Modelling and Production Optimisation of Oil Reservoirs | Dariusz Lerch
| | Abstract | Constrained Numerical Optimisation is a very wide and broad field of interest which nowadays can be utilised for solving many engineering problems, where some adjustment of the input values is necessary for obtaining more ecient results from the system. A very challenging part of it is constraining the problem by relating it to mathematical model which represents the real life system. In most cases such a model is a set of differential - algebraic equations (DAEs), taking states of the system as function arguments, for which we look for the most optimal input variables (controls). It is very important that such a model both preserves the physical properties of the system which occur in the real world, e.g. conservation of mass, momentum, energy and is not too complex at the same time so it can be computed in a straightforward manner. Handling mentioned requirements in case of production optimisation of oil reservoirs imposed common usage of shooting methods in both academic and industrial communities for these problems since they eliminate the presence of state variables in the optimisation algorithm and consequently reduce the size of the problem which is very big mainly due to spacial and time discretisation. In this thesis we focus on applying, still unexplored by oil communities and competent to shooting methods, direct collocation approach in order to optimise oil production under water-flooding in a natural subsurface oil reservoir in secondary recovery phase.
We used an Interior Point Optimiser (Ipopt), which is a software package targeted for large scale non-linear optimisation that was set up in Visual Studio integrated development environment (IDE) and C++ object oriented programming language (OOPL). Before tackling oil problem, we tested simultaneous method in Ipopt on a well known nonlinear problem of Van Der Pol oscillator. Then we implemented a two-phase (water-oil) immiscible flow model for an isothermal reservoir with isotropic permeability properties based on mass conservation principle for the each phase. We discretised the model
in space by using finite volume method (FVM) and used the two point flux approximation (TPFA) and the single point upstream (SPU) scheme for flux computation. We discretised a new model formulation in time by using implicit scheme backward Euler method. Next we presented that obtained reformulation preserves the mass conservation properties used for model derivation. We implemented a numerical approach with the aim of the future usage by non-linear model predictive control (NMPC) framework and smart-well technology in order to maximise the Net Present Value (NPV) of oil production, which is a function of controllable inputs such as injection rates at the injection wells and bottom whole pressures (BHPs) at the production wells. The optimisation is based on interior point algorithm in the line search framework with the BFGS quasi-Newton method that computes an approximation of the inverse of the Hessian given the first order gradient. The Jacobian of the constraints in the sparse format is obtained analytically by utilising the open structure supported by simultaneous method and direct access to the first order derivatives.
The results from the simultaneous method investigated in this work, present that it has the clear and merit potential for upstream production optimisation of oil reservoirs. | | Type | Master's thesis [Academic thesis] | | Year | 2012 | | Publisher | Technical University of Denmark, DTU Informatics, E-mail: reception@imm.dtu.dk | | Address | Asmussens Alle, Building 305, DK-2800 Kgs. Lyngby, Denmark | | Series | IMM-M.Sc.-2012-124 | | Note | | | Electronic version(s) | [pdf] | | Publication link | http://www.imm.dtu.dk/English.aspx | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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