landfilldesign.com
Geocomposite Gas Pressure Relief Layer under Surface Impoundments  - Design Calculator

Problem Statement

This calculator determines the transmissivity of a geocomposite layer required to release pressure built up due to gas entrapment. Such gas may be caused by the decay of organics within the subgrade or rising water table. Proper design and use of a geocomposite underdrain can eliminate the potential for whaling.

Solutions

Flow Rate

The gas flow rate under the pond's liner is a function of the mass flux of the gas and the pond's length. The mass flux of gas under the pond is site specific and varies spacially and temporally in a given pond. The gas flow rate under the pond is defined as follows:

Eq. (1)

ΦPG

 Pond gas flux (m3/s/m2)

qPG

 Pond gas flow rate (m3/s/m)

L

 Pond length (m)

s

 Slope (m/m)

Required Relief Layer Transmissivity

The required gas transmissivity for PG relief layer is based on PG flow rate (qPG) and gas gradient (i).

Eq. (2)


Eq. (3)

where:

θrequired PG

 Required PG layer transmissivity (m3/s/m)

qPG

 Flow rate (m3/s/m)

i

 Gas Gradient (m/m)

umax

 Allowed mas gas pressure (KPa)

γgp

 Unit weight fo gas (KN/m3)

Eq. (4)

where:

θultimate PG

 Ultimate PG layer transmissivity (m2/s)

FS

 Overall factor of safety

RFin

 Intrusion Reduction Factor

RFcr

 Creep Reduction Factor

RFcc

 Chemical Clogging Reduction Factor

RFbc

Biological Clogging Reduction Factor

TSF

Total Serviceability Factor = FS * RFin * RFcr * RFcc * RFbc

Hydraulic Transmissivity vs. PG Transmissivity

The gas transmissivity can be converted to a hydraulic transmissivity for the same drainage medium. The intrinsic permeability variables for common liquids and gases are listed in Table 1.

Eq. (5)

where:

θH20

 Hydraulic transmissivity (m2/s)

θGAS

 gas transmissivity (m2/s)

μgas

 Dynamic viscosity of gas (N-s/m2)
μH20 Dynamic viscosity of water (N-s/m2)
γGAS Unit weight of gas (kN/m3)

γH20

 Unit weight of water (kN/m3)
 

Table 1. - Intrinsic Permeability Variables for Common Fluids and Gases (70oF)
  Density, ρ Unit Weight, γ Dynamic Viscosity, μ  Kinematic Viscosity, υ
  slug/ft3 kg/m3 pcf N/m3 Centipoise lb-s/ft2 N-s/m2 ft2/s m2/s
Water 1.94 1000 62.4 9800 1.01 2.12E-5 1.01E-3 1.09E-5 1.01E-6
Air 2.34E-3 1.2 .0753 11.8 .018 3.78E-7 1.79E-5 1.63E-4 1.48E-5
CO2 3.55E-3 1.83 .114 17.9 .015 3.15E-7 1.50E-5 8.88E-5 8.21E-6
Methane 1.29E-3 .666 .0416 6.54 .011 2.31E-7 1.10E-5 1.79E-4 1.65E-5
LFG(*) 2.53E-3 1.31 .0815 12.8 .0132 2.77E-7 1.32E-5 1.09E-4 1.01E-5

*55% CO2  ,45% CH4



Input Values
Gas Relief Layer underneath Ponds
Φpond m3/s/m2
L m
umax KPa
γgp kN/m3
Reduction Factors and Safety Factor
Surface Systems
RFin 1.0 - 1.2
RFcr 1.1 - 1.4
RFcc 1.0 - 1.2
RFbc 1.2 - 1.5
FS 2.0 - 3.0


References

Richardson, G.N. and Zhao, A., (2000), "Gas Transmission in Geocomposite Systems", Geotechnical Fabrics Report, March, pp. 20-23, 2000.

Thiel, R.S. (1998), "Design Methodology for a Gas Pressure Relief Layer Below a Geomembrane Landfill Cover to Improve Slope Stability", Geosynthetic International, Vol. 5, No. 6 pp. 589-617.


 Copyright 2001 Advanced Geotech Systems.  All rights reserved.