Method for visualization of fluid filtration in heterogeneous porous medium
A method and system for visualization of a direction of a fluid flow in heterogeneous porous medium in hydrocarbon reservoirs based on the streamlines. The method allows for constructing the detailed and accurate model of a direction and a volume of the fluids being transferred between the wells and can be used for analysis of waterflooding and hydrodynamic connectivity between the wells used in oil and gas reservoirs with a large number of wells. The visualization method can be used both for analysis of instantaneous fluid flows at the current calculation step of hydrodynamic simulator and for analysis of fluid flows accumulated over several calculation steps.
1. A computer-implemented method of visualization of fluid flow direction in heterogeneous porous medium in hydrocarbon reservoirs based on streamlines, the method comprising:
determining streamlines using particles tracing on a basis of a three-dimensional pressure map and a reservoir porosity and a permeability properties;
determining pairs of injection and production wells having fluid flow between them, on a basis of a plurality of streamlines;
building a graph of fluid flows between the injection and the production wells, having the injection and the production wells serve as graph vertices connected by an edge; and
visualizing the graph edges in a form of curves constructed by a spline-based interpolation of points obtained from the plurality of the streamlines using segments represented by quadratic Bezier curves,
wherein a midpoint of a streamline of the plurality of the streamlines is a point, where a particle appears in a halfway distance interval, which the particle covers from beginning to end of the streamline, and
wherein the midpoint coordinates (x2, y2) of Bezier curve are calculated as:
x 2=2* x _center_mass−0.5*( x 1+ x 3),
y 2=2* y _center_mass−0.5*( y 1+ y 3),
where (x1, y1) are coordinates of a first control point, (x_center_mass, y_center_mass) are coordinates of a point which is a projection onto a two-dimensional map of a center of mass of a set of points, where each point corresponds to the midpoint of one of the streamlines of the plurality of the streamlines connecting the injection and the production wells, and (x3, y3) are coordinates of a third control point.
2. The method of claim 1 , wherein the graph is simulated on a two-dimensional map of a field.
3. The method of 2 , wherein the two-dimensional map of the field is constructed by projecting of a field hydrodynamic model three-dimensional grid onto a plane or onto a cross section.
4. The method of claim 1 , wherein the interpolation of points is a polynomial interpolation.
5. The method of claim 1 , wherein the interpolation with splines is an interpolation with cubic splines.
6. The method of claim 1 , wherein the interpolation with splines is an interpolation with B-splines.
7. The method of claim 1 , wherein each N-th point of the streamline, along which the particle travel from the injection well to the production well within the shortest time, is used to construct a set of the interpolation points.
8. The method of claim 1 , where the interpolation is performed on a set of points, where each point is a center of mass of a set of points representing locations of particles corresponding to different streamlines at certain points in time.
9. The method of claim 1 , where the interpolation is performed on a set of points, where each point is the center of mass of a set of points representing locations of particles corresponding to different streamlines at points in time corresponding to an equal percentage of a distance covered from the injection and production wells.
10. The method of claim 1 , wherein the interpolation of points is an interpolation used with a quadratic Bezier curve constructed by three control points,
wherein:
a first point is a projection of an upper boundary coordinate of an injection well upper perforated interval onto a two-dimensional map;
a second point is taken so that the Bezier curve passes through a point, which is a projection onto a two-dimensional map of a center of mass of a set of points, where each point corresponds to the midpoint of one of the streamlines connecting the injection and the production wells; and
the third point is a projection of an upper boundary coordinate of a production well upper perforated interval onto a two-dimensional map.
11. The method of claim 1 , wherein any subset of the edges and the verticies of the graph of the fluid flows is visualized.
12. The method of claim 11 , wherein the edges to which the fluid flow volume corresponds within specified limits, are selected as a subset of the graph edges to be visualized.
13. The method of claim 1 , wherein the fluid flows accumulated in several calculation steps of a hydrodynamic simulator are visualized.
14. The method of claim 13 , wherein the interpolation is performed on the points which are the centers of mass for the interpolation points used at different times.
15. A computer-implemented system for visualization of fluid flow direction in heterogeneous porous medium in hydrocarbon reservoirs, based on streamlines, the system comprising:
at least one processor,
a memory coupled to the processor;
a computer programmable logic stored in the memory and executed on the processor, the logic is configured to execute the steps of claim 1 .