Gridding and Well Modelling in Reservoir Simulation

Gridding in Reservoir Simulation

o Gridding Process: is simply one of chopping into a (large) number of smaller spatial blocks which then the numerical block to block flow calculations are performed.

o This process of dividing up the reservoir into such blocks is known as spatial discretisation.

o Type of grids: Cartesian Grid, Radial Grid, Distorted Grid (Corner Point Geometry), and Hybrid Grid

o Dimension of Grids: 1D, 2D, and 3D

Cartesian Grid(a). 1D horizontal grid

(b). 1D vertical grid

Cartesian Grid(c). 2D areal grid

Cartesian Grid(d). 2D areal grid (cross sectional model showing

a water front in a waterflood)

Cartesian Grid(e). 3D cartesian grid (Modelling reservoir with

several layers)

Radial Grid

(a) 1D Radial Grid

(b) 2D Radial Grid

Radial Grid

(c) 3D Radial Grid

Accuracy of Simulations and Numerical Dispersion

• Numerical dispersion is essentially an error due to the fact that we use a grid block approximation for solving the flow equations.

Numerical Dispersion Error

Effect of grid on water breakthrough time-numerical dispersion

Dt = 1: No fluid flowed from block to block [Krw (Swc) = 0]Dt = 2: Fluid flows from block i=1 to block i = 2After only Dt = 5 water has reached block 5.

One method of reducing numerical dispersion is to increase the number of grid blocks.

Numerical Dispersion Error

If we take more grid blocks (Dx decreases), the we will locate the front more accurately. Indeed, taking more and more blocks we will gradually get closer to the analytical (correct) solution.

Effect of Grid Orietation• The distance between

wells I-P1 and I-P2 are the same.

• The flow between I-P2 is more tortuous.

• The I-P1 orientation tends to lead to somewhat earlier breakthrough and a less optimistic recovery that the I-P2 orientation.

Effect of Grid Orietation Error

• As for numerical dispersion, some grid refinement can help to reduce the grid orientation effect.

The Effect of Vertical Grid Refinement of Recovery in a Waterflood in a 2D Cross-Sectional Model

Extrapolation of Predicted Waterflood Recovery Efficiency for 2D Stratified Model C Sand Base Case

The Effect of Vertical Grid Refinement of Recovery in a MWAG Displacement in a 2D Cross-Sectional Model

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

The Effect of Vertical Grid Refinement of Recovery in a Gas flooding in a 2D Cross-Sectional Model

These results show that 200 layers are needed to fully resolve the gas “tongue” at the top of the reservoir. Clearly, if we just guesses that 5 vertical blocks would be enough and did not check, then our calculation would be significantly in error.

Local Grid Refinement (LGR)

To represent regions with rapidly changing waterfront will require a finer grid than will be required for relatively stagnant regions of the system.The application of some local grid refinement (LGR) may be much more appropriate.

Hybrid Grid LGR

Hybrid grids are mixed geometry combinations grids which are used to improve the modelling of flows in different regions. The most common use of hybrid grids are cartesian/radial combination.

Distorted Grids and Corner Point Geometry

Corner Point Geometry

Complex reservoir model constructed using corner point geometry

Issues in Chossing a Reservoir Simulation Grid

i. Grid Dimension: refers to whether we should use a 1D, 2D or 3D grid structure.

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 radial, distorted grid. This choice aso includes where local grid refinement 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.

A 2D x/z cross-sectional model may be used to study the effect of vertical heterogeneity (layering) for example – on 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.

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.

Issues in Chossing a Reservoir Simulation Grid

Well in Reservoir Simulation

Cartesian grid cut from a 3D freservoir modelshowing two horizontal wells going through the system; two vertical wells also shown.

Hierarchies of Well and Well Controls

• For a single well:– Set the well flowing pressure and calculate the flows– Set the flows and calculate the well flowing pressure

• For a simple injector/producer pair:– At the injector: Fix the water injection rate but with

(upper) limits on the well flowing pressure.– At the producer: Set the well flowing pressure and

allowing the calculation of the oil and water phase flows (Qo and Qw).

Estimation of Flow Rate Injected and Produced

Since Bo > Bw, then the volumetric production rate of oil (in stb/day) is lower than the injected water rate (in stb/day).

What volume of injected water must we inject to exactly replace the reservoir volume of oil and waterphases?