The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Global warming and climate change concerns have triggered global efforts to reduce the concentration of atmospheric carbon dioxide (CO2). Carbon dioxide capture and storage (CCS) is considered a crucial strategy for meeting CO2 emission reduction targets. In this paper, various aspects of CCS are reviewed and discussed including the state of the art technologies for CO2 capture, separation, transport, storage, leakage, monitoring, and life cycle analysis. The selection of specific CO2 capture technology heavily depends on the type of CO2 generating plant and fuel used. Among those CO2 separation processes, absorption is the most mature and commonly adopted due to its higher efficiency and lower cost. Pipeline is considered to be the most viable solution for large volume of CO2 transport. Among those geological formations for CO2 storage, enhanced oil recovery is mature and has been practiced for many years but its economical viability for anthropogenic sources needs to be demonstrated. There are growing interests in CO2 storage in saline aquifers due to their enormous potential storage capacity and several projects are in the pipeline for demonstration of its viability. There are multiple hurdles to CCS deployment including the absence of a clear business case for CCS investment and the absence of robust economic incentives to support the additional high capital and operating costs of the whole CCS process.

https://www.elsevier.com/__data/assets/pdf_file/0005/96980/Current-status-carbon-capture.pdf

An overview of current status of carbon dioxide capture and storage technologies

Coalbed methane: A review

This article reviews the storage of captured CO2 in coal seams. Other geologic formations, such as depleted petroleum reservoirs, deep saline aquifers and others have received considerable attention as sites for sequestering CO2. This review focuses on geologic sequestration of CO2 in unmineable coalbeds as the geologic host. Key issues for geologic sequestration include potential storage capacity, the storage integrity of the geologic host, and the chemical and physical processes initiated by the deep underground injection of CO2. The review topics include (i) the estimated CO2 storage capacity of coal, along with the estimated amount and composition of coalbed gas; (ii) an evaluation of the coal seam properties relevant to CO2 sequestration, such as density, surface area, porosity, diffusion, permeability, transport, rank, adsorption/desorption, shrinkage/swelling, and thermochemical reactions; and (iii) a treatment of how coalbed methane (CBM) recovery and CO2-enhanced coalbed methane (ECBM) recovery a...

Sequestration of Carbon Dioxide in Coal with Enhanced Coalbed Methane RecoveryA Review

[1] Relative permeabilities are the key descriptors in classical formulations of multiphase flow in porous media. Experimental evidence and an analysis of pore-scale physics demonstrate conclusively that relative permeabilities are not single functions of fluid saturations and that they display strong hysteresis effects. In this paper, we evaluate the relevance of relative permeability hysteresis when modeling geological CO2 sequestration processes. Here we concentrate on CO2 injection in saline aquifers. In this setting the CO2 is the nonwetting phase, and capillary trapping of the CO2 is an essential mechanism after the injection phase during the lateral and upward migration of the CO2 plume. We demonstrate the importance of accounting for CO2 trapping in the relative permeability model for predicting the distribution and mobility of CO2 in the formation. We conclude that modeling of relative permeability hysteresis is required to assess accurately the amount of CO2 that is immobilized by capillary trapping and therefore is not available to leak. We also demonstrate how the mechanism of capillary trapping can be exploited (e.g., by controlling the injection rate or alternating water and CO2 injection) to improve the overall effectiveness of the injection project.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005WR004806

Impact of relative permeability hysteresis on geological CO2 storage

A mathematical formulation, applicable to both numerical simulation and transient well analysis that describes the flow of gas in very tight porous media and includes a dual-mechanism transport of gas is developed. Gas is assumed to be traveling under the influence of a concentration field and a pressure field. Transport through the concentration field is a Knudsen flow process and is modeled with Fick's law of diffusion. Transport through the pressure field is a laminar process and is modeled with Darcy's law (inertial/turbulent effects are ignored). The combination of these two flow mechanisms rigorously yields a composition-, pressure-, and saturation-dependent slippage factor. The pressure dependence arises from treating the gas as a real gas. The derived dynamic slippage is most applicable in reservoirs with permeabilities less than or equal to0.01 md. The results indicate that in reservoirs of this type, differences between recoveries after 10 years of production with the dynamic-slip and constant-slip approaches were as great as 10%, depending on the initial gas saturation. If an economic production rate is considered, differences as great as 30% can be expected.

Dynamic gas slippage: a unique dual-mechanism approach to the flow of gas in tight formations.

One primary goal of any enhanced recovery project is to maximize the ability of the fluids to flow through a porous medium (i.e., the reservoir). This paper discusses the effect of capillary number, a dimensionless group describing the ratio of viscous to capillary forces, on twophase (oil-water) relative permeability curves. Specifically, a series of steady-state relative permeability measurements were carried out to determine whether the capillary number causes changes in the two-phase permeabilities or whether one of its constituents, such as flow velocity, fluid viscosity, or interfacial tension (IFT), is the controlling variable.

Effect of Capillary Number and Its Constituents on Two-Phase Relative Permeability Curves

The goal of this study is to determine the effect of the capillary number on two-phase (oil-water) relative permeability curves Specifically, a series of steady-state relative permeability measurements were carried out to determine if the capillary number causes changes in the two-phase permeabilities or if any one of its constituents, such as flow velocity, fluid viscosity, or interfacial tension, are the controlling variables For the core tests, run in fired Berea sandstone, a Soltrol 170 oil-calcium chloride brine-isopropyl alcohol-glycerin system was utilized Alcohol was the interfacial tension reducer and glycerin was the wetting phase viscosifier The non-wetting phase (oil) relative permeability showed little correlation with the capillary number As the interfacial tension decreased below 20 dynes/cm, the oil permeability increased dramatically However, as the wetting phase viscosity increased, the non-wetting phase demonstrated less ability to flow For the wetting phase (water) relative permeability, the opposite capillary number effect was shown For both the tension decrease and the viscosity increase, ie, a capillary number rise, the water permeability increased, but not as much as with the oil curves No velocity effects were noted for the range studied A relative permeability model was then developed from the experimental data, based on fluidmore » saturations, interfacial tension, fluid viscosities, and the residual saturations, using regression analysis The applicability of these regression models were then tested with the aid of a two-phase reservoir simulator« less

The effect of the capillary number and its constituents on two-phase relative permeability curves

Production Analysis of Tight-Gas and Shale-Gas Reservoirs Using the Dynamic-Slippage Concept

Described in this paper are the mathematical and numerical developments for a series of finite difference models which simulate the two-phase, transient behavior of coal seam degasification wells. Included in this series are models for unstimulated, as well as hydraulically stimulated, wells. The hydraulically stimulated wells are assumed to have either a single infinite or finite conductivity vertical fracture. The natural fracture system of the coal seam, the butt and face cleat, is identified with a porous network and assigned effective porosities, nominally less than ten percent, and absolute permeabilities, generally less than 25 md with values extending into the microdarcy range. A time dependent sorption term has been included to describe the phenomenon of gas desorbing from the coal matrix to the porous network. The coal seam is then modeled with the mathematics of multiphase flow through porous media. All models described in this paper are single well, mesh centered models in radial-cylindrical coordinate geometry. The fully implicit, generalized Newton-Raphson procedure has been employed to solve the coupled, nonlinear equations generated by the models. An intensive sensitivity analysis of the models is included. All models have been verified with successful history matches against stimulated and unstimulated methane drainage wellsmore » producing from coal gas reservoirs.« less

Turgay Ertekin

Papers

Dynamic gas slippage: a unique dual-mechanism approach to the flow of gas in tight formations.

Effect of Capillary Number and Its Constituents on Two-Phase Relative Permeability Curves

The effect of the capillary number and its constituents on two-phase relative permeability curves

Production Analysis of Tight-Gas and Shale-Gas Reservoirs Using the Dynamic-Slippage Concept

Numerical simulation of the transient behavior of coal-seam degasification wells