Effect Of Boundary Shape Research Articles

Mechanical anisotropy on reduced ballistic limit of phosphorene by cone wave reflection：A computational study

Two-dimensional materials, such as phosphorene, exhibit exceptional electrical and mechanical properties, offering promising prospects for both electronic and mechanical applications. To design more mechanically reliable devices using phosphorene, exploring its mechanical performance, especially impact resistance, is necessary. Here, coarse-grained molecular dynamics simulations are presented to study the mechanical responses of phosphorene under ballistic impact. Interestingly, size-dependent behaviors have been observed, which could be attributed to a coupling effect of cone wave reflection and membrane size. Owing to significant differences in Young’s modulus between the armchair and zigzag direction in phosphorene, mechanical wave propagation exhibits substantial anisotropy in a single-layer phosphorene membrane. A critical membrane size has been identified, below which cone wave reflections from the boundaries can induce perforation: a phenomenon particularly relevant to micro-ballistic testing of two-dimensional material membranes. The effect of boundary shape on reduction in ballistic limit has been studied, in which all the phosphorene sheets in the study are elliptical while the axial ratio of the ellipses is varied from 0.54 to 1.85. The axial ratio 0.69 is proven to maximize the strain amplification induced by cone wave reflection, thus leading to the biggest reduction in ballistic impact for phosphorene. A unitless indicator based on atomic Green-Lagrange strain has been proposed, which can effectively quantify the boundary shape effect on the reduced ballistic limit. Our findings provide timely guidance for the design of future nanodevices using phosphorene with high impact resistance.

Semi-analytical modeling of transient pressure behaviour for a multifractured horizontal well in a gas reservoir with a complex fracture network by considering effects of slippage, stress-sensitivity, and gas adsorption/desorption

A semi-analytical technique has been developed, validated, and applied to quantify the pressure behaviour of a multifractured horizontal well (MFHW) in a gas reservoir with discrete fracture networks and an arbitrary boundary. Considering stress-sensitivity and the slippage effect in the matrix subsystem, a pseudo-pressure is incorporated into the gas flow equations. To weaken the strong nonlinearity from such a combined effect, the dual-reciprocity boundary element method (DRBEM) is applied to efficiently and effectively linearize the governing equations by replacing the nonlinear function with a series of particular solutions. Comparing with the boundary element method (BEM), not only can the DRBEM be used to obtain the accurate solution in any space and time domains, but also it is flexible to deal with the nonlinearity restriction in the governing equations. The finite volume method (FVM) is then adopted to simulate gas flow behaviour in the fracture subsystem with different fracture geometries. Not only can the proposed model be applied to a complex fracture network and operating schedules, but also capture complex gas flow behaviour including the Langmuir sorption, slippage effect, and stress-sensitive effect in a gas reservoir with a discrete fracture network and an arbitrary boundary. The mathematical formulations have been validated and then extended to field applications. A strong stress-sensitive effect is found to result in a large pressure drop and offset the permeability-enhancing effect from the slippage effect. In addition, a decrease in pressure drop derived from gas desorption would restrict the stress-sensitive effect. Furthermore, it can be found that each individual factor imposes a significant impact on the linear flow and boundary dominated flow regimes. On the basis of a mutual interference, the combined effect (i.e., stress-sensitivity, slippage effect, and gas adsorption/desorption) may be weaker than that of each individual factor. In the late boundary-dominated flow regime, the effect of boundary shape becomes more obvious on the pressure distribution curves since the pressure wave would reach the boundaries near fractures within a relatively short time.

Modeling transient pressure behaviour of a multi-fractured horizontal well in a reservoir with an arbitrary boundary and different fracture networks by considering stress-sensitive effect

Combining horizontal drilling together with hydraulic fracturing greatly improves the economic viability of exploiting a tight reservoir, while the stress-sensitive effect raises the significant difficulty to accurately evaluate its well performance. In this paper, a semi-analytical model is proposed to evaluate transient pressure behaviour of a multi-fractured horizontal well (MFHW) in a naturally fractured reservoir with an arbitrary boundary and different fracture networks under stress-sensitive effect. More specifically, the boundary element method coupled with the Pedrosa's transform formulation is used to obtain accurate solutions of the nonlinear equations incorporated with stress-sensitive effect in an arbitrary-shaped reservoir with single-zone or two-zone matrix subsystems. Meanwhile, the Laplace-transform finite difference method can be utilized to semi-analytically deal with the nonlinear fracture subsystems consisting of primary, secondary, and natural fractures by dividing complex fracture networks into small fracture segments. The convergence-skin effect is then introduced to represent the radial flow pattern in hydraulic fractures near a horizontal wellbore. Not only can the effects of stress-sensitivity in the matrix and different fracture subsystems be respectively examined, but also the corresponding pressure responses together with pressure derivative curves are obtained. Such coupled theoretical formulations have been verified and then extended for field applications. The semi-analytical solution is found to be more accurate and reasonable than the solution with the uniform permeability modulus, while the stress-sensitivity has a dominant impact on the intermediate- and late-time flow periods. The convergence-skin effect can be aggravated in the late-time period by considering the inherent stress-sensitivity in a hydraulic fracture, especially at low fracture conductivity. Based on the sensitivity analysis associated with different networks, the initial fracture conductivity in primary and secondary fractures imposes a great impact on the early-stage bilinear flow and fluid feed regimes, while the initial fracture conductivity in natural fractures makes a difference to the transient pressure response in the transition flow regime. As the minimum fracture conductivity in the primary fractures decreases, such an influence becomes more dominant during the late-time flow period. However, the minimum fracture conductivity in secondary and natural fractures has an inappreciable effect on the flow regime. In the late-time flow period, the effect of boundary shape becomes more obvious on the type curves, especially for a relatively small reservoir compared with the size of a horizontal well intercepted by multiple hydraulic fractures. For a reservoir with two-zone systems, the smaller the mobility ratio in the two zones is, the earlier the boundary-dominated flow in the outer zone will commence. Not only does this study facilitate understanding the respective contribution of stress-sensitivity and convergence-skin effect on the well production, but also the newly proposed models can be applied to optimally design a hydraulic fracturing operation under various constraints.

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

AbstractThis study presents a Laplace‐transform‐based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin‐type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi‐analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two‐zone and three‐zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two‐zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two‐zone aquifers is investigated. Finally the drawdown distribution in three‐zone aquifers with arbitrarily shaped boundary for constant‐rate tests (CRT) and flow rate distribution for constant‐head tests (CHT) are analyzed.

Transient pressure response of fractured horizontal wells in tight gas reservoirs with arbitrary shapes by the boundary element method

Horizontal wells and hydraulic fracturing are the key techniques to develop tight gas reservoirs efficiently, but the related researches on the pressure of such wells in arbitrary shaped reservoirs are rare. On this background, this paper extends the boundary element method (BEM) into application to study a multiple fractured horizontal well (MFHW) in arbitrary shaped tight gas reservoirs. By discretizing the outer boundary as well as the fractures, the boundary integral equation can be derived through coupling the fundamental solution of the Helmholtz equation with the dimensionless diffusivity equation. Thereafter, the coefficient matrix, including the fluxes and pressure on the boundaries, can be assembled, and the bottomhole pressure can be computed simultaneously. In this study, by comparison with some semi-analytical solution cases, the accuracy of the results from the BEM was validated. Also, the pressure response and its derivative type curves for a MFHW in an elliptical drainage area were also analyzed, and the effects of reservoir shape, fracture number together with fracture distribution on type curves were examined, respectively. The results suggest that the reservoir shape has a weak effect on the type curves for a MFHW in a large drainage area. If the reservoir size is not large enough comparing to the size of MFHW, the effects of boundary shape could become more obvious and the pressure wave would propagate to the closer boundary (i.e., the minor axis is small) in a relatively short time, which leads to earlier boundary reflection flow period.

Effect of Boundary Shape on Performance of the Ultrasonic Buffer Rod Without Clad

Boundary shape is one of the important factors that affects the performance of ultrasonic buffer rods. To provide unclad buffer rods for some certain cases, the paper investigates the effect of the rod outline shape on the signal-to-noise ratio (SNR) of ultrasonic signals based on the models built with Wave 2500, and found that the rods with an outline of a steep gradient play a very important role in eliminating the trailing noise. By only improving the rod's outline, the SNR of ultrasonic signals could be enhanced greatly.

The Effect of Boundary Shape and Minima Selection on Single Limb Stance Postural Stability

The effect of time-to-boundary minima selection and stability limit definition was investigated during eyes open and eyes closed condition single-limb stance postural stability. Anteroposterior and mediolateral time-to-boundary were computed using the mean and standard deviation (SD) of all time-to-boundary minima during a trial, and the mean and SD of only the 10 absolute time-to-boundary minima. Time-to-boundary with rectangular, trapezoidal, and multisegmented polygon defined stability limits were also calculated. Spearman's rank correlation coefficient test results revealed significant medium-large correlations between anteroposterior and mediolateral time-to-boundary scores calculated using both the mean and SD of the 10 absolute time-to-boundary minima and of all the time-to-boundary minima. Friedman test results revealed significant mediolateral time-to-boundary differences between boundary shape definitions. Follow-up Wilcoxon signed rank test results revealed significant differences between the rectangular boundary shape and both the trapezoidal and multisegmented polygon shapes during the eyes open and eyes closed conditions when both the mean and the SD of the time-to-boundary minima were used to represent postural stability. Significant differences were also revealed between the trapezoidal and multisegmented polygon definitions during the eyes open condition when the SD of the time-to-boundary minima was used to represent postural stability. Based on these findings, the overall results (i.e., stable versus unstable participants or groups) of studies computing postural stability using different minima selection can be compared. With respect to boundary shape, the trapezoid or multisegmented polygon shapes may be more appropriate than the rectangular shape as they more closely represent the anatomical shape of the stance foot.

Influence of boundary shape on interaction process of plasma jet and liquid media

The effects of boundary shape on the propagation form of the plasma jet in liquid media are studied. The construction and consecutive expansion processes of plasma jet in liquid are recorded by high speed digital camera system. The results indicate that the expansion construction of plasma jet in li quid is a typical Taylor cavity, and the axial expansion velocity of Taylor cavity in stepped-wall chamber is greater than that in cylindrical chamber. Based on the experiments, numerical simulations of the interaction of non-steady plasma jet wit h liquid media are carried out. The change characteristics of pressure and velocity in plasma jet flow field have been obtained.