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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Residence time distribution ： ウィキペディア英語版 Residence time distribution The residence time distribution (RTD) of a chemical reactor is a probability distribution function that describes the amount of time a fluid element could spend inside the reactor. Chemical engineers use the RTD to characterize the mixing and flow within reactors and to compare the behavior of real reactors to their ideal models. This is useful, not only for troubleshooting existing reactors, but in estimating the yield of a given reaction and designing future reactors. The concept was first proposed by MacMullin and Weber in 1935, but was not used extensively until P.V. Danckwerts analyzed a number of important RTDs in 1953. ==Theory== The theory of residence time distributions generally begins with three assumptions: # the reactor is at steady-state, # transports at the inlet and the outlet takes place only by advection, and # the flow is incompressible. The incompressibility assumption is not required, but compressible flows are more difficult to work with and less common in chemical processes. A further level of complexity is required for multi-phase reactors, where a separate RTD will describe the flow of each phase, for example bubbling air through a liquid. The distribution of residence times is represented by an exit age distribution, $E(t)$. The function $E(t)$ has the units of time−1 and is defined such that : $\backslash int\_^\backslash infty\; E(t)\backslash ,\; dt\; =\; 1$. The fraction of the fluid that spends a given duration, $t$ inside the reactor is given by the value of $E(t)\; dt$. The fraction of the fluid that leaves the reactor with an age less than $t\_1$ is : $\backslash int\_^\; E(t)\backslash ,\; dt$. The fraction of the fluid that leaves the reactor with an age greater than $t\_1$ is : $\backslash int\_^\backslash infty\; E(t)\backslash ,\; dt\; =\; 1-\backslash int\_^\; E(t)\backslash ,\; dt$. The average residence time is given by the first moment of the age distribution: : $\backslash bar\; t\; =\; \backslash int\_^\backslash infty\; t\; \backslash cdot\; E(t)\backslash ,\; dt$. If there are no dead, or stagnant, zones within the reactor then $\backslash bar\; t$ will be equal to $\backslash tau$, the residence time calculated from the total reactor volume and the volumetric flow rate of the fluid: : $\backslash tau\; =\; \backslash frac$. The higher order central moments can provide significant information about the behavior of the function $E(t)$. For example, the second central moment indicates the variance ($\backslash sigma^2$), the degree of dispersion around the mean. : $\backslash sigma^2\; =\; \backslash int\_^\backslash infty\; (t-\; \backslash bar\; t)^2\; \backslash cdot\; E(t)\backslash ,\; dt$ The third central moment indicates the skewness of the RTD and the fourth central moment indicates the kurtosis (the "peakedness"). One can also define an internal age distribution $I(t)$ that describes the reactor contents. This function has a similar definition as $E(t)$: the fraction of fluid within the reactor with an age of $t$ is $I(t)\; dt$. As shown by Danckwerts, the relation between $E(t)$ and $I(t)$ can be found from the mass balance: : $I(t)\; =\; \backslash frac\backslash left(1-\backslash int\_0^t\; E(t)\backslash \; dt\backslash right)\; \backslash qquad\; E(t)\; =\; -\backslash tau\; \backslash frac$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Residence time distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.