Effects of Soil Conditions on Solar Pond Performance

SERl/TP-253-257 UC Ctegory: 59c DE8496 Effects of Soil Conditions on Solr Pond Performnce Cecile Leboeuf Did H Johnson Jnury 984 To be presented t Americn Society of Mechnicl Engineers Solr Energy Diision Sixth Annul Technicl Conference 8-2 April 984 Ls Vegs, Ned Prepred under Tsk No 424 FTP No 49 Solr Energy Reserch nstitute A Diision of Midwest Reserch nstitute 67 Cole Boulerd Golden, Colordo 84 Prepred for the US Deprtment of Energy Contrct No DE-AC2-83CH93

Printed in the United Sttes of Americ Ailble from: Ntionl Technicl nformtion Serice US Deprtment of Commerce 5285 Port Royl Rod Springfield, VA 226 Price: Microfiche A Printed Copy A2 NOTCE This report ws prepred s n ccount of work sponsored by the United Sttes Goernment Neither the United Sttes nor the United Sttes Deprtment of Energy, nor ny of their employees, nor ny of their contrctors, subcontrctors, or their employees, mkes ny wrrnty, express or implied, or ssumes ny legl libility or responsibility for the ccurcy, completeness or usefulness of ny informtion, pprtus, product or process disclosed, or represents tht its use would not infringe pritely owned rights

SER/TP-253-257 uncr or SOL CONDTONS ON SOLAR POND PERFORMANCE CM Leboeuf DR Johnson Solr Energy Reserch nstitute Golden, Colordo ABSTRACT A recent effort to design one-cre solr pond t the U s Air Force Acdemy brought up seerl reserch issues pertining to solr pond performnce prediction This report ddresses those issues nterctions of the pond with the soil below it he historiclly been estimted using ery simplistic techniques tht tend to ignore soil composition, moisture content, nd the coupled het nd moisture trnsport phenomen This study exmines the models of soil therml conductiity nd het nd mss trnsport in soils under imposed temperture grdients to ssess the potentil pplicbility of these models to solr pond modeling n ddition, computer simultion code is deeloped tht incorportes the soil therml conductiity model Using the code, prmetric nlysis ws performed illustrting the impct of this property on pond behior nd the importnce of experimentl model erifiction for the rnge of soil tempertures experienced in solr ponds mplictions of the combined het nd moisture moement theory on solr pond performnce re presented NOMENCLATURE CJ specific het of liquid wter (J kg- c-l) isotherml moisture diffusiity m2 5- oc- ) De therml moisture diffusiity m2 s - ) De isotherml por diffusiity (m2 s-) shpe fctor for the ir - filled pores (dimensionless) shpe fctor for the ith soil component (dimensionless) h reltie humidity of ir - filled pores (dimensionless) K hydrulic conductiity (m s - ) L T PJ ltent het of poriztion (J kg-) het flux (W m-2) moisture flux (kg m-2 s-) temperture (c) ir weighting fctor (dimensionless) weighting fctor for the th soil component (dimensionless) olume frction of ir in the soil (m3 m-3) olume frction of the ith soil component (m3 m-3) soil field cpcity (m3 m-3) olume frction of wter in the soil (m3 m-3) o um! ric liquid (m m ) moisture content in the soil effectie soil therml conductiity (W m- c-l) therml conductiity of ir (W m- c-l) pprent t!l_ erm \ conductiity of the ir - filled pores (W m- c- ) therm! cqnductiity of the ith soil componnt (W m- oc-) therml cond y t 3 y trnsfer (Wm c ) due to por ltent het ltent het trnsfer effect in pores with % reltie humidity (W m- c-) therml conductiity of wter (W m-l c-) density of liquid wter (kg m-3) soil porosity (dimensionless)

SER/TP-253-257 NTRODUCTON Moing ground wter will often be present t some depth below the bottom of solr pond Het will e conducted from the pond through the soil to the ground wter nd hence trnsported wy from the pond Thus, the therml conductiity of the soil below solr pond is n importnt fctor in determining its performnce Preious studies of the therml performnce of solr ponds he considered soil therml conductiity to be independent of temperture nd he usully used lues ner tht of pure wter (=6 W m- c- ) () Howeer, soil conductiity depends on porosity, - moisture content, soil mkeup, nd temperture n ddition, het nd moisture fluxes in the ground my be coupled A flux of het cused by temperture grdient cn cuse flux of moisture The resulting redistribution of moisture will ffect the locl therml conductiity This pper uses preiously deeloped model of solr pond therml performnce (2) modified to include widely ccepted model of soil the!rnl conductiity (3) to ssess the effects of soil temperture, moisture c-;;-ntent, nd mkeup on performnce n ddition recognized theory of coupled het nd moisture trnsport (4) is used to determine the conditions under which the temperture grdients tht typiclly exist below solr pond might ffect the distribution of moisture The pper concludes with summry of results nd recommendtions for further THEORY Solr Pond Therml Performnce work The two-dimensionl ersion of SOLPOND (2), simulton progrm for slinity grdient solr ponds, ws used in this study This progrm mode ls the trnsient therml performnce of solr pond using the lumped prmeter electricl circuit nlogy s depicted in Fgure Absorption of solr rdition within ech element is modeled by current source, The current source in the storge lyer lso ccounts for the energy deliered by the pond The user supplies the following inputs: upper conection lyer, nonconecting lyer, nd storge lyer depths; wether dt; lod dt; opticl trnsmission; simultion time step; therml conductiities; nd het cpcities The upper conecting lyer nd the storge lyer re ech described by single node The number of nodes used to model the grdient lyer nd ground re selected by the user To oid numericl oerstbility, implicit finite difference equtions compute the time solution Dynmics of the nonconecting lyer re not modeled, t is ssumed tht the pond storge temperture neer exceeds l c nd tht excess energy is extrcted when necessry to oid oerheting, Soil Therml Conductiity where t x n t + W + WW ixi\ wx> i=l n + x w wixi + wx i=l () n is the number of indiidul solid constituents; - w - nd - i re the therml conductiities of the wter, ir, nd solid prticles, respectiely W nd i W re weighting fctors; nd X, nd X re the i olume frctions of wter, soil prticles, nd ir, respectiely The three min clssifictions of soi\ constit uents re cly nd silt (tlo = 293 W m- c- ), qurtz l snd (t = W m- c- ), nd orgnic mtter 2 nd (t 8l = 25 W m-l c ) Therml conductiities of wter nd ir re both functions of temperture, ccording to the following expressions: nd fw 55 + 2 34 x -3 T x - -5 2 T ; (2) >- = 2 37 + 6,4 x -S T, (3) where T is the temperture in c nd - nd '- re in o w m- c-, w The weighting fctors depend on the orienttion nd distribution of soil grnules nd ir pockets These re ssumed to be rndomly distributed nd orientedellipsoids such tht:, t [ nd 2 + Ai + ( --,- - l) gi (- i r, - + -i - )( >-w Aw - Zg,) l 2 ] W +, -p -p + r ) + (; )( - 2g ) - L ' - g w where g nd g re shpe fctors corresponding to the i soil grnules nd ir pockets, respectiely, nd - is p the pprent therml conductiity of the ir-filled pores (4) (5) The shpe fctors re difficult to determine becuse of the unpredictble ribility in soil structure nd pore size; hence they pose mjor uncertinty in computing weighting fctors The empiriclly determined lue of g is, 25 for most soils The ir shpe fctor is bsed on the work of de Vries ( 5), i which split the soil into two regions by moisture content, When olumetric moisture con tent is boe the soil field cpcity X (the olumetric moisture content r i:etined by the soil fter flooding), g is defined s X g = 333-298 -r- (6) A widely ccepted nd experimentlly erified physicl model for soil therml conductiity ws deeloped by de Vries (3) This model ssumes tht soil is mde up of grins Of so l id mterils imbedded in continuous medium, which is either wter or ir n prtilly sturted soils, wter is the continuous medium with pockets of ir imbedded in it, n ery dry soils (less thn 5% moisture content by olume), it: is considered the continuous medium with drops of wter imbedded in it The effectie soil therml conductiity for prtilly sturted soil is defined s where > is the porosity (the rtio of the soil bulk density to the erge density of the soil mterils) Below field cpcity, g is defined s Xw ' g 3 + X (g 3) (7) - r where g is the lue for g resulting from Eq 6 when the olfimetric moisture content is exctly equl to the field cpcity The pprent therml conductiity of the irfilled pores is defined s 2

SER/TP-253-257 Ambient Temperture Surfce,_, lo-\ Grdient )-'::c--+ Storge Typicl Section / \ \, \ '-, Ground TempertCre / --- --- Figure Therml Model Schemtic of Three-Dimensionl Solr Pond > > + p > where > is the therml conductiity due to por ltent het trnsfer The lue of > depends on the degree of sturtion of the ir-filled pores, nd is gien s where h is the reltie humidity ii}; the ir-filled pores, expressed s frction, nd > is the ltent het trnsfer due to por flow when the reltie humidity of the pores s % de Vries (_) presents dt on the lue of > s function of temperture which cn be fitted With the following exponentil expression (2): >5 (8) (9) = 223 exp (568 T) () Coupled Het nd Moisture Trnsport Although none of the existing theories completely describes the behior of coupled moisture nd het trnsport in soils, seerl he been erified for certin field conditions A widely ccepted theory ws deeloped by Phi::ip nd de Vries ( 4) This theory considers tht flux of moisture q m in the soil is cused by the ction of grity nd grdients of temperture T nd moisture content ei so tht () where Pi is the density of liquid wter, De is the isotherml moisture diffusiity, or is the therml moisture diffusiity, n K is+ the hydrulic conductiity Similrly, flux or het qh in the soil is cused by grdient in temperture nd moisture content nd by the sensible het crried by flux of moisture so tht + + + + qh = >r - PtLDeV9t + Ct(T - T o) qm ' (2) where L is the ltent het of poriztion, Ci is the specific het of liquid wter, De is the isotherml por diffusiity, nd T is the reference temperture PARAMETRC STUDES Effect of Te ture, Mc>isture Content, nd Soil Hke-Up on The :;r Conductiity of Soils n the theory section, we defined three tmperture-dependent ribles (>, w nd > ) tht influence the effectie soil therml conductiity These prmeters re plotted ersus temperture in Figure s 2 The > l cure crosses the 't > cure t 6 c nd rises shrpl therefter, indic itg the dominnce of por het trnsport in the ir-filled pores t eleted tempertures The theory of soil therml conductiity hs trdicionlly been pplied to soils below 4, such s encountered in griculturl pplictions or nlysis of buried trnsmission cbles Solr ponds, howeer, re designed to operte with storge zone tempertures pproching l c The derth of therml conductiity dt for soils boe 4 c, together with the rdicl difference in the reltionship of the temperture-dependent ribles in this rnge, mkes it impertie tht the de Vries model be erified under solr pond operting conditions before designs re bsed on it The effects of moisture content, soil mkeup, nd temperture on therml conductiity re shown in 3

SER/TP-253-257 i3 e 'i!:: : ;:; () - 3 25 2 5 5 A,, A;;'----!' /' ------- --,,;L ---- -- A, ---- 2 3 4 5 6 7 8 Temperture (C) Figure z Therml Conductiity of Air, Wter, Sturted Vpor Figures 3 nd 4 n both figures, the fltness of the cures t 6 C occurs s result of the cross-oer of - w nd - s shown in Figure 2 At oc, the por trnsport is dominnt, so tht s the pores become filled th wter, the effectie conductiity ctully decreses The sndy soil shown in Figure 3 hs higher oerll therml conductiity thn the finergrined clyey soil shown in Figure 4, with ymxi um _ lue t 8 C nd 25% sturtion of 38 W m c Een the clyey soil conductiity reches 24 W m- c-l t these conditions, which is pproximtely 2-/2 times the conductiity of the sme soil t 2 c nd the sme moisture content ' nd Effects of Soil Conditions on Solr Pond Performnce n performing the following nlyses, we kept certin ssumptions constnt We chose Colordo Springs, Colo, for the solr pond site Wether dt for Colordo Springs, including dily erge dry bulb nd incident rdition for typicl yer, were deried from hourly sttistics on the Erstz TMY (Typicl Meteorologicl Yer) dt set, which is ilble from the Ntionl Climtic Center A 3-dy time step ws used in ll performnce simultions Energy extrcted from the pond ws mesured per unit re Unless otherwise specified, constnt therml lod of 3 W m -2 is imposed on ech solr pond simultion The -surfce conecting lyer thickness ws ssumed to be 4 m, nd the grdient zone depth ws 2 m SOLPOND, computerized solr pond therml performnce simultion code (2), ws used in this study to predict pond behior fie ground storge nodes re used, with n ssumed infinite cpcity sink het t temperture of 2 C nd depth of m To put the ground het loss issue into proper perspectie, we conducted n nlysis of the proportion of het losses from pond tht re to the ground We ssumed constnt soil therml c onductiity The nnul temperture profile of the pond for specific configurtion nd fixed energy extrction rte is one illustrtie mesure of the effect of pond het losses on performnce f the pond hs no side-wll or grond het losses (soil therml conductiity <<l w 9 m- c - L ), the temperture profile for the bse-cse pond (which hs storge zone 25 m thick nd therml energy extrction rte of 3 W m -2 ) is shown s the uppermost cure of Figure 5 The next cure represents pond tht hs negligible edge losses but suffers erticl ground losses to soil with conductiity of - - W m C (This lue is commonly used in performnce prediction if no other site-specific soil dt is ilble) As the pond becomes smller, edge losses begin to be significnt, s eidenced by the decresed temperture profiles for the -m, 3-m, nd -m dimeter ponds While this does not fully brcket performnce (ie, it could be worse), Figure 5 does proide n indiction of the importnce of ground het losses to solr pond performnce Mny spce-conditioning or industril process lods being considered for solr pond pplictions he prescribed minimum temperture below which they cnnot be sered For this reson it is dntgeous to design pond in which the temperture will not fll below specified minimum during typicl yer A thick storge zone smooths out ritions in mbient conditions nd cn, therefore, mintin higher pond minimum temperture thn thin storge zone Howeer, the mximum tempertures chieed re lower in pond with thick storge zone To exmine the effect of ground therml conductiity on storge zone sizing, we exmine got conductiities rnging from 2 to 2 W m C nd storge zone thicknesses from 5 to 3 m; we then determined the minimum operting temperture of the pond for ech set of conditions These dt re shown in Figure 6 As the conductiity increses, the benefits gined by thickening the storge zone tend to decrese Thus for site which is known to he high soil therml conductiity, het losses to the ground tend to offset ny improements gined by incresing the storge zone beyond bout 2 m for these conditions i3 e 4 35 3 25 'i!:: :: tl 2 5 () ;;; E Q; - 25 :f 5 ;:; g () o / --,,,,--- -- ---------- oc ------------------o c / 4 C _ - --- -- - 2 c ' -- -- / ' // / /,-, ' Soil Type: % Cly 9% Snd 2 3 4 5 Percentge of Wter Filled Voids Figure 3 Soil Therml Conductiity-Sndy Soil /,,,, f= 5 / /---- -- ------ - - c ;, -:-- --------------6 C /, ----4 C,/ _- - -- - -,, / // / /,,, //,,,-:::, L::_:-:::-::: Soil Type: 9% Cly, % Snd 2 c on----t--:;2 :-----, 4 -,--- 5 - J Percentge of Wter-Filled Voids Figure 4 Soil Therml Conductiity-Clyey Soil 6 j 6 4

SER/TP-253-257 No]rO«ndlosses! A tw m- ci No edge losses (A W m- c -m dim pond A W'm-CJ tkes plce t _ bout 2% of sturtion From 2% to 22% of sturtion, the erge temperture drops less steeply Beyond 22%, the sndy - soil cure lso flttens out, but t leel bout 7 C lower thn the cure for cly '3-mdimpondf\ : tw m-cj - -mdm pond(a - Wirn-''Cl Energy Eucuon 3 w:m Grdient: 2 m Storge 25 m Surfce m F M A M J J A S O N D Month Figure 5 Effect of Ground Therml Conductiity nd 8 - >-- u; = o = 2 c ') ') Figure 6 Pond Size on Annul Temperture Profile Grdient, 2 rn 5 Surfce m m = 72 m Lod 3 W;rr 2 Storge Lyer Dpth m Site Colordo Springs 25 3 Effect of Ground Therml Conductiity on Dependence of Mlnilllum Temperture on Storge Lyer Depth The de Vries model for soil therml conductiity hs not been erified in the temperture rnge of soils beneth solr ponds t displys some peculirities in this rnge becuse of the exponentil nture of the por trnsport ter<n Howeer, we chose to use the de Vries model with our solr pond therml performnce si:nultion code to determine the potentil impct of temperture- nd moisture - dependent therml conductiity model on the prediction of solr pond behior With the two progrms integrted, it is possible to updte lues of soil therml conductiity for ech of the fie ground nodes t ech time step, bsed on nodl tempertures of the preceding itertion Using two soil types, one sndy (9% snd nd % cly by weight) nd one clyey (9% cly nd % snd by weight), we he exmined solr pond performnce for rious lues of moisture content The pond performnce is mesured by its erge nnul storge temperture in c (bsed on pond with 4-m surfce lyer, 2-m grdient, 2-m storge zone, nd n energy extrction rte of 3 W m - 2 ) The mo is tu re content of the soil is shown by percentge of sturtion (percentge of oid spces filled with wter) Figure 7 shows the reltionship between pond storge temperture nd soil sturtion As expected, the solr pond on clyey soil mintins higher temperture thn the pond on sndy soil The erge temperture of the pond on clyey soil decreses firly steeply until the soil moisture content is bout 22% of sturtion Beyond 22% of sturtion, little drop in erge pond temperture is seen A similr effect is seen for the sndy soil cse, but the chnge in slope of the erge temperture first Coupled Het nd Moisture Trnsfer We N'ish to determine the conditions under which the temperture grdient set up in the soil by the precuse redistribution of sence of solr pond might the soil moisture content 4 from tht which existed before the pond ws in plce To do this we will determine the impct of n imposed temperture grdient in the soil on the resultnt stedy - stte moisture grdient under conditions of zero moisture flux n this cse, the one-dimensionl form of Eq becomes d9 dt = -D9 dz - 'r dz + K, (2) 4 or d9 'r dt K 'dz = - D e (rz +Dr) o3> Therefore, if the rtio K/Ur is Jch less thn dr dz, then the stedy-stte temperture grdient will he profound effect on the stedy-stte moisture grdient Figure 8 shows the behior of K s function of moisture content 9 for Yolo light cly t 2 c Very limited dt exist on the temperture dependence of hydrulic conductiity, prticulrly boe 3 c Figure 9 shows the behior of Ur for Yolo cl d' s function of olumetric moisture co f tent t 2 C K ries considerbly, from m s- t 9 75 m3 m-3 to - 3 >< 8 m s- t 9 = 45 m3 m-3 or is firly constnt in this rnge of 9 t pproximtely x lo- m2 l 2 3 s- c- A typicl temperture grdient beneth solr pond is 23 c m-l ccording to Meyer nd Hedstrom <D Using these lues, nd for 9 up to bout 2%,! < 2 3 C m- l «= 23 o c m -l Dr dz but for 9 greter thn bout 45 m3-3 Hence the influence of the temperture grdient on the moisture grdient in the soil will be significnt for reltiely dry soils but not for reltiely wet soils (ssuming the soil to be Yolo cly) 85 ' ''\ ' \ ---- 9% Snd ioo,o Cly Lo = 3 Wtm 9% Cly % Snd --:?------ Percentge of Wter-Fte Voids -- Figure 7 Effect of Moisture Content on Pond Storge Temperture 5

SER/TP-253-257 These results suggest tht combined het nd moisture flux my be n importnt considertion for mny solr ponds Figure 7 shows tht for our exmple, solr pond erge nnul storge temperture decresed from 83 c to 73 C s the moisture content of underlying soil went from % to 2% of sturtion for light cly soil, ssuming no interction between het flux nd moisture distribution f the temperture grdients set up by solr pond interct with the moisture content to drie moisture wy from the bottom of the pond, then n insulting region of low therml conductiity might be creted below the pond, preenting such drstic reduction in performnce This possibility remins s specultion until dt on soil properties cn be obtined t solr pond operting tempertures (so c) A literture serch by the uthors hs filed to uncoer such dt () -9 o, - E en _J -2L-- -ii-o 2 3 4 5 Volumetric Moisture Content B (m3/m') Figure 9 Therml Moisture Diffusiities for Yolo Cly t 2 C SUMMARY AND RECOMMENDATONS Het lost through the soil to moing ground wter cn he significnt effect on solr pond performnce The mount of het lost will depend on the soil therml conductiity, which is function of moisture content, soil mkeup, porosity, nd temperture Prmetric studies using n ccepted model of soil therml conductiity show tht under t,he rnge of solr pond operting co nditions moisture content' soil mkeup, nd temperture he significnt effects on solr pond performnce Howeer, these results depend on extrpoltion of dt from pproximtely 3 c to solr pond operting tempertures ner 8 C becuse sufficient dt on soil therml properties t higher tempertures re not ilble t is lso possible tht the flux of het from the solr pond through the soil to the ground wter my cuse redistribution of moisture in the soil below the pond with corresponding effect on soil therml conductiity This possibility is sup- ported by n ccepted theory of coupled het (td moisture trnsport in soils but lso depends on extrpoltion of dt from bout 3 c to solr pond operting tempertures (bout 8 C) A literture serch by the uthors hs filed to uncoer sufficient dt on soil therml properties to completely elute soil therml conductiity nd coupled het nd moisture moement t solr pond operting conditions We recommend tht such dt be obtined becuse of the potentil importnce of these subjects in understnding solr pond therml performnce REFERENCES (f) --- E -; 8 ' '2 Q-3 o-4 < c g Jyde, T S, nd Henderson, J, Slt Concentrtion Grdient Solr Ponds--Modeling nd Optimiztion, SER/TP-35-277, June 979 Presented t the Annul Meeting of the nterntionl Solr Energy Society, Atlnt, GA, My 28-June, 979 2 Henderson, J,, nd Leboeuf, C M, SOLPOND - A Simultion Progrm for Slinity Grdient Solr Ponds, SER/TP-35-559, Jn 98 Presented t the Second Annul Systems Simultion nd Economics Anlysis Conference, Sn Diego, CA, Jn 23-25, 98 3 de Vries, D A, Simultneous Trnsfer of Het nd Moisture in Porous Medi, Trnsctions Americn Geophysicl Union, Vol 39, No 5, Oct 958 4 Philip, J R, nd de Vries, D A, Moisture Moement in Porous Mterils Under Temperture Grdients, Trnsctions Americn Geophysicl Union, Vol 38, No 2, Apr 957 5 de Vries, D A Therml Properties of Soils, Physics of Plnt Enironment, W R Vn Wijk, ed, North Hollnd Publishing Co, Amsterdm, 963 o-5 2 3 4 5 B(m3m3) Figure 8 Vrition of Hydrulic Conductiity with Moisture ContentYolo Cly 6 Wlter, W R, Sbey, J D, nd Hmpton, D R, Studies of Het Trnsfer nd Wter Migrtion in Soils, DOE/CS/339-Tl, 98, Colordo Stte Uniersity, Ft Collins, CO 7 Meyer, K A, nd Hedstrom, J C, Estimtes of Ground Conductiity for the DOE-USAFA Experimentl Solr Pond, LA-UR-82-294, 982, Los Almos Ntionl Lbortory, Los Almos, NM 6