertical shaft quantity summation;QMAXFor vertical shaft flow summation, Unit m3/h。
The technical scheme of the application is described in detail below by specific embodiment:
By taking certain concrete garbage category sludge gas collection vertical shaft design as an example, a kind of refuse landfill of the present invention is described in detail It is distributed with vertical shaft and running optimizatin method for designing.
Specific landfill yard overview:The landfill yard is located at Wuhan City, Hubei Province, and reservoir area is the 4th landfill area, day processes rubbish About 2000 tons, floor space about 2.75 × 104m2.Jing Field Research data shows that the basic parameter of the reservoir area is:Garbage loading embeading Age is 1.3 years, average landfill depth 23.8m, and vertical shaft seal section is 1m, fills area planar figure as shown in Figure 4.Shaft structure shows It is intended to referring to accompanying drawing 2, the pumping strength relationship of vertical shaft seal section, punching segment length and evacuating valve position is received to the gas of vertical shaft Collection ability, therefore, appropriate design punching segment length and pumping intensity can significantly improve the collection efficiency of vertical shaft.
By live exhaustive test, test obtains the region heap body permeability from 1.05 × 10- 13m2Arrive
2.3×10- 11m2.Tested by gas on-site pressure monitoring, obtaining junk-heap body gas production rate is
8.15×10- 4m3/(m3/ h) --- i.e. rubbish produces 8.15 × 10 per hour per cubic meter- 4The natural pond of cubic meter
Gas.
Based on the basic parameter in the 4th landfill area, different pumping intensity, different punching segment length and difference are calculated respectively Vertical shaft flow under the conditions of permeability in single vertical shaft running, by all permeability k value, punching length value h and pumping Intensity level PwWith corresponding vertical shaft flow value QwData on flows storehouse is set up after statistics, 1 is shown in Table.
Table 1
Sample values 1 2 3 S-2 S-1 S
Permeability k (10-12m2) 1.5 2 2.5 1.5 2 2.5
Punching segment length h 6 6 6 10 10 10
Pumping intensity Pw -0.5 -0.5 -0.5 -1 -1 -1
Vertical shaft flow Qw 13.2 15.1 17.3 20.5 22.3 24.4
Referring to accompanying drawing 4, modeling is optimized to multiple vertical shaft flows using BP neural network, in model with permeability, beat Hole length, pumping intensity and flow are optimization input variable, become by optimization output of well spacing, punching segment length and pumping intensity Amount, with vertical shaft flow and well spaced relationship, well spacing reasonable function scope (wherein vertical shaft well spacing schematic diagram is shown in accompanying drawing 3), erects Well yield is constraints less than reservoir area biogas quantum of output, turns to target with vertical shaft maximum flow, obtains the same luck of multiple vertical shafts Optimum vertical shaft well spacing, punching segment length and pumping intensity under the conditions of row.By the permeability k value in multiple vertical shafts, punching section Length value h and pumping intensity level PwWith corresponding vertical shaft flow value Q 'wStatistics forms data on flows storehouse, is shown in Table 2.
Table 2
Sample values 1 2 3 S-2 S-1 S
Permeability k (10-12m2) 1.0 1.0 1.0 9.0 9.0 9.0
Punching segment length h 4 4 4 16 16 16
Pumping intensity Pw -0.5 -0.5 -0.5 -1 -1 -1
Vertical shaft flow Q 'w 14.5 15.7 17.1 32.4 34.5 35.9
After optimum results meet the constraint condition and optimization aim, well spacing L, the punching of multiple vertical shafts under optimal conditionss are obtained Segment length h is respectively:34.5m, 13.8m.Pumping intensity Pw(the first two years):- 1.83kPa (First Year), -1.31kPa (second Year).Optimum well spacing 34.5m, optimum punching segment length 13.8m according to the multiple vertical shafts in optimum results, in above-mentioned landfill Reservoir area carries out Construction of Silo, according to the optimum pumping intensity Q in optimum resultswOperation silo system, the flow to silo system It is monitored.Monitoring result shows:Actual collection amount and reservoir area biogas quantum of output ratio reached at first 2 years 84.9% and 87.0%, this shows the collection efficiency of the silo system with the Optimization Design design apparently higher than current other storehouses of the country The collection efficiency in area.
The technical scheme provided in the embodiment of the present application, at least has the following technical effect that:
It is distributed by above-mentioned vertical shaft and running optimizatin method for designing, asks for obtaining pumping intensity level, the well spacing of optimum Value and the length value that punches, save design time.Multiple vertical shaft running optimizatin designs can be according to specific landfill yard reservoir area work Condition is designed, and engineer applied has more preferable adaptability and motility.Multiple vertical shaft running optimizatin designs are based on collection efficiency What principle of optimality was carried out, vertical shaft is realized by controlling pumping intensity, well spacing, punching length and collect the maximization of efficiency, keep away The excessive construction delay for being evacuated and causing is exempted from, has simplified technique and ensure that the continuous service of vertical shaft collection.The optimization design side Method not only solves vertical shaft and collects that gas efficiency is low, the chaotic problem of vertical shaft distribution arrangement, and also a saving a large amount of manpowers, thing Power, financial resources.The Optimization Design is used in the different refuse landfills of different regions, the vertical shaft designed can be managed The collection efficiency thought, significantly improves garbage category sludge gas collection efficiency, increased the economic benefit of marsh gas power generation engineering, very The good demand for having adapted to garbage category sludge gas generating.
Above-described specific embodiment, has been carried out further to the purpose of the present invention, technical scheme and beneficial effect Describe in detail, the be should be understood that specific embodiment that the foregoing is only the present invention is not limited to this Bright, all any modification, equivalent substitution and improvements within the spirit and principles in the present invention, done etc. should be included in the present invention Protection domain within.

Claims (3)

1. a kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing, it is characterised in that comprised the following steps:
S1:Determine the basic parameter of refuse landfill vertical shaft place reservoir area;
S2:Determine the permeability and gas production rate of the reservoir area junk-heap body;
S3:According to the basic parameter, permeability and gas production rate, with the first Optimization Design Method, the single rubbish is calculated The gas pressure value of landfill yard vertical shaft, meanwhile, calculate different pumping intensity, punching segment length and the permeability corresponding The flow value of the single refuse landfill vertical shaft, and set up data on flows storehouse;
S4:According to the data on flows storehouse, with the second Optimization Design Method, the optimum well of multiple refuse landfill vertical shafts is determined Spacing, punching segment length and pumping intensity;
S5:Landfill yard garbage loading embeading is carried out with the optimum well spacing of vertical shaft and punching segment length according to the plurality of refuse landfill Field Construction of Silo, runs the plurality of refuse landfill vertical shaft according to the optimum pumping intensity;
First Optimization Design Method in step S3 includes:
According to permeability and gas production rate, gas pressure value is determined with methane migration equation of continuity;The methane migration connects Continuous property equation is:Wherein, permeabilities of the k for junk-heap body;ε is constant;QgFor aerogenesis speed Rate;
Determine in single refuse landfill vertical shaft running with single refuse landfill vertical shaft flow rate calculation formula and flow The excursion of amount;Wherein, the single refuse landfill vertical shaft flow rate calculation formula is:QwFor refuse landfill vertical shaft flow, cubic unit m/h;μ is transported for mixed gas Coefficient of kinematic viscosity, unit for Pa Sec;RwFor refuse landfill vertical shaft radius, unit rice;P is gas pressure, unit handkerchief;Pw To be evacuated intensity level, unit is handkerchief;H is punching segment length, unit rice;RiFor the refuse landfill vertical shaft radius of influence, unit Rice;
The corresponding gas pressure p is calculated with the methane migration equation of continuity;By the calculated gas Body pressure p and permeability value k, punching length value h and pumping intensity level Pw, with the single refuse landfill vertical shaft Flow rate calculation formula calculates corresponding refuse landfill vertical shaft flow value Qw
Second Optimization Design Method in step S4 is:With permeability value, punching length value, pumping intensity level and rubbish Rubbish landfill yard vertical shaft flow value is optimization input variable, with refuse landfill between vertical shaft flow and well spaced relationship formula, well It is constraints away from reasonable function scale relationships formula, refuse landfill vertical shaft discharge relation formula, with refuse landfill vertical shaft Flow summation maximum turns to target, obtain optimum well spacing of the plurality of refuse landfill vertical shaft simultaneously under service condition, Punching segment length and pumping intensity;
Wherein, the refuse landfill vertical shaft flow with well spaced relationship is:Q'wFor Individual well gas flow under the conditions of the pumping simultaneously of multiple refuse landfill vertical shafts, cubic unit m/h;μ is mixed gas Kinematic coefficient of viscosity, unit Pa Sec;L be well spacing, unit rice;RwFor refuse landfill vertical shaft radius, unit rice;P is The gas pressure, unit handkerchief;PwTo be evacuated intensity, unit handkerchief;H is punching segment length, unit rice;
The well spacing reasonable function scale relationships formula is:Wherein, H is reservoir area depth, and unit is rice;
The refuse landfill vertical shaft discharge relation formula is:Wherein, QgFor refuse landfill With the gas production of vertical shaft overlay area, cubic unit m/h;Q′wjFor the flow of jth mouth refuse landfill vertical shaft, unit Cube m/h;N is refuse landfill vertical shaft quantity summation;QMAXFor refuse landfill vertical shaft flow summation, unit is stood Square m/h.
2. method for designing as claimed in claim 1, it is characterised in that:
The junk data and warehouse-in data filled out by reservoir area by the basic parameter of reservoir area described in step S1 determines;The base This parameter includes:Reservoir area depth, garbage loading embeading age.
3. method for designing as claimed in claim 1, it is characterised in that:
Permeability in step S2 determines that by exhaustive test gas production rate is determined by gas pressure monitoring test.
CN201510075248.9A 2015-02-12 2015-02-12 A kind of refuse landfill is distributed with vertical shaft and running optimizatin method for designing Active CN104680009B (en)

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CN109085307B (en) * 2018-09-18 2023-12-22 中国科学院武汉岩土力学研究所 Multi-parameter collection and detection device for refuse landfill gas

Citations (2)

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Publication number Priority date Publication date Assignee Title
CN201760436U (en) * 2010-03-01 2011-03-16 北京环卫集团环境研究发展有限公司 Garbage landfill gas discharging and collecting system
CN102400473A (en) * 2011-08-08 2012-04-04 南京大学 Construction method for gas suction vertical shaft of waste landfill gas and collection device

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CN201760436U (en) * 2010-03-01 2011-03-16 北京环卫集团环境研究发展有限公司 Garbage landfill gas discharging and collecting system
CN102400473A (en) * 2011-08-08 2012-04-04 南京大学 Construction method for gas suction vertical shaft of waste landfill gas and collection device

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Title
垃圾填埋场填埋气竖井收集系统设计优化;彭绪亚等;《环境污染治理技术与设备》;20030331;第4卷(第3期);6-8 *

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