Abstract:
Disclosed is a method of modelling a subsurface volume, and a corresponding computer program and apparatus. The method comprises defining a regular planar grid of regularly arranged locations in the two dimensions substantially parallel to the surface, and calculating a plurality of one dimensional arrays, each one dimensional array extending from a different one of the regularly arranged locations, in the direction from surface to subsurface. Each of the one dimensional arrays comprises a plurality of one dimensional cells, wherein the cells are delineated according to actual geological features of the subsurface volume.

Description:
[0001]    The present disclosure relates to methods of subsurface modelling and in particular to gridding techniques used in subsurface modelling. 
         [0002]    Subsurface models may comprise, for example, reservoir flow, basin, and geo-mechanical models. These comprise gridded 3D representations of the physical space of the subsurface, which may be used as inputs to a simulator thereby allowing the prediction of a range of physical properties as a function of controlled or un-controlled boundary conditions. 
         [0003]    In a subsurface model the reservoir may be represented by an array of discrete cells, delineated by a grid which may be regular or irregular. The array of cells is usually three-dimensional, although 1D and 2D models are sometimes used. Values for attributes such as porosity, permeability and water saturation are associated with each cell. The value of each attribute is implicitly deemed to apply uniformly throughout the volume of the reservoir represented by the cell. 
         [0004]    A subsurface model may be described in terms of a seismic grid and a reservoir grid. The seismic grid tends to be a regular grid of relatively low resolution when compared to the reservoir grid. The reservoir grid is an irregular grid with grid boundaries defined, at least in part, by geologic features of the subsurface. Transferring information obtained at seismic scale to the reservoir grid is typically performed directly by a painting technique i.e. directly using geometry to correlate the position in the seismic dataset to the position in the reservoir grid 
         [0005]    It is desirable to improve on these gridding techniques. 
       SUMMARY OF INVENTION 
       [0006]    In a first aspect of the invention there is provided a method of modelling a subsurface volume comprising: defining a regular planar grid comprising regularly arranged locations, in the two dimensions substantially parallel to the surface; calculating a plurality of one dimensional arrays, each one dimensional array extending from a different one of said regularly arranged locations, in the dimension substantially perpendicular to said planar grid; each of said one dimensional arrays comprising a plurality of one dimensional cells, wherein said cells are delineated according to actual geological features of the subsurface volume. 
         [0007]    Other aspects of the invention comprise a computer program comprising computer readable instructions which, when run on suitable computer apparatus, cause the computer apparatus to perform the method of the first aspect; and an apparatus specifically adapted to carry out all the steps of any of the method of the first aspect. 
         [0008]    Other non-essential features of the invention are as claimed in the appended dependent claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    Embodiments of the invention will now be described, by way of example only, by reference to the accompanying drawings, in which: 
           [0010]      FIG. 1  is a representation of part of a typical reservoir grid; 
           [0011]      FIG. 2  is a representation of part of a hybrid grid according to an embodiment of the invention, with reservoir grid layering also shown; 
           [0012]      FIG. 3  is an illustration of one pillar of the hybrid grid of  FIG. 2  with reservoir grid layering also shown; 
           [0013]      FIG. 4  is an illustration of two pillars of the hybrid grid of  FIG. 2  with reservoir grid layering also shown; 
           [0014]      FIG. 5  is a flow diagram illustrating a method of constructing the hybrid grid of  FIG. 2 ; and 
           [0015]      FIG. 6  illustrates a further method of constructing the hybrid grid of  FIG. 2 . 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0016]    A subsurface model may be described in terms of a seismic grid and a reservoir grid (and possibly also a geologic grid). The seismic grid is typically a uniform, regular grid (in x, y and z, where each seismic trace is in the z direction, i.e. from surface to subsurface) which divides the subsurface volume into a plurality of regularly sized and arranged cells. 
         [0017]    The reservoir grid is an irregular grid of cells with cell boundaries defined, at least in part, by geologic features of the subsurface.  FIG. 1  illustrates a part of such a grid. The grid is fairly irregular in the x and y directions, and is more markedly irregular in the z direction. In particular, the boundary of each cell  100  is defined in the z direction by each layer boundary of the subsurface. In this way, the reservoir grid describes the subsurface geology in terms of the reservoir layers, represented by the various z planes of the reservoir grid. 
         [0018]    The reservoir grid is somewhat large and unwieldy due to its irregular nature. To address this, a “hybrid grid” has been devised, which provides a compromise solution between using a seismic dataset regularly sampled in the x,y,z directions and an irregularly sampled reservoir grid. The hybrid grid is regular in the x and y directions, in a similar manner to the seismic grid, while maintaining the irregular layered approach in the z direction of the reservoir grid. In one embodiment the hybrid grid may share the same sampling rate (definition) in the x-y plane as the seismic grid from which it is constructed. 
         [0019]      FIG. 2  illustrates such a hybrid grid. At each regularly spaced intersection  200  on the x-y plane is a vertical 1D array or “pillar”  210  extending in the z direction (where the z direction is the direction from surface to subsurface). Each pillar is composed of a set of 1D cells  220 , each cell having its upper and lower boundaries defined by the layer boundaries  230  (or faults) of the subsurface. The layer boundaries are shown on the diagram for illustration. The top boundary of one cell is the bottom boundary of the cell immediately above and the bottom boundary of one cell is the top boundary of the cell immediately below it. A single pillar  210  is shown in  FIG. 3 . Here, the top boundary  300  of cell n is the bottom boundary of cell n−1 and the bottom boundary  310  of cell n is the top boundary of cell n+1. 
         [0020]    The hybrid grid comprises an array of these vertical pillars. There is no topological link in the hybrid grid other than the link between pillars, that is their positions relative to each other in the x-y plane. In this aspect they are equivalent to 3D datasets. Different pillars within a single hybrid grid may comprise a different number of cells. This can be seen in  FIG. 4 , which shows two adjacent pillars  400   a ,  400   b.  Pillar  400   a  is comprised of 6 cells and pillar  400   b  is comprised of 5 cells. 
         [0021]    A hybrid grid cell may comprise a number of properties (cell centred) in a similar manner to a reservoir grid. Some properties may be of Boolean type with the cell having a true or false value for this property, which is hence called a region. 
         [0022]      FIG. 5  is a flowchart illustrating how a hybrid grid can be created from a geometry  500  (origin, unit vector in the x,y dimensions, step in x,y dimensions) and a reservoir grid  510 . In this case a rasterization of the reservoir grid is performed  520  in order to construct the pillars. To do this, a layer property is created in the hybrid grid. The layer property comprises attributing to each cell of the hybrid grid  530 , the corresponding layer number of the reservoir grid for that cell. The output of this method is the hybrid grid  540 . 
         [0023]    The rasterization process  520  consists of determining every intersection through a reservoir layer of the reservoir grid (in the z-direction), at each pillar position (x,y location). A cell is created for the given pillar each time a layer is intersected, the cell being attributed with the appropriate layer number from the reservoir grid. 
         [0024]    As illustrated in  FIG. 4 , each reservoir layer may be intersected once, more than once, or not at all at a given x,y location. The numbers in parentheses are the reservoir grid layer numbers. The number shown next to each cell is the layer number attributed to that cell. Layer ( 2 ) is shown shaded for illustration. In the specific example shown, pillar  400   b  passes once through each of reservoir layers ( 0 )-( 4 ). Pillar  400   a  passes through reservoir layers ( 1 ) and ( 2 ) twice, through reservoir layers ( 3 ) and ( 4 ) once and does not pass through layer ( 0 ) at all. Consequently, the cell number of the hybrid grid (counting in the z-direction) does not necessarily correspond to the layer number attributed to that cell. 
         [0025]    It should be understood that the reservoir grid description illustrated here (with quadrangular cells) is only provided as an example, and any other reservoir grid description (i.e. an unstructured grid) can be used to create a hybrid grid provided that the notion of layers exists. 
         [0026]    It should also be understood that the hybrid grid could be defined either with the pseudo vertical direction as depth or time. 
         [0027]    As an alternative to the methodology of  FIG. 5 , the hybrid grid may be constructed from a regular geometry, a set of horizons (with the number of horizons known) and a number of sedimentological rules attached to the horizons. The sedimentological rules may categorise the horizons according to whether they are “parallel to top”, “parallel to base” or “proportional”. “Top” and “Base” may refer to the surface and lowermost horizon respectively, or else could refer to one or more reference horizons. 
         [0028]      FIG. 6  illustrates this methodology. It shows a set of horizons, including four reference horizons  610   a - 610   d  (shown bold) and sub-horizons  600 . The sub-horizons labelled “parallel to top” and “parallel to base” are both referenced to reference horizon  610   b.  The sub-horizons labelled proportional are referenced to reference horizons  610   c  and  610   d.  Three pillars  620   a,    620   b,    620   c  of the resultant hybrid grid are also shown. 
         [0029]    This method of construction of a hybrid grid is similar to the method already described using a reservoir grid. A main difference is that the layer property is not defined. At each pillar location defined by the regular geometry in the x-y plane, each intersection with the reference horizons  610   a - 610   d  is determined. The positions of the sub-horizons between each pair of adjacent ones of these computed intersections is then determined according to the sedimentological rules and the known number of sub-horizons between each pair of reference horizons, thus defining the positions of the cells. This process will be readily apparent to the skilled person. 
         [0030]    The hybrid grid is a much smaller object compare to reservoir grid (only pillars and properties are stored) and therefore it can have an extremely high lateral resolution. Compared to seismic cube, the hybrid grid has the advantage of retaining the layer notion, which is the most important geological feature. Any kind of fault can be handled without difficulty. 
         [0031]    The hybrid grid (in the time domain) is a good support for seismic inversion. It can be used to parameterize the inversion, which means that the inversion results can be directly attributed to each identified layer of the hybrid grid. To transfer the inversion results to the reservoir grid (in depth) there is no need for a time to depth conversion: as all that is needed is to attribute the value for a layer from the hybrid grid to the corresponding layer in the reservoir grid. However, as the seismic data is generally coarser (in the z/time direction) than the reservoir/hybrid grid, two or more adjacent layers of the hybrid grid may be collapsed in a single layer for the sake of the inversion. If so, it is necessary to distribute the inversion results obtained at the coarse layer to the finer layers of the reservoir grid. 
         [0032]    The construction of the original hybrid grid either from a reservoir grid or from a set of layers generally results in a smooth version of the hybrid grid. During the inversion, it is possible to adapt the layer thicknesses of the hybrid grid to match the actual seismic data. The new information concerning the geometry of the grid can be used to update the geometry of the reservoir grid. 
         [0033]    The hybrid grid is also a good support for the loop back problem i.e. regenerating seismic data from a geological model or a reservoir grid. For that purpose, first a hybrid grid is constructed using the reservoir grid. The seismic response can then be computed from the hybrid grid. As a result of the coarse lateral resolution of the reservoir grid, many adjacent cells of the same layer of the hybrid grid will have the same elastic values and therefore many of the computed seismic traces will be the same. Actual seismic response is not pointwise (e.g. Fresnel zone effect) and therefore the response at any given xy position is a mixture of the responses of neighbouring cells. This can be simulated by mean filtering the elastic properties of each layer of the hybrid grid. 
         [0034]    The hybrid grid is a good intermediary for transferring information from a seismic dataset to a reservoir grid because it decouples the lateral upscaling from the vertical down scaling problem. When converting from seismic data to hybrid grid, only data in the z direction needs to be considered (since the lateral resolution of hybrid grid and seismic is exactly the same). Consequently transferring information from a hybrid grid to reservoir grid requires only lateral upscaling in a layer by layer manner. When converting in the opposite direction the hybrid grid makes it possible to consider in a first step (conversion of a reservoir grid to hybrid grid), only data in the x and y directions; and in a subsequent step to consider only the data in the vertical direction (transfer of information from the hybrid grid to seismic support). 
         [0035]    One or more steps of the methods and concepts described herein may be embodied in the form of computer readable instructions for running on suitable computer apparatus, or in the form of a computer system comprising at least a storage means for storing program instructions embodying the concepts described herein and a processing unit for performing the instructions. As is conventional, the storage means may comprise a computer memory (of any sort), and/or disk drive, optical drive or similar. Such a computer system may also comprise a display unit and one or more input/output devices. 
         [0036]    The concepts described herein find utility in all aspects of surveillance, monitoring, optimisation and prediction of hydrocarbon reservoir and well systems, and may aid in, and form part of, methods for extracting hydrocarbons from such hydrocarbon reservoir and well systems. 
         [0037]    It should be appreciated that the above description is for illustration only and other embodiments and variations may be envisaged without departing from the spirit and scope of the invention.