Grid blocks

Reservoir simulation is a technique in which a computer-based mathematical representation of the reservoir is constructed and then used to predict its dynamic behaviour. The reservoir is gridded up into a number of grid blocks. The reservoir rock properties (porosity, saturation, and permeability), and the fluid properties (viscosity and the PVT properties) are specified for each grid block. 

The number and shape of the grid blocks in the model depend upon the objectives of the simulation. A 100 grid block model may be sufficient to confirm rate dependent processes described in the previous section, but a full field simulation to be used to optimise well locations and perforation intervals for a large field may contain up to 100,000 grid blocks. The larger the model, the more time consuming to build, and slower to run on the computer. 

Figure 8.18 Typical grid block configurations for reservoir simulation...

If for example we discretize the region over which the PDE is to be solved into M grid blocks, use of finite differences (or any other discretization scheme) to approximate the spatial derivatives in Equation 10.1 yields the following system of ODEs ... 

Figure 1. A single realization of a synthetic reservoir cross-section containing sand (light) and shales (dark). The lengths, thicknesses and center coordinates of the shales are independent, random events taken from known distribution functions. Shales are accumulated until a pre-specified global degree of shale area/total area (f 0.24 in this case) is attained. The light boxes correspond to grid blocks. (Reproduced from Ref. 2.)...

Heller points to grid blocks axis is in grid block units. 

Whatever the geologic causes, there are several purely statistical inferences to be drawn from Figure 16 which bear directly on the issue of reservoir simulation. The size of grid four may be a natural choice for the grid block size in a deterministic simulation model. Such a selection would minimize the variation between blocks and may, in fact, make stochastic assignments of secondary importance (thus, reducing the differences between realizations). The variation of the fifth scale would be incorporated as pseudo functions or megascopic dispersivity into individual blocks. 

The computer simulation program which was available for miscible flood simulation is the Todd, Dietrich Qiase Multiflood Simulator (28). This simulator provides for seven components, of which the third is expected to be carbon dioxide and the seventh water. The third component is allowed to dissolve in the water in accordance with the partial pressure of the third component in the non-aqueous phase or pdiases. It is typically expected that the first two components will be gas components, while the fourth, fifth, and sixth will be oil components. There is provision for limited solubility of the sixth component in the non-aqueous liquid p ase, so that under specified conditions of mol fraction of other components (such as carbon dioxide) the solubility of the sixth component is reduced and some of that component may be precipitated or adsorbed in the pore space. It is possible to make the solubility of the sixth component a function of the amount of precipitated or adsorbed component six within each grid block of the mathematical model of the reservoir. This implies, conversely, a dependence of the amount adsorbed or precipitated on the concentration (mol fraction) of the sixth component in the liquid non-aqueous j ase, hence it is possible to use an adsorption isotherm to determine the degree of adsorption. 

FIGURE 9.3. Numerical values for the calculated electron density (a) at grid points, and (b) a two-dimensional plot, showing how contours are drawn in two dimensions. The level of contours (in electrons per cubic A) can be calculated if the volume of each three-dimensional grid block is known in A , and the absolute scale is know for the electron density (from the Wilson plot initially, and then from the subsequent lecist-squares refinement). 

The grid blocks tested are listed in Table 4.1. The recovery factors (RF) from each grid shown in the table are all greater than 99.48% at one pore volume (PV) of injection. That means, at least from the recovery factor point of view, all these models provide reasonably accurate results (close to theoretical RF of 100% for the built base model with the mobilities of displacing and displaced fluids being equal). 

Here, So and Sm are the oil and microemulsion phase saturations, respectively, present in a specific location (a grid block in simulation). They are not necessarily equal or larger than their respective residual saturations. The normalized saturation is now... 

The grid blocks used are 100 x 1 x 1, which is a ID model, and the length is 0.75 ft. Some of the reservoir and fluid properties and some of the surfactant data are listed in Table 8.1. The viscosity of polymer solutions at different concentrations is presented in Figure 8.5. The polymer adsorption data are shown in Figure 8.6. The microemulsion viscosity is shown in Figure 8.7, and the capillary desaturation curves are shown in Figure 8.8. 

Shell (48) used a simple foam model (49) for their Bishop Fee pilot. The foam generation rate was matched by using an effective surfactant partition coefficient that took into account surfactant losses and foam generation inefficiencies. The value of this coefficient was selected so that the numerical surfactant propagation rate was equal to the actual growth rate. Foam was considered to exist in grid blocks where steam was present and the surfactant concentration was at least 0.1 wt%. The foam mobility was assumed to be the gas-phase relative permeability divided by the steam viscosity and the MRF. The MRF increased with increasing surfactant concentration. The predicted incremental oil production [5.5% of the... 

In order to handle separate yet interacting processes in fractures and matrix, the dual permeability method has been adopted, such that each grid block is divided into matrix and fracture continua, characterized by their own pressure, temperature, liquid saturation, water and gas chemistry, and mineralogy. Simulations of THC processes include coupling between heat, water, and vapor flow aqueous and gaseous species transport kinetic and equilibrium mineral-water reactions and feedback of mineral... 

Figure 3. Modeled CO2 concentrations in fractures and matrix compared to measured values from boreholes (corrected for vapor condensation) (a) Borehole interval 74-3 (average of bounding grid blocks) (b) Borehole interval 75-3 (c) Borehole interval 76-3.

This type of reaction allows the way in which the DAVY lamp for miners works, to be explained the grid blocks the exit of the free radicals present in the flame. 

Figure 9.23 Examples of (a) slit block, (b) grid block, and (c) honeycomb block packing structures (Kolev, 2006).

In order to finite-difference the model partial differential equations, we need values of the state variables at discrete distances, yi,V2, --yN, and zi,Z2,...Zn, and at discrete times, 0, Ai, 2At,..., (n/ — l)At. Here N is the number of grid blocks along the quadrant boundar>% At is the time step, and n/ = t/fAt. The reservoir quadrant is therefore replaced by a system of grid blocks shown in Figure 8.37. The integer i is used as the index in the y direction, and the integer j as the index in the z direction. In addition, the index n is used to denote time. Hence pe use the following notation to identify a process variable... 

The model region for the computer model is shown in Fig. 25.3 (left). Only the major grid blocks are shown, the model contains 9,709 finite elements and 39,688 nodes with eight incident wave directions (indicated as 1 to 8). The Crescent City harbor is shown in Fig. 25.3 (right) with five locations of special interest as A, B,... 

The simulation region is shown in Fig. 25.15 (left). The radius of the outside semi-circle of the domain is about 4 km. To provide clarity only the major grid blocks are shown. The present grid system contains 72,955 nodes and 17,823 elements. The bathymetry was obtained from the field survey data conducted by HMTC and other organization commissioned for this region. 

In the particular case of equal grid block sizes (Ax = Ax, = Ax.+j/2) multiplying across Equation 8.14 by the cell volume of block i Ax l) to convert to volumetric flow rates then ... 

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