Methods of determining front propagation within a subsurface volume
Disclosed is a method of determining front propagation within a subsurface volume such as a reservoir. The subsurface volume includes a plurality of cells and at least one geological fault. The method includes performing a fast marching algorithm so as to determine the front propagation in terms of the time of arrival of the front at a particular cell from one or more neighboring cells which make up the neighborhood of the particular cell. For each faulted cell that is adjacent a geological fault, the neighborhood of the faulted cell is defined as including only its geometric neighbors, where the geometric neighbors are those cells that are in contact with the faulted cell in a geometric sense, regardless of stratification.
1. A method of determining front propagation within a subsurface volume, the subsurface volume being discretised into a plurality of cells, the method comprising steps of:
performing a fast marching algorithm so as to determine the front propagation in terms of a time of arrival of the front at a particular cell from at least one neighbouring cells which make up a neighbourhood of the particular cell, wherein the fast marching algorithm is performed to obtain an expression of a drained volume as a function of diffusive time of flight;
converting the expression to simulate a pressure variation induced by a well test;
performing a plurality of well test simulations using the fast marching algorithm;
performing a comparison of resultant data from each of the well test simulations and resultant data from a measured well test on the subsurface volume in order to rank the resultant data from the well test simulations according to whether they reproduce most closely the resultant data from the measured well test; and
selecting a subset of the plurality of well test simulations according to the ranking of the resultant data from the well test simulations.
2. The method as claimed in claim 1 , wherein the fast marching algorithm is performed to solve an eikonal equation.
3. The method as claimed in claim 1 , wherein the comparison step is performed by computing a distance between different sets of resultant data obtained from different well test simulations.
4. The method as claimed in claim 3 , wherein the computing of distance between different sets of resultant data obtained from different well test simulations comprises using a dynamic time warping algorithm which associates every data point of the resultant data from a first of the well test simulations or measured well test to a corresponding data point of the resultant data from a second of the well test simulations or measured well test.
5. The method as claimed in claim 4 , further comprising steps of:
constructing a set of vectors associating data points from the first of the well test simulations or measured well test to a corresponding data point from the second of the well test simulations or measured well test; and
computing the distance between the data from the first of the well test simulations or measured well test and the second of the well test simulations or measured well test as a trace of a covariance of the difference between the every vector of the set of vectors and a vector which is the mean vector of the set of vectors.
6. The method as claimed in claim 1 , further comprising a step of using the subset of well test simulations in volumetric studies to estimate a porous volume in the subsurface volume and/or a volume of hydrocarbon or water present within the subsurface volume.
7. The method as claimed in claim 1 , further comprising a step of using the subset of well test simulations to predict a fluid flow in a geological reservoir and hydrocarbon and/or water production from the geological reservoir.