Upscaling



King Abdulaziz University

Faculty of Earth Sciences

Department of Petroleum Geology & Sedimentology

Building 4D Geological Models

(Dynamic Models)

of Petroleum Reservoirs

Supervised by:

Dr. Hassan S. Naji

Submitted by:

Ihab Y. Babbo

1430 - 1431

Simulation

To simulate fluid flow in a reservoir, we first need a geological model of the reservoir.  This model will have to be described in such a way that the data can be used for numerical computations. This is done by “gridding” the reservoir, which divides the reservoir into a finite set of homogeneous grid cells. Each of these cells contains data for each of the geological parameters in that cell.

Next we need a description of the fluids in the reservoir. This is done by describing the so-called relative permeability functions and the PVT data. Relative permeability functions are a description of how the fluids flow relative to each other. The PVT data represent how pressure and volume of the fluids relate. We also have to describe where the fluid phases are present in the reservoir – this is done by describing where their contacts are sitting.

We need to apply a force to the fluids and this is done by setting locations of wells and their production/injection rates. Lastly, we must specify the time period for the simulation and how many time steps we would like to use.

The flow of fluids is governed by three basic physical principles:

• Mass is neither created nor destroyed, that is Conservation of Mass.

• The rate of change of momentum of a portion of the fluid equals the force applied to it, or Conservation of Momentum.

• Energy is neither created nor destroyed, that is Conservation of Energy.

Conservation of Mass

The first principle is modeled by a so called partial differential equation that says that if there is a difference between flow into and out of a tiny volume of space, this will either cause a build-up or a draw down of mass in this tiny volume.

Conservation of Momentum

The second principle is approximated by an experimental law, called Darcy’s law, that relate the pressure difference (force) across a porous rock containing a fluid and the resulting velocity (momentum) of this fluid. This experimental law is also represented by a partial differential equation that is combined with the equation based on the first principle to form a set of partial differential equations that is the mathematical description of the flow of fluids through a porous media.

Conservation of Energy

The third principle is approximated by a relationship between Pressure, Volume and Temperature (PVT) for the rock and the fluids. The PVT data is represented by a set of tables for each reservoir.

General information on streamline simulation

FrontSim is a streamline simulator. This numerical method first solves the pressure, then computes the streamlines and thereafter computes the changes in saturation along the streamlines. The equations for saturations are solved as several one dimensional problems along streamlines, as opposed to solving one large three dimensional problem. Consequently, FrontSim can be very fast and hence capable of handling grids with millions of grid cells.

For reservoirs where the movement of the fluids is mostly driven by the potential field induced by producing wells, FrontSim is particularly efficient. Examples include:

• Water flooding.

• Highly heterogeneous reservoirs.

Since FrontSim can be run on large models is also a good tool for:

• Screening of large geological models.

• Validation of up-scaled models.

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Streamline Calculation

Given the fluid pressure in each of the cells, we can find the streamlines by selecting a number of so called starting points in the reservoir. Beginning at these starting points, we find the lowest pressure (or alternatively the highest) in close vicinity of the starting point, such as the steepest downhill we can find, and follow this downhill to the next point, etc. This process will eventually lead us to a producing well. When we have gone through this process for all the starting points, the reservoir should be covered by streamlines.

Streamline representation

Since the streamlines describe the direction of flow at the moment in time that they are computed, they can be used as a computational tool to move the fluids along. The streamlines can be seen as a set of tubes representing the total reservoir volume and through which the fluids are moving. The tubes have exactly the same geological properties as the underlying geological model has. This approach divides the fluid flow into a set of 1-dimensional models and therefore reduces the problem to a computational simplicity that can have significant advantages. Since each streamline carries about the same volume, the density of the streamlines is an indication of the velocity of the fluid.

Streamline simulation advantages

The sequential process described above (solve pressure – move fluids along streamlines) constitutes one time step. An advantage with this approach is that the time steps can be very long and therefore the computational effort needed can be reduced.

The obvious advantage of a streamline method is the possibility it offers to do relatively quick simulations on large geologically and architecturally complex models.  This is the main reason that the streamline method is a popular tool for validating up-scaling methods, measuring uncertainty, screening and ranking different model scenarios. Another advantage of the streamline method is the visual information it gives about the fluid flow pattern and connectivity in the reservoir. This can be used to study the effects of different well patterns on the flow, and to monitor which volumes, wells and boundaries that support a specific well at any given time.

Streamline Time dependency

Even though a streamline simulation can be significantly faster than standard simulations, it can still be a time consuming affair if we want to model in detail all physical properties available in FrontSim. Some of the most important time dependencies are discussed below.

Number of Cells

The size of the model represented by the number of cells, will impact the time it will take to compute the pressure and move the fluids along. For example, for a model with 1 million grid cells it might take up to several minutes to compute the pressure and move the fluids one time step, depending somewhat on the complexity of the fluid description and the computational speed of the processor of your PC. Also, the memory requirement might be in the order of 1 gigabyte (Gb).

Fluid description

The fluid description will impact the CPU time. The fastest model will be a low compressible 2-phase model (oil/water). The low compressibility will cause the pressure solution to be easier to solve and the requirement for time steps for accuracy is low.  In addition, if the mobility and densities of the fluids are close, one time step might still result in a reasonably accurate (also from engineering perspective, that is, standard simulation) simulation result. For a one million-grid cell model, one time step might require 3 minutes of computer time with a state-of-the-art PC.

Time steps

The number of time steps and the length of each time step will influence both the result and the time it will take to achieve a result. As we introduce more detail in the fluid description, we also potentially introduce a need to use more and shorter time steps. Such a factor is gravity segregation. To be accurate, more time steps are required even though FrontSim will include the effect in a one time step solution.

Compressibility

Another factor is the compressibility introduced when using a 3-phase oil/water/gas model. To achieve close to engineering accuracy, we will have to enable the gravity segregation and use many time steps. In addition, the non-linearity of the model will cause more computational effort per time step. Note that FrontSim’s streamline concept will allow the user to use only one long time step (possibly years), even for this type of model, but the engineering accuracy defined by standard simulation will be degraded.

The resulting set of partial differential equations cannot be solved by any analytical means due to its typical complexity in geometry, rock property and fluid description. Instead, a so called numerical approximation is used. Many types of numerical methods are available to solve these equations. Most use some form of a finite difference/volume method that divides the geometry into many small subsections called cells containing rock and fluid properties. These cells cover the whole domain and the fluid flow is represented as relationships between these cells. These relationships result in an equation system with a number of unknowns on the order of number of cells or higher. This equation system will have to be solved for every time step during the simulation. These methods might require very many small time steps, and because of this, a reservoir simulation process can be a very time consuming affair depending on the geological detail represented and fluid property modeled.

Import ECLIPSE / FrontSim data and results

Existing ECLIPSE and FrontSim data and results files created outside of Petrel can be imported into Petrel. Petrel will read directly from the simulator output files, and results will be accessed directly via the index created by the simulator.

Petrel will on import of the simulator files generate Petrel objects for controlling and edit the simulator input and output files from within Petrel.

How to import simulation data

1.  Right click in the Cases pane and select Import (on tree) from the context menu.

2.  Select files of type (ECLIPSE / FrontSim data and results, Petrel Summary Data, VIP summary ASCII) and the file(s) to import.

3.  Click OK. In the case of importing ECLIPSE and FrontSim data and results, Petrel will automatically select the various input and results files if they are located in the same directory. In the Import ECLIPSE / FrontSim run dialog you can also select to browse for this input if they are located elsewhere.

4.  In the top of the dialog select which simulator the simulation files are defined for. This will aid Petrel in the import and conversion of the simulation files into Petrel objects.

5.  Click OK to continue with the import.

 In the bottom of the Import ECLIPSE / FrontSim run dialog you can specify some import settings. The option Automate handling of import settings will let Petrel automatically choose the suitable import settings for the selected import files. The coordinate system settings are based on the presence of the MAXPAGES keyword and the grid geometry is automatically converted to the project unit system. Furthermore, unknown keywords are logged in the log window and faults are auto detected. To manually control the import settings, turn off the checkbox in front of the option and click on the Advanced… button.

Quality Control of Imported Data

After importing data into Petrel to build 3D models, it is very important that all the input data is quality controlled before the data is used to create new data.

Visualizing

The best way to quality check the input data is to visualize different data together in the 3D Display window to look for data inconsistencies. This is a unique way of comparing data from different sources e.g. interpreted seismic lines can be compared (in 3D) to seismic data, well logs and well tops. Another great feature in Petrel is the possibility to zoom in between different surfaces and inspect how the layers between surfaces look.

Visualization of the data is a very important feature in Petrel and is described in more detail in Visualization.

Statistics

Another important data tool that can be performed in Petrel is to inspect the statistics for objects both imported and created in Petrel. Each data object in Petrel has a Settings window, which consists of different tabs with different options. The settings windows for every object in Petrel are described in detail in Settings for objects in the Input tab. The Statistics window is a tab that is available in every settings window. The settings window can be opened by double clicking on an object in the Petrel panes or by clicking on the object with the right mouse button and select Settings from the context menu.

To check the statistics of an object in Petrel, open the settings window and select the Statistics tab. In the statistics tab the max and min coordinates of the X-, Y- and Z- axis are listed, together with different information about the object, e.g. number of closed and open polygons in a polygon data-set or number of well logs with min and max values for a well.

The important part to check in the statistics is that the values are within the area that you expect them to be. Check that the log curves look reasonable and that the min and max values for a log curve are within the expected values.

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