基于不可逆热力学原理的油藏多孔介质耦合作用模型

油藏多孔介质渗流过程存在多场耦合作用,目前的一些研究方法和分析模型具有一定局限性。本文将不可逆热力学原理应用于油藏复杂渗流过程,在局域平衡和连续性假设基础上,提出了基于表征单元体(Representative Elementary Volume,简称REV)的元胞描述方法;推导出了多孔介质渗流过程考虑导热和扩散作用的耦合方程;基于所建模型,分析了稠油热采过程的熵产变化特性。稠油热采过程除包括热传导和扩散耦合作用外,还包括黏滞流动和化学反应等不可逆过程,可根据本文模型扩展。     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

强迫耗散系统的有序结构和系统的发展(Ⅰ)，最小熵产生原理和有序结构

一个系统的发展总是由不可逆热力过程和非线性动力过程所驱动.将大气动力学方程组同考虑了动能变化的Gibbs关系结合起来构建的熵平衡方程，才能更好地描述大气系统的不可逆热力过程和非线性动力过程.至今非平衡态热力学仅利用Onsager线性唯象关系证明了最小熵产生原理.利用新建立的熵平衡方程和大气动力学方程的性质证明，最小熵产生原理在热力学线性区和非线性区都是普遍成立的.且当热量输送平衡、水汽输送平衡和动量输送平衡时，系统达到不可逆过程最弱的最小熵产生热力学状态.当系统又是动力平衡且无平流时，这种最小熵产生态就是 关键词： 非线性热力学 熵产生 最小熵产生原理 有序结构     

不同目的热优化目标函数:热量传递势容损耗与熵产

热量传递势容(势容)反映了物体的导热能力,在导热过程中势容有损耗,对应于势容损耗最小的导热过程效率最高,传热速率最大。熵反映了过程的不可逆性,在导热过程中熵有增加(熵产),对应于熵产最小的过程是系统做有用功的能力((?))损失最小的过程。以势容损耗和熵产为目标函数,分别对导热平板和圆形导热管进行了导热优化计算。以势容损耗作为目标函数的优化,要求沿传热方向温度的梯度为常数,结果是系统具有最大的导热能力。以熵产作为目标函数的优化,要求沿传热方向温度的自然对数的梯度为常数,结果是系统具有最小的(?)损耗。     

辐射热力学中光量子的熵和光子气的熵

本文根据已证明了的光谱等效温度Tλ方程和光量子能量,首次导出了光量子熵常数sλ为3.72680×10-23 J.K-1,并证明通过sλ算出的黑体等效温度等于黑体辐射温度,验证了光量子熵常数结论的正确性;此外,给出了闭口系平衡态空腔辐射场光子气的熵和熵变方程,首次提出开口系辐射流的熵,接收器的净辐射熵差的计算式.本文的结果,为非平衡态辐射热力学体系提供了新的理论基础,对研究辐射能与其它能量转化中不可逆损失将提供有益帮助.     

热流演化方程及其推证

在经典的输运过程中,各向同性的均匀介质中的热传导方程,可从Fourier定律 J=—K T(1)和热流的能量守恒方程推得.得到的热传导方程为式中C是传热介质每单位体积的比热,K是热传导系数,T是介质的温度.(3)式在偏微分方程中属抛物线型,它预示热扰动(热波)将以一个无限大速度传播,这显然不符合实验事实.实际上波速是决不能超过热载体的速度的.Vernotte[1]正视了这一点,早在1958年就建议把(1)式修正成如下最简单的热流演化方程:式中τ了是弛豫时间.(4)式的合理性是显然的,因为按(2)式和(4)式可得在偏微分方程中,(5)式属于双曲线型,它预示着热扰…     

基于热质理论的热波传递现象研究

基于热质的概念应用牛顿力学原理建屯了热质输运的控制方程,推导得到了普适的导热定律.在惯性力可以忽略时它即退化为傅立叶导热定律,反映出非傅立叶导热现象的本质是热质的惯性引起的.当热流和温度对空间的惯性以及温度对时间的惯性可以忽略时,所得到的导热定律可以退化为CV模型.对热波传递的数值分析表明:当热扰动和热流都比较小时,热流在空间加速的惯性可以忽略,基丁热质理论的热波方程和CV模型符合得很好;但是,在描述较大的热扰动时,由于热流的空间加速惯性不能够被忽略,CV模型的结果在两个温度波峰叠加时会出现负温度的非物理现象,而基于热质理论的普适导热定律的结果则克服了这一缺陷.     

太阳能热发电系统蓄热过程熵产分析

蓄热技术是平衡热量供应和需求的有效手段,可以提高系统的热稳定性和延长工作时间。应用于太阳能高温热发电中的单罐斜温层蓄热系统越来越受到重视。本文从热力学第二定律出发对蓄热系统的不可逆损失进行了研究,分析了蓄热过程中蓄热材料的密度、导热系数、颗粒直径和熔盐的流速等参数对蓄热系统熵产的影响。结果表明当蓄热材料密度较小,导热系数较小、蓄热球颗粒直径较小时,系统的熵产值较小;当熔盐流速较低时,系统的熵产值也较小。     

正六边形板式换热器的热力学分析

本文提出了一种新型的正六边形球面肋板式换热器,并对该换热器进行了基于熵产数的热力学分析。通过数学推导给出了换热器中局部熵产的计算公式,该公式是数值模拟计算求解换热器中局部熵产和总熵产的通用公式。借助数值分析软件ANSYS CFX 12.0,建立了换热器的三维物理模型,采用有限容积法对流体在球面肋形成的流道中的流动进行了热力学分析。得到了板片上由有限温差导热和阻力引起的熵产的具体分布情况,以及熵产数随雷诺数的变化规律,为后续板片的优化设计工作提供了参考。     

热质的运动和传递-最低热质能耗散原理和热质运动方程

过增元基于质能方程提出了热质的概念.在非平衡热力学中,存在最低能量耗散原理,根据该原理可以导出热传导,扩散及粘性流动等不可逆输运过程的方程式.当采用热质模型对传热现象进行描述时,发现热质的运动也满足最小作用量原理:最低热质能耗散原理,根据该原理可以推导得出热质运动的动量守恒方程。     

Entropy Production for a Class of Inverse SRB Measures

We study the entropy production for inverse SRB measures for a class of hyperbolic folded repellers presenting both expanding and contracting directions. We prove that for most such maps we obtain strictly negative entropy production of the respective inverse SRB measures. Moreover we provide concrete examples of hyperbolic folded repellers where this happens.     

Nonequilibrium quantum impurities: from entropy production to information theory

Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This Letter discusses these issues in the context of quantum impurity models. We use simple thermodynamic arguments to define the rate of entropy production sigma and show that sigma has a simple information-theoretic interpretation in terms of nonequilibrium distribution functions. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady state. We conclude by applying these ideas to the resonance level model and the Kondo model.     

Construction of BGK Models with a Family of Kinetic Entropies for a Given System of Conservation Laws

We introduce a general framework for kinetic BGK models. We assume to be given a system of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK models that lead to this system in the hydrodynamic limit, and that are compatible with the whole family of entropies. This is obtained by a new characterization of Maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family of entropies. We deduce a general procedure to construct such BGK models, and we show how classical examples enter the framework. We apply our theory to isentropic gas dynamics and full gas dynamics, and in both cases we obtain new BGK models satisfying all entropy inequalities.     

Entropy of averaging for compressible two-pressure two-phase flow models

We propose here a new closure for compressible two-pressure two-phase flow models, which satisfies conservation requirements, boundary conditions at the edges of the mixing zone, hyperbolic stability (real eigenvalues for the characteristic version of the equations of motion) and an entropy inequality. Except for the latter, these properties are direct consequences of the proposed closures. The entropy, which is the main focus of this Letter, inequality (as opposed to entropy conservation for microphysically adiabatic processes) implies positivity for the entropy of averaging.     

Regularization of Quantum Relative Entropy in Finite Dimensions and Application to Entropy Production

The fundamental concept of relative entropy is extended to a functional that is regular-valued also on arbitrary pairs of nonfaithful states of open quantum systems. This regularized version preserves almost all important properties of ordinary relative entropy such as joint convexity and contractivity under completely positive quantum dynamical semigroup time evolution. On this basis a generalized formula for entropy production is proposed, the applicability of which is tested in models of irreversible processes. The dynamics of the latter is determined by either Markovian or non-Markovian master equations and involves all types of states.     

Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.     

Onsager Relations and Eulerian Hydrodynamic Limit for Systems with Several Conservation Laws

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities whenever a stationary measure with product structure exists. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of the conserved variables) is a globally convex Lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit. As concrete examples we also present a number of models modeling deposition (or domain growth) phenomena. The Onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel. The fact that equilibrium thermodynamic entropy is Lax entropy for the arising Euler equations was noticed earlier in the context of Hamiltonian systems with weak noise, see ref. 7.     

Entropy production in open volume-preserving systems

We describe a mechanism leading to positive entropy production in volume-preserving systems under nonequilibrium conditions. We consider volume-preserving systems sustaining a diffusion process like the multibaker map or the Lorentz gas. A continuous flux of particles is imposed across the system resulting in a steady gradient of concentration. In the limit where such flux boundary conditions are imposed at arbitrarily separated boundaries for a fixed gradient, the invariant measure becomes singular. For instance, in the multibaker map, the limit invariant measure has a cumulative function given in terms of the nondifferentiable Takagi function. Because of this singularity of the invariant measure, the entropy must be defined as a coarse-grained entropy instead of the fined-grained Gibbs entropy, which would require the existence of a regular measure with a density. The coarse-grained entropy production is then shown to be asymptotically positive and, moreover, given by the entropy production expected from irreversible thermodynamics.     

Jacobi fields on statistical manifolds of negative curvature

Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively.     

Entropy Production and Information Gain¶in Axiom-A Systems

Anosov systems are mathematical models for chaotic systems in statistical mechanics and fluid dynamics. Most of these systems enjoy the property of positive entropy production. We introduce the concept of specific information gain (or specific relative entropy) h(μ₊,μ₋) in Anosov systems and prove that it is identical to the entropy production rate e _p (μ₊) defined by Ruelle and Gallavotti in Anosov systems. From this point of view, the entropy production rate e _p (μ₊ characterizes the degree of macroscopic irreversibility of the system. Received: 2 August 1999 / Accepted: 14 April 2000