Experimental test and theoretical calculation of the fracture height limit of gas pipe flow to Darcy flow

Low-speed flow experiments in which ultra-fine copper tubes are used to simulate micro-fractures in carbonate strata are conducted to analyze the variations of gas flow state in fractures of different fracture heights,determine flow state transition limit and transition interval,and establish the calculation method of flow state transition limit.The results show that the ideal Hagen-Poiseuille flow is the main form of gas flow in large fractures.Due to the decrease of fracture height,the gas flow in the fracture changes from Hagen-Poiseuille flow with ideal smooth seam surface to non-Hagen-Poiseuille flow,and the critical point of the transition is the boundary of flow state transition.After the fracture height continues to decrease to a certain extent below the boundary of the flow state transition fracture height,the form of gas flow gradually changes to the ideal Darcy flow,thus the transition interval of the gas flow state in the closing process of fracture can be determined.Based on the three-dimensional microconvex body scanning of the fracture surface,the material properties of fracture and properties of fluid in the fracture,a method for calculating the boundary of flow state transition is established.The experimental test and theoretical calculation show that the limit of the fracture height for the transition from pipe flow to Darcy flow is about twice the sum of the maximum height of the microconvex bodies on the upper and lower sides of the fracture.

A granular-biomass high temperature pyrolysis model based on the Darcy flow

We established a model for the chemical reaction kinetics of biomass pyrolysis via the hightemperature thermal cracking of liquid products. We divided the condensable volatiles into two groups, based on the characteristics of the liquid prdoducts., tar and biomass oil. The effects of temperature, residence time, particle size, velocity, pressure, and other parameters on biomass pyrolysis and high-temperature tar cracking were investigated numerically, and the results were compared with experimental data. The simulation results showed a large endothermic pyrolysis reaction effect on temperature and the reaction process. The pyrolysis reaction zone had a constant temperature period in several layers near the center of large biomass particles. A purely physical heating process was observed before and after this period, according to the temperature index curve.

Similarity Solutions for Laminar Boundary Layer Flow of Darcian Fluid over Horizontal Plate with a Convective Boundary Condition

This paper considers the problem of hydrodynamics and thermal boundary layers of Darcy flow over horizontal surface embedded in a porous medium. The solutions of such problems for the cases of uniform surface temperature and variable surface temperature have been studied and analysed in many papers. This paper, however, attempts to find similarity solutions for the Darcy flow problem with a convective boundary condition at the plate surface. It is found that the solution is possible when the heat transfer coefficient is proportional to x–2/3. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process. Analytical expressions are provided for local surface heat flux and total surface heat transfer rate while the flow variables are discussed graphically.

A New Unified Stabilized Mixed Finite Element Method of the Stokes-Darcy Coupled Problem: Isotropic Discretization

In this paper, we develop an a-priori error analysis of a new unified mixed finite element method for the coupling of fluid flow with porous media flow in RN, N ∈ {2,3}, on isotropic meshes. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. The approach utilizes a modification of the Darcy problem which allows us to apply a variant nonconforming Crouzeix-Raviart finite element to the whole coupled Stokes-Darcy problem. The well-posedness of the finite element scheme and its convergence analysis are derived. Finally, the numerical experiments are presented, which confirm the excellent stability and accuracy of our method.

Forward modeling of tight sandstone permeability based on mud intrusion depth and its application in the south of the Ordos Basin

Permeability is an important index in reservoir evaluation,oil and gas accumulation control,and production effi ciency.At present,permeability can be obtained through several methods.However,these methods are not suitable for tight sandstone in general because the pore type in tight sandstone is mainly secondary pores and has the characteristics of low porosity and permeability,high capillary pressure,and high irreducible water saturation.Mud invasion depth is closely related to permeability during drilling.In general,the greater the permeability,the shallower the mud invasion depth,and the smaller the permeability,the deeper the mud invasion depth.Therefore,this paper builds a model to predict the permeability of tight sandstone using mud invasion depth.The model is based on the improvement of the Darcy flow equation to obtain permeability using mud invasion depth inversion of array induction logging.The influence of various permeability factors on the model is analyzed by numerical simulation.The model is used to predict the permeability of tight sandstone in the south of the Ordos Basin.The predicted permeability is highly consistent with the core analysis permeability,which verifi es the reliability of the method.

Experimental study of the transition from non-Darcian to Darcy behavior for flow through a single fracture

Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of the evolution of the flow pattern at places far from the outlet. The relationship between the hydraulic gradient and the flow velocity at different points, and the proportion evolution of the linear and nonlinear portions in the Forchheimer formula are then discussed. Three major conclusions are obtained. First, the non-Darcian flow exists in a single fracture in different laboratory tests. Better fitting accuracy is obtained by using the Forchheimer formula than by using the Darcy law. Second, the proportion of the Darcy flow increases with the increase of the observation scale. In places far enough, the Darcy flow prevails, and the critical velocity between the non-Darcian flow and the Darcy flow decreases as the fracture aperture increases. Third, when the fracture aperture increases, the critical Reynolds number between the non-Darcian flow and the Darcy flow decreases.

A Uniformly Stable Nonconforming FEM Based on Weighted Interior Penalties for Darcy-Stokes-Brinkman Equations

A nonconforming rectangular finite element method is proposed to solve a fluid structure interaction problem characterized by the Darcy-Stokes-Brinkman Equation with discontinuous coefficients across the interface of different structures.A uniformly stable mixed finite element together with Nitsche-type matching condi-tions that automatically adapt to the coupling of different sub-problem combinations are utilized in the discrete algorithm.Compared with other finite element methods in the literature,the new method has some distinguished advantages and features.The Boland-Nicolaides trick is used in proving the inf-sup condition for the multi-domain discrete problem.Optimal error estimates are derived for the coupled prob-lem by analyzing the approximation errors and the consistency errors.Numerical examples are also provided to confirm the theoretical results.