# SW—Soil and Water: Sorption of Phosphorus by Soil, Part 1: Principles, Equations and Models

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<ul><li><p>Biosystems Engineering (2002) 82 (1), 124w</p><p>G</p><p>n</p><p>n</p><p>information about sorption onto such colloids. Equations are considered for processes, column experiments</p><p>1.</p><p>muif&MptodethWthpsoinwsom</p><p>.</p><p>l</p><p>15and P dynamics systems studies. Isotherm equations representing fast reversible sorption have been identied.Instantaneous equilibrium can be assumed for most applications of the fast sorption equations, with theexception of surface erosion studies. Details of some very complex mechanistic models of the slow reactionand deposition processes are presented and discussed. Some simpler equations for these processes fromexisting eld-scale P dynamics models are also presented. It is concluded that, at least in the short term, themechanistic approach is too complex for incorporation into a systems model of the whole range of Pprocesses, and that further development should represent time-dependent processes by adaptation of thesimple equations. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved</p><p>Introduction</p><p>Plant nutrients from chemical fertilizer or animalanure are positive assets if retained in the soil forptake by plants, but become environmental pollutantsleached into watercourses or groundwater (McGechanWu, 1998; McGechan & Lewis, 1998, 2000; Lewis &cGechan, 1998). There has been much attention in theast devoted to nitrogen as a nutrient and pollutant, dueits high solubility and leachability through eld</p><p>rains and to groundwater (McGechan et al., 1997; Wual., 1998), and its high potential for conversion to</p><p>armful volatile or gaseous emissions (McGechan &u, 1998). Attention is currently moving more towardse less soluble and non-volatile contaminating nutrienthosphorus (P). The study of P as a plant nutrient and</p><p>addresses sorption of P by soil components, and somefeatures of P sorption which make the process complexcompared to sorption of other reactive chemicals.Weather-driven simulation modelling has become an</p><p>important component of studies of soil nutrients, bothfor crop growth and for their losses by leaching tobecome environmental pollutants. Such modellingstudies using the soil nitrogen dynamics model SOILN(Johnsson et al., 1987) and other models have beendescribed for nitrogen as a nutrient and pollutant by Wuand McGechan (1998a, 1998b) and Wu et al. (1998)The authors, Lewis and McGechan, have also reviewedthe eld-scale models GLEAMS, ANIMO andCENTURY, which are being used to study P (as welas nitrogen) cycling processes. Their review covers thewhole range of transformation and transport processesdoi:10.1006/bioe.2002.0054, available online at http://wwSW}Soil and Water</p><p>REVIEW</p><p>Sorption of Phosphorus by Soil, Part</p><p>M. B. McGecha</p><p>Environment Division, SAC, West Mains Road, Edinburgh EH9 3J</p><p>(Received 26 January 2001; accepte</p><p>The very extensive literature on phosphorus (P) sorptequations and parameter values for use in a soil P dysorption of P onto surface sites, and various slower pbelow surfaces of iron or aluminium oxide mineralsconsidered to take place both onto static soil componetransport in sediments moving in surface runo owsfacilitated through soil P pollution ows have only recil component is complicated by its long residence timethe ground due to sorption, and its tendency to moveith soil water in colloidal or particulate form. Unlike alute such as nitrate, there can be restrictions onovements of colloids in soil pores. This paper</p><p>37-5110/02/$35.00 1.idealibrary.com on</p><p>PAPER</p><p>1: Principles, Equations and Models</p><p>n; D. R. Lewis</p><p>, UK; e-mail of corresponding author: m.mcgechan@ed.sac.ac.uk</p><p>d in revised form 1 February 2002)</p><p>ion studies is reviewed with the intention of selectingamics model. Processes considered are fast reversiblerocesses including reactions which deposit P at depthin soil or precipitate calcium phosphate. Sorption ists and onto mobile sediments or colloids. Phosphorushas been extensively studied, but problems of colloidently received attention. There is almost no publishedapplicable to P in the soil, including a short descriptionof sorption processes. However, due to the complexityof sorption processes for P and the extensive publishedliterature on it, this topic is the subject of a moredetailed review in the current paper, including models</p><p># 2002 Silsoe Research Institute. Published byElsevier Science Ltd. All rights reserved</p></li><li><p>M. B. MCGECHAN; D. R. LEWIS2Notation</p><p>A coecient in Eqn (20) (Hansen et al.,1999)</p><p>Aa coecient in Eqn (22) (Barrow, 1974b)Alox oxalate-extractable aluminium content,</p><p>mmol kg1 or mg kg1</p><p>[Alox+Feox] oxalate-extractable aluminium plus ironcontent, mmol kg1</p><p>Ar coecient in the Arrhenius equation,Eqn (22) (Barrow & Shaw, 1975a)</p><p>As specic surface area of soil particles inEqn (58) (Sharpley & Ahuja, 1983),cm2 g1</p><p>a0a3 tted coecients in Eqn (40)ab proportion of P converted to an ineec-</p><p>tive form [in Eqn (21), Barrow 1974a]ad coecient in diusivity function in Eqn</p><p>(58) (Sharpley & Ahuja, 1983)ar coecient in Eqn (60) (Ahuja et al.,</p><p>1982)as coecient in Eqn (34) (Sharpley, 1982)aw slope constant in Eqn (57) (Sharpley &</p><p>Ahuja, 1982)B coecient in Eqn (20) (Hansen et al.,</p><p>1999)B1, B2, B3 coecients in Eqn (23) (Barrow & Shaw,</p><p>1975a)Bsat base saturation by ammonium acetate</p><p>method in GLEAMS, %b1 exponent in the Freundlich sorption</p><p>isotherm equation, Eqn (2)b2 exponent in time-dependent term of the</p><p>Freundlich sorption isotherm equation,Eqn (5), and of desorption equation,Eqn (52)</p><p>b3 third exponent in Eqn (52) (Barrow,1979)</p><p>bk coecient in Eqn (7) (Kuo, 1988)br coecient in Eqn (60) (Ahuja et al.,</p><p>1982)C concentration of P in solution, mg l1</p><p>%CC average concentration of P in runowater [Eqn (60), Ahuja et al., 1982]</p><p>Ce concentration of P at the interfacebetween oxide and phosphate [Eqn(41)], mg l1</p><p>Cd,0 Limiting concentration of P in solu-tion for no desorption (Barrow, 1979),mg l1</p><p>Ci, Ci1 concentrations of P in solution at times tiand ti1 [Eqn (37), Barrow, 1983a]</p><p>C0 concentration of P in solution at timezero, mg l1</p><p>C0,0 coecient representing limiting concen-tration of P in solution for zero deso-rption time (Barrow, 1979)</p><p>Cd,0 composite coecient in desorption equa-tions, Eqns (50) and (52) (Barrow, 1979)</p><p>Cro instantaneous concentration of desorbedP in runo water, Eqn (59) (Sharpleyet al., 1981a)</p><p>Ct concentration of P in solution at time tin Eqn (23) (Barrow & Shaw, 1975a),mg l1</p><p>CCaCO3 calcium carbonate concentration inGLEAMS</p><p>CL clay content of soil, %cr coecient in Eqn (60) (Ahuja et al.,</p><p>1982)D diusion coecient</p><p>DSSP degree of saturation with P, %E energy of activation of chemical compo-</p><p>nent [in Eqns (7) and (14), Kuo, 1988 andEqn (28), Barrow 1974a]</p><p>Er kinetic energy of rainfall per unit areaper unit time in Eqn (60) (Ahuja et al.,1982)</p><p>eT rate constant adjustment factor for soiltemperature in EPIC and GLEAMS</p><p>es power coecient in Eqn (60) (Ahujaet al., 1982)</p><p>ey rate constant adjustment factor for soilwater content in EPIC and GLEAMS</p><p>F the FaradayFeox oxalate-extractable iron content,</p><p>mmol kg1 or mg kg1</p><p>f fraction of sorption sites that take partin the fast sorption process (Chen et al.,1996)</p><p>fb parameter in Eqns (37) and (38) (Bar-row, 1983a)</p><p>fl fraction of fertilizer P labile after 6months incubation period in EPIC</p><p>fs diusion impedance factor (Nye &Staunton, 1994)</p><p>I integral with respect to time of dier-ences in P concentration in solution andat the interface between oxide andphosphate within a particle, Eqn (40)</p><p>Ir rainfall intensity, cm h1</p><p>i index for summation in generalizedisotherm equation, Eqn (15) (Goldberg& Sposito, 1984)</p><p>is coecient in Eqn (34) (Sharpley, 1982)j index for summation in Eqns (84) and (87)K coecient in Eqn (23) (Barrow & Shaw,</p><p>1975a)K2,j, K3, j coecients in ANIMO, Eqn (84)</p><p>(Schoumans, 1995)Ks constant in Eqn (56) (Sharpley et al.,</p><p>1981b)</p></li><li><p>SORPTION OF PHOSPHORUS 3k1, k2, k3, k4 coecients in multiple-component sorp-tion and desorption equations</p><p>kb the Langmuir coecient in Eqn (18)(Barrow, 1983a)</p><p>kE1, kE2 coecients in the Elovich sorption iso-therm equation, Eqn (16)</p><p>kF coecient in the Freundlich sorptionisotherm equation, Eqn (2)</p><p>ki coecient in generalized sorption iso-therm equation, Eqn (15)</p><p>kL coecient in the Langmuir sorptionisotherm equation, Eqn (6), lmg1 [P]</p><p>kL1, kL2 coecients in two-component Langmuirsorption isotherm equation, Eqn (11),lmg1 [P]</p><p>kT1, kT2 coecients in the Temkin sorption iso-therm equation, Eqn (1)</p><p>kZ2, kZ3 coecients in kinetic form of Langmuirsorption isotherm equation, as presentedby Van der Zee et al. (1989a), Eqns (9)and (10)</p><p>L length of slope in Eqn (60) (Ahuja et al.,1982)</p><p>M mass of soil in interaction zone [Eqns(59) and (60)], kg</p><p>m proportion of added P in solution attime zero in Eqn. (25) (Barrow & Shaw,1975a)</p><p>md Power coecient in diusivityfunction in Eqn (58) (Sharpley &Ahuja, 1983)</p><p>mr Power coecient in Eqn (60) (Ahujaet al., 1982)</p><p>m1, m2 coecients in electrostatic potentialequations (Barrow, 1983a, 1983b)</p><p>n number of components in generalizedisotherm equation, Eqn (15) (Goldberg& Sposito, 1984)</p><p>nb power coecient in Eqns (21) and (29)(Barrow & Shaw, 1975b)</p><p>nr power coecient in Eqn (60) (Ahujaet al., 1982)</p><p>OM organic matter, %Pact active P pool in EPIC and GLEAMSPacto previous value of Pact in Eqn (86)Pd quantity of P desorbed, g [P] kg</p><p>1 [soil]Pfe fertilizer P added, g [P] kg</p><p>1 [soil]Pilf labile P after fertilization and incubation</p><p>in EPIC and GLEAMSPili initial labile P (prior to fertilization)Plab labile P pool in EPIC and GLEAMSPom minimum quantity of desorbable P in</p><p>Eqn (57) (Sharpley & Ahuja, 1982)Pox oxalate-extractable P content,</p><p>mmol kg1 or mg kg1</p><p>Psp proportion of added P which remainslabile after incubation in EPIC andGLEAMS</p><p>Pspcl clay content related proportion of addedP which remains labile after incubationin ICECREAM</p><p>Pspph soil pH related proportion of added Pwhich remains labile after incubation inICECREAM</p><p>Pstab stable deposited P poolP0 initial quantity of desorbable P in Eqn</p><p>(56) (Sharpley et al., 1981a, 1981b)pH pH in GLEAMSQ quantity of P sorbed on surface sorption</p><p>sites, including that sorbed by fast time-dependent processes, mg [P] kg1 [soil]</p><p>Qe equilibrium value of quantity of P sorbedon surface sorption sites, mg [P]kg1 [soil][Eqn (43), Raats et al., 1982]</p><p>Qmax maximum P sorption capacity for sur-face sorption sites, including that sorbedby fast time-dependent processes, mg[P] kg1 [soil]</p><p>Qmax,1,Qmax,2</p><p>maximum P sorption capacity for sur-face sorption sites in two-componentLangmuir sorption isotherm equation,Eqn (11), mg [P] kg1 [soil]</p><p>Q0 surface-sorbed P in soil prior to the startof a soil P test, Eqn (3)</p><p>Qr runo rate per unit area in Eqn (60)(Ahuja et al., 1982)</p><p>q coecient in Eqns (31) and (32) (Bar-row, 1983b)</p><p>R universal gas constantRas ow rate for slow P adsorption in EPIC</p><p>and GLEAMS, kg ha1 day1</p><p>Rla ow rate for rapid P adsorption in EPICand GLEAMS, kg ha1 day1</p><p>S quantity of P deposited below sorptionsurfaces by slow reaction, or quantitysorbed by time-dependent processeswhich include slow deposition, g[P] kg1 [soil]</p><p>S1, S2, S3 three components of S (for j=1, 2 and 3)given by Eqn (87) (Schoumans, 1995)</p><p>Sl angle of slope in Eqn (60) (Ahuja et al.,1982), %</p><p>Smax maximum quantity of P deposited belowsorption surfaces by slow reaction, ormaximum quantity sorbed by time-de-pendent processes which includes slowdeposition, g [P] kg1 [soil]</p><p>Stot quantity of P sorbed on surface sorptionsites plus that deposited below sorptionsurfaces by slow reaction, g [P] kg1</p><p>[soil]s coecient in Eqn (34) (Sharpley, 1982)T absolute temperature, K</p><p>T1, T2 temperatures in Eqn (32) (Barrow 1983c)Tc soil temperature, 8Ct time, day</p></li><li><p>2</p><p>M. B. MCGECHAN; D. R. LEWIS4of sorption processes applied to laboratory experiments.The availability and usefulness of data for estimatingparameters of equations which may be incorporated intoeld-scale models is later assessed in a follow-on Part 2of this paper (McGechan, 2002).</p><p>2. General principles of phosphorus sorption</p><p>Sorption is the process by which reactive chemicalsbecome attached to surfaces, sometimes of otherwiserelatively harmless solids. Small particles have a largespecic surface area, so tend physically to have a highsorption capacity (but this is further modied by theirchemistry). In addition to those on immobile particles inthe soil matrix, there are competing sorption sites onotherwise non-polluting sediments and colloids whichmove relatively freely in water ows along the surface orthrough the soil. Small soil particles readily becomedetached to become mobile sediments or colloids, andland-spread manures and wastes contain additionalcolloidal material. However, attention in the extensiveliterature has been directed mainly to sorption onto</p><p>immobile soil components, with a few references tosorption onto sediments moving in surface runoows.In common with other reactive chemicals, the extent</p><p>to which P is adsorbed relative to that in solution ishighly non-linear, as energy levels vary between dierentbinding sites on the solid surfaces, high-energy sitesbecoming occupied before low-energy sites. This non-linearity is commonly represented mathematically by anumber of alternative equations (isotherms), withlogarithmic or other transformations to make linearapproximations.For P (which may dier from some other reactive</p><p>chemicals), the sorption process is complicated for onemain reason. Apparent sorption of P can be thought ofas being a combination of several processes, including afast (almost instantaneous) reversible true sorptionprocess on soil particle surfaces, plus various slowertime-dependent processes, some of which lead todeposition of P at a depth below the surface of particles.These slower processes can be further subdivided intorelatively faster and very slow components, and aredescribed by various authors as slow adsorption, the</p><p>HPO4 (Barrow, 1983a)as power constant in Eqn (56) (Sharpley</p><p>et al., 1981a, 1981b)b rate constant in kinematic sorption</p><p>isotherm equations, and also in Eqn(45) (Raats et al., 1982)</p><p>1993)rd dry bulk density of soil, gm</p><p>3</p><p>s standard deviation of electrostaticpotential (Barrow, 1983a)t1, t2 time periods in Eqn (32) (Barrow &Shaw, 1983b)</p><p>td desorption time, h (Barrow, 1979)tL lag time which elapses before the slow</p><p>deposition process becomes establishedin Eqn (20) (Hansen et al., 1999)</p><p>t0 start of time period, dayV constant relating quantity of desorbable</p><p>P to eective concentration in Eqn (58)(Sharpley & Ahuja, 1983)</p><p>Vr total rain volume in the rainfall event perunit area in Eqn (60) (Ahuja et al., 1982)</p><p>v water velocity in convection/dispersionequation</p><p>W water:soil ratio in Eqn (56) (Sharpleyet al., 1981a, 1981b)</p><p>Wk interaction energy in Eqn (14) (Kuo,1988)</p><p>z depth in soil in convection/dispersionequation</p><p>zi valency, including sign (2 for HPO42)</p><p>zk number of nearest neighbour surround-ing a central phosphate species in Eqn(14) (Kuo, 1988)</p><p>a proportion of phosphate present asbas rate constant for slow adsorption inEPIC, day1</p><p>bb rate constant in Eqn (21) (Barrow 1974a)be rate variable [Eqns (43) and (45), Raats</p><p>et al., 1982]bs power constant in Eqn (56) (Sh...</p></li></ul>

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