scholarly journals Semianalytical Solution of the Nonlinear Dual-Porosity Flow Model with the Quadratic Pressure Gradient Term

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang-Tao Li ◽  
Ren-Shi Nie ◽  
Yong-Lu Jia ◽  
Dan-Ling Wang
Keyword(s):  
Pressure Gradient ◽  
Flow Model ◽  
Flow Behavior ◽  
Nonlinear Flow ◽  
Dual Porosity ◽  
Model Parameters ◽  
Gradient Term ◽  
Well Production ◽  
Pressure Gradient Term ◽  
Naturally Fractured

The nonlinear dual-porosity flow model, specifically considering the quadratic pressure gradient term, wellbore storage coefficient, well skin factor, and interporosity flow of matrix to natural fractures, was established for well production in a naturally fractured formation and then solved using a semianalytical method, including Laplace transform and a transformation of the pressure function. Analytical solution of the model in Laplace space was converted to numerical solution in real space using Stehfest numerical inversion. Nonlinear flow process for well production in a naturally fractured formation with different external boundaries was simulated and analyzed using standard pressure curves. Influence of the quadratic pressure gradient coefficient on pressure curves was studied qualitatively and quantitatively in conditions of a group of fixed model parameters. The research results show that the semianalytical modelling method is applicable in simulating the nonlinear dual-porosity flow behavior.

scholarly journals Investigation on Nonlinear Flow Behavior through Rock Rough Fractures Based on Experiments and Proposed 3-Dimensional Numerical Simulation

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-34
Author(s):  
Xianshan Liu ◽  
Man Li ◽  
Nandou Zeng ◽  
Tao Li
Keyword(s):  
Pressure Gradient ◽  
Friction Factor ◽  
Flow Behavior ◽  
Nonlinear Flow ◽  
Wall Friction ◽  
Cloud Data ◽  
3 Dimensional ◽  
Relative Roughness ◽  
Seepage Characteristics ◽  
Relationship Of

Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient ∇ P and flow rate Q , and the critical Reynolds number( Re c ) and wall friction factor ( f ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data ∇ P ~ Q decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of f , Re , and relative roughness indicated that f increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that f could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient B in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.

scholarly journals Inherent dissipation of upwind-biased potential temperature advection and its feedback on model dynamics

2021 ◽  
Author(s):  
Almut Gaßmann
Keyword(s):  
Energy Conservation ◽  
Pressure Gradient ◽  
Potential Temperature ◽  
Gradient Term ◽  
Advection Scheme ◽  
Temperature Advection ◽  
Advection Schemes ◽  
Pressure Gradient Term ◽  
Diffusive Fluxes ◽  
Total Energy Conservation

<p>Higher order upwind biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and anti-diffusive fluxes are interpreted here as the effect of irreversible sub-gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes.</p><p>The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one-dimensional advection-dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core.</p>

scholarly journals Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet

2021 ◽  
Vol 26 (3) ◽  
pp. 104-118
Author(s):  
A.N. Kashif ◽  
F. Salah ◽  
D.S. Sankar ◽  
M.D.N. Izyan ◽  
K.K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Maxwell Fluid ◽  
Gradient Term ◽  
Pressure Gradient Term ◽  
Layer Flow

Abstract The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

scholarly journals Nonlinear flow model for well production in an underground formation

2013 ◽  
Vol 20 (3) ◽  
pp. 311-327 ◽  
Author(s):  
J. C. Guo ◽  
R. S. Nie
Keyword(s):  
Fluid Flow ◽  
Liquid Flow ◽  
Gas Flow ◽  
Flow Model ◽  
Transient Flow ◽  
Nonlinear Models ◽  
Nonlinear Flow ◽  
Pressure Transients ◽  
Well Production ◽  
Nonlinear Transient

Abstract. Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water). The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

Sign in / Sign up

Export Citation Format

Share Document