Simulated Annealing for Interpreting Gas/Water Laboratory Corefloods
- Ahmed Ouenes (New Mexico Inst. of Mining and Technology) | Guy Fasanino (Gaz de France) | R.L. Lee (New Mexico Inst. of Mining and Technology)
- Document ID
- Society of Petroleum Engineers
- SPE Annual Technical Conference and Exhibition, 4-7 October, Washington, D.C.
- Publication Date
- Document Type
- Conference Paper
- 1992. Society of Petroleum Engineers
- 5.4.1 Waterflooding, 4.1.5 Processing Equipment, 1.6.9 Coring, Fishing, 5.6.3 Deterministic Methods, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 5.1.5 Geologic Modeling, 5.1 Reservoir Characterisation, 5.3.1 Flow in Porous Media, 4.3.4 Scale, 4.1.2 Separation and Treating, 5.5.8 History Matching, 5.3.2 Multiphase Flow
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This paper presents a new approach for the simultaneous estimation of relative permeability and capillary pressure curves from two-phase laboratory corefloods. The new technique enables us to retrieve a discrete representation of the flow functions by using a discrete optimization method called simulated annealing. The number of discrete points for each flow curve can be very high and yet will not affect the convergence of the algorithm specially designed for multidimensional optimization problems. Moreover, the algorithm is totally independent from the forward model; therefore, changes in the objective function, boundary conditions, or numerical scheme do not affect the formulation of the optimization problem. Simulated annealing as a global optimization method does not require the evaluation of objective function gradients. Hence, costly gradient computations by finite differences or lengthy derivations of adjoint equations for the optimal control theory are not necessary. The flow functions are estimated after minimizing a least-squares objective function containing all available and reliable experimental data obtained from standard drainage or imbibition experiments. The automatic history-matching code is demonstrated with actual and synthetic experiments, and good matching is obtained for various cases tested. Since the convergence of the algorithm is no longer the major concern, other physical problems such as end effect and the dependence of relative permeability curves on the flow rate are addressed.
The concept of relative permeability for two-phase flow was obtained by extending Darcy's equation of the single phase flow. In practice, these curves are retrieved by analyzing the data obtained from laboratory corefloods. Many experimental problems (end effect, fingering, etc.) arise during this analysis and tend to induce errors in the estimation. Because of the impact of these curves on multi-phase flow calculations, other methods must be used in order to overcome the underlying problems.
Two experimental methods can be used to determine relative permeability curves: steady-state and unsteady-state. The steady-state method establishes a constant fractional flow of wetting and non-wetting phases along the core. This method has many disadvantages, the most notable from a practical point of view, is that it is time consuming. In the unsteady-state method, only the displacing phase is injected. The pressure drop along the core and the cumulative recovery of the displaced phase are monitored. This method is based on the Buckley-Leverett theory and Welge interpretation, both of which do not take into account the capillarity. The Johnson-Bossler-Naumman (JBN) and Jones-Roszelle procedures are two similar explicit methods, derived from the previous theory and used routinely in petrophysical laboratories. The neglect of capillarity can be justified when the end effect is negligible by using high injection flow rates. Rapoport and Leas suggested a scaling criterion to achieve the domination of viscous forces on the capillary forces. However, such a criterion cannot totally negate the capillary effects. To obtain more accurate relative permeability curves, which account for capillarity, many authors introduced implicit or numerical methods to retrieve permeability curves from coreflood data.
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