Interrelationships Between Flux,Membrane Properties,and Soil Water Transport in a Subsurface Pervaporation Irrigation System

Abstract

Oil and natural gas-produced waters are by-products of energy development that present unique challenges to the energy industry and impacted landowners. Conventionally, produced waters are typically saline and therefore must be desalinated to some extent before beneficial reuse. Subsurface pervaporation irrigation combines desalination with beneficial reuse in the form of crop irrigation. This investigation studied factors governing water flux for two membranes, one polyether ester (PEE) and one cellulose triacetate (CTA), for use in subsurface pervaporation irrigation. Water flux was determined to be a function of membrane properties (thickness, hydrophilicity) and environmental variables (vapor pressure gradient, soil texture, soil clay content). Specific water fluxes ranged from a maximum of 6.77×10⁻² L/[m²·day·Pa] for CTA membranes to a minimum of 7.97×10⁻³ L/[m²·day·Pa] for PEE membranes. Fluxes increased as water vapor pressure in the soil adjacent to the membrane decreased. Total soil water potential and its specific components, matric potential and osmotic potential, influenced flux. Clayey and peaty soils have a lower matric potential than sand for the same soil water content, which translated to a lower vapor pressure and hence higher flux for clayey/peaty soils.

Introduction

Agriculture accounts for ∼70% of freshwater withdrawals worldwide (FAO, 2000; Rosegrant et al., 2005). As the global population continues to grow, the stresses placed on finite water supplies will only increase (Vorosmarty et al., 2000; Means et al., 2005; Jones, 2009; Fuller and Harhay, 2010; Chartres et al., 2011; Younos et al., 2013; Singh et al., 2014). Produced water is cogenerated during oil and/or natural gas production and generally comprises formation water and process flows like the flowback portion of hydraulic fracturing fluids. Presently, ∼2 billion gallons of produced water are generated in the United States every day (Veil, 2004; Benko and Drewes, 2008; Clark and Veil, 2009; Interior, 2011; Veil and Clark, 2011). Increased oil and natural gas development has led to a variety of water issues, primary among them is how to sustainably manage these enormous quantities of produced waters (Veil, 2004; Benko and Drewes, 2008; Gregory et al., 2011; Wilson and VanBriesen, 2012). For many areas, produced water represents an enormous untapped resource if it can be treated to an acceptable standard. Current produced water management practices include deep well injection (Tofflemire and Brezner, 1971; Bridgeman, 1980; Mogharabi, 1991; Fritsche, 2000), evaporators/brine crystallizers (Roos et al., 2003; Macedonio et al., 2013), and membrane technologies (Cakmakci et al., 2008; Mondal and WickramasingHe, 2008; Mondal et al., 2008; Welch, 2009; Hickenbottom et al., 2013; McGinnis et al., 2013; Ozgun et al., 2013; Phuntsho et al., 2013; Coday et al., 2014; Zhang et al., 2014). Although each is effective in its own right, they are all associated with various characteristics that inhibit their use in applications outside of centralized water management centers. This inhibits the beneficial reuse of produced waters in many regions experiencing rapid development of oil and gas resources. An alternative approach involves combining desalination directly with the beneficial reuse application. One such approach is subsurface pervaporation irrigation.

Pervaporation is a nonpressure-driven membrane process that has been in use since the 1950s for separating alcohol and organic solvents from water (Lipski and Cote, 1990; Marin et al., 1996; Jiraratananon et al., 2002; Kittur et al., 2005; Naidu and Aminabhavi, 2005; Huang et al., 2009; Li et al., 2010). In pervaporation, mass transport is driven by a difference in chemical potential across the membrane (e.g., a vapor pressure gradient) (Shao and Huang, 2007) with transport being described by the solution-diffusion model (Wijmans and Baker, 1995). Pervaporation differs from conventional membrane processes, in that the permeate changes phase from liquid to vapor on the permeate side of the membrane (Jonquieres et al., 2002; Shao and Huang, 2007). Because it is a nonpressure-driven membrane process, there has recently been a spike in interest in using pervaporation for desalination (Korngold and Korin, 1993; Korin et al., 1996; Korngold et al., 1996; Zwijnenberg et al., 2005; Quinones-Bolanos et al., 2005a, 2005b; Quinones-Bolanos and Zhou, 2006; Xie et al., 2011; Drobek et al., 2012; Sule et al., 2013; Todman et al., 2013a, 2013b; Huth et al., 2014). Researchers have looked at subsurface pervaporation irrigation as a way to combine water treatment (desalination) with beneficial reuse (Quinones-Bolanos et al., 2005a, 2005b; Quinones-Bolanos and Zhou, 2006; Sule et al., 2013; Todman et al., 2013a, 2013b).

Subsurface pervaporation irrigation utilizes tubular, semipermeable, and hydrophilic membrane materials in place of conventional drip tape. When considering using produced water or any other saline feed stream for irrigation, desalination is likely necessary to preserve plant health and soil characteristics. For produced water applications before the pervaporation irrigation system, select water constituents would have to be removed before the water enters the tubular membranes as these materials are known to result in severe membrane fouling. Examples of such materials include synthetic and naturally occurring organic compounds (Alzahrani et al., 2013), microbes/biological by-products (Alzahrani et al., 2013; Alzahrani and Mohammad, 2014), and particulates (Alzahrani and Mohammad, 2014). Mineral scaling within the tubular pervaporation membranes can be mitigated through acidification of the feed water to increase the solubility of the sparingly soluble salts to control mineral scaling (Le Gouellec and Elimelech, 2002; He et al., 2008). The likelihood of scaling will increase as the water becomes concentrated in the irrigation system. For this reason, the irrigation system will be periodically flushed with acidified water, or some cleaning solution, to remove those solids and precipitates that have accumulated within the tubular membranes. The nature and frequency of such cleaning events will be a function of the raw water quality and process operation.

Previous studies (Zwijnenberg et al., 2005; Quinones-Bolanos et al., 2005a, 2005b; Quinones-Bolanos and Zhou, 2006) have investigated subsurface pervaporation irrigation, with only a fraction of those using oil and gas-produced waters as source waters (Zwijnenberg et al., 2005; Sule et al., 2013). Quinones-Bolanos et al. (2005b) determined that water flux increased with decreasing humidity in the soil while achieving a max flux of 4 L/[m²·day]. Fluxes decreased with increasing feed water salinity. This was attributed to concentration polarization at the membrane surface and possible interference with water dissolution into the membrane polymer. Quinones-Bolanos et al. (2005a) examined the performance of a pervaporation membrane in a soil box, where the membrane was buried in two types of soils (a loam soil and a loamy sand) and a desiccant was used to simulate a plant root (a water sink). Flux was determined to be inversely proportional to the soil moisture content. Tests done by Sule et al. (2013) measured fluxes in topsoil of about 5×10⁻¹ L/[m²·day] compared with 2.04×10⁻¹ L/[m²·day] in sand. The higher flux measured in the topsoil was credited to the topsoil's ability to adsorb more water relative to the sand. Water adsorption by the soil purportedly drew the moisture away from the membrane and, in turn, created a higher vapor pressure gradient. Previous subsurface pervaporation irrigation experiments (Todman et al., 2013b) and simulations (Todman et al., 2013a) explored water transport through soil media from a buried pervaporation membrane. Water transport was assumed to occur in both liquid and vapor phases. Vapor flow through dry soils was determined to be more significant than liquid flow. Relationships between the membrane and soil properties and the resulting flux were not explored in detail in these earlier efforts. While a vapor pressure gradient is often cited as the primary driver for mass transport in subsurface pervaporation irrigation, it has not yet been evaluated in detail. This is particularly true for clayey soils, which are the most common types of soils in agricultural applications.

The objective of this study was to evaluate and study the interrelationships between flux, membrane properties, and moisture transport in the soil as applied to the desalination performance of a subsurface pervaporation irrigation process. The properties investigated included the soil type (soil texture, clay content, hydraulic conductivity), soil volumetric moisture content in the immediate vicinity of the tube (vapor pressure gradient), and membrane hydrophilicity. The results from the subsurface soil pervaporation experiments were compared with simulations done using the HYDRUS-2D model to better understand the movement of moisture within the soil. The soil moisture content within the wetted zone around the pervaporation membrane was analyzed to determine the feasibility of the irrigation membrane to practically irrigate crops.

Materials and Methods

Pervaporation membranes

Two different pervaporation membranes were studied in this investigation. The first was a polyether ester (PEE) membrane manufactured by Du Pont (de Nemours, Geneva). The tubular PEE membrane (diameter=2.14 cm) is nonporous and hydrophilic (Huth et al., 2014) and has a corrugated structure to enhance its mechanical strength for use in subsurface environments. Samples of different linear densities (mass per length of tubing) were examined (50, 70, and 90 g/m). The thicknesses of the top corrugations for the three linear densities were 0.2, 0.3, and 0.4 mm, respectively. The thicknesses of the bottom corrugation for the three linear densities were 0.6, 0.7, and 0.9 mm, respectively. The bulk density of the PEE membrane was 1.19 g/cm³. The second membrane was a cellulose triacetate (CTA) membrane supplied by Hydration Technology Innovations (Albany, OR). The CTA membrane is a composite membrane with an embedded polyester mesh for mechanical support. The active layer (CTA) thickness was ∼10 μm, and the total thickness of the membrane (CTA+polyester mesh) was 115 μm. The bulk density of the CTA membrane was ∼1.31 g/cm³. The pure water contact angle values for the flat-sheet PEE (linear density 50 g/m) and CTA membranes were 11.8°±4.7° and 46.2°±2.6°, respectively.

Bench-scale soil subsurface pervaporation tests

Subsurface pervaporation irrigation tests were conducted to determine the effect of membrane thickness, soil type, and environmental conditions (initial soil water content, relative humidity [RH] of headspace) on water flux. In addition, the transport of moisture from the membrane throughout the surrounding soil was studied. A schematic of the irrigation test apparatus used in this study is given in Figure 1. The total depth of the box was 30 cm, with 10 cm of headspace (headspace volume=0.13 m³) within the box. The tubular PEE (length, l=1 m, cross-sectional area, A_x=1.103 m²) or CTA (l=0.91 m, A_x=0.0828 m²) membrane was attached to watertight fittings inside the box, at a depth of 10 cm from the box bottom, and surrounded by 0.25 m³ of soil (total soil height was 20 cm from the bottom of the box to the top of the soil). An airline was used to circulate dry air through the box (1 L/min) to maintain the RH in the box at <2%.

FIG. 1.

Experimental setup used for bench-scale subsurface pervaporation irrigation tests. Note that the recycle line was only used in one test with the clay loam soil to study the effect of feed mixing on membrane performance. The feed water used in all the tests was coal bed methane (CBM)-produced water (T_avg.=22°C, TDS_initial=1,230 mg/L, pH_initial=7.91).

Soil types used in the experiments included silica sand garden soil and a clay loam soil. The silica sand (AquaQuartz, Wedron, IL) was Grade No. 20 with a particle diameter range of 0.45–0.55 mm. The initial water content of the sand was 0.05 m³/m³. The clay loam soil was obtained from Rawlins, WY. The clay loam comprised ∼30% sand, 30% silt, and 40% clay. It had an initial water content of 0.08 m³/m³. The garden soil used in the tests was obtained from Miracle-Gro^® (Marysville, OH). It is a blend of organic materials, sphagnum peat moss, and nutrients. The initial water content of the garden soils used in the tests varied between 0.05 and 0.11 m³/m³. The soil water retention properties for the sand and the clay loam were taken from the HYDRUS-2D database for standard sand and clay loam soils (Carsel and Parrish, 1988; Van Genuchten et al., 1991; Schaap et al., 2001). These properties are listed in Table 1. These soil properties were used to calculate the vapor pressure of water in the soil, which in turn helped us to calculate the vapor pressure gradient, experienced by water in the pervaporation tube placed in a soil medium and the specific pervaporation flux. Because the garden soil is a commercial blend of materials, it has not been well characterized in the literature and subsequently there were no available data for calculating the soil water retention parameters. This prevented the calculation of a vapor pressure gradient, and in turn the specific flux, for the pervaporation membranes in the garden soil. Thus, water transport behavior in the garden soil was not modeled using the HYDRUS-2D software.

Table 1.

Soil Hydraulic Function Parameters and Initial Conditions for Different Soils Used in the HYDRUS-2D Simulations

Model input parameter	Sand	Clay loam
van Genuchten–Mualem (van Genuchten, 1980) model parameters
Residual soil water content, θ_r (cm³/cm³)	0.045	0.075
Saturated soil water content, θ_s (cm³/cm³)	0.43	0.39
Saturated soil hydraulic conductivity, K_s (cm/day)	712.8	31.44
Soil water characteristic curve shape parameter, α (1/cm)	0.145	0.059
Empirical pore tortuosity/connectivity parameter, l	0.5	0.5
Soil water characteristic curve shape parameter, n	2.68	1.48
Average initial soil water content (cm³/cm³)	0.05	0.08

The feed water tank was placed on a mass balance so that the flux could be calculated as a function of time (change in mass over time). The feed tank was placed at an elevation above the tubing to provide positive water pressure relative to the atmosphere (∼2.8 kPa) inside the pervaporation tubing. Twelve Decagon 5TE (Pullman, WA) soil capacitance probes were placed within the soil box at various depths and distances from the pervaporation tubing to monitor soil moisture content, electrical conductivity (EC), and temperature. Probes were also placed in the headspace within the box to measure the temperature and RH of the air above the soil. One probe was attached to the lid of the box, and the other probe was placed on the soil surface. Samples were periodically drawn from inside the tubular pervaporation membranes using the sample collection port (Fig. 1). The EC of the drawn samples was measured to calculate salt rejection. In select tests with the clay loam soil, the feed water was recycled through the tubular membrane using a peristaltic pump (cross-flow velocity=0.053 m/s) to study the effects of mixing on membrane performance.

The specific flux for a pervaporation membrane is determined according to Eq. (1). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}J_ { sp } = \frac { v } { SA_ { m } *t* \Delta VP } \quad\quad { \rm Eq. } \ ( 1 )\end{align*} \end{document}

where J_sp is the specific water flux (L/[m² day·Pa]); v is the volume of water processed by the membrane (L); SA_m is the surface area of the feed side of the membrane through which component i is processed (m²); t is the time over which the permeation took place (day); and ΔVP is the transmembrane vapor pressure gradient (Pa). The vapor pressure gradient is the difference in vapor pressure between the water inside the membrane and the water present in the soil. The vapor pressure of water in the soil is calculated based on the pressure head of water in the soil, which is a function of the soil properties, as follows: The volumetric water content (θ) and temperature of the soil at any given time are determined using the capacitance probes. The soil pressure head is determined from the volumetric water content using van Genuchten's equation [Eq. (2)], provided we know the soil water retention properties (θ_s—saturated water content of the soil; θ_r—residual water content of the soil; and n, α—shape parameters). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}\theta ( h ) = \theta_r + \frac { \theta_s - \theta_r } { ( 1 + \mid \alpha h \mid^n ) ^m } \quad\quad { \rm Eq. } \ ( 2 )\end{align*} \end{document}

The RH of water in the soil is directly related to the soil pressure head and is determined as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}ln ( R. \ H ) = \frac { hMg } { RT } \quad\quad { \rm Eq. } \ ( 3 )\end{align*} \end{document}

where R.H is the RH of water in the soil; h is the soil pressure head (m); M is molar mass of water (kg); g is the acceleration due to gravity (m/s²); R is the universal gas constant; and T is the absolute temperature (K). The vapor pressure of water in the soil is determined based on the temperature and RH of the soil.

Test solutions

Tests were carried out using model electrolyte (sodium chloride) solutions and produced water samples collected from operating coal bed methane (CBM) wells. CBM water samples were collected from an active well site in the Powder River Basin (Sheridan, WY). The produced water samples were not treated (e.g., filtered) before use in the subsurface irrigation experiments. The average pH of the CBM water was 7.9±0.2, indicating that it was marginally alkaline. The mean total dissolved solids (TDS) concentration of the CBM water was 1,500 mg/L, making it mildly brackish. The TDS primarily comprise sodium and bicarbonate ions. The CBM water was classified as a soft water with a total hardness of 66.2 mg/L as CaCO₃. The total organic carbon concentration in the CBM water was 19 mg/L.

Modeling of liquid water transport in soil

The movement and distribution of liquid water from the permeate side of the pervaporation membrane through the sand or clay loam were modeled using HYDRUS-2D (Simunek et al., 1999). HYDRUS-2D is a computer software package widely used in the soil sciences field for simulating water, heat, and/or solute movement in two-dimensional (2D), variably saturated porous soils (Skaggs et al., 2004; Kandelous and Simunek, 2010; Bufon et al., 2012; Nakhaei and Simunek, 2014). In our simulations, the flux was assumed to be uniform across the entire length of the tubular membranes. It was therefore possible to conceptualize the pervaporation tubing as a line source, with water infiltration and redistribution across the soil then being 2D (vertical plane) processes. Assuming a homogeneous and isotropic soil, the governing equation for liquid water transport through the soil is the 2D Richards equation: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} \frac { \partial \theta } { \partial t } = \frac { \partial } { \partial x } \left[ K ( h ) \frac { \partial h } { \partial x } \right] + \frac { \partial } { \partial z } \left[ K ( h ) \frac { \partial h } { \partial z } + K ( h ) \right] \ {\rm Eq.} \ (4) \end{align*} \end{document}

where θ is the volumetric water content; h is the soil water pressure head; t is the time; x is the horizontal space coordinate; z is the vertical space coordinate; and K is the hydraulic conductivity of the soil. The soil hydraulic properties were modeled using the van Genuchten–Mualem constitutive relationship given as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}\begin{align*}& \theta(h) = \begin{cases} \theta_r + \frac {\theta_s - \theta_r} {(1 + \mid \alpha h \mid^n)^m} \ {h < 0} \\ {\theta_s} \qquad\qquad\qquad h \ge 0 \end{cases} \\& K (h) = K_s {S^l_e} \left[1 - \left(1 - {S^{l / m}_e} \right)^m \right] ^2 \quad\quad {\rm Eq.} \ (5)\end{align*}\end{document}

The effective saturation S_e is given as follows: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}S_e = \frac { \theta - \theta_r } { \theta_s - \theta_r } , \ m = 1 - 1 / n\end{align*} \end{document}

where θ_s is the saturated water content of the soil; θ_r is the residual water content of the soil; K_s is the saturated hydraulic conductivity of the soil; and n, α, and l are shape parameters. K_s, n, α, and l are related to the pore size distribution, tortuosity, and pore connectivity of the soil. HYDRUS-2D uses the Galerkin finite element method to solve Eq. (4) (Simunek et al., 1999). Variables used in the model for the two different soil types are summarized in Table 1. The van Genuchten–Mualem soil transport parameters used in the simulations were obtained from the HYDRUS-2D database for standard sand and clay loam soils (Carsel and Parrish, 1988; Van Genuchten et al., 1991; Schaap et al., 2001). The initial water content used in the simulations was 0.05 m³/m³ for the sand and 0.08 m³/m³ for clay loam soil. These values were based on the average initial moisture content of the different soils as measured by the 5TE soil probes. The three-dimensional soil profile illustrated in Figure 1 can thus be simplified to a 2D domain in the y-z plane considering the pervaporation tubing to be a line source of water. Because the pervaporation tubing was placed at the center of the soil box, assuming symmetry, only one half of the 2D domain in the y-z plane needs to be simulated. In our simulations, only the right side of the presumed symmetric profile was simulated. The tubing is represented as a half-circle on the boundary curved inward toward the interior of the mesh. The half-circle has a 1 cm radius and is 10 cm above the bottom boundary (Fig. 2). The transport domain considered for the simulations was rectangular (width, w=43 cm, depth, d=20 cm, discretized into elements). The pervaporation tubing boundary had a variable water flux, q (cm/day), which was determined experimentally from the subsurface pervaporation irrigation tests conducted with the silica sand and clay loam soils, respectively. The remaining portion of the left boundary was a zero flux boundary condition due to the symmetry of the profile, as was the upper boundary reflecting our assumption that surface evaporation was insignificant (i.e., evaporation was assumed to be less than 5% of the water application rate). Model simulations were executed for 30 days (sand) and 42 days (clay loam) to be consistent with the experiments.

FIG. 2.

Numerical modeling setup of two-dimensional soil plane, indicating boundary conditions used in HYDRUS-2D. The half-circle on the left hand boundary represents the pervaporation membrane tube and the incoming water flux.

Results and Discussion

Previous studies have generally assumed that water is transported through the soil that surrounds a buried pervaporation membrane only in the liquid phase (Quinones-Bolanos et al., 2005b; Quinones-Bolanos and Zhou, 2006). In a typical pervaporation process, the upstream side of the membrane is at ambient pressure, while the downstream side is under vacuum or a lower vapor pressure. This facilitates evaporation of the selective component (water) from the permeate side of the membrane. In a subsurface environment, the membrane is surrounded by soil, making for much different conditions than conventional pervaporation. Water transport in soil can occur by two mechanisms, that is, liquid flow along the solid surfaces and vapor flow through the connected air phase (Churaev et al., 2000). Only in extremely dry soil conditions (desert/arid) will the bulk connectivity of water in the liquid phase break down, which would promote water transport in the vapor phase across the soil even if to a lesser extent when compared with water transport in the liquid phase (Churaev et al., 2000). Water vapor flows in soil due to the soil water content variations are miniscule because the vapor pressure in most soils approaches the saturated vapor pressure at soil water contents greater than the residual water content of the soil (Puri et al., 1925). For example, in sand, the equilibrium humidity is greater than 99.5% even at a suction pressure of 600 MPa (Hillel, 1998). Hence, we assumed that water in the soil would exist only in the liquid phase in the immediate vicinity of the membrane that greets the water permeating across the membrane barrier.

Irrespective of the soil type (silica sand, garden soil, or clay loam) and system properties (temperature, feed water chemistry/composition, and initial soil water content), the water fluxes for the tubular PEE membranes reached comparable steady-state values (Fig. 3). The steady-state water fluxes for all tests ranged from 0.174–0.574 L/[m²·day]. The fluxes that were measured in all the three soils were elevated at the beginning of each test (t<1 day) compared with the steady-state value that was achieved after 1 day. The higher flux measured at the beginning of each test is attributed to a combination of factors depending on the soil properties. In the sand and garden soils, the elevated flux at the beginning of the test was attributed solely to the adsorption of water by the tubular membrane. The PEE membrane adsorbs some volume of water, resulting in an elevated, but declining flux over the beginning of the test (t<1 day).

FIG. 3.

Temporal variations in water flux (L/[m²·day]) through the tubular polyether ester (PEE) membrane (thickness=650 μm) in garden soil, clay loam, and sand. Feed water used for tests was CBM-produced water (T_avg.=22°C, TDS_initial=1,230 mg/L, pH_initial=7.91).

Previously (Huth et al., 2014), we have determined that the tubular PEE membrane adsorbs 35.4%±2.5% of its dry weight in water when filled with the CBM-produced water. The membrane became fully saturated with water after 24 h, which correlated with the elevated flux measured in the sand and garden soils. Considering adsorption of water only, the length of the PEE membrane used in the tests (1 m) would theoretically adsorb 30.6 g of water over the initial 24-h period based on a water adsorption by weight of 35%. The amount of water permeated across the PEE membrane in the sand, garden soil, and clay loam was 25.1, 75.4, and 91.2 g, respectively, in a 24-h period. Thus, the initial flux measured for the PEE membrane in the sand is entirely attributable to membrane swelling. Conversely, other factors must be playing a role for the PEE membrane when buried in the garden soil or clay loam. For example, in clay loam, the corresponding average flux corrected for swelling during the 24-h period was 0.616 L/[m²·day], which is about 2,000–3,000 times the average flux measured. This value compares favorably to the average fluxes measured in the clay loam over the duration of the test −0.408 L/[m²·day]. The amount of water that permeated across the garden soil and clay in 1 day is due to a combination of water adsorption by the membrane, whereas the rest can be attributed to the additional osmotic potential of the garden soil and clay loam, as explained later.

Representative, specific water flux values as a function of time for the tubular PEE and CTA membranes buried in a clay loam soil are summarized in Fig. 4. The specific flux for the CTA membrane was 4×that for the PEE membrane under the same environmental conditions and using the same feed solution over the respective test durations. The higher water flux that was measured for the CTA membrane agrees with earlier results for flat-sheet PEE and CTA membranes (Huth et al., 2014) and is attributed to the thinner active layer for the CTA membrane (10 μm vs. 650 μm). Water flux as a function of the thicknesses of the PEE membranes was also examined in our earlier study (Huth et al., 2014) and was found to be inversely proportional to the water flux in accordance with Fick's law. A further consideration is the hydraulic resistance to mass transport imparted by the two types of membranes. The driving force for water transport is thus a combination of the difference in pressure heads between the water inside the tubular membrane, the soil matric potential, and a difference in vapor pressure between the soil and feed water inside the tubular membrane. The matric suction for dry soils (volumetric water content, θ<10%) can range from 10 kPa for sandy soils to 100,000 kPa for clayey soils (Hillel, 1998; Warrick, 2002).

FIG. 4.

Temporal variation of specific flux (L/[m²·day·Pa]) for the tubular PEE (650 μm) and cellulose triacetate (CTA) membranes (active layer thickness −10 μm) when buried in clay loam soil. The feed water used was CBM-produced water (T_avg.=22°C, TDS_initial=1,230 mg/L, pH_initial=7.91).

Results from dead-end filtration experiments (see Supplementary Data) have shown that a hydraulic pressure of 1,750 kPa was required to achieve water transport across a 20-μm-thick PEE membrane in the absence of a vapor pressure gradient. A hydraulic pressure of just 350 kPa was enough to achieve permeation across the CTA membrane. The CTA membrane had a contact angle with water of 11.8°±4.7°, which is much lower than that measured for the PEE membrane (48.4°±5.12°), indicative of a more hydrophilic surface and a higher affinity for water. For pervaporation processes, the volume fraction of water (φ_i) in the membrane is related to the activity of water (a_i) and the sorption model parameter (k_i). The diffusion coefficient of water in the membrane is directly proportional to the volume fraction of water in the membrane (Ortiz et al., 2005). A more hydrophilic surface thus equals a larger diffusion coefficient and hence a higher flux in accordance with Fick's law. Now that the effect of membrane properties on the water flux has been established, the role of the soil composition and properties on the flux in a subsurface irrigation setup is explored.

Variations in temperature can be considered negligible as we are considering a specific flux (normalized over vapor pressure gradient), and the vapor pressure is a function of temperature. The water flux reached its steady-state value much quicker with sand and garden soil (Fig. 3) in comparison with the clay loam where it took about 10 days (Fig. 5). The notable difference in times required to reach a steady-state flux in the sand and garden soils compared with the clay loam was attributed to the fact that the clay loam was dry at the beginning of the test—initial moisture content of 0.08 m³/m³ compared with typical clay loam soils, which have a residual water content of about 0.10 m³/m³. This, combined with the fact that the clay loam has the highest clay content of all the soils tested, allows for a sort of wicking effect—removing moisture from the vicinity of the membrane. This wicking effect, also known as capillary action, is due to adhesion (attraction between the water molecules) and cohesion (attraction between the water and the ions present in the clay). Due to the capillary effect, the water penetrating the clayey soil tends to spread out laterally rather than vertically (Brouwer et al., 1985).

FIG. 5.

Temporal variations in specific flux L/[m²·day·Pa] (red line) and vapor pressure Pa (black line) through the tubular PEE membrane (thickness=650 μm) in clay loam soil. Feed water used for the test was CBM-produced water (T_avg.=22°C, TDS_initial=1,230 mg/L, pH_initial=7.91).

The driving force for traditional pervaporation processes is the vapor pressure gradient (ΔVP). The initial flux through the PEE membrane (t<2 days) when surrounded by garden soil and clay loam soil was found to be greater than the flux through the PEE tubing when surrounded by sand (Fig. 3). One explanation for this is that the water in the garden soil and clay loam has a much lower vapor pressure when compared with the sand during the beginning of the test. The vapor pressure of water in a given soil is affected by the type of soil (pressure head of the soil based on the volumetric water content) (Fredlund and Rahardjo, 1993). Total water potential is defined as the potential energy of water per unit volume relative to pure water at reference conditions. Water potential quantifies the ability/tendency of water to move from one point to another in soil due to a combination of driving forces like osmosis, gravity, pressure, or capillary action. Clayey and peaty soils exhibit adsorption by forming hydration envelopes over the soil particle surfaces. The water potential of the clayey/peaty soil is influenced by the electric double layer that surrounds, and the exchangeable ions present in, the soil (osmotic potential) (Hillel, 1998; Warrick, 2002). Peaty (garden soil) and clayey soils (clay loam) have a higher total water potential compared with sandy soils as they have an added effect of the osmotic potential when compared with sand, which only has a matric potential (Binkley and Fisher, 2012).

Hence, for the same initial moisture content of the soil, the garden soil (peat) and the clay loam soil will have a lower pressure head and hence a lower vapor pressure. The lower vapor pressure in the immediate vicinity of the pervaporation membrane corresponds to a higher driving force (vapor pressure gradient) at the beginning of the test, which will result in a higher water flux according to Fick's Law. However, as the soil continued hydrating (receiving the permeate water from the PEE membrane tube), the lower hydraulic conductivity of the clay loam and garden soils in comparison with the sand ensured that the water content in the soil surrounding the PEE membrane increased, thereby decreasing the vapor pressure of water in the soil surrounding the PEE membrane. This reduction in vapor pressure was reflected in the reduced specific flux rate for the clay loam and garden soils when compared with the sand as the test progressed (2<t<30 days).

The HYDRUS-2D simulations for our subsurface pervaporation irrigation system using the PEE membrane with sand and clay loam as the soil medium predict that clayey soils are better suited for irrigation as they support higher volumetric moisture contents owing to the lower hydraulic conductivity of the clay relative to the sand. Figure 6 depicts the moisture distribution within the soil after 30 days of operation with the silica sand and the clay loam soil. As expected, we see that the lower hydraulic conductivity of the clay loam results in regions of much higher volumetric content in the immediate vicinity around the PEE tubing (Fig. 6a) than the sand (Fig. 6b). In addition, the moisture front in the clay loam advances slowly and laterally in comparison with the sand, which shows rapid advancement of the moisture front together with more vertical movement. The rate at which the water permeates across the membrane is directly proportional to the vapor pressure gradient existing across the membrane barrier. The flux should theoretically decrease with time as the volumetric moisture content increases in the soil immediately surrounding the membrane (as water permeates across the pervaporation tubing into the surrounding soil). Moisture present in the soil though is not stationary and is conducted across the soil (hydraulic conductivity). This property, which redistributes the moisture across the entire soil profile, helps in maintaining a relatively constant moisture content in the soil near the membrane. This in turn maintains a sufficient vapor pressure gradient, which serves as the driving force for continued water permeation across the membrane. This redistribution effect would be assisted with the presence of a plant, which acts as a water sink, which in turn would result in the formation of a steady-state vapor pressure gradient between the water inside the pervaporation tubing and the moisture in the soil.

FIG. 6.

Surface plots of simulated water distribution, resulting from flux from the PEE membrane (thickness=650 μm) in the soil at the end of 30 days of testing with (a) silica sand and (b) clay loam soils surrounding the subsurface pervaporation irrigation tubing.

Water movement is directly related to the size of the pores in a soil. The smaller pores in clayey soils provide for the slow movement of water in all directions by capillary action. On the contrary, the larger pores in sandy soils make water drain downward due to gravity. Even though it seems like the moisture front has moved a shorter distance (Fig. 6) in the clay loam soil compared with the sand, it is important to note that the initial moisture content of the clay loam soil (0.08 m³/m³) is much higher than that of the sand (0.05 m³/m³). The lower hydraulic conductivity of the clay loam soil, together with the high affinity between the water and the clay present in the soil, slows down the movement of the moisture front away from the pervaporation tube. This can be an advantage for irrigating crops as the moisture front can be localized around the root system of the plants. The pervaporation irrigation tubes can be spaced much wider in clay loam than sandy soils to maintain the necessary moisture levels for irrigation. The experimentally measured soil water content was more closely predicted by the simulations (HYDRUS-2D) with sand than with the clay loam soil (Fig. 7). It is reasonable to conclude that HYDRUS-2D can in fact predict the movement of moisture within the soil.

FIG. 7.

Comparison of experimental and predicted soil water contents at individual soil probe locations at days 1, 15, and 30 for two different soils—sand and clay loam—with the PEE membrane (thickness=650 μm).

It was not possible to collect permeate samples from the soil to directly calculate the salt rejection by the membranes. Instead, salt rejection was calculated by relating the conductivity values of the initial feed and that of the reject water to the known concentration factor at any given time according to Eq. (6). \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*}C_r = CF^*C_f \quad\quad {\rm Eq.} \quad\quad ( 6 )\end{align*} \end{document}

where CF is the concentration factor (unitless); C_r is the conductivity of the reject water inside the pervaporation tubing (mS/cm); and C_f is the initial conductivity of the feed water (mS/cm). The conductivity of the reject water can be calculated by assuming a rejection efficiency and using the known concentration factor. If the assumed rejection efficiency is correct, then the calculated and measured conductivity values for the reject water will result in a linear relationship between the two values. Representative calculated and measured conductivity values for reject water in soil box tests using the PEE and CTA membranes buried in clay loam were plotted against the measured reject conductivity values and the results are presented in Figure 8. The goodness of fit (R² values) between the theoretical and actual conductivity values for the reject waters for both the PEE (R²=0.9972) and CTA (R²=0.9799) membranes supports our assumption of 100% salt rejection by the two pervaporation membranes. Based on these analyses, both membranes reject salt at efficiencies approaching 100%, indicating that nearly pure water entered into the surrounding soil. These findings are in agreement with our earlier findings for the PEE membrane, where salt rejection approached 100% (Huth et al., 2014).

FIG. 8.

Calculated versus measured conductivity values for reject water in representative soil box experiments using PEE and CTA membranes buried in clay loam. Feed water used for tests was CBM-produced water (T_avg.=22°C, TDS_initial=1,230 mg/L, pH_initial=7.9).

The effect of temperature and increasing feed salinity on the permeate fluxes of the PEE and CTA membranes was studied using flat-sheet membrane samples (seeSupplementary Data). It was found that the flux decreased with increasing salinity and increased with increasing feed temperature. An increase in the feed temperature creates a higher vapor pressure gradient and hence a higher driving force for transport corresponding with a higher flux, whereas an increase in feed salinity decreases the vapor pressure of water in the feed and hence lowers the driving force for transport across the membrane.

The range in water flux values achieved in this work suggests that the technology is suitable for meeting the water demands of select crops under appropriate climatic and soil conditions. For example, the maximum evapotranspiration rate/water demand for crops such as alfalfa (Honaman et al., 1998; Tolk et al., 2006; Djaman and Irmak, 2013), cotton (Thorp et al., 2014; Bai et al., 2015), and castor beans (Marenco-Centeno et al., 2012; Lima et al., 2013) is between 0.8 and 1 mm/day in a loamy sand. This range in values translates into a water application rate range of 0.8–1.0 L/day per square meter of land. The average flux values measured for the PEE membrane in sand and clay loam ranged from 0.45 to 0.39 L/[m²·day], while the flux for the CTA membrane in clay loam was 2.74 L/[m²·day]. Based on the surface area/unit length of the CTA membrane (0.0828 m²/m), we would require 5.4 m of the CTA membrane for a 1 m² plot of soil generally characterized as clay loam to meet the daily water demand of any of the above-mentioned crops. Similarly, using the surface area/unit length value for the PEE membrane (1.103 m²/m), we would require between 30 and 34 m of the PEE membrane in sand and clay loam, respectively, to provide the necessary water for the above-mentioned crops in a 1 m² plot. This example scenario is based on a number of assumptions and represents areas of ongoing research, such as quantifying the zone of influence that singular and multiple tubular membranes impart in various soils. This unknown quantity will affect the spacing requirements for the membranes for different crop/soil combinations.

Conclusions

Flux results for the subsurface pervaporation experiments indicate a very good potential for long-term use in subsurface irrigation as there was no noticeable loss in membrane performance observed for the duration of the tests (≤42 days). The pervaporation-specific flux was found to directly increase with an increase in temperature. The tubular pervaporation membranes were found to show consistent permeate flux regardless of feed water salinity (feed concentration increase due to permeate removal) and soil type surrounding the tubing, although permeate flux was found to generally increase as the RH and surrounding soil moisture decreased. The water fluxes achieved with the CTA membrane were higher than that of the PEE membranes and were attributed to the thinner active layer and increased hydrophilicity of the CTA membrane. Ionic conductivity of the soil did not increase during the tests, indicating no salt leakage and thus very good salt rejection capabilities. The effect of clay content in real soils with regard to increasing pervaporation water flux due to the additional osmotic potential and the subsequent decrease in flux due to the water accumulation in the vicinity of the membrane owing to the lower hydraulic conductivity of clay is something that needs to be further explored. The soil water content distributions predicted using HYDRUS-2D were found to be in very good agreement with the experimental results.

Footnotes

Acknowledgments

The authors gratefully acknowledge the funding provided for this project by the Research Partnership to Secure Energy for America (RPSEA, Project No. 09123–11) and the University of Wyoming's School of Energy Resources. The authors would also like to thank KC Harvey and Associates for providing the clay loam soil and valuable insight on the soil properties. Their gratitude also goes to DuPont™ and Hydration Technology Innovations for supplying the membrane samples. Finally, they wish to thank Dr. Thijs Kelleners from the University of Wyoming for his assistance with the HYDRUS-2D modeling and valuable suggestions.

Author Disclosure Statement

No competing financial interests exist.

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