Supporting Information

Thermolytic Osmotic Heat Engine for Low-grade Heat Harvesting:

Thermodynamic Investigation and Potential Application Exploration

Xin Tong1,2*, Su Liu1,2, Junchen Yan1,2, Osvaldo A. Broesicke1,2, Yongsheng Chen1, and John Crittenden1,2*

1School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United

States2Brook Byers Institute for Sustainable Systems, Georgia Institute of Technology, Atlanta, GA 30332, United

States

*Corresponding authors:

Xin Tong, Phone.: +1 847 868 5499, E-mail address: xin.tong@ce.gatech.edu.

John Crittenden, Phone.: +1 404 894 7895, E-mail address: john.crittenden@ce.gatech.edu.

SI1. Derivation of the maximum specific energy from PRO

S1

Figure S2 shows a scheme of a counter-current flow PRO system operated under a

constant hydraulic pressure of ΔP. The calculation of specific energy has been done by previous

studies [1, 2], and here we follow the previous derivation procedure and then apply the derived

equations in our system to calculate the extractable energy from the PRO system. According to

the previous study, two different regimes can be identified for the counter-current flow operation

based on the feed flow rate fraction (φ) [2]. When the feed flow rate fraction is small, the PRO

operation is considered to be in the feed limiting regime (FLR). The feed solution concentration

reaches a critical concentration (cF*) which is a function of the draw solution (influent)

concentration (cD,0) and the applied hydraulic pressure (ΔP):

c F, f=cF¿ =cD ,0−

ΔPυRT (S1)

When the feed solution concentration (cF) reaches cF* at some point in the membrane module, the

osmotic pressure difference (between the draw solution and the feed solution) equals the applied

hydraulic pressure. Beyond that point, both effective driving force and membrane water flux

vanish.

On the other hand, the draw limiting regime (DLR) can also be identified. When the feed

flow rate fraction is high, the draw solution concentration decreases to a critical draw

concentration (cD*) at some point in the membrane module. Beyond that point, the hydraulic

pressure equals the osmotic pressure difference and no water transport occurs. The critical

concentration is related to the feed solution (influent) concentration (cF,0) and the applied

hydraulic pressure (ΔP):

c D, f=cD¿ =cF ,0+

ΔPυRT (S5)

S2

Here, we define the feed recovery rate, γ, as the ratio of QPRO over the feed solution

(influent) flow rate QF,0. In addition, the membrane area is assumed to be large enough so that the

critical concentration (cF* or cD

*) can be achieved. Based on equation (1), the specific energy

generation (total energy generated normalized by the volumetric flow rate) (wg) can then be

expressed as:

wg=W g

Qtot=ΔPφγ (S6)

where Wg is the total energy generated from PRO, and Qtot is the total volumetric flow rate of the

mixed solution (volumetric flow rate of feed and draw solutions combined).

When the PRO is operated in FLR, by combining equation (S4) and mass balance on

solute in the feed solution (QF cF=QF , f cF ,f ):

γ FLR=1−c F

c F¿ (S7)

The specific energy can then be given by:

wg , FLR=ΔPφ γ FLR=ΔPφ(1−c F

c F¿ ) (S8)

In the FLR, cD should be larger (or equal to) cD*, since cD

* is the lowest value that cD,f can achieve.

For the PRO to operate in FLR, the above constrains need to be fulfilled, which leads to:

φ ≤ φFLR=cF

¿

c D+c F (S9)

S3

When feed solution is limited and the PRO operation is in DLR, by combing equation

(S5) and mass balance, the feed recovery rate (γ) can be expressed as:

γ DLR=1−φ

φ(c F

c F¿ −1) (S10)

Similarly, the specific energy can be given by:

wg , DLR=ΔPφ γ DLR=ΔP(1−φ)(cF

cF¿ −1) (S11)

In the DLR, cf should be smaller (or equal to) cF*, since cF

* is the highest value that cF,f can

achieve:

φ ≥ φDLR=cF

¿

cD+c F (S12)

In eqn (S8), wg,FLR is a monotonically increasing function with respect to φ, and the

highest value that φ can achieve is φFLR (according to equation (S9)), so the maximum specific

energy is achieved (for FLR) when the feed flow rate fraction equals φFLR. Analogously, eDLR is a

monotonically decreasing function with respect to φ, and the lowest value that φ can achieve is

φDLR (according to equation (S12)), so the highest specific energy in the DLR is obtained when

the feed flow rate fraction equals φDLR. In addition, by comparing equation (S9) and equation

(S12), φFLR and φDLR are the same as long as the other operating conditions (cD, cF and ΔP) keep

unchanged. The maximum specific energy can then be expressed as:

wg , max=ΔPcD, 0−cF, 0−ΔP /(υRT )

cD ,0+c F , 0 (3)

S4

The corresponding optimal feed flow rate fraction is also the critical feed flow rate fraction

which divides the FLR and DLR:

φopt=cF

¿

cD ,0+cF ,0=

c D,0−ΔP /(υRT )cD, 0+cF ,0

(S13)

SI2. Calculation of density of the solutions

The density of the working solution (NH4HCO3 solution) at various solute concentrations

can be calculated by [3, 4]:

ρm= 1w solvent

ρ solvent+

w solute

ρ solute

(S14)

where ρm is the density of the solution, ρsolvent is the density of the solvent (water), ρsolute is the

density of the solute (NH4HCO3), wsolvent is the mass fraction of the solvent, and wsolute is the mass

fraction of the solute. The density of the solute can be estimated using [3]:

ρ solute=(c0 (1−w solvent )+c1) e¿ ¿¿ (S15)

where t is the temperature in degrees Celsius (°C), c0 to c4 are dimensionless empirical

coefficients. The values of the empirical coefficients depend on the solute, for NH4HCO3 the

following values are used: c0=1.731 4 , c1=91.0521, c2=0.6811, c3=0.0027, and

c4=1657.29199 [3]. The determined solution density as a function of solution concentration is

shown in Figure S3.

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Figure S1. Maximum specific energy generation in PRO as a function of the applied hydraulic pressure for different draw solution concentrations (the feed solution is DI water).

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Figure S2. Schematic view of a counter-current flow PRO module. The draw solution is pressurized to a constant hydraulic pressure of ΔP, and the pressure is maintained across the PRO module. The draw solution flows into the module (from left) with a volumetric flow rate of QD,0 and a solute concentration of cD,0, and flows out (from right) with a volumetric flow rate of QD,f and a solute concentration of cD,f. The feed solution flows into the module (from right) with a volumetric flow rate of QF,0 and a solute concentration of cF,0, and flows out (from left) with a volumetric flow rate of QF,f and a solute concentration of cF,f.

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Figure S3. (a) Density and (b) osmotic coefficient of NH4HCO3 solution as a function of the molar concentration of the solution.

S8

Figure S4. (a) Activity of solute and (b) activity of water as a function of the molar concentration of NH4HCO3 solution.

S9

Figure S5. Comparison between modeling predicted global maximum specific energy generation (w*

g,max) in this study and literature reported values. The change of global maximum specific energy generation (w*

g,max) with the change of the draw solution concentration is shown in the figure. The solid line represents the values from this study, the feed and draw solutions are NH4HCO3 solutions. The red dots represent the values from a previous study (values with the draw solution concentrations of 0.6 M and 1.2 M are shown) [2], and the feed and draw solutions are NaCl solutions. The feed solution concentration is 0.015 M. Since the previous study assumed the osmotic coefficient (ϕ) equals 1, the higher specific energy values were resulted. Thus, ϕ of a few different values (1, 0.9, 0.8, and 0.7) were taken, and the maximum specific energy values were re-calculated for better comparison.

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Figure S6. Schematic view of an osmotic heat engine (OHE) to harvest solar-thermal energy. The heat exchanger (incorporating stripping column) is connected to a thermal storage tank (TST). The TST is used to store the solar energy in the form of thermal energy.

S11

Figure S7. Real-time direct solar irradiance data of five different cities (Atlanta, Las Vegas, Los Angeles, Miami and Phoenix) for the year 2015 [5].

S12

Table S1. Properties of the different streams in the osmotic heat engine (OHE) (power generation capacity = 1.4 kW, TH = 313.15 K, CD,0 = 2 M and CD,0 = 0.5 M).

Stream T (K) P (kPa) C (M) m (kg/s) a Ns (mol/s) Nw (mol/s) as aw

1 293.15 3544 2 59.48 3.528 98 0.76 0.952 293.15 101.325 0.5 59.84 0.882 98 0.28 0.983 293.15 3544 1.25 59.48 3.528 156.8 0.56 0.974 293.15 101.325 1.25 59.84 0.882 39.2 0.56 0.975 293.15 3544 1.25 59.48 1.323 58.8 0.56 0.976 293.15 346 1.25 59.84 2.205 98 0.56 0.977 293.15 3544 1.25 59.48 2.205 98 0.56 0.978 317.15 346 1.25 3.58 2.205 98 0.56 0.979 293.15 101.325 1.25 115.74 2.205 98 0.56 0.9710 323.15 346 0.5 59.48 0.882 98 0.28 0.9811 293.15 1181.3 1.25 56.26 1.323 58.8 0.56 0.9712 293.15 346 0.5 56.26 0.882 98 0.28 0.9813 293.15 508 1.25 59.48 3.528 156.8 0.56 0.9714 309.18 508 2 115.74 3.528 98 0.76 0.9515 293.15 508 2 115.74 3.528 98 0.76 0.9516 293.15 508 1.25 3.58 1.323 58.8 0.56 0.9717 - - - - - - - -18 - - - - - - - -19 - - - - - - - -

NH3+CO2 - - - - - - - -a Mass flow rate of the stream.

Note: Mass flow rate of the different streams were calculated by multiplying the volumetric flow rate by the density of solutions (shown in Figure S3). Activity of water (aw) and solute (as) were determined by using equations (6) – (10) (shown in Figure S4).

S13

Table S2. Determined chemical exergy and exergy of the different streams in the osmotic heat engine (OHE) (power generation capacity = 1.4 kW, TH = 313.15 K, CD,0 = 2 M and CD,0 = 0.5 M).

Stream Efch (kW) Ef (kW)

1 0.0026 6.75792 6.7977 6.49763 4.0637 12.89074 1.0159 1.01595 1.5239 5.16766 2.5398 2.97147 2.5398 8.61278 2.5398 10.14429 2.5398 2.539810 6.7977 18.042411 1.5239 2.667012 6.7977 7.229313 4.0637 5.211514 0.0026 4.034615 0.0026 0.720016 1.5239 1.954317 - 1.400318 - 0.431619 - 8.6754

NH3+CO2 - 0.7771Note: The gaseous species in the Stream (NH3+CO2) were considered to have behavior of ideal gas, and the entropy and enthalpy values were taken from literature [6].

S14

Table S3. Embodied energy of a solar-thermal osmotic heat engine (OHE) with power generation capacity of 1.2 kW (the embodied energy of the flat-plate solar collector is not included).

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Turbine 2.14 kW

Reinforcing Steel 22 kg 40 880Steel, low-alloyed 37 kg 38 1406

Chromium steel 18/8 8 kg 38 304Copper 2 kg 100 200

Aluminum 1 kg 179 179Iron-nickel-chromium alloy 1 kg 30 30

Polyethylene, HDPE, granulate 1 kg 12.7 12.7Pressure exchanger 172.8a m3/kg

Fiberglass 1 kg 17 17Epoxy Resin 1 kg 113 113

Alumina Ceramic 3 kg 20 60Aluminum 1 kg 170 170

Stainless Steel 2 kg 40 80Titanium 0.1 kg 650 65

Pump (draw side) 0.03 kWStainless steel hot rolled coil 0.03 kg 38 1.14

Copper 0.01 kg 100 1Pump (feed side) N/A kW

Stainless steel hot rolled coil 0 kg 38 0Copper 0 kg 100 0

PRO membrane 19 m2

Poly (ether sulfone) 2 kg 86 172N-methyl-2-pyrrolidone 38 kg 81 3078

diamine mono-piperazine 15 kg 100 1500trimesoylchloride 19 kg 85 1615

Hexane 38 kg 0.4 15.2Polyester mesh (draw side) 5 kg 79 395Polyester tricot (feed side) 14 kg 79 1106

PRO membrane vesselFiberglass (shell) 0.2 kg 17 3.4

Epoxy Resin (shell) 0.2 kg 113 22.6PVC (shell) 0.1 kg 80 8

PVC (end caps) 0.1 kg 80 8Heat sink 3.31 kW

Steel, low-alloyed 1.6 kg 38 60.8Chromium 0.4 kg 38 15.2

Nickel, 99.5% 0.2 kg 180 36a Total flowrate through the pressure exchanger.

S15

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Heat exchanger (1) 9.27 kW

Copper tube 24 kg 60 1440Nickel, 99.5% 3 kg 180 540

Heat exchanger (2)b 6.86 kWCopper tube 19 kg 60 1140

Nickel, 99.5% 2 kg 180 360Thermal storage tank 3 m3

Stainless steel 19 kg 50 950glass wool 9 kg 114 1026Aluminium 23 kg 254 5842

Addition 10% for contingencies 2319

Total 25513b Heat exchanger (2) is the one that incorporated with stripping column.

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Table S4. Embodied energy of an osmotic heat engine (OHE) with power generation capacity of 200 kW (the embodied energy of the flat-plate solar collector is not included).

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Turbine 357 kW

Reinforcing Steel 3670 kg 40 146800Steel, low-alloyed 6107 kg 38 232066

Chromium steel 18/8 1331 kg 38 50578Copper 360 kg 100 36000

Aluminum 204 kg 179 36516Iron-nickel-chromium alloy 109 kg 30 3270

Polyethylene, HDPE, granulate 90 kg 12.7 1143Pressure exchanger 28800 m3/kg

Fiberglass 241 kg 17 4097Epoxy Resin 241 kg 113 27233

Alumina Ceramic 465 kg 20 9300Aluminum 106 kg 170 18020

Stainless Steel 343 kg 40 13720Titanium 17 kg 650 11050

Pump (draw side) 4.4 kWStainless steel hot rolled coil 4.8 kg 38 182.4

Copper 1.6 kg 100 160Pump (feed side) 0.2 kW

Stainless steel hot rolled coil 0.1 kg 38 7.6Copper 0.1 kg 100 10

PRO membrane 2942 m2

Poly (ether sulfone) 294 kg 86 25284N-methyl-2-pyrrolidone 5839 kg 81 472959

diamine mono-piperazine 2353 kg 100 235300trimesoylchloride 2942 kg 85 250070

Hexane 5883 kg 0.4 2353Polyester mesh (draw side) 804 kg 79 63516Polyester tricot (feed side) 2150 kg 79 169850

PRO membrane vesselFiberglass (shell) 36 kg 17 612

Epoxy Resin (shell) 36 kg 113 4068PVC (shell) 18 kg 80 1440

PVC (end caps) 6 kg 80 480Heat sink 552 kW

Steel, low-alloyed 267 kg 38 10146Chromium 69 kg 38 2622

Nickel, 99.5% 39 kg 180 7020

S17

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Heat exchanger (1) 1544 kW

Copper tube 1416 kg 60 84960Nickel, 99.5% 168 kg 180 30240

Heat exchanger (2) 1143 kWCopper tube 1115 kg 60 66900

Nickel, 99.5% 132 kg 180 23760Addition 10% for

contingencies 209469

Total 2304158

S18

Table S5. Embodied energy of an osmotic heat engine (OHE) with power generation capacity of 5 MW (the embodied energy of the flat-plate solar collector is not included).

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Turbine 8929 kW

Reinforcing Steel 92733 kg 40 3709320Steel, low-alloyed 152745 kg 38 5804310

Chromium steel 18/8 33293 kg 38 1265134Copper 9000 kg 100 900000

Aluminum 5107 kg 179 914153Iron-nickel-chromium alloy 2714 kg 30 81420

Polyethylene, HDPE, granulate 2251 kg 12.7 28587.7Pressure exchanger 720000 m3/kg

Fiberglass 6023 kg 17 102391Epoxy Resin 6023 kg 113 680599

Alumina Ceramic 11634 kg 20 232680Aluminum 2640 kg 170 448800

Stainless Steel 8581 kg 40 343240Titanium 413 kg 650 268450

Pump (draw side) 178 kWStainless steel hot rolled coil 194 kg 38 7372

Copper 65 kg 100 6500Pump (feed side) 10 kW

Stainless steel hot rolled coil 10 kg 38 380Copper 65 kg 100 400

PRO membrane 131340 m2

Poly (ether sulfone) 13134 kg 86 1129524N-methyl-2-pyrrolidone 260682 kg 81 21115242

diamine mono-piperazine 105071 kg 100 10507100trimesoylchloride 131340 kg 85 11163900

Hexane 262677 kg 0.4 105070.8Polyester mesh (draw side) 35875 kg 79 2834125Polyester tricot (feed side) 95994 kg 79 7583526

PRO membrane vesselFiberglass (shell) 1587 kg 17 26979

Epoxy Resin (shell) 1587 kg 113 179331PVC (shell) 794 kg 80 63520

PVC (end caps) 243 kg 80 19440Heat sink 13806 kW

Steel, low-alloyed 6678 kg 38 253764Chromium 1726 kg 38 65588

Nickel, 99.5% 976 kg 180 175680

S19

Equipment/ Material Quantity Unit Energy intensity (MJ/kg) Embodied energy (MJ)Heat exchanger (1) 38607 kW

Copper tube 18593 kg 60 1115580Nickel, 99.5% 2205 kg 180 396900

Heat exchanger (2) 28571 kWCopper tube 14640 kg 60 878400

Nickel, 99.5% 1733 kg 180 311940Addition 10% for

contingencies 7508347

Total 82591813

S20

Table S6. Embodied energy of flat-plate solar collectors for different cities.

Location Quantity Unit Energy intensity (MJ/m2)[7] Embodied energy (MJ)Atlanta 291 m2 1732 504012

Las Vegas 185 m2 1732 320420Los Angeles 251 m2 1732 434732

Miami 313 m2 1732 542116Phoenix 186 m2 1732 322152

S21

References

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