scholarly journals Nonlinear Moving Boundary Model of Low-Permeability Reservoir

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8445
Author(s):  
Xiarong Jiao ◽  
Shan Jiang ◽  
Hong Liu
Keyword(s):  
Linear Model ◽  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Outer Boundary ◽  
Low Permeability ◽  
Gas Seepage ◽  
Boundary Model ◽  
Low Permeability Reservoirs

At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant pressure outer boundary and closed outer boundary are compared with the analytical solutions. The calculation results show that it is reliable to solve the oil-gas seepage equation with the moving boundary nonlinear equation. To deal with the difficulty in solving analytical solutions for low-permeability reservoirs and numerical solutions of moving boundaries, a quasi-linear model and a nonlinear moving boundary model were proposed based on the characteristics of low-permeability reservoirs. The production decline curve chart of the quasi-linear model and the recovery factor calculation chart were drawn, and the sweep radius calculation formula was also established. The research results can provide a theoretical reference for the policy-making of development technology in low-permeability reservoirs.

Moving Boundary Model for Leaching of Nuclear Waste Glass

1984 ◽  
Vol 44 ◽  
Author(s):  
T. Banba ◽  
T. Murakami ◽  
H. Kimura
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Surface Layers ◽  
Proposed Model ◽  
Film Mass Transfer ◽  
Leaching Experiments ◽  
Trial And Error Method ◽  
Boundary Model ◽  
Fundamental Equations ◽  
Error Method

AbstractThe leaching experiments of Soxhlet type have been carried out[l, 2] and on the basis of the results we developed the mathematical leaching model which used one dimensional diffusion and could treat the growth of surface layers. The model adopted the following assumptions: 1) The velocity of the bulk glass-surfacé layers boundary depends on time alone. 2) Some of the diffusing substances are immobilized in the surface layers by an irreversible first-order reaction. 3) A fictitious film exists at the solution-surface layers interface. The fundamental equations were established based on these assumptions and the numerical solutions were obtained by the Crank-Nicholson implicit method. The values of the diffusion coefficient, the reaction rate and the film mass transfer coefficient were obtained by a trial-and-error method. The applicability of the model was confirmed by the fact that the leaching mechanisms deduced from the calculated results were consistent with those mechanisms deduced from the experimental results. The present study showed the proposed model was valid for calculation of the leach rates of waste glasses when surface layers grew during leaching, and the study also indicated which parameters should be measured experimentally to predict the leach rates.

scholarly journals Analytical Solutions for Non-Darcy Transient Flow with the Threshold Pressure Gradient in Multiple-Porosity Media

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Erhui Luo ◽  
Xiaodong Wang ◽  
Yongle Hu ◽  
Jianjun Wang ◽  
Li Liu
Keyword(s):  
Mathematical Model ◽  
Pressure Gradient ◽  
Transient Response ◽  
Moving Boundary ◽  
Low Permeability ◽  
Threshold Pressure ◽  
Threshold Pressure Gradient ◽  
Pressure Transient ◽  
Multiple Porosity ◽  
Low Permeability Reservoirs

Low-velocity non-Darcy flow can be described by using the threshold pressure gradient (TPG) in low-permeability porous media. The existence of the TPG yields a moving boundary so that fluid starts to flow inside this boundary when the pressure gradient overcomes the viscous forces, and beyond this boundary, there will be no flow. A mathematical model of considering the TPG is developed to describe the flow mechanism in multiple-porosity media. By defining new dimensionless variables, the nonlinear mathematical model can be solved analytically. This new approach has been validated with several approximate formulas and numerical tools. The diffusion of the moving boundary varying with time is analyzed in detail in multiple-porosity media, and then the effect of the moving boundary on pressure transient response is investigated and compared with that of the traditional three boundary types (closed boundary, infinite-pressure boundary, and constant-pressure boundary). Sensitivity analysis is conducted to study the effect of the TPG on pressure and pressure derivative curves and rate decline curves for single-porosity media, dual-porosity media, and triple-porosity media, respectively. The results show that the moving boundary exerts a significant influence on reservoir performance at a relatively early time, unlike the other three boundary types, and only a boundary-dominated effect at the late time. The larger the threshold pressure gradient, the smaller the diffusion distance of the moving boundary and the rate of this well at a given dimensionless time. At the same time, the pressure transient response exhibits a higher upward trend because of a larger TPG. All behavior response might be explained by more pressure drop consumed in low-permeability reservoirs. The finding is helpful to understand the performance of low-permeability multiple-porosity media and guide the reasonable development of low-permeability reservoirs.

ASSESSMENT OF OIL WELL PRODUCTIVITY IN LOW-PERMEABILITY RESERVOIRS IN THE FIELDS OF EASTERN SIBERIA

2017 ◽  
pp. 30-36
Author(s):  
R. V. Urvantsev ◽  
S. E. Cheban
Keyword(s):  
Oil Recovery ◽  
Large Scale ◽  
Oil And Gas ◽  
Oil Extraction ◽  
Low Permeability ◽  
Oil Well ◽  
Eastern Siberia ◽  
Development Costs ◽  
Traditional Fields ◽  
Low Permeability Reservoirs

The 21st century witnessed the development of the oil extraction industry in Russia due to the intensifica- tion of its production at the existing traditional fields of Western Siberia, the Volga region and other oil-extracting regions, and due discovering new oil and gas provinces. At that time the path to the development of fields in Eastern Siberia was already paved. The large-scale discoveries of a number of fields made here in the 70s-80s of the 20th century are only being developed now. The process of development itself is rather slow in view of a number of reasons. Create a problem of high cost value of oil extraction in the region. One of the major tasks is obtaining the maximum oil recovery factor while reducing the development costs. The carbonate layer lying within the Katangsky suite is low-permeability, and its inventories are categorised as hard to recover. Now, the object is at a stage of trial development,which foregrounds researches on selecting the effective methods of oil extraction.

Theoretical analysis of pressure-bearing performance on compression packer in low permeability reservoirs

2021 ◽  
Vol 191 ◽  
pp. 104325
Author(s):  
Yanwen Zhang ◽  
Hanxiang Wang ◽  
Jiaqi Che ◽  
Mingchao Du ◽  
Mingjie Dou ◽  
...  
Keyword(s):  
Theoretical Analysis ◽  
Low Permeability ◽  
Low Permeability Reservoirs

The Seepage Pressure Distribution and the Capacity of Low-Permeability Reservoirs Gas

2013 ◽  
Vol 734-737 ◽  
pp. 1317-1323
Author(s):  
Liang Dong Yan ◽  
Zhi Juan Gao
Keyword(s):  
Mathematical Model ◽  
Pressure Distribution ◽  
Low Permeability ◽  
Flow State ◽  
Klinkenberg Effect ◽  
Gas Reservoirs ◽  
Gas Well ◽  
Seepage Pressure ◽  
Slippage Effect ◽  
Low Permeability Reservoirs

Low-permeability gas reservoirs are influenced by slippage effect (Klinkenberg effect) , which leads to the different of gas in low-permeability and conventional reservoirs. According to the mechanism and mathematical model of slippage effect, the pressure distribution and flow state of flow in low-permeability gas reservoirs, and the capacity of low-permeability gas well are simulated by using the actual production datum.

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