CHARACTERISTIC DIFFERENCE METHODS FOR TWO-PHASE DISPLACEMENT IN NATURALLY FRACTURED RESERVOIRS

In this paper we shall give the characteristic difference methods for two phase displace meat problem in naturally fractured reservoirs.We shall prove the existence,uniqueness of the ap proximate solution and a priori discrete L2-error estimates.

THE UPWIND OPERATOR SPLITTING FINITE DIFFERENCE METHOD FOR COMPRESSIBLE TWO-PHASE DISPLACEMENT PROBLEM AND ANALYSIS

For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.

Stability analysis of the moving interface in piston- and non-piston-like displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axisymmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.

The characteristic finite difference fractional steps methods for compressible two-phase displacement problem

For compressible two-phase displacement problem, a kind of characteristic finite difference fractional steps schemes is put forward and thick and thin grids are used to form a complete set. Some techniques, such as piecewise biquadratic interpolation, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L^2 norm are derived to determine the error in the approximate solution.

Characteristic finite element scheme and analysis the three-dimensional two-phase displacement semi-definite problem

NUMERICAL simulation of the two-phase (oil and water) displacement problem is the mathematical basis of energy sources. For two-dimensional positive problem, Douglas et al. put forward the well-known characteristic finite difference method and characteristic finite element method. However, for numerical analysis there exist some difficulties. They assumed that the problem is periodic and the diffusion matrix of the concentration equation is positive difinite

The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem

For compressible two-phase displacement problem,the modified upwind finite difference fractionalsteps schemes are put forward.Some techniques,such as calculus of variations,commutative law of multiplicationof difference operators,decomposition of high order difference operators,the theory of prior estimates and tech-niques are used.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.Thismethod has already been applied to the numerical simulation of seawater intrusion and migration-accumulationof oil resources.

Quantitative Characterization of Interlayer Interference in Multi-Layered Sandstone Reservoirs Offshore China

X oilfield is a typical multi-layer sandstone reservoir in offshore China. In the early stage, in order to obtain economic oil production, directional well was used to adopt a set of multi-layer combined production, which resulted in serious interlayer interference, water injection inrush and low reserve utilization. Based on the theory of single-phase unstable seepage flow and the theory of oil-water two-phase non-piston displacement, the author innovatively established a mathematical model of interlayer dynamic interference in multilayer sandstone reservoirs, revealed the influence law of main controlling factors such as permeability, viscosity, starting pressure gradient and reservoir type on interlayer interference, and innovatively formed a quantitative characterization theory of interlayer interference in multilayer combined oil production. The technical demarcation of offshore multi-zone combined oil production reservoir system is formulated and the recombination of oil field development system is guided.

Numerical Simulation of Dissolved Oxygen Supersaturation Flow over the Three Gorges Dam Spillway

The dissolved oxygen concentration in a flow changes with distance downstream of the spillway crest and depends on the geometric configuration of the spillway and the hydraulic and operating conditions.A mathematical model was developed to simulate the turbulent structure of the flow over the spillway of the Three Gorges Dam at the 145 m reservoir water level to study the aeration characteristics and the gas transport.The model was calibrated and verified with measured data.The analysis of distribution of the aeration and the dissolved oxygen showed that the downstream water level,upstream dissolved oxygen content,and the flow discharge all affect the dissolved oxygen saturation downstream of the sluicing dam.The simulation provides guidance for controlling the dissolved oxygen supersaturation and environmentally friendly operation of the Three Gorges Dam.