The Role of Nitrate Diffusion in Determining the Order and Rate of Denitrification in Flooded Soil: II. Theoretical Analysis and Interpretation

Additional Index Words: rate constant, zero-order reaction, firstorder reaction, submerged soil, available carbon. A theoretical analysis of denitrification occurring in submerged soil in a test tube, when assumed to be a zero-order reaction with available ———————————————————— organic carbon nonlimiting, appears to be a first-order reaction if the __ , , , , c effects of diffusion are neglected? In this case, denitrification appears R ESEARCHERS have attempted to measure the order of to be a first-order reaction because denitriflcation occurs at a faster ^ the denitrification reaction and the rate constant of rate than the diffusive flux can supply NO3--N to the soa. After some denitrification in the laboratory. Traditionally, this has length of time, the concentration of NO3~-N in the lower portion of been done by submerging soil in a test tube or beaker where the flood-water-soil interface will be equal to the concentration in the 62 is first eliminated from the system and then measuring flood-water. After which time, denitrification occurs only in the upper the disappearance of NO3~-N from the system. Analysis of portion of the soil sample. When the role of diffusion is neglected, it is the resulting data most often leads the researcher to generally assumed that denitrification occurs uniformly throughout conclude that denitrification is a first-order reaction, i.e., the soil sample. It is for this reason that denitrification can appear to dc/df = _fc]C where c is concentratiOn of NO3~-N in the be a first^rder reaction when it may actually be a zero-order ^ f [& ^ ^ k Js ̂ mte constant rf ̂ finjt. reaction. The true order of reaction and rate constant of demtnficaH t tion in a test tube can be evaluated experimentally by eliminating the ______ floodwater above the soil sample; with this experimental geometry 'Contribution from the Kentucky Agric. Exp. Stn. as Journal Article some of the confounding effects of diffusion of NC>3~-N can be no. (77-3-26) and from the Louisiana Agric. Exp. Stn. and is published minimized. If diffusion is neglected, not only is the order of reaction with the approval of the Directors. Received 28 Feb. 1977. Approved 7 misjudged but the depth of floodwater above the soil has a significant °professor of Agronomy, Univ. of Kentucky, Lexington, KY 40506 and effect on the magnitude of the calculated rate constant of the apparent Post-Doctoral Research Associate and Professor, Agronomy Dep. Louifirst-order reaction also. siana State Univ., Baton Rouge, LA 70803. PHILLIPS ET AL.: NITRATE DIFFUSION AND DENITRIFICATION IN FLOODED SOIL: II. 273 Standford et al. (1975) measured denitrification rates in about 30 soils. Their procedure was approximately that outlined above, i.e., NO3~-N as KNO3 and distilled water were added to the soils in containers which were stoppered and incubated after which time NO3~-N disappearance was measured with time. A depth of about 3 cm of water was maintained above the samples. They plotted percent of initial nitrate remaining (which is equivalent to /u,g of NO3~ in the system/g of oven-dry soil) v. time and concluded that denitrification in their study of 30 soils generally followed first-order reaction kinetics better than zero-order reaction kinetics. Mahendrappa and Smith (1967) found that maximum denitrification rates under fully anaerobic conditions occurred at specific soil moisture contents. The time required to denitrify all the added NO3~-N was considerably longer when the soil water content was greater than saturation than when the soil was less than saturated. They felt the increased time required was due to a difference in distribution of organisms and/or N compounds in the two soil moisture treatments. In their paper it could not be determined if floodwater existed above the soil of their high moisture treatment. If, in fact, floodwater did exist above their soil samples then, as will be seen later, their findings could be explained by the effect of diffusion of N03~-N. Kirda et al. (1974) and Starr et al. (1974) assumed that denitrification, as well as nitrification, is a first-order reaction during steady leaching of N in soil columns. They were successful in modeling N transport and distribution in soil columns assuming that denitrification and nitrification are first-order reactions. However, Starr and Parlange (1976) hypothesized and illustrated to some degree that the kinetics of nitrogen transformations in Kirda et al. (1974) and Starr et al. (1974) could have as easily been modeled using zero-order kinetics for the nitrogen transformations. Doner et al. (1974) leached Hanford sandy loam with NO3~-N for 3 weeks; quasi-steady-state conditions were obtained during the last 12 days of the experiment. They concluded that denitrification followed zero-order kinetics until the NO3~-N concentration reached some low concentration below which the order of reaction of denitrification was other than zero. Nommik (1956) and Bremner and Shaw (1958) concluded that NO3~-N concentration had little influence on rate of denitrification. Their conclusion implies that denitrification under their experimental conditions was a zeroorder reaction. In contrast, if denitrification were a firstorder reaction, then NO3~-N concentration must influence the rate of denitrification. The data of Patrick (1960) shows denitrification to be a zero-order reaction when an aqueous suspension of soil plus NO3~-N is agitated without floodwater and maintained under anaerobic conditions. The objective of this study was to show by theoretical analysis that denitrification, when occurring in submerged soil with available organic carbon nonlimiting and with a uniform concentration of NO3~-N in the floodwater, appears to be a first-order biological reaction when in fact it may be a zero-order biological reaction. THEORY The geometry to be considered is shown in Fig. 1. It is assumed the soil is in an anaerobic state with denitrification occurring as a zero-order biological reaction, i.e., dCldt = —k where C is NO3 N concentration, t is time, and k is the zero-order rate constant. The depth of the soil is assumed to be infinite with the soilfloodwater interface at x = 0, and with overlying floodwater of depth, a. We are further assuming that significant denitrification does not occur in the floodwater and that the initial concentration of NO3~-N in the soil solution and floodwater is equal. As soon as denitrification begins in the anaerobic soil, there will exist a concentration gradient and then NO3~-N will diffuse from the floodwater to the soil. Consequently, the concentration of NO3~N at x = 0, the floodwater-soil interface, will decrease with time. Even though the concentration of NO3~-N in the floodwater will decrease with time, it is assumed that the concentration will remain uniform throughout the depth of floodwater due to mixing in response to density and temperature gradients. The partial, second-order differential equation describing concentration of NO3~-N as a function of soil depth and time where transport is due to denitrification as a zero-order reaction is given by Eq. [1]