Seismic to simulation

Encyclopedia

**Seismic to Simulation**is the process and associated techniques used to develop highly accurate static and dynamic 3D models of hydrocarbon reservoirs for use in predicting future production, placing additional wells, and evaluating alternative reservoir management scenarios. The process is successful if the model accurately reflects the original well logs

Well logging

Well logging, also known as borehole logging is the practice of making a detailed record of the geologic formations penetrated by a borehole. The log may be based either on visual inspection of samples brought to the surface or on physical measurements made by instruments lowered into the hole...

, seismic data and production history.

## Introduction

Reservoir models are constructed to gain a better understanding of the subsurface that leads to informed well placement, reserves estimation and production planning. Models are based on measurements taken in the field, including well logs, seismic surveysReflection seismology

Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite/Tovex, a specialized air gun or a...

, and production history.

Seismic to simulation enables the quantitative integration of all field data into an updateable reservoir model built by a team of geologists, geophysicists, and engineers. Key techniques used in the process include integrated petrophysics and rock physics to determine the range of lithotypes and rock properties, geostatistical

Geostatistics

Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...

inversion to determine a set of plausible seismic-derived rock property models at sufficient vertical resolution and heterogeneity for flow simulation, stratigraphic

Stratigraphy

Stratigraphy, a branch of geology, studies rock layers and layering . It is primarily used in the study of sedimentary and layered volcanic rocks....

grid transfer to accurately move seismic-derived data to the geologic model, and flow simulation for model validation and ranking to determine the model that best fits all the data.

## Rock Physics and Petrophysics

The first step in seismic to simulation is establishing a relationship between petrophysical key rock properties and elastic propertiesElastic modulus

An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically when a force is applied to it...

of the rock. This is required in order to find common ground between the well logs and seismic data.

Well logs are measured in depth and provide high resolution vertical data, but no insight into the inter-well space. Seismic are measured in time and provide great lateral detail but is quite limited in its vertical resolution. When correlated, well logs and seismic can be used to create a fine-scale 3D model of the subsurface.

Insight into the rock properties comes from a combination of basic geologic understanding and well bore measurements. Based on an understanding of how the area was formed over time, geologists can predict the types of rock likely to be present and how rapidly they vary spatially. Well log and core measurements

Core sample

A core sample is a cylindrical section of a naturally occurring substance. Most core samples are obtained by drilling with special drills into the substance, for example sediment or rock, with a hollow steel tube called a core drill. The hole made for the core sample is called the "core hole". A...

provide samples to verify and fine-tune that understanding.

Seismic data is used by petrophysicists to identify the tops of various lithotypes and the distribution of rock properties in the inter-well space using seismic inversion attributes such as impedance

Acoustic impedance

The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...

. Seismic surveys measure acoustic impedance contrasts between rock layers. As different geologic structures are encountered, the sound wave reflects

Reflection seismology

Reflection seismology is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite/Tovex, a specialized air gun or a...

and refracts

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

as a function of the impedance contrast between the layers. Acoustic impedance varies by rock type and can therefore be correlated to rock properties using rock physics relationships between the inversion attributes and petrophysical properties such as porosity

Porosity

Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...

, lithology

Lithology

The lithology of a rock unit is a description of its physical characteristics visible at outcrop, in hand or core samples or with low magnification microscopy, such as colour, texture, grain size, or composition. It may be either a detailed description of these characteristics or be a summary of...

, water saturation

Water content

Water content or moisture content is the quantity of water contained in a material, such as soil , rock, ceramics, fruit, or wood. Water content is used in a wide range of scientific and technical areas, and is expressed as a ratio, which can range from 0 to the value of the materials' porosity at...

, and permeability.

Once well logs are properly conditioned and edited, a petrophysical rock model is generated that can be used to derive the effective elastic rock properties from fluid and mineral parameters as well as rock structure information. The model parameters are calibrated by comparison of the synthetic to the available elastic sonic

Sonic logging

Sonic logging shows a formation’s interval transit time, designated Dt. It is a measure of a formation’s capacity to transmit sound waves. Geologically, this capacity varies with lithology and rock textures, notably porosity....

logs. Calculations are performed following a number of rock physics algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s including: Xu & White, Greenberg & Castagna, Gassmann, Gardner, modified upper and lower Hashin-Shtrikman, and Batzle & Wang.

When the petrophysical rock model is complete, a statistical database is created to describe the rock types and their known properties such as porosity and permeability. Lithotypes are described, along with their distinct elastic properties.

## MCMC Geostatistical Inversion

In the next step of seismic to simulation, seismic inversion techniques combine well and seismic data to produce multiple equally plausible 3D models of the elastic properties of the reservoir. Seismic data is transformed to elastic property log(s) at every trace. Deterministic inversion techniques are used to provide a good overall view of the porosity over the field, and serve as a quality control check. To obtain greater detail needed for complex geology, additional stochastic inversion is then employed.Geostatistical inversion procedures detect and delineate thin reservoirs otherwise poorly defined. Markov chain Monte Carlo

Markov chain Monte Carlo

Markov chain Monte Carlo methods are a class of algorithms for sampling from probability distributions based on constructing a Markov chain that has the desired distribution as its equilibrium distribution. The state of the chain after a large number of steps is then used as a sample of the...

(MCMC) based geostatistical inversion addresses the vertical scaling problem by creating seismic derived rock properties with vertical sampling compatible to geologic models.

All field data is incorporated into the geostatistical inversion process through the use of probability distribution function

Probability distribution function

Depending upon which text is consulted, a probability distribution function is any of:* a probability distribution function,* a cumulative distribution function,* a probability mass function, or* a probability density function....

s (PDFs). Each PDF describes a particular input data in geostatistical terms using histogram

Histogram

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson...

s and variogram

Variogram

In spatial statistics the theoretical variogram 2\gamma is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z...

s, which identify the odds of a given value at a specific place and the overall expected scale and texture based on geologic insight.

Once constructed, the PDFs are combined using Bayesian inference

Bayesian inference

In statistics, Bayesian inference is a method of statistical inference. It is often used in science and engineering to determine model parameters, make predictions about unknown variables, and to perform model selection...

, resulting in a posterior PDF that conforms to everything that is known about the field. A weighting system is used within the algorithm, making the process more objective.

From the posterior PDF, realization

Realization

realization and realisation may be:* Realization , a sport climbing route in Ceüse, France* Realization , the pricing of security at market value* Realization , an actually observed value of random variable...

s are generated using a Markov chain Monte Carlo algorithm. These realizations are statistically fair and produce models of high detail, accuracy and realism. Rock properties like porosity can be cosimulated from the elastic properties determined by the geostatistical inversion. This process is iterated until a best fit model is identified.

Inversion parameters are tuned by running the inversion many times with and without well data. Without the well data, the inversions are running in blind-well mode. These blind-well mode inversions test the reliability of the constrained inversion and remove potential biased.

This statistical approach creates multiple, equi-probable models consistent with the seismic, wells, and geology

Geology

Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

. Geostatistical inversion simultaneously inverts for impedance and discrete properties types, and other petrophysical properties such as porosity can then be jointly cosimulated.

The output volumes are at a sample rate consistent with the reservoir model because making synthetics of finely sampled models is the same as from well logs. Inversion properties are consistent with well log properties because the histograms used to generate the output rock properties from the inversion are based on well log values for those rock properties.

Uncertainty is quantified by using random seeds to generate slightly differing realizations, particularly for areas of interest. This process improves the understanding of uncertainty and risk within the model.

## Stratigraphic Grid Transfer

Following geostatistical inversion and in preparation for history matching and flow simulation, the static model is re-gridded and up-scaled. The transfer simultaneously converts time to depth for the various properties and transfers them in 3D from the seismic grid to a corner-point gridCorner-point grid

In geometry, a corner-point grid is a tessellation an Euclidean 3D volume where the base cell has 6 faces .A set of straight lines defined by their end points define the pillars of the corner-point grid. The pillars have a lexiographical ordering that determines neighbouring pillars. On each...

. The relative locations of properties are preserved, ensuring data points in the seismic grid arrive in the correct stratigraphic layer in the corner point grid.

The static model built from seismic is typically orthogonal but flow simulators expect corner point grids. The corner point grid consists of cubes that are usually much coarser in the horizontal direction and each corner of the cube is arbitrarily defined to follow the major features in the grid. Converting directly from orthogonal to corner point can cause problems such as creating discontinuity in fluid flow.

An intermediate stratigraphic grid ensures that important structures are not misrepresented in the transfer. The stratigraphic grid has the same number of cells as the orthogonal seismic grid, but the boundaries are defined by stratigraphic surfaces and the cells follow the stratigraphic organization. This is a stratigraphic representation of the seismic data using the seismic interpretation to define the layers. The stratigraphic grid model is then mapped to the corner point grid by adjusting the zones.

Using the porosity and permeability models and a saturation height function, initial saturation models are built. If volumetric calculations identify problems in the model, changes are made in the petrophysical model without causing the model to stray from the original input data. For example, sealing faults are added for greater compartmentalization.

## Model Validation and Ranking

In the last step of seismic to simulation, flow simulation continues the integration process by bringing in the production history. This provides a further validation of the static model against history. A representative set of the model realizations from the geostatistical inversion are history matched against production data. If the properties in the model are realistic, simulated well bottom hole pressure behavior should match historical (measured) well bottom hole pressure. Production flow rates and other engineering data should also match.Based on the quality of the match, some models are eliminated. After the initial history match process, dynamic well parameters are adjusted as needed for each of the remaining models to improve the match. The final model represents the best match to original field measurements and production data and is then used in drilling decisions and production planning.

## Further reading

- "Building Highly Detailed, Realistic 3D Numerical Models of Rock and Reservoir Properties: Rigorous Incorporation of All Data Reduces Uncertainty", Fugro-Jason White Paper, 2008.

- Contreras, A., Torres-Verdin, C., "AVA sensitivity analysis and inversion of 3D pre-stack seismic data to delineate a mixed carbonate-siliciclas tic reservoir in the Barinas-Apure Basin, Venezuela".

- Contreras, A., Torres-Verdin, C., Kvien, K., Fasnacht, T., Chesters, W., "AVA Stochastic Inversion of Pre-Stack Seismic Data and Well Logs for 3D Reservoir Modeling", EAGE 2005.

- Deutsch, C. Geostatistical Reservoir Modeling, New York: Oxford University Press, 2002, 376 pages.

- Jarvis, K., Folkers, A., Saussus, D., "Reservoir compartment prediction of the Simpson field from the geostatistical inversion of AVO seismic data", ASEG 2007.

- Leggett, M., Chesters, W., "Joint AVO Inversion with Geostatistical Simulation", CSEG National Convention, 2005.

- Sams, M., Saussus, D., "Comparison of uncertainty estimates from deterministic and geostatistical inversion", SEG Annual Conference, 2008.

- Soni, S., Littmann, W., Timko, D., Karkooti, H., Karimi, S., Kazemshiroodi, S. "An Integrated Case Study from Seismic to Simulation through Geostatistical Inversion", SPE 118178.

- Stephen, K., MacBeth, C. "Reducing Reservoir Prediction Uncertainty by Updating a Stochastic Model Using Seismic History Matching", SPE Reservoir Evaluation & Engineering, December 2008.

- Zou, Y., Bentley, L., Lines, L. "Integration of reservoir simulation with time-lapse seismic modeling", 2004 CSEG National Convention.

## External links

- American Association of Petroleum Geologists
- Australian Society of Exploration Geophysicists (ASEG)
- European Association of Geoscientists and Engineers
- Petrel Seismic to Simulation
- Fugro-Jason
- Fugro
- Petroleum Exploration Society of Australia (PESA)
- Society of Exploration Geophysicists
- Society of Petroleum Engineers
- Society of Petrophysicists and Well Log Analysts (SPWLA)
- The University of Texas at Austin Petroleum and Geoscience Engineering Reading Room
- Geological Survey Publications Warehouse