Explicit methods for fast, accurate solution of advection dominated transport equations.
A typical streamline-based transport solver consists of the following steps:
choose a set of seed points
trace streamlines from seed points backwards to injectors and forwards to producers
map saturations and properties from the grid to the streamlines
solve one-dimensional transport equation along streamlines
map resulting saturation distributions back to grid.
Choosing seed points. Seed points should preferably be chosen so that every cell is traversed by at least one streamline, this may be hard to achieve in low-flow regions without a seed point strategy designed to guarantee this.
Tracing streamlines. This can be hard for complex grid topologies and geometries, for instance on corner-point grids with faults. In particular, one must handle non-conforming grids, and velocity fields only defined by face fluxes.
Our current streamline-based solvers are capable of:
fast tracing of streamlines on simplicial, cartesian and corner-point grids (with faults)
efficient and accurate solution of one-dimensional equations by front-tracking methods.
Generalized travel-time inversion (GTTI) is a very efficient method for history matching. The GTTI method is robust and computationally efficient. Unlike conventional ‘amplitude’ matching, which can be highly nonlinear, it has been shown that the travel-time inversion has quasilinear properties. As a result, the minimization proceeds rapidly even if the initial model is not close to the solution. Second, travel-time sensitivities are typically distributed more uniform between wells compared to ‘amplitude’ sensitivities that tend to be localized near the wells. This prevents over-correction in the near-well regions. Finally, in practical field applications, production data are often characterized by multiple peaks. Under such conditions, the travel-time inversion can prevent the solution from converging to secondary peaks in the production response.
As many othermethods for data integration, GTTI is based on the use of production response sensitivities. Using a streamline formulation, accurate approximations to such sensitivities can be computed analytically based on a single flow simulation. To this end, one uses time-of-flight sensitivties that describe the change in time-of-flight caused by small perturbations in reservoir properties such as porosity and permeability. Production response sensitivites can then be obtained by simplifying the flow physics and assuming a monotone Buckley-Leverett displacement along each streamline.
History matching using 2500 days of production data. The last 500 days are predicted based on the history match.
History matching 2475 days of water-cut data from the 69 producers, each operating with a constant rate fulfilling the total voidage rate induced by 32 water injectors. The modell contains 1 048 576 active cells and a satisfactory history match was obtained within 17 minutes on a standard PC. Key technologies:travel-time inversion and multiscale pressure solver.
Published November 17, 2009
A portfolio of strategic research projects funded by the Research Council of Norway