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Eliana Gomez |
A Numerical Simulation is a recreation math of a natural process. Using numerical simulations we study physical processes in engineering, economic and even biological. The field of numerical simulations is therefore a large interdisciplinary field of research. Some scientific problems are studied primarily by using numerical simulations as the problems of chaos , fractality or complexity and in general all fields of nature governed by systems of nonlinear equations or not easily reproducible in the laboratory.Simulation of flow fields.
The general equation of conservation of mass:
Darcy's Law expresses the flow of fluids in terms of pressure and gravity:
Darcy's law is valid only for low flow rates, where turbulence and inertia are negligible. Darcy's law generalizes the multi-phase flow, oil, water, gas in porous media:
Bj parameters values of parameters related to surface conditions (indicated by the S) and reservoir conditions (indicated by the index R). The parameters are defined as relations of volumes:
Rs = [VDG / Vo] S.
Bj relations and mass transfer Rs, depends on the pressure multistage pj j = o, w, g. Although the compressibility of water is small, the ratio Bw = f (pw) can be approximated by the following equation:
Similar expressions for Bo, Bg, Rs, and nj are empirical and discussed by Aziz and Settari (1979).
The coefficients in equation (4) express transimisibilidades and are defined as:
The Oil and gas viscosity depends strongly on the pressure and temperature. The dependence of the pressure again is empirical and developed by Aziz and Settari (1979). The temperature dependence of viscosity is especially important in processes such as heat recovery steam injection. In general, dependence on the temperature approaches very well through the following equation:
Finally, the porosity is often dependent on pressure:
where cR is the total compressibility of the rock.
Equations:
Tied in situ volumes of the equation q (1) qa production volumes as they appear on the wellhead standard surface conditions.
Comments from wells. In a field experiment, petroleum engineers control the pressure in the well. Well tests are performed by changing the pressure in the well and watching the reaction of the pressure in the reservoir (and their respective effect on the pressure well controlled). These experiments attempt to estimate the local reservoir transmissibility but has to account for the "skin effect": changes in the rock surrounding the well. Additionally, petroleum engineers record production volumes in the wells. Production volumes in the wells depend on the reservoir pressure p and pressure downhole well PWF:
Where d is transmissibility. Each grid point represents a homogenous cell in the basement.
The following figure shows snapshots of a reservoir transmissibility constant pressure and variable sources. The pressure pulses fade in time as you would expect from a solution of parabolic differential equation.
Fig 1. Snapshots of a flow simulator for a medium of transmission and sources of constant pressure points randomly. The panel shows the pressure field as time increases from left to right and from top to bottom. A source generates the momentum fades over time.
References:
- Landa, JL, 1997, Reservoir parameter estimation constrained to pressure transients, performance history, and saturation in distributed data: Petroleum Engineering Department Stanford
- Aziz, K., and Settari, A., 1979, Petroleum reservoir simulation: Applied Science Publishers.
- Raghavan, R., 1993, Well test analysis: Prentice Hall.
- Wave propagation in an hydrocarbon reservoir exploitation During: In a preliminary, Integrated study. Stanford Exploration Project 03/09/1999
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