General Background

This section focuses on the importance of reservoir simulation. The relevance of simulators in the industry will be examined briefly. In addition, a little information about the concepts of numerical and analytical methods will be given. Lastly, a comparison between the two methods, and a quick look at the benefits and limitations of both will be considered.

2.1. Reservoir Simulation

Reservoir simulation is referred to as “the process of inferring the behavior of a real reservoir from the performance of a mathematical model of that physical system” (Soleng & Holden, 1998). It has become ingrained in the oil and gas industry. So much so, that most aspects of reservoir engineering problems are and can be solved using simulators. There is a simulator for everything from well testing to EOR (Enhanced Oil Recovery) predictions (Islam, Hossain, Mousavizadegan, Mustafiz, & Abou-Kassam, 2016).

Simulation is a combination of physics, mathematics, and computer programming, coming together to develop a tool for estimating and predicting hydrocarbon behavior under various situations and operations. Figure 2.1 details the necessary steps that are involved when developing a reservoir simulator (Odeh, 1982). The purpose of simulators are to take an environment and all the necessary forces and characteristics, and then simulate/imitate the reaction and feedback of the environment and all the elements involved given a set boundary.

Figure 2.1: The major steps involved in reservoir simulation development and procedure (Odeh, 1982)

A very similar objective is present for the reservoir; to simulate the behavior of all the components involved (fluids, geo-mechanics, etc.) without the cost or effort of testing it in real life. However, what makes reservoir simulators so different from most others is largely by the fact that the

portrayal and model of the reservoir, coupled with the boundary conditions and flow calculations of

porous media, have a great deal of uncertainty. The pore systems and the flow patterns through

them occurs on a level of detail that is near impossible to model or even characterize (Pettersen,

2006).

General Background

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Figure 2.2: A regular Cartesian grid pattern (Pettersen, 2006)

The structure of the pore system is so complex and unsystematic, that without the possibility to scan or extract the reservoir on the nano scale, the system will remain largely unknown. On the other hand, even if it were possible to achieve such a level of detail in the model, it would result in a problem that is too large and intensive to solve for computers presently. The uncertainty that is incorporated in these calculations is what make them so increasingly difficult to simulate accurately (Peaceman, 1977).

These problems occur essentially due to; the generalization and upscaling from micro scale to macro scale from subsurface data such as seismic and well logs, and the simplification and/or uncertainty in the model and calculations themselves. However, despite these hindrances, reservoir simulation is

commonly used with great success. It is still one of the fundamental parts used for decision making in

the industry. Not only can yield vital information about the reservoir and the flow patterns, but also

highlight areas that need to be investigated further (Carlson, 2006).

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2.2. Gridding in Reservoir Simulation

A reservoir description is a model that maps the geology of a region. The geological data is often obtained from well logs, seismic, or other similar techniques. This is then used to create a geological model, which is often of fine scale reflecting the input information, such as core samples. Though, through upscaling and over generalization of the data, coupled with the necessity of having manageable computations, leads to simulators having to have a coarser scale. As such, simulators grid the

information, where some statistical method is applied, and makes it more feasible to perform calculations on (Soleng & Holden, 1998). Gridding is an essential part of any numerical reservoir simulation.

Figure 2.3: A regular Cartesian grid pattern as found in a reservoir model. Varying grid lengths and dipping structures are taken into account when creating such a model (Pettersen, 2006)

When reservoir simulators were first being introduced into the industry, Cartesian grids

(rectangular/cuboidal) were what was most commonly used (Cao, 2002). Radial grids were then later

developed to simulate flow near the well bore (Pedrosa & Aziz, 1985), and then local grid refinement

General Background

6 | P a g e was established to attain higher accuracy in regions of either high flow or where more information is available (Nacul, 1991). Not too long thereafter, a technique referred to as corner point gridding was developed and introduced to the industry (Ponting, 1989). This ushered a new and radical way of approaching the subject matter of gridding. Corner point gridding made it possible to design grid blocks that are non-rectangular (Peaceman, 1996), making it possible to model faults and other intricate geological features more accurately and with more precise geometry.

Figure 2.4: An example of an unstructured grid, where faults and multilateral wells can be seen as well (Cao, 2002)

In the last few decades, there has been a large focus on unstructured grids (Aavatsmark, Barkve, &

Mannseth, 1998). Similar to the concept of corner point gridding, unstructured grids can adapt to

geological features. The way in which it can achieve that is by allowing the grids to be flexible in nature,

non-orthogonal, and can contain multiple points. This allows for not only being able to model complex

geological structures, but also be used to varying sizes for the grid blocks, performing similarly if not

better than local grid refinement and corner point gridding (Prévost, Lepage, Durlofsky, & Mallet, 2005).

Background Research

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