# Reservoir Simulation Learning Objectives Chapter 1 – Introduction and Case Studies

*Be able to describe what is meant by a simulation model, saying what analytical models and numerical models are.

Simulation models are a representation of a real system and because of their simplified nature, allow calculations to be made giving insight into the real system.

Analytical Models are defined by their ability to be solved by using mathematical techniques.

Numerical Models are defined by the complexity in solving their equations and are usually carried out by a computer. Numerical models approximate the real model by carrying out a large number of calculations across unit steps of interest (time steps for example).

*Be familiar with what specifically a reservoir simulation model is.

A numerical reservoir simulation model represents a petroleum reservoir by subdividing the total area into grid blocks. Each block represents a local part of the reservoir and has assigned uniform values (porosity, permeability etc.) which are constant for each time period calculation though they adjust with time to reflect the changing properties of the reservoir.

Each block is connected and calculations are performed for each individual section.

A reservoir simulation model requires several inputs to be run. Reservoir properties must be input (porosity, permeability, injection rates, bottom hole pressure limits etc.), numerical features are then assigned (these include grid block resolution, shape and time step size). Finally, the desired outputs are selected to be exported to file once the numerical model is completed.

*Be able to describe the simplifications and issues that arise in going from the description of a real reservoir to a reservoir simulation model

The simplifications when going from a real reservoir to a reservoir simulation model are inherent in the uniform values assigned to different variables for each grid block. As we approach an infinitesimally small grid block we approach the real reservoir, due to the computing power required to perform numerical calculations it is not possible to complete complex numerical analysis at such a fine grid block resolution. Therefore, we must assume a constant value of each variable for the given time step and given grid block size. This is the core simplification. In reality, each of the variables will be changing with time and will vary across the grid block.

Issues that arise are when we look at the forward predictions for reservoir simulation – we cannot know for certain if they are correct. It is important to assess the various uncertainties of each of the data inputs in the given model.

Reservoir simulation models are weakest during the initial appraisal stages of a reservoir because there is very little data and little or no performance history.

*Be able to describe why and in what circumstances simple or complex reservoir models are required to model reservoir processes

Why are simple or complex models required to model reservoir processes?

Well, we use them to model a reservoir that cannot be modelled by analytical or experimental methods. Why do we want to model it? So we can gain valuable information about how we expect the reservoir to perform or data that is otherwise of interest. Total field cumulative oil production profile with time, average field pressure as a function of time and individual well pressures over time are just a few of the outputs we are interested in.

In what circumstances are simple or complex reservoir models required?

The answer lies in the minimum level of modelling required to answer the question that we are trying to address. Complex models are used for complex questions whereas simple models are used for simple questions. It is important to note that the model should be consistent with the amount of reliable data we have – as they say trash in equals trash out. One must have reliable data in order to get a reliable solution, there’s no use having a complex model and using unreliable data as the output will be just as unreliable.

A few different types of reservoir models outlined in the text include:

The Tank Model

This model assumes average values of reservoir properties across the entire area of the reservoir.

The Simple Sector Model

The reservoir model is broken up into sections where the variables are likely to be significantly different and average values are taken for each section (example: section off oil zone and aquifer zone, and the different flanks).

Fine Grid Simulation Model

This guy requires the greatest computational power. Grids are small and there is a fine resolution across the entirety of the reservoir. Grids resolution can be made increasingly fine around areas where values are likely to vary significantly, and coarse throughout areas where variables are relatively uniform. The effect of this is to increase computational efficiency.

*Be able to list what input data is required and where this may be found

The input data that is required comprises of:

• Fluid and rock properties
• Numerical factors (grid block resolution, time step sizes, grid shape)
• Reliable field well controls (injection rates, bottom hole pressure constraints etc.)

Fluid and rock properties are taken from formation evaluation procedures and core samples. Numerical factors are determined based on the complexity of the required model. Field Well Controls can be taken from production tests.

*Be able to describe several examples of typical outputs of reservoir simulations and say how these are of use in reservoir development

We can break up reservoir simulation models into the stages of a well life cycle:

1. Appraisal Stage

During the appraisal stage reservoir simulation is used to design the overall field development plan. Numerical analysis is run with different values for original oil in place (STOIIP), reservoir parameters (permeability, porosity and effect of aquifer etc.) and major changes in geology of the reservoir (distribution and presence of shale, different fault structures etc.).

Future predicted performances of the well are then generated and we receive cases for optimistic, pessimistic and most probable from which development plans can be created.

The several examples of typical outputs of reservoir simulations can include average field pressure; total field cumulative oil, water and gas production profiles with time; individual well pressures (bottom hole or wellhead) over time; and spatial distribution of oil, water and gas saturations throughout the reservoir as functions of time – just to list a few.

1. Mature Field Development

Reservoir simulation is used as a reservoir management tool during this stage of a well’s life. Since the well has been producing for some time, the reservoir engineer has access to pressure, GORs and cumulative oil production data which they can use to update the reservoir model and evaluate future development options.

1. Late Field Development

Reservoir simulation may be performed during the final stages of a well’s life however it is either completely up to the discretion of the operating company or the regulatory framework of the country in which they operate. Some countries require companies to produce reservoir simulations as part of their ongoing operations. If this is not the case, a company may choose to perform a final reservoir simulation to investigate potential recovery measures and extend the production life. Other times, the cost of running a simulation will outweigh the possible economic benefits and the well will be plugged and abandoned.

*Know the meaning of all the highlighted terms – or terms referred to in the Glossary – in Chapter 1 e.g. history matching, black oil model, transmissibility, pseudo relative permeability etc.

History Matching

The process of adjusting inputs based on performance data to generate a model that more closely reflects the real world scenario. The most common updates are made to field and individual well cumulative production, watercuts and pressures.

Black Oil Model

The black oil model is a classification system of transport equations used to simulate recovery processes. It is most commonly used in modeling immiscible two and three phase component systems.

Transmissibility

Refers to the measure of how easily fluid passes between two grid blocks. Harmonic average between blocks is used to determine the single phase part of transmissibility. Arithmetic average is used for average relative permeability when we have more than one phase.

Pseudo Relative Permeability

Pseudo-relative permeability accounts for: the effects of small scale heterogeneity, the balance of different forces (gravity/viscous and capillary) and numerical affects such as numerical dispersion. It is the effective relative permeability in the simulation model at the grid block scale.

*Be able to describe and discuss the main changes in reservoir simulation over the last 40 years from the 60’s to the present – and say why these have occurred

Changes have occurred primarily due to greater computer processing power and the adoption of new ideas in areas such as geostatistics and reservoir description.

Computer Power

CPU

Processing power has increased and so more complex numerical analysis can be performed leading to finer resolution of grid blocks and smaller time steps.

Parallel Processing

Computer processing power has also increased due to parallel processing. The idea is to distribute the simulation calculation around a number of processors, which perform different parts of the computational problem simultaneously. We can then observe if the problem becomes linearly faster with the number of parallel processors, if this is the case then it is said to be scalable. If the addition of processors increases computational speed in a linear fashion then it is said to have excellent “parallelises” and relates to the efficiency of additional processing power used in parallel.

Visualization

Huge improvements have been seen in visualization techniques. This allows users to more conveniently observe data, to generate more powerful visual models and gain greater insight into the data.

Geostatistics

Mining and mineral geostatistics processes have been adapted to the petroleum industry in the past 10 to 15 years. Pixel-based point geostatistical techniques and object based modelling have been developed and applied in various reservoirs.

Upscaling

Upscaling is the substitution of a heterogeneous property region of fine grid cells with an equivalent homogeneous region with single coarse-grid cell with effective property values. It is an averaging procedure where the fine resolution of the grid blocks is approximated by a coarse-scale model with averages taken for static and dynamic reservoir parameters.

Organisational changes in the oil industry

• More integrated approach to geology/engineering/geophysics
• Organizational changes in the form of downsizing and outsourcing reservoir simulation (makes for good business for smaller consultant)
• Companies have shifted from heavy investment in ‘in-house’ R&D to focusing more of development. Companies now tend to support universities and independent outside organisations to develop technology, except probably for Schlumberger.

*Know in detail and be able to compare the differences between what reservoir simulations can do at the appraisal and in the mature stages of reservoir development

At the appraisal stage reservoir simulations can at best only give an educated guess at the likely outcomes because the input data is riddled with uncertainties. Though the data should not be scoffed at and instantly dismissed, when combined with statistical likelihoods the data can present a useful picture of the upper and lower boundaries of recovery and the most likely scenario from which future actions can be planned. At the appraisal stage we typically determine:

• the nature of the reservoir recovery plan
• the nature of the facility required to develop the field
• nature and capacities of plant equipment for injection and separation
• the different types and number of wells to be drilled
• sequence of the drilling program

Mature stages of reservoir development uses history matching to update the reservoir model. At this stage we are more interested in enhancing the field development strategy by adjusting infill drilling and injection scheme plans. We can also determine the usefulness of smaller projects like drilling an attic horizontal well or working over 2 or 3 existing vertical/slanted wells.

*Have an elementary knowledge of how uncertainty is handled in reservoir simulation

We plot the cumulative oil recovery for the most probably case, a range of cases within 50% probability and a range of cases with a 90% probability. From this we can get an idea of the maximum and minimum anticipated values for cumulative oil recovery.

In addition to this, a spider plot is created which plots the variation in recovery against the percentage change in input value. This is valuable in determining the most important input quantity that has the greatest impact on recovery result. We can then spend time and effort on reducing the uncertainty of the most impactful input parameter and achieve a less uncertain model.

*Know all the types of reservoir simulation models and what type of problem or reservoir process each is used to model

Black Oil Model

The black oil model is used for single, two and three phase reservoir processes and is the most commonly used formulation of the reservoir simulation equations. It treats each of the phases as mass components and only gas is allowed to dissolve in the oil and water. The pressure dependent nature of gas solubility is incorporated into the black oil model through gas solubility factors Rso and Rsw.

The black oil model is used to approximate:

• Capillary imbibition processes
• Immiscible gas injection
• Waterflooding including viscous, capillary and gravity forces (secondary recovery)
• Primary depletion recovery (solution gas drive)
• Immiscible water-gas-oil recovery process

Compositional Model

The model defines compositions based on component paraffin series (C1, C2, C3 etc.). It is required when there is a significant inter-phase mass transfer effect in the fluid displacement process as it accounts for mass conservation, whereas the black oil model does not.

Compositional model can approximate:

• Gas injection with oil mobilization by first contact or developed miscibility (CO2 flooding)
• Modelling of gas injection into near critical reservoirs
• Gas recycling processes in condensate reservoirs

Chemical Flood Model

The chemical flood model estimates polymer or surfactant displacement processes. Due to the high cost nature of these displacement processes, the chemical flood model is rarely used and will only be used when polymer flooding or surfactant flooding are economically viable (high oil price). Chemical flood models can be extended to model foam flooding.

Chemical flood model is used to estimate:

• Polymer flooding
• Polymer/surfactant flooding
• Low-tension polymer flooding
• Alkali flooding
• Foam flooding

Thermal Model

Thermal recovery methods reduce the viscosity of heavy oils by adding heat in the form of injected steam or by actually combusting the oil. Thermal approximations therefore model:

• Steam soaks where steam is injected into the well, the well is shut in to allow the heat to spread, then the well is brought back into production with the freshly mobilized oil because of a reduction in viscosity.
• Steam drive where steam is continuously injected. The viscosity of the oil is reduced and mobility increases driving more oil out.
• In Situ combustion where air or as is injected and an actual combustion takes place underground. This is not a common oil recovery method. Imagine the field day the newspapers and media outlets would have if it were.

Dual-Porosity Models of Fractured Systems

This model has been developed to approximate multiphase flow in fractured systems where the oil flows in fractures but is stored in the rock matrix.

Coupled Hydraulic, Thermal Fracturing and Fluid Flow Models

These models estimate the effect of mechanical stresses and deformations on fluid flow. They are still in the early research stages.

*Know or be able to work out the equations for the mass of a phase or component in a grid block for a black oil or compositional model

For a black oil model:

For the compositional model:

Cjj is the mass concentration of component I in phase j (j = gas, oil or water), dimensions of mass/unit volume of phase.

Vp is the pore volume.