Seismic Reservoir Modeling

Theory, Examples, and Algorithms

Dario Grana, Tapan Mukerji, Philippe Doyen

• Publisher: Wiley-Blackwell
• Year: 2021
• ISBN:
  9781119086192
• Edition: 1
• Topic: Ciencias físicas
• Subtopic: Geología y ciencias de la Tierra

Seismic reservoir characterizationaimsto build 3-dimensional models of rock and fluid properties, including elastic and petrophysicalvariables, to describe andmonitor the state of the subsurfacefor hydrocarbonexploration andproduction andforCO? sequestration. Rock physics modeling and seismic wave propagation theory provide a set of physical equations to predict the seismic response of subsurface rocks based on their elastic and petrophysical properties. However, the rock and fluid properties are generally unknown and surface geophysical measurements areoftenthe only available data to constrain reservoir models far away from well control. Therefore, reservoirproperties are generally estimated from geophysical data as a solution of an inverse problem, by combining rock physics and seismic models with inverse theory and geostatistical methods, in the context of the geologicalmodelingof the subsurface. A probabilistic approach to the inverse problem provides the probability distribution of rock and fluid properties given the measured geophysical data and allows quantifying the uncertainty of the predicted results. The reservoir characterization problem includes both discrete properties, such as facies or rock types, and continuous properties, such as porosity, mineral volumes, fluid saturations, seismic velocities and density.

Seismic Reservoir Modeling: Theory, Examples and Algorithms presentsthe main concepts and methods of seismic reservoir characterization. The book presents an overview ofrock physics models that link the petrophysical properties to the elastic properties in porous rocksand a review of themost common geostatistical methods to interpolate and simulate multiple realizations of subsurface propertiesconditionedon a limited number of direct and indirect measurementsbased onspatial correlation models.Thecore of the bookfocuses onBayesian inverse methods for the prediction ofelasticpetrophysical properties from seismic data using analytical and numerical statistical methods.The authors presentbasic and advancedmethodologies of the current state of the art in seismic reservoir characterizationand illustrate themthrough expository examples as well as real data applications to hydrocarbon reservoirs and CO?sequestration studies.

1
Review of Probability and Statistics

Statistics and probability notions and methods are commonly used in geophysics studies to describe the uncertainty in the data, model variables, and model predictions. Statistics and probability are two branches of mathematics that are often used together in applied science to estimate parameters and predict the most probable outcome of a physical model as well as its uncertainty. Statistical methods aim to build numerical models for variables whose values are uncertain (e.g. seismic velocities or porosity in the subsurface) from measurements of observable data (e.g. measurements of rock properties in core samples and boreholes). Probability is then used to make predictions about unknown events (e.g. porosity value at a new location) based on the statistical models for uncertain variables. In reservoir modeling, for example, we can use statistics to create multiple reservoir models of porosity and water saturation using direct measurements at the well locations and indirect measurements provided by geophysical data, and then apply probability concepts and tools to make predictions about the total volume of hydrocarbon or water in the reservoir. The predictions are generally expressed in the form of a probability distribution or a set of statistical estimators such as the most‐likely value and its variability. For example, the total fluid volume can be described by a Gaussian distribution that is completely defined by two parameters, the mean and the variance, that represent the most‐likely value and the uncertainty of the property prediction, respectively. Probability and statistics have a vast literature (Papoulis and Pillai 2002), and it is not the intent here to do a comprehensive review. Our goal in this chapter is to review some basic concepts and establish the notation and terminology that will be used in the following chapters.

1.1 Introduction to Probability and Statistics

The basic concept that differentiates statistics and probability from other branches of mathematics is the notion of the random variable. A random variable is a mathematical variable such that the outcome is unknown but the likelihood of each of the possible outcomes is known. For example, the value of the P‐wave velocity at a given location in the reservoir might be unknown owing to...