Tight gas is one important unconventional hydrocarbon resource that is stored in tight sandstone, whose mechanical property greatly influences the tight gas production process and is commonly believed to be simply elastic when designing the stimulation plan. However, the experimental evidence provided in this work surprisingly shows that tight sandstone can deform in a viscoelastic way. Such an unexpected observation poses a challenge in accurately modelling the deformation process. We solve this problem by adopting the fractional Maxwell model to successfully derive the constitutive equation of tight sandstone, based on which not only all the experimental data can be interpreted quantitatively, but also reasonable and consistent predictions as to tight sandstone’s long-term deformation behaviour can be made. We then investigate the typicality of our results in China’s Changqing oilfield, which is one major centre of tight gas production and where the rock samples for experiments are obtained. It is estimated that a non-negligible portion of 18% tight sandstone samples in this area will probably display viscoelasticity. Finally, our work implies that the mechanical properties of other materials may also need further scrutiny to possibly uncover any unexpected behaviour, overlooking which may result in misleading predictions.

We uncover an optimization principle for the finite-time heat-work conversion process performed between two finite-sized heat reservoirs in the nonlinear response regime that is characterized by rather generic flux-force relations. We solve the problem of maximizing work output in a given time interval by means of the variational method. Moreover, in the limiting case that the cold reservoir is infinite, we find the corresponding optimized process can be determined by a single quantity, which plays the role similar to that of the Hamiltonian in classical mechanics. Some theoretical implications are discussed consequently, under the generalized tight-coupling condition which applies to both linear and nonlinear response cases. Our results can hopefully help design and control realistic thermodynamical processes.

A necessary condition to optimize work output is obtained for general heat engines working between two finite-sized heat reservoirs in a given period of time $\tau$, with the amount of heat received from the hot reservoir being fixed for all possible realizations of the process. It states that $T_{\mathrm{c}}\dot{\sigma }$ should be a constant during the optimized process, where $T_{\mathrm{c}}$ is the temperature of the cold reservoir, which could be time dependent, and $\dot{\sigma }$ is the entropy production rate of the two reservoirs. Further optimizing $\tau$ gives the maximum time-averaged power output; the corresponding thermodynamical efficiency, however, is found to be generally not equal to half of the maximum efficiency due to the finiteness of the sizes of two reservoirs. Our results are obtained within the framework of Onsager's theory of linear irreversible thermodynamics and under the tight-coupling condition. The findings in this work may potentially be applied in the optimization of realistic thermodynamical processes.

Anomalous transport in porous media is commonly believed to be induced by the highly complex pore space geometry. However, this phenomenon is also observed in porous media with rather simple pore structure. In order to answer how ubiquitous can anomalous transport be in porous media, we in this work systematically investigate the solute transport process in a simple porous medium model with minimal structural randomness. The porosities we consider range widely from 0.30 up to 0.85, and we find by lattice Boltzmann simulations that the solute transport process can be anomalous in all cases at high Péclet numbers. We use the continuous time random walk theory to quantitatively explain the observed scaling relations of the process. A plausible hydrodynamic origin of anomalous transport in simple porous media is proposed as a complement to its widely accepted geometric origin in complex porous media. Our results, together with previous findings, provide evidence that anomalous transport is indeed ubiquitous in porous media. Consequently, attentions should be paid when modelling solute transport by the classical advection-diffusion equation, which could lead to systematic error.