Boundary Condition Treatment in a Transient Flow Model
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- Master's theses (TN-IEP) 
Transient flow modelling used for hydraulic calculations and well control evaluations is a vital part to the safety in the industry to properly prepare and build correct procedures when constructing wells. Modeling liquid and gas flow is complex and it’s important to keep introducing new, efficient ideas to reduce model uncertainties and run time. This can help reduce numerical liabilities, risk and cost. The objective in this thesis has been to implement a new way of treating the boundary conditions in a transient flow model and compare it to more widely used methods. In addition, demanding benchmark cases have been developed to properly test the different boundary condition treatment methods against one another. The AUSMV scheme is used for modeling the flow and pressures in the work in this thesis. The AUSMV scheme uses a simplified transient drift flux model for two-phase flow to predict flow and pressures in the system. Water and air are used instead of oil and gas to reduce the model complexity and instead put focus on the boundary treatment. The model makes a variety of assumptions and include conservation of mass and momentum and is supplied with closure laws. Previous work with AUSMV scheme has mostly used a zero-order extrapolation technique to treat the boundary condition. The first-order extrapolation technique has been introduced recently to improve upon the zero-order. With the work in this thesis, it would be possible to avoid the use of extrapolating the mid-cell value to the boundary completely. The compatibility relations method uses characteristics that transport information from the interior computational domain toward the boundary. On the outgoing boundary, the characteristic compatibility relations together with the imposed physical conditions are used to determine the unknown variables at the boundary points. For a horizontal pipeline with an open end, when considering pressure pulse propagation both the use of compatibility relations method and first-order extrapolation technique worked well. However, the compatibility relations method seems to work slightly better avoiding some unphysical oscillation that was seen initially in the simulation. For a closed well with a migrating kick, the compatibility relations method had no clear benefit over first-order extrapolation technique. The compatibility relations method even had some stability issue for a finer grid. For the open hole cases (case 3 and case 4), a kick is migrating on its own or being circulated out. This leads to an unloading situation where the liquid in front of the kick is forced out of the well violently before the gas breaches through. For the rough grid of 25 cells, there were large differences in results when comparing zero-order and first order extrapolation techniques and compatibility relations method. However, for a fine grid of 100 cells, all models seem to give the same results regarding pressure development. However, there was a difference in maximum liquid and gas flowrates predicted between the boundary condition treatment methods. Compatibility relations method tended to predict a lower maximum liquid flowrate and higher maximum gas flowrate. The input of using a sufficiently refined grid was demonstrated. This reduces numerical diffusion and the difference between the different boundary condition treatment methods are reduced. One can also note that for rough grids, the zero-order extrapolation technique tended to be more unstable. In general, increasing the number of cells in the well will have a greater impact than which boundary condition treatment is chosen. The reason for this is reduced numerical diffusion which is an important factor in simulation results accuracy. In addition, with an increased number of cells, the numerical errors that were introduced with a zero-order extrapolation technique (when considering large gas expansion effect) is reduced. There was a tendency that first-order extrapolation technique in combination with a rough grid produced more numerical problems. There was an issue with extra gas being added in the system for all simulations (except case 1). It was always a similar amount gas being added and it happened early in the simulation. However, this issue is unlikely to have anything to do with the newly implemented boundary condition treatment as it was present whether the compatibility relations method was used or not. There was also a compatibility relations method stability issues for case 2 when using a refined grid. These issues were not solved and needs further investigation.
Master's thesis in Petroleum engineering