Projects per year

### Abstract

With an increasing demand for oil and diculties in nding new major oil
elds, research on methods to improve oil recovery from existing elds is
more necessary now than ever. The subject of this thesis is to construct
ecient numerical methods for simulation and optimization of oil recovery
with emphasis on optimal control of water ooding with the use of smartwell
technology.
We have implemented immiscible ow of water and oil in isothermal reservoirs
with isotropic heterogenous permeability elds. We use the method
of lines for solution of the partial differential equation (PDE) system that
governs the uid ow. We discretize the the two-phase ow model spatially
using the nite volume method (FVM), and we use the two point
ux approximation (TPFA) and the single-point upstream (SPU) scheme
for computing the uxes.
We propose a new formulation of the differential equation system that arise
as a consequence of the spatial discretization of the two-phase ow model.
Upon discretization in time, the proposed equation system ensures the mass
conserving property of the two-phase ow model. For the solution of the spatially
discretized two-phase ow model, we develop mass conserving explicit
singly diagonally implicit Runge-Kutta (ESDIRK) methods with embedded
error estimators for adaptive step size control. We demonstrate that high
order ESDIRK methods are more ecient than the low-order methods most
commonly used in reservoir simulators. Most commercial reservoir simulation
tools use step size control, which is based on heuristics. These can
neither deliver solutions with predetermined accuracy or guarantee the convergence in the modied Newton iterations. We have established predictive
step size control based on error estimates, which can be calculated from the
embedded ESDIRK methods. We change the step size control in order to
minimize the computational cost per simulation.
We implement a numerical method for nonlinear model predictive control
(NMPC) along with smart-well technology to maximize the net present
value (NPV) of an oil reservoir. The optimization is based on quasi-Newton
sequential quadratic programming (SQP) with line-search and BFGS approximations
of the Hessian, and the adjoint method for ecient computation
of the gradients. We demonstrate that the application of NMPC for
optimal control of smart-wells has the potential to increase the economic
value of an oil reservoir.

Original language | English |
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Place of Publication | Kgs. Lyngby, Denmark |
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Publisher | Technical University of Denmark |

Number of pages | 186 |

Publication status | Published - 2011 |

Series | IMM-PHD-2011 |
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Number | 265 |

## Projects

- 1 Finished

## Numerical Methods for Simulation and Optimization of Enhanced Oil Recovery Methods

Völcker, C., Jørgensen, J. B., Thomsen, P. G., Engsig-Karup, A. P., Foss, B. A. & Kristensen, M. R.

01/01/2008 → 24/08/2012

Project: PhD

## Cite this

Völcker, C. (2011).

*Production Optimization of Oil Reservoirs*. Technical University of Denmark. IMM-PHD-2011, No. 265