CFL criterion / IMPES -- CFD Online Discussion Forums CFL criterion / IMPES -- CFD Online Discussion Forums

Impes method simulation dating, presentation on theme: "undersaturated oil-gas simulation impes solution"— presentation transcript:

If error is greater then tolerance continue with iterations Iteration defines a stepwise process in which we continue towards some specified goal by making changes to input parameters. A finite difference numerical model with independent fracture grid has been developed and applied successfully to a coalbed methane reservoir.

Several numerical techniques are incorporated to speed up the program convergence and cut down the number of iterations per time step, thus greatly improving iterative model performance. Learn basic principles of Reservoir Simulation Size in megabytes: Criteria for undersaturated oil conditions.

The gas-oil ratio, GOR, at the surface, is for undersaturated systems equal to the solution gas-oil ratio: A predictive stepsize adjustment rule based on error estimates and convergence control of the integrated iterative solver is presented.

A finite difference scheme is a way of approximating derivatives of a function. Good parallel scalability enables the iterative method to solve large problems with millions of elements and highly heterogeneous reservoir properties.

Iteratively coupled reservoir simulation for multiphase flow in porous media

Continue 13 Boundary Conditions Constant gas injection rate Again, a gas rate term is already included in the gas equation. Numerical dispersion and numerical diffusion are interchangeable. In this dissertation, an iterative coupling approach is proposed and developed to solve multiphase flow problems targeting the efficient, robust and accurate simulation of the hydrocarbon recovery process.

We begin by following a particular algorithm and taking a specific number of steps to get the answer. The idea of convergence is that as we progress through iterations our input data is becoming more accurate and resultantly the error reduces, giving us increasingly more accurate results.

Continue The oil mass balance is written so that its continuity equation includes the liquid part only, while the gas mass balance includes the solution gas in the reservoir, and thus all free gas at the surface: We establish predictive stepsize control impes method simulation dating to high order methods for dating a gibson les paul custom discretization in reservoir simulation.

A Note on IMPES and Some IMPES-Based Simulation Models - OnePetro

They are sets of non-linear algebraic equations because we have unknown pressure as the solution and the coefficients are also unknown saturations. More where, for the oil equation: Continue For an under-saturated oil, the oil pressure is per definition higher than the bubble impes method simulation dating pressure: Jon Kleppe Assistant s: Several numerical examples have been tested using the iterative approach, the fully implicit method, and the IMPES method.

Given the natural numbering scheme and these values, you can then draw up a table with j values along the y axis and i values along the x axis. The terms must be included in the appropriate coefficients in the pressure solution.


Thus, for a constant surface oil production rate of Qoi positive in a well in grid block i: The iterative method is developed for parallel implementation, and several test cases have been run on parallel clusters with large numbers of processors.

The exploitation of an oil field is a complex and multidisciplinary task, which demands a lot of prior knowledge, time, and money.

At the end of each time step, actual oil rate and GOR are computed. In the following we will use the oil equation for this purpose: If dependent variables are defined by coupled sets of equations, and a matrix or iterative technique is needed to obtain the solution, the numerical method is implicit.

The derivative terms to be computed numerically for each time step based on the input table to the model, now are: The solution gas-oil ratio, on the other hand, is now a function of bubble point pressure only, and not on oil pressure: It requires a first guess x 0 and an expression for the derivative of x v at iteration v.

Continue In a block with a well of this type, the following matrix coefficients are modified: Again, the pressure equation may now be solved for oil pressures by using Gaussian elimination. Or we can apply an algorithm. A good reservoir characterization is deemed essential in the accomplishment of Enhanced Oil Recovery EOR processes in order to estimate accurately the properties of the porous medium affecting the flow properties.

Iteratively coupled reservoir simulation for multiphase flow in porous media

Based on theories and methods from oil-gas geology and mechanics of flow through porous media, this paper presents a two-phase, 3D flow and hydraulic fracturing model of dual-porosity media. Continue Although we have single phase flow, we will keep the relative permeability in the equations in case it is not equal to one.

We try to improve the predictive stepsize control through an extended communication between the convergence rate, the error control and the stepsize. Current reservoir simulators apply timestepping algorithms that are based on safeguarded heuristics, and can neither guarantee convergence in the underlying equation solver, nor provide estimates of the relations between convergence, integration error and stepsizes.

However, if the amount of gas in solution varies, such as in the case of gas injection into an under-saturated reservoir, we need to keep track of the bubble point pressure, or saturation pressure, of the oil in order to account for the gas as well as in order to be able to compute the oil properties.

However, in tems of controlling the integration error, the low order of the FIM method leads to small integration steps, while the explicit treatment of the saturation may restrict the stepsizes for the IMPES scheme. Continue For the last term, we use the standard approximation: Comparison results show that independent fracture grid is more effective than equivalent percolation resistance method in production fitting.

The error time may have some scaling issues weighing the pressure and saturation terms because of the units of pressure If the error is less than the tolerance the process is complete.

2 Dimensional Streamline Simulation

The terms appearing in the rate expressions will again have to be included in the appropriate matrix coefficients when solving for pressures. Continue For the gas equation, we only have the solution gas terms, which may be approximated just as for the solution gas term of the saturated equation: Reservoir simulation and numerical techniques were then included in the pre-development and follow-up studies as an effective tool to determine the productivity and future behavior of the oil field.

The FIM method offers unconditionally stability in the sense of discrete approximations, while the IMPES scheme benefits from the explicit treatment of the saturation. The well constant is as before given by: Next What are the primary unknowns when solving the undersaturated equations?

Write the equations for undersatrated flow.

Chapter 6 – Numerical Methods in Reservoir Simulation Learning Objectives

This dissertation investigates advanced linear solvers for high performance computers HPC for reservoir simulation. But these alone do not guarantee the success of the project. Linear solvers take the greatest portion of CPU time in reservoir simulations. Continue The two first terms above are identical to the two first terms of the saturated oil equation, with the exception that the derivative of the inverse formation volume factor is now a partial derivative, and that the the gas saturation is now zero.