A new theoretical solution of the effect of atmospheric pressure on water level

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The nonlinear oil–water two-phase flow behavior for a horizontal well in triple media carbonate reservoir

Carbonate reservoir is one of the important reservoirs in the world. Because of the characteristics of carbonate reservoir, horizontal well has become a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A mathematical model for a oil–water two-phase flow horizontal well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes are presented in this article. A semi-analytical solution is obtained in the Laplace domain using source function theory, Laplace transformation, and superposition principle. Analysis of transient pressure responses indicates that seven characteristic flow periods of horizontal well in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug and fracture system, horizontal section length, and horizontal well position can significantly influence the transient pressure responses of horizontal well in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir by type curve matching.     

Scattering of plane P waves by a semi-cylindrical hill： analytical solution

An analytical solution for scattering of plane P waves by a semi-cylindrical hill was derived by using the wave function expansion method, and convergence of the solution and accuracy of truncation were verified. The effect of incident frequency and incident angle on the surface motion of the hill was discussed, and it was shown that a hill greatly amplifies incident plane P waves, and maximum horizontal displacement amplitudes appear mostly at the inclined incidence of waves, which are located at the half-space; and maximum vertical displacement amplitudes emerge mostly at the vertical incidence of waves, which are situated at the hill.     

Scattering of Rayleigh waves by a shallow circular alluvial valley： High-frequency solution

Introduction The effect of local site conditions on wave propagation is one of the most attractive topics in engineering seismology. It may be resolved by either a numerical method or an analytical method. Numerical methods include the finite difference, finite element, boundary element method, etc. The analytical method is the wave function expansion method. The advantage of these numerical methods is that they can be applied to local inhomogeneity of arbitrary shapes, but analytical method …     

Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry

The semi-empirical Kozeny–Carman (KC) equation is the most famous permeability–porosity relation, which is widely used in the field of flow in porous media and is the starting point for many other permeability models. However, this relation has many limitations from its inception, and the KC constant is an empirical parameter which was proved to be not a constant. In this paper, we briefly reviewed the KC equation, its modifications and various models for the KC constant. We then derived an analytical expression for the permeability in homogeneous porous media based on the fractal characters of porous media and capillary model. The proposed model is expressed as a function of fractal dimensions, porosity and maximum pore size. The analytical KC constant with no empirical constant is obtained from the assumption of square geometrical model. Furthermore, a distinct linear scaling law between the dimensionless permeability and porosity is found. It is also shown that our analytical permeability is more closely related to the microstructures (fractal dimensions, porosity and maximum pore size), compared to those obtained from conventional methods and models.     

Precision calculation of crustal deformation induced by radial steady laminellar flow of underground water from single well in multi-layered structural aquifers

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Dimensional analysis of two-phase flow including a rate-dependent capillary pressure–saturation relationship

The macroscopic modelling of two-phase flow processes in subsurface hydrosystems or industrial applications on the Darcy scale usually requires a constitutive relationship between capillary pressure and saturation, the P_c(S_w) relationship. Traditionally, it is assumed that a unique relation between P_c and S_w exists independently of the flow conditions as long as hysteretic effects can be neglected. Recently, this assumption has been questioned and alternative formulations have been suggested. For example, the extended P_c(S_w) relationship by Hassanizadeh and Gray [Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990;13(4):169–86] proposes that the difference between the phase pressures to the equilibrium capillary pressure is a linear function of the rate of change of saturation, thereby introducing a constant of proportionality, the coefficient τ. It is desirable to identify cases where the extended relationship needs to be considered. Consequently, a dimensional analysis is performed on the basis of the two-phase balance equations. In addition to the well-known capillary and gravitational number, the dimensional analysis yields a new dimensionless number. The dynamic number Dy quantifies the ratio of dynamic capillary to viscous forces. Relating the dynamic to the capillary as well as the gravitational number gives the new numbers DyC and DyG, respectively. For given sets of fluid and porous medium parameters, the dimensionless numbers Dy and DyC are interpreted as functions of the characteristic length and flow velocity. The simulation of an imbibition process provides insight into the interpretation of the characteristic length scale. The most promising choice for this length scale seems to be the front width. We conclude that consideration of the extended P_c(S_w) relationship may be important for porous media with high permeability, small entry pressure and high coefficient τ when systems with a small characteristic length (e.g. steep front) and small characteristic time scale are under investigation.     

A new method of testing pile using dynamic P-S-curve made by amplitude of wave train

Introduction To the impact pattern, the dynamic test with high strain is generally grouped into two kinds.One is stricken by hammer and another is by rocket. The former is widely used and the latter isused widely abroad and seldom used at home. To the analyzing method, it is also divided into twokinds. One is the method of wave equation and another is the method of experimental formula.The methods of Smith, Case and Capwap and other improved methods belong to the former, andthe methods …     

Role of wave–mean flow interaction in sun–climate connections: Historical overview and some new interpretations and results

Quasi-decadal variations in solar irradiance – termed the 11-year solar cycle (SC) – have been linked to variations in a variety of atmospheric circulation features, including the polar vortex, the Brewer–Dobson circulation, and the quasi-biennial oscillation. These features share an underlying commonality: they are all rooted in wave–mean flow interaction. The purpose of this paper is to provide a historical overview of the connection between the SC and wave–mean flow interaction and to propose a more complete theoretical framework for solar modulated wave–mean flow interaction that includes both zonal-mean and zonally asymmetric ozone as intermediaries for communicating variations in solar spectral irradiance to the climate system. We solve a quasi-geostrophic model using the WKB formalism to highlight the physics connecting the SC to planetary wave-drag. Numerical results show the importance of the zonally asymmetric ozone field in mediating the effects of solar variability to the wave-driven circulation in the middle atmosphere.     

Soil–structure interaction for a SDOF oscillator supported by a flexible foundation embedded in a half-space: Closed-form solution for incident plane SH-waves

A closed-form analytical solution is presented for the dynamic response of a SDOF oscillator, supported by a flexible foundation embedded in an elastic half-space, and excited by plane SH waves. The solution is obtained by the wave function expansion method. The solution is verified for the special case of a rigid foundation by comparison with published results. The model is used to investigate the effect of the foundation flexibility on the system response. The results show that the effect is significant for both foundation response and structural relative response. For a system with more flexible foundation, the radiation damping is smaller, the foundation response is larger, especially for obliquely incident waves, while the structural relative response is smaller, and the system frequency shifts towards lower frequencies. This simple model may be helpful to obtain insight into the effects of soil–structure interaction for a slim structure on an extended flexible foundation.     

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Simulations of flow for a discrete-fracture model in fractured porous rocks have gradually become more practical, as a consequence of increased computer power and improved simulation and characterization techniques. Discrete-fracture models can be formulated in a lower-dimensional framework, where the fractures are modeled in a lower dimension than the matrix, or in an equi-dimensional form, where the fractures and the matrix have the same dimension.     

Impacts of groundwater flow on the evolution of a thermokarst lake in the permafrost–dominated region on the Qinghai–Tibet plateau

As a result of global warming induced permafrost degradation in recent decades, thermokarst lakes in the Qinghai–Tibet plateau (QTP) have been regulating local hydrological and ecological processes. Simulations with coupled moisture–heat numerical models in the Beiluhe basin (located in the hinterland of permafrost regions on the QTP) have provided insights into the interaction between groundwater flow and the freeze–thaw process. A total of 30 modified SUTRA scenarios were established to examine the effects of hydrodynamic forces, permeability, and climate on thermokarst lakes. The results indicate that the hydrodynamic condition variables regulate the permafrost degradation around the lakes. In case groundwater recharges to the lake, a low–temperature groundwater flow stimulates the expansion of the surrounding thawing regions through thermal convection. The thawing rate of the permafrost underlying the lake intensifies when groundwater is discharged from the lake. Under different permeability conditions, spatiotemporal variations in the active layer thickness significantly influence the occurrence of an open talik at the lake bottom. A warmer and wetter climate will inevitably lead to a sharp decrease in the upper limit of the surrounding permafrost, with a continual decrease in the duration of open talik events. Overall, our results underscore that comprehensive consideration of the relevant hydrologic processes is critical for improving the understanding of environmental and ecological changes in cold environments.     

Reduction of peak ground velocity by nonlinear soil response–Ⅱ:excitation by a P-wave pulse

We study the reduction of peak velocity on the ground surface of a soil valley caused by loss of wave energy by large nonlinear strains and strain localization inside the valley, for excitation by a half-sine P-wave pulse. This study is a follow up to our previous study of out of plane response for excitation by an SH-pulse. In this paper, we consider the inplane response, and assume that the soil material does not support tension, but the normal stress at a point in the soil can be compression(negative) or zero. A point in the soil with zero stress behaves as a stress-free point, it does not transmit normal stress and appears as a crack point. Because of this, along with the nonlinear response associated with compression and shear, the in-plane response in this study is more complex than that of the out-of-plane SH response. We study the interplay of two opposing effects:(i) jump in impedance from a higher value(half-space) to a lower value(valley), which amplifies the linear motions at the free surface of the valley, and(ii) the occurrence of nonlinear zones in the valley, which reduce the motion at the valley surface.     

A physical interpretation of the deterministic fractal–multifractal method as a realization of a generalized multiplicative cascade

In this study, we attempt to offer a solid physical basis for the deterministic fractal–multifractal (FM) approach in geophysics (Puente, Phys Let A 161:441–447, 1992; J Hydrol 187:65–80, 1996). We show how the geometric construction of derived measures, as Platonic projections of fractal interpolating functions transforming multinomial multifractal measures, naturally defines a non-trivial cascade process that may be interpreted as a particular realization of a random multiplicative cascade. In such a light, we argue that the FM approach is as “physical” as any other phenomenological approach based on Richardson’s eddies splitting, which indeed lead to well-accepted models of the intermittencies of nature, as it happens, for instance, when rainfall is interpreted as a quasi-passive tracer in a turbulent flow. Although neither a fractal interpolating function nor the specific multipliers of a random multiplicative cascade can be measured physically, we show how a fractal transformation “cuts through” plausible scenarios to produce a suitable realization that reflects specific arrangements of energies (masses) as seen in nature. This explains why the FM approach properly captures the spectrum of singularities and other statistical features of given data sets. As the FM approach faithfully encodes data sets with compression ratios typically exceeding 100:1, such a property further enhances its “physical simplicity.” We also provide a connection between the FM approach and advection–diffusion processes.     

Calibration of a rainfall–runoff model at regional scale by optimising river discharge statistics: Performance analysis for the average/low flow regime

Traditional procedures for rainfall–runoff model calibration are generally based on the fit of individual values of simulated and observed hydrographs. We use here an alternative option that is carried out by matching, in the optimisation process, a set of streamflow statistics. Such an approach has the significant advantage to enable also a straightforward regional calibration of model parameters, based on the regionalisation of the selected statistics. The minimisation of the set of objective functions is carried out by using the AMALGAM algorithm, leading to the identification of behavioural parameter sets. The procedure is applied to a set of river basins located in central Italy: the basins are treated alternatively as gauged and ungauged and, as a term of comparison, the results obtained with a traditional time-domain calibration are also presented. With respect to previous applications of analogous procedures, we investigate here the identification of the target statistics depending on the purposes of the application, and in particular when the focus is on the reproduction of the low-flows. The results show that a suitable choice of the statistics to be optimised leads to interesting results in real world case studies as far as the reproduction of the different flow regimes is concerned.     

A new definition of strong motion duration and related parameters affecting the response of medium–long period structures

This study presents a new definition of the strong motion duration combining the alternative bracketed and significant duration definitions. Based on the time integral of the absolute ground velocity, a new index is defined, as cumulative absolute displacement (CAD), and used to estimate the strong motion duration. The proposed bracketed-significant duration t_bs is found to be well correlated with the strong motion part of the records, especially in the case of near-source events. The duration t_bs and the CAD index are used to assess the anticipated structural behavior of medium–long period structures.