Abstract
A new residence-time distribution (RTD) function has been developed and applied to quantitative dye studies as an alternative to the traditional advection-dispersion equation (AdDE). The new method is based on a jointly combined four-parameter gamma probability density function (PDF). The gamma residence-time distribution (RTD) function and its first and second moments are derived from the individual two-parameter gamma distributions of randomly distributed variables, tracer travel distance, and linear velocity, which are based on their relationship with time. The gamma RTD function was used on a steady-state, nonideal system modeled as a plug-flow reactor (PFR) in the laboratory to validate the effectiveness of the model. The normalized forms of the gamma RTD and the advection-dispersion equation RTD were compared with the normalized tracer RTD. The normalized gamma RTD had a lower mean-absolute deviation (MAD) (0.16) than the normalized form of the advection-dispersion equation (0.26) when compared to the normalized tracer RTD. The gamma RTD function is tied back to the actual physical site due to its randomly distributed variables. The results validate using the gamma RTD as a suitable alternative to the advection-dispersion equation for quantitative tracer studies of non-ideal flow systems.
Highlights
Researchers have used the distribution of residence times to examine the characteristics of a nonideal ow reactor or system. e residence-time distribution (RTD) was rst proposed to analyze chemical reactor performance in a paper by MacMullin and Weber in 1935 [1,2,3]
Discharge samples of the simulated PFR were collected at 20-minute intervals and analyzed using uorometry and inductively coupled plasma optical emission spectrometry (ICP-OES) for rhodamine and zinc chloride, respectively. e rhodamine WT-20 tracer data was applied to the gamma and advection-dispersion equation (AdDE) RTD models
E results of the tracer study were used to develop the residence-time distribution (RTD) function. e RTD function (EEEEEE) for contaminant molecules in a non-ideal ow system is a probability density function (PDF) which can be interpreted to de ne the probability that contaminant particles present in the in uent at time equals zero will arrive at the effluent a er a time. e RTD is depicted as a plot of EEEEEE versus time as time goes from zero to in nity [2,3,4, 6,7,8]
Summary
Researchers have used the distribution of residence times to examine the characteristics of a nonideal ow reactor or system. e residence-time distribution (RTD) was rst proposed to analyze chemical reactor performance in a paper by MacMullin and Weber in 1935 [1,2,3]. Is jointly combined four-parameter gamma model allows for more exibility to account for the nonlinear aspects [30, 31] of a non-ideal ow system than the single parameter AdDE model; the gamma distribution’s two parameters To address this issue, the gamma distribution for the RTD was derived based on the assumption that the tracer travel distance and linear velocity of the system were gamma-distributed random variables. We are assuming that the time domain is steady state rather than transient. e authors in [2, 5,6,7,8] provide a thorough explanation of non-ideal ow systems
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