Determination of Soil Hydraulic Parameters with CyclicIrrigation Tests

Communar, Gregory; Friedman, Shmulik P.

doi:10.2136/vzj2013.09.0168

Cited by 11 publications

(11 citation statements)

References 42 publications

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“…Introducing the dimensionless variables:

\begin{matrix} left \\ \frac{R}{r} = \frac{Z}{z} = \frac{H_{normalw}}{{normalϕ}_{normalw}} = \frac{α_{normala}}{2} \\ ρ = {(R^{2} + Z^{2})}^{1 / 2} \\ \frac{T}{t} = \frac{α_{normala} k_{normala}}{4} \\ and \\ Φ = \frac{8 π φ}{α_{normala} Q_{0}} \end{matrix}

the solution for the nondimensional (ND) MFP resulting from a periodic harmonic variation in the air‐discharge rate

Q (t) = Q_{0} + Q_{0} \sin (ω t)

where ω = 2π/ t c [T −1 ] is the radian frequency (angular velocity) and t c [T] is the cycle period during which Q oscillates in the range of 0 ≤ Q ≤ 2 Q 0 , for a buried point source located at Z = 0, was given by Communar and Friedman (2014), where it was described as

{normalΦ}_{\infty} = \frac{1}{2} ({normalΦ}_{\infty}^{normalC} + {normalΦ}_{\infty}^{normalp})

with the superscripts C and P denoting the constant and periodic flux terms, respectively. The MFP resulting from the constant flux term (Φ ∞ C ) is (Philip, 1968)

{normalΦ}_{\infty}^{normalC} = \frac{\exp (Z - ρ)}{normalρ}

{normalΦ}_{\infty}^{normalP} = \frac{\exp (Z - {normalμ}_{1} ρ)}{normalρ} \sin ({normalω}_{0} T - {normalμ}_{2} ρ)

where ω 0 = 4ω/α a k a is the dimensionless radian frequency and the coefficients μ 1 and μ 2 are

\begin{array}{l} left<...> \end{array}

…”

Section: Model Assumptionsmentioning

confidence: 99%

“…Unlike the harmonic air injection described above, which requires special equipment, square‐wave (step‐input) air injection is more practical and easier to implement. Cyclic‐step air injection with equal on and off times (50% duty cycle) can be represented as a Fourier sine series of the aforementioned harmonic air injection (Communar and Friedman, 2014):

Q (t) = Q_{0} + Q_{0} \sum_{m = 1}^{\infty} \frac{4 \sin ({normalω}_{normalm} t)}{2 m - 1}

comprised of only odd‐number harmonics: ω m = (2 m − 1)ω. Thus, the MFP resulting from cyclic step‐input air injection into an infinite soil domain is

\begin{matrix} left \\ {normalΦ}_{\infty, p u l s} = \frac{\exp (Z - ρ)}{2 ρ} \\ + \frac{4}{normalπ} \sum_{m = 1}^{\infty} \frac{\exp (Z - {normalμ}_{m, 1} ρ)}{(2 m - 1) ρ} \sin ({normalω}_{m, 0} T - {normalμ}_{m, 2} ρ) \end{matrix}

where μ m,1 and μ m,2 are determined by Eq.…”

Section: Model Assumptionsmentioning

confidence: 99%

“…7, Z 0 = 1) below the soil surface is between 31 cm for constant‐rate air injection (or very short cycle periods) and 44 cm for long cycles using step‐pulse or harmonic air injection. Communar and Friedman (2014) suggested a simple field method to determine the soil parameters ( k w and α w ) for the purpose of drip‐irrigation design, based on measuring the time shift and amplitude of the capillary head (using a tensiometer) at a fixed depth below the source dripper. This simple procedure cannot be easily transformed for assessing the soil parameters for air flow because in this case much smaller, undetectable time shifts and air pressure amplitudes are expected (Fig.…”

Section: Model Assumptionsmentioning

confidence: 99%

“…The general solution (j ¥ ) of Eq. [6] for a point source buried in an infinite domain and emitting at an arbitrary rate Q(t) = Q 0 f (t) with a constant Q 0 [L 3 T −1 ] was given by Carslaw and Jaeger (1959): where w = 2p/t c [T −1 ] is the radian frequency (angular velocity) and t c [T] is the cycle period during which Q oscillates in the range of 0 £ Q £ 2Q 0 , for a buried point source located at Z = 0, was given by Communar and Friedman (2014), where it was described as…”

Section: Harmonic Air Injection From a Point Source Into An Ininite Smentioning

confidence: 99%

“…Unlike the harmonic air injection described above, which requires special equipment, square-wave (stepinput) air injection is more practical and easier to implement. Cyclic-step air injection with equal on and off times (50% duty cycle) can be represented as a Fourier sine series of the aforementioned harmonic air injection (Communar and Friedman, 2014):…”

Section: Square-wave (Step-input) Air Injectionmentioning

confidence: 99%

See 4 more Smart Citations

Bounds to Air‐Flow Patterns during Cyclic Air Injection into Partially Saturated Soils Inferred from Extremum States

Ben‐Noah

Friedman

2019

Vadose Zone Journal

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Core Ideas The problem of periodic air injection from a point source into the soil is analyzed. Air content and pressure are bounded by extremum states of instantaneous water relaxation. Air‐flow pattern determined by two soil parameters and cycle period. Use of simplified analytical solutions enables a preliminary design of an aeration system. Soil‐aeration procedures are widely used as an environmental practice for soil and groundwater remediation (removal of volatile compounds and enhancement of biological treatment) and less frequently as an agricultural practice to prevent root O2 deficiency. Analytical solutions to problems of air flow in the soil allow a phenomenological analysis of the physical problem and the effects of the governing parameters, which in turn enables a more systematic design tool for soil‐aeration systems. We present solutions for the air‐pressure distributions resulting from harmonic (sinusoidal) or square‐wave (step‐pulse) air injection into infinite and semi‐infinite (with an atmospheric pressure at the soil surface) soil domains. The approach presented here suggests using exact (analytical) solutions to extreme (unrealistic) conditions, setting the boundaries of the physical span of the flow problem. The simplified analytical solutions, based on assuming instantaneous water relaxation or, alternatively, assuming stagnant water are used to analyze the effects of different air‐injection modes (constant, harmonic, and step‐pulse) on the air‐pressure distribution and radius of influence (ROI) for different values of the governing parameters: source depth, cycle period, and the soil's air‐conductivity parameters. For long cycle periods, square‐pulse and harmonic air injection can increase the maximal ROI compared with that resulting from steady air injection.

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“…Introducing the dimensionless variables:

\begin{matrix} left \\ \frac{R}{r} = \frac{Z}{z} = \frac{H_{normalw}}{{normalϕ}_{normalw}} = \frac{α_{normala}}{2} \\ ρ = {(R^{2} + Z^{2})}^{1 / 2} \\ \frac{T}{t} = \frac{α_{normala} k_{normala}}{4} \\ and \\ Φ = \frac{8 π φ}{α_{normala} Q_{0}} \end{matrix}

the solution for the nondimensional (ND) MFP resulting from a periodic harmonic variation in the air‐discharge rate

Q (t) = Q_{0} + Q_{0} \sin (ω t)

{normalΦ}_{\infty} = \frac{1}{2} ({normalΦ}_{\infty}^{normalC} + {normalΦ}_{\infty}^{normalp})

with the superscripts C and P denoting the constant and periodic flux terms, respectively. The MFP resulting from the constant flux term (Φ ∞ C ) is (Philip, 1968)

{normalΦ}_{\infty}^{normalC} = \frac{\exp (Z - ρ)}{normalρ}

{normalΦ}_{\infty}^{normalP} = \frac{\exp (Z - {normalμ}_{1} ρ)}{normalρ} \sin ({normalω}_{0} T - {normalμ}_{2} ρ)

where ω 0 = 4ω/α a k a is the dimensionless radian frequency and the coefficients μ 1 and μ 2 are

\begin{array}{l} left<...> \end{array}

…”

Section: Model Assumptionsmentioning

confidence: 99%

Q (t) = Q_{0} + Q_{0} \sum_{m = 1}^{\infty} \frac{4 \sin ({normalω}_{normalm} t)}{2 m - 1}

comprised of only odd‐number harmonics: ω m = (2 m − 1)ω. Thus, the MFP resulting from cyclic step‐input air injection into an infinite soil domain is