Madrid: aproximación general a la innovación

2.6 Issues in Choosing a Reservoir Simulation Grid

The main issues in choosing a grid for a given reservoir simulation calculation are as follows:

(i) Grid Dimension: Refers to whether we should use a 1D, 2D or 3D grid structure;

Figure 13

Corner point geometry

Figure 14

Complex reservoir model constructed using corner point geometry

4 4

Gridding And Well Modelling

(ii) Grid Geometry/Structure: The next issue is whether we should use a simple Cartesian grid (x, y, z) or some other grid structure such as r/z. This choice also includes where local grid refinement, a distorted grid or corner point geometry is appropriate;

(iii) Grid Fineness/Coarseness: How many grid blocks do we need to use? This asks whether a few hundred or thousand is adequate or whether we need 10s or 100s of thousands for an adequate simulation calculation.

We remind the student of the advice in Chapter 1. This was to carry out the reservoir simulation calculation keeping firmly in mind the question which had to be answered or the decision which had to be taken. Therefore, the issues of grid dimension, type and fineness are directly related to the appropriate question/decision. However, as we will see, there are several technical considerations that can guide us in these choices.

Essentially, all 3 choices (grid dimension, type and fineness) depend strongly on the problem we are trying to solve. Consider the issues of grid dimension and type together. A 2D x/z cross-sectional model (with dip if necessary) may be used to study the effects of vertical heterogeneity - layering for example - on the sweep efficiency or water breakthrough time. For a near-well coning study, an r/z grid is usually more appropriate since it more closely resembles the geometry of the near well radial flow.

2D x/z grids are also used to generate pseudo relative permeabilities for possible use in 2D areal models. For full field simulations, 3D grids are generally used which in most models are still probably Cartesian with varying grid spacing in all three dimensions.

In recent years, other types of grid such as distorted or corner point grids are being applied - especially if a geocellular model has been generated as part of the reservoir description process. Such guides are also applied in some studies to model major faults in reservoirs. Flow through major faults can lead to communication between non neighbour blocks and this can be modelled in some simulators by defining non-neighbour grid block connections as shown schematically in Figure 15.

Fault

L2 L1

L3

L4

L2L1

L3

L4

The issue of grid fineness/coarseness, or how many grid blocks to use in a given simulation, can sometimes be quite subtle as we will show below. However, in many practical calculations, some “reasonable” and practical number of grid block is chosen by the engineer. Then, this can be checked by refining the grid and seeing if the answers are close enough to the coarser calculation. If, as we carry out this grid

Figure 15

Grid system at a fault which may have non-neighbour connections

4 4

Gridding And Well Modelling

refinement, the answer - e.g. recovery profiles and water etc. - no longer changes, the calculation is said to be “converged” and is probably quite reliable. By “reliable”, we mean that the grid errors are probably a small contribution of to the overall uncertainties of the whole calculation. If the grid is far from being converged, then comparisons between different sensitivity calculations may be masked by numerical errors. These various points are illustrated by the two examples below.

The two examples used to show the importance of the number of grid blocks are:

(i) Example 1: the effect of vertical grid fineness (i.e. NZ blocks) on a miscible water-alternating-gas (MWAG) process.

(ii) Example 2: resolving the vertical equilibrium (VE) limit of a gas displacement calculation.

Example 1: Figures 16(a) and 16(b) shows the recovery results (at a given time or pore volume throughput) for both a waterflood and an MWAG flood in the same system each as a function of 1/NZ. The difference between the two calculations is the incremental oil recovered by the MWAG process. The economics of performing MWAG depends on how large this difference is. The purpose of plotting this vs.

(1/NZ) is that we can extrapolate this to zero i.e., effectively to NZ → ∞. Taking the results at NZ = 2 (1/NZ = 0.5) shows an incremental recovery of (72% - 36%)

= 36% of STOIIP which is a huge increase and would make such a project very attractive. However, as we refine the vertical grid, the waterflood recovery increases while the MWAG recovery decreases, i.e. the calculations move closer together and the incremental oil is greatly reduced. Indeed, as we extrapolate to (1/NZ) = 0, we see that the incremental oil is only (47.5% - 47%) = 0.5% which is well within the error band of the calculation. So, rather than having a very attractive project, we appear to have a completely marginal or non-existent improved oil recovery scheme.

Certainly, performing just one coarse grid calculation and taking the results at face value would be very misleading in this case.

Example 2: The vertical equilibrium (VE) condition in a gas flood is where the gas if fully segregated by gravity from the oil. This limit has a simple analytical form (not discussed here) which can be written down without doing a grid block calculation. However, we can test the numerical simulation by seeing how many blocks (NZ again) we need to correctly reproduce the VE limit. The answer is rather surprising as shown by the results in Figure 17. These results show that 200 layers are needed to fully resolve the gas “tongue” at the top of the reservoir. Clearly, if we just guessed that 5 vertical blocks would be enough and did not check, then our calculation would be significantly in error.

The two examples above illustrate how the number of blocks chosen for a simulation can strongly affect the results. It shows the need to check that a calculation has converged or that changing the number of grid blocks does not significantly change the answers.

4 4

Gridding And Well Modelling

Figure 16: (a) Extrapolation of Predicted Waterflood Recovery Efficiency for 2D Stratified Model C Sand Base Case

Process ==> Waterflooding

1/_nzgrid blocks

Recovery Efficiency, %ooIP

Vertical Grid Refinement NX

As vertical grid is refined --> 0

Homogeneous Model, kv/kh = 0.1 Stratified Model, 1.2 HCPVI, kv/kh = 0.02 Homogeneous Model, kv/kh = 0.01

100

Recovery Efficiency, %ooIP

Vertical Grid RefinementNX

As vertical grid is refined --> 0

Homogeneous Model, kv/kh = 0.1

Variable Width Homogeneous Model, side solver Stratified Model, 25% slug, 1.2 HCPVI, kv/kh = 0.02 Homogeneous Model, kv/kh = 0.01

Process ==> Wiscible Water - Alternating - Gas (MWAG) 1 Extrapolated RE = 27.6%

Extrapolated RE = 35.3%

(b) Extrapolation of Predicted MWAG Recovery Efficiency for 2D Stratified Model C Sand Base Case

Process ==> Waterflooding

1/_nzgrid blocks

Recovery Efficiency, %ooIP

Vertical Grid Refinement NX

As vertical grid is refined --> 0

Homogeneous Model, kv/kh = 0.1 Stratified Model, 1.2 HCPVI, kv/kh = 0.02 Homogeneous Model, kv/kh = 0.01

100

Recovery Efficiency, %ooIP

Vertical Grid RefinementNX

As vertical grid is refined --> 0

Homogeneous Model, kv/kh = 0.1

Variable Width Homogeneous Model, side solver Stratified Model, 25% slug, 1.2 HCPVI, kv/kh = 0.02 Homogeneous Model, kv/kh = 0.01

Process ==> Wiscible Water - Alternating - Gas (MWAG) 1 Extrapolated RE = 27.6%

Extrapolated RE = 35.3%

Figure 16

The effect of vertical grid refinement on recovery in (a) a waterflood and (b) a MWAG displacement in a 2D cross-sectional model

4 4

Gridding And Well Modelling

0 0.2 0.4 0.6 0.8 1 PVI

Recovery factor

0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

fine grid : 5 layers fine grid : 25 layers fine grid : 50 layers fine grid : 200 layers coarse grid

VE Limit Oil

x

x

Gravity Dominated

x

x x

x

x x x x x

x x

x x x x x

x x x

x x x

x x x x

Gas