Network science is a broadly interdisciplinary field, pulling from computer science, mathematics, statistics, and more. The data scientist working with networks thus needs a broad base of knowledge, as network data calls for—and is analyzed with—many computational and mathematical tools. One needs good working knowledge in programming, including data structures and algorithms to effectively analyze networks. In addition to graph theory, probability theory is the foundation for any statistical modeling and data analysis. Linear algebra provides another foundation for network analysis and modeling because matrices are often the most natural way to represent graphs. Although this book assumes that readers are familiar with the basics of these topics, here we review the computational and mathematical concepts and notation that will be used throughout the book. You can use this chapter as a starting point for catching up on the basics, or as reference while delving into the book.

In this chapter, we discuss how to represent network data inside a computer, with some examples of computational tasks and the data structures that enable those computations. When working with network data using code, you have many choices of data structures---but which ones are best for our given goals? Writing your own code to process network data can be valuable, yet existing libraries, which feature extensively-tested and efficiently-engineered functionalities, are worth considering as well. Python and R, both excellent programming languages for data science, come well-equipped with third-party libraries for working with network data, and we describe some examples. We also discuss choosing and using typical file formats for storing network data, as many standard formats exist.

The notes in this appendix provide a brief and limited overview of R syntax, semantics, and the R package system, as background for working with the R code included in the text. It is intended for use alongside R help pages and the wealth of tutorial material that is available online.

This chapter explains how the mathematical models from Chapter 4 are implemented and integrated to form a full simulator. To this end, we introduce data structures to represent fluid behavior, the reservoir state, boundary conditions, source terms, and wells. We then explain in detail how the two-point flux approximation (TPFA) scheme is implemented in MRST for general unstructured grids. We also outline the basic solver used to compute time-of-flight and tracer partitions. We end the chapter by presenting a few examples that demonstrate how to set up simulations in MRST and set appropriate boundary conditions, source terms, or well models. The examples include the famous quarter-five spot problem, a corner-point grid with four intersecting faults, and a model of a shallow-marine reservoir (SAIGUP).

Generating a coarser volumetric description of the reservoir rock is a common task in reservoir engineering. This chapter discusses how to partition a fine grid model into a smaller set of coarse blocks. After the partition, the coarse blocks will each consist of a finite collection of cells from the underlying fine model. Through a series of examples, we demonstrate a variety of different partition methods. Whereas the simplest methods only utilize the geometry or topology of the grid, the more advanced methods can compute partitions that adapt to petrophysical properties, fluid contacts, flow fields, near-well regions, or underlying geological properties like depositional environments, flow units, rock types, etc.

The chapter explains how you can generate grid models to represent subsurface reservoirs. We outline a number of elementary grid types: structured/rectilinear grids, fictitious domains, Delaunay triangulations, and Voronoi grids. We then explain stratigraphic grids that are commonly used to model real subsurface formations, including in particular corner-point and perpendicular bisector (PEBI) grids. We explain how such grids are represented in MRST using a data structure for general unstructured grids, and we discuss how to compute geometric properties like volumes, face areas, face normals, etc. We end the chapter by presenting an overview of alternative gridding techniques, including composite grids, multiblock grids, and control-point and boundary conformal grids.