# Analytical Solutions For 1D Displacement By Gases

## Abstract/Contents

- Abstract
- Analytical solutions are obtained for a mathematical model of gas injection processes into porous media for enhanced oil recovery. The problem considered is one-dimensional, multicomponent, two-phase gas/oil displacement. The basic assumptions are isothermal flow with no dispersion, gravity and capillary forces at constant pressure and temperature. The mathematical model leads to an eigenvalue problem, which is solved to find a unique path connecting the injection gas point and initial oil point on a muticomponent phase diagram.Two important cases are compared throughout this study: (1) systems in which there is no volume change as components move between phases and (2) systems where volume is not conserved. For the first case (no volume change) the mathematical model is simplified, since there is no spatial variation in the flow velocity for this case. However, the solution algorithm is generally the same for both cases. It has some modifications, though, for the case of volume change on mixing to account for the fact that the flow velocities are not known until the solution construction has reached the initial and injection points.A tie-line intersection approach is used to find a solution for an arbitrary number of components in the oil or injection gas. Although there are two types of composition variations in a solution called shocks and rarefactions, only shocks are considered to connect adjacent tie lines. The jump points from one tie line to another, which constitute a solution, are found by solving the shock material balances. For the two cases mentioned above there are different shock balances, nevertheless, they reduce to the same (or almost the same) form which represents a simple nonlinear equation. The shocks from the injection or initial points into the two-phase region require a special treatment, however. Several solution examples are also provided. The comparison of the two cases, volume change and no volume change, is given for all of them. Certain speculations as to how they differ and how the volume change assumption affects the solution profile are made to infer what physics contributes to the behavior observed in the solutions.

## Description

Type of resource | text |
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Date created | June 2000 |

## Creators/Contributors

Author | Ermakov, Pavel |
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Primary advisor | Orr Jr., Franklin M. |

Degree granting institution | Stanford University, Department of Petroleum Engineering |

## Subjects

Subject | School of Earth Energy & Environmental Sciences |
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Genre | Thesis |

## Bibliographic information

## Access conditions

- Use and reproduction
- User agrees that, where applicable, content will not be used to identify or to otherwise infringe the privacy or confidentiality rights of individuals. Content distributed via the Stanford Digital Repository may be subject to additional license and use restrictions applied by the depositor.

## Preferred citation

- Preferred Citation
- Ermakov, Pavel. (2000). Analytical Solutions For 1D Displacement By Gases. Stanford Digital Repository. Available at: https://purl.stanford.edu/ns902xy8961

## Collection

Master's Theses, Doerr School of Sustainability

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