Research Area: Improved recovery# Reservoir Simulation in Challenging Reservoir

Project Number: 6355
### Objective

Project Duration: 1. August 2013- 31. July 2016

Project Director: Trond Kvamsdal, NTNU

Division Head: Svein Børre Torp

Technical contact person, Statoil: Alf Birger Rustad, e-mail abir@statoil.com

The main objective of this project is to identify and resolve some of the main challenges in reservoir simulation related to low productivity reservoirs from an industrial mathematics perspective. The overall goal is to enable better predictions of reservoir performance for key problems, and at the same time keep the simulation time at a reasonably low level. As of today, three central challenges have been identified:

1. The first task is to consider steady state upscaling of relative permeability in oil-water systems. General steady state upscaling on a control volume requires running a full simulation on the volume until steady state is reached. This gives the saturation distribution, which is to be used further in the upscaling process. Full simulation is computationally very demanding. Along with the general steady state upscaling, two approximation approaches have been developed. The first assumes capillary equilibrium, i.e., that the capillary pressure is constant throughout the model. This approximation is expected to be feasible on small scales or in regions with low flow rate. The second approximation assumes that viscous forces are dominant, so that capillary and gravitational forces can be neglected. This is expected to be a good approximation in regions with high flow rate. Based on experience it is expected that general steady state upscaling will converge towards the capillary equilibrium approach as the flow rate decreases, and equivalently that general steady state upscaling will converge towards the viscous limit approach as the flow rate increases. We will therefore study this effect and examine the rate of convergence. General steady state upscaling is much slower than the two approximation approaches, but it is expected to be more accurate. Thus, it is valuable to examine at which flow rates it is acceptable to use the two approximation approaches rather than general steady state upscaling.

2. The second identified challenge is well productivity in low productivity reservoirs. The fluid velocity and the pressure differences are typically high in near well regions, causing extra numerical challenges. Fracturing of reservoir zones near production wells is now a commonly used technique to increase inflow into the wells in shale-gas reservoirs. The fractures are typically very small compared to the surrounding media and have much higher permeability. To be able to model this, small discretization cells are needed to capture the effect of the fractures. Small discretization cells are known to result in numerical difficulties. Numerical methods such as the mimetic finite difference method and mortar methods have shown to be promising on such problems. Research and development of these applied to near well simulation with fracturing will therefore be the second aspect of this project. Poroelasticity and fracture propagation will also be considered.

3. The third identified challenge is the ability to upscale and simulate flow predictively in highly heterogeneous reservoirs for oil-gas systems. Gas-injection in low productivity reservoirs for increased oil recovery has proven to be effective in some cases. These processes are not fully understood and simulation has shown to be challenging. One task is therefore to improve the current simulation tools so that the fluid flow can be better predicted. This also includes developing upscaling methods, realising that solving the upscaling problem for compositional flow is very challenging, and in general is beyond what can be expected from this project. Another aspect of gas injection is precipitation of condensates when the gas is exposed to high initial pressures while pressures drop rapidly close to injectors. The effect is usually termed condensate drop-out and can have devastating effects on well-productivity. One of the fundamental challenges in predicting this behaviour is the need for fully compositional formulation. Compositional effects are well known in the industry to cause prolonged simulation times and convergence problems for reservoir simulation.

**Publications:**

[1] Odsæter, L.H., Berg, C.F., Rustad, A.B.: Rate dependency in steady-state upscaling. *Transport in Porous Media *110(3), 565-589 (2015)

[2] Odsæter, L. H., Kvamsdal, T., and Wheeler, M. F. A postprocessing technique to produce locally conservative flux. In *28th Nordic Seminar on Computational Mechanics *(October 2015), pp. 129-132.

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