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Accurate estimation of permeability is critical for oil and gas reservoir development and management, as it controls production rate. After assessing numerical techniques ranging from pore network modeling (PNM) to the lattice Boltzmann method (LBM), an AI-based workflow is developed for a quick and accurate estimation of the permeability of a complex carbonate rock from its X-ray micro-computed tomography (micro-CT) image. Following features engineering using both image processing and PNM, we trained and tested the workflow on thousands of segmented 3D micro-CT images using both shallow and deep learning algorithms to assess the permeability. A broad variety of supervised learning algorithms are implemented and tested, including linear regression, support vector regression, improved gradient boosting, and convolutional neural networks. Additionally, we explored a hybrid physics-driven neural network that takes into account both the X-ray micro-CT images and petrophysical properties. Finally, we found that the predicted permeability of a complex carbonate by machine learning (ML) agrees very well with that of a more computationally-intensive voxel-based direct simulation. In addition, the ML model developed here provides a substantial reduction in computation time by roughly three orders of magnitude compared to that of the LBM. This paper highlights the crucial role played by features engineering in predicting petrophysical properties by machine and deep learning. The proposed framework, integrating diverse learning algorithms, rock imaging, and modeling, has the potential to quickly and accurately estimate petrophysical properties to aid in reservoir simulation and characterization.

Accumulation of liquids in gas-condensate reservoirs may lead to a vertical flow of liquid caused by density difference in the presence of gravity. In this paper, the effect of this vertical flow on the prediction of production data has been investigated. To achieve this goal, a single-layer synthetic cylindrical reservoir is considered and, the flows are simulated with and without vertical direction grid blocks with two lean and rich fluids. The governing equations of the so-called Modified Black-Oil (MBO) model are solved in a cylinder sector using the open-source Matlab Reservoir Simulation Toolbox (MRST). When the vertical flow is taken into consideration, the results show that gravity may lead to migration of liquid condensates to lower regions and the production rates decrease as a consequence of wellbore partially blockage especially for the rich fluid. In addition, gravity may cause a non-linear effect on the flow behavior and increase in the condensates production rates. All results are also obtained for three values of critical liquid condensate saturation to show the effect of this parameter on the production. It has been shown that neglecting the vertical flow may cause significant errors in the result of production, i.e. up to 25% when the fluid is rich and the critical condensate saturation is 0.15. To generalize the effect of the reservoir thickness, dimensional analysis is carried out which yields a similarity parameter. The findings of this study can help for a better understanding of near well flow in gas-condensate reservoirs. Based on this study, in applications in which the reservoir gas is rich in condensate and the thickness of the reservoir layer or the vertical permeability is high enough, it is recommended that the gravity effect is taken into account by enough grid points in the vertical direction in each layer.

Natural gas reservoir simulation, as a physics-based numerical method, needs to be carried out with a high level of precision. If not, it may be highly misleading and cause substantial losses, poor estimation of ultimate recovery factor, and wasted effort. Although simple simulations often provide acceptable approximations, there is a continued desire to develop more sophisticated simulation strategies and techniques. Given the capabilities of Machine Learning (ML) and their general acceptance in recent decades, this chapter considers the application of these techniques to gas reservoir simulations. The aspiration ML technics should be capable of providing some improvements in terms of both accuracy and speed. The simulation of gas reservoirs (dry gas, wet gas, and retrograde gas-condensate) is introduced along with its fundamental concepts and governing equations. More specific and advanced concepts of applying ML in modern reservoir simulation models are described and justified, particularly with respect to history matching and proxy models. Reservoir simulation assisted by machine learning is becoming increasingly applied to assess suitably of reservoirs for carbon capture and sequestration associated with enhanced gas recovery. Such applications, and the ability to improve reservoir performance via production efficiency, make ML-assisted reservoir simulation a valuable approach for improving the sustainability of natural gas reservoirs. The concepts are reinforced using a case study applying two ML models providing dew point pressure predictions for gas condensate reservoirs. Banner headline Reservoir simulation methods applied to gas reservoirs are reviewed and the key influencing variables identified. Machine Learning (ML) methods can be applied in various ways to improve the performance of gas reservoir simulations, especially in respect to history matching and proxy modeling. Additionally, ML can assist the CO2 sequestration and enhanced gas recovery, well placement optimization, production optimization, estimation of gas production, dew point prediction in gas condensate reservoirs, and pressure and rate transient analysis.

Down-flush hydrodynamic movement of fluids at at transitional zones towards areas with low pressure gradients have been reported to directly influence the accurate prediction of petroleum reservoir’s production performances over time. Fluctuations in the fluid-fluid interactions and pressure changes around the reference line was the major cause for the discrepancy. In this research, a sensitivity study on the influence of hydrodynamic tilt factor h to oil, water and gas production was carried-out by means of the commercial software Eclipse Black oil simulator using the openSource Norne field data. The constant h is a function of the corrected shut-in pressure, fluid specific gravity at contact base-lines, pressure at the reference elevation and at the oil-water contact. The error in the contact depth was captured using the difference between the initial and calculated true vertical depths of the fluid’s contact zones. The obtained information was fed into the simulator to model the process dynamics. Findings revealed that the error margin for the first case h A (gas-oil contact) was insignificant. However, a mean deviation in the reservoir’s production predictions of atleast 8% for approximately a 6.5% change in the interacting fluids density was attained in-contrast to the base case.

Large investments are required for the positioning and drilling of oil and gas wells, implying that decisions related to these activities may be significantly aided by sound and proven mathematical-oriented methods. The use of intuitive engineering judgement alone cannot guarantee sustainable profitability over long periods, especially under geological (reservoir model) uncertainty. To capture significant uncertainty sources in the subsurface geology of the reservoir considered in this study, geostatistical model realisations are obtained using available information (permeabilities and porosities). We use specialised algorithms of the MATLAB Reservoir Simulation Toolbox (MRST, interfaced with PETREL™) in order to determine optimal petroleum production well locations and production rates and thus maximise the field oil recovery. The developed computational workflow has been applied to a realistic case study, for which robust optimality is demonstrated using the worst-case realisation for determining optimal well locations.

The dolostone of the Cambrian Longwangmiao Formation has been a significant gas exploration area in Sichuan Basin. In Gaoshiti-Moxi regions, a giant gas pool with thousands of billion cubic meters' reserve has been discovered. However, the origin of the reservoir and the distribution patterns are still disputed, eventually constraining the dolostone exploration of the Longwangmiao Formation. This paper focuses on the characteristics, origin, and distribution patterns of the dolostone reservoir in the Longwangmiao Formation based on: the outcrop geological survey, cores, thin-sections observation, reservoir geochemical characteristics study, and reservoir simulation experiments. As a result, two realizations were acquired: (1) The Cambrian Longwangmiao Formation could be divided into upper and lower part in Sichuan Basin. Based on the two parts of the Longwangmiao Formation, two lithofacies paleogeographic maps were generated. In addition, the carbonate slope sedimentary models were established. The grainstone shoals are mainly distributed in the shallow slope of the upper part in the Longwangmiao Formation. (2) The grainstone shoals are the developing basis of the dolostone reservoir in the Longwangmiao Formation. Moreover, the contemporaneous dissolution was a critical factor of grainstone shoal reservoir development in the Longwangmiao Formation. Controlled by the exposure surface, the dissolution vugs are not only extensively distributed, but also successively developed along the contemporaneous pore zones. Hence, the distribution patterns could be predicted. The geological understandings of the origin of dolostone reservoir in the Longwangmiao Formation show that the reservoir distributed in the areas of karstification in the Gaoshiti-Moxi regions, as well as the widespread grainstone shoals in the whole basin, are the potential exploration targets. Keywords: Sichuan Basin, Longwangmiao Formation, Carbonate slope, Dolograinstone shoal reservoir, Genesis and distribution of reservoir

Coal seams with high CO2 gas contents can be difficult to drain gas for outburst management. Coal has a high affinity for CO2 with adsorption capacities typically twice that of CH4. This paper presents an analysis of nitrogen injection into coal to enhance drainage of high CO2 gas contents. Core flooding experiments were conducted where nitrogen was injected into coal core samples from two Australian coal mining basins with initial CO2 gas contents and pressures that could be encountered during underground mining. Nitrogen effectively displaced the CO2 with mass balance analysis finding there was only approximately 6%–7% of the original CO2 gas content residual at the end of the core flood. Using a modified version of the SIMED II reservoir simulator, the core flooding experiments were history matched to determine the nitrogen and methane sorption times. It was found that a triple porosity model (a simple extension of the Warren and Root dual porosity model) was required to accurately describe the core flood observations. The estimated model properties were then used in reservoir simulation studies comparing enhanced drainage with conventional drainage with underground in seam boreholes. For the cases considered, underground in seam boreholes were found to provide shorter drainage lead times than enhanced drainage to meet a safe gas content for outburst management. Keywords: Gas drainage, High CO2, ECBM, Reservoir simulation

This study aims to show that utilization of captured carbon dioxide from the power and industrial sectors for enhanced oil recovery (CO2-EOR) can be a key means of supporting global climate change ambitions. Normative business scenarios are developed to support the economic evaluation of CO2-EOR under different contexts. A reservoir simulation model provides a realistic basis for economic input parameters and has been developed to support the determination of scenarios in which energy price variations, production tax rates and carbon dioxide prices will make CO2-EOR economically viable. The scenarios are used to test CO2-EOR project economics under a variety of oil prices. Projects are shown to be resilient and profitable investments, though arguably not all projects may lead to long-term CO2 storage. Through the scenarios it is shown that stakeholders, particularly the global citizen, have the ability to significantly impact CO2-EOR project investments. Keywords: Climate change, Carbon capture and storage, Energy scenario, Energy strategy

In this chapter, the embedded discrete fracture model (EDFM) is further developed to simulate fractures in geologically complex reservoirs represented by corner-point grids. Corner-point grids have the capability to model complex geological features, such as faults and irregular reservoir boundaries. As an industry-standard, they are widely used in the simulation of different types of reservoirs, including both conventional and unconventional reservoirs. It is necessary to effectively simulate natural and hydraulic fractures in such reservoirs. As a result of the high flexibility in the definition of corner-point grids, there are difficulties in terms of geometrical calculations for the application of the EDFM in corner-point grids. Geometrical algorithms are presented in this chapter to solve these challenges. Transmissibility factor formulations are also extended to handle different scenarios of connections between fracture segments. Several case studies are presented to demonstrate the accuracy and effectiveness of the EDFM for modeling complex fractures in field-scale reservoir simulation studies with corner-point grids.

In this chapter, a two-step methodology is introduced to investigate the feasibility of using three different miscible gases in EOR from unconventional reservoirs: CO2, lean gases, and rich gases. The integrated procedure presented in this chapter includes reservoir simulation and history matching of some miscible-gases used in EOR projects. The objective is to provide a proper evaluation of the molecular diffusivity of such gases in the field level of unconventional liquid-rich reservoirs (ULR). First, numerical simulation methods of compositional models are introduced, which are incorporated into the local grid refinement of hydraulic fractures. This chapter also presents an analysis of diffusion effects using an LS-LR-DK (logarithmically spaced, locally refined, and dual permeability) model. Second, the history matching process is conducted by incorporating different molar-diffusivity rates to find the correct diffusivity level in the field scale by matching the simulation models with the EOR pilot tests conducted in the Bakken formation of North Dakota, Montana, and South Saskatchewan. The main purpose of this chapter is to provide selection criteria for the proper type of miscible gases in terms of EOR in ULR.

This chapter presents the effect of nanopore confinement on phase behavior and pressure-volume-temperature (PVT) properties of unconventional reservoir fluids. The impacts of pore confinement on the production performance of shale wells during the primary production stage are also discussed. Moreover, the positive and negative impacts of nanopore confinement on different enhanced oil recovery methods are extensively explained. This chapter presents how pore confinement should be implemented in the reservoir simulation to accurately mimic the performance of miscible gas injection in unconventional reservoirs.

Reservoir simulation on Darcy’s scale provides an upscale view of the various processes that are involved in engineering applications. This point of view facilitates greatly the description and the simulation on this relatively direct level. Several algorithms and corresponding solvers have been proposed in the petroleum industry to model and calculate phenomena seen at Darcy’s scale, and plenty of software have been developed using these solvers to help process managing and production estimations. In this chapter, we will go over the notations and model equations of finite element methods (FEMs), first, that are well accepted in Darcy’s scale reservoir simulation, and we will show the equivalence between FEMs and finite-difference methods (FDMs).

This chapter presents discretization of 1-D, 2-D, and 3-D reservoirs using block-centered grids in Cartesian and radial-cylindrical coordinate systems. As the name implies, the gridblock dimensions are selected first, followed by the placement of points in central locations of the blocks. In this, the distance between block boundaries is the defining variable in space. In contrast, the gridpoints (or nodes) are selected first in the point-distributed grid, which is discussed in Chapter 5 . Chapter 2 introduced the terminology for reservoir discretization into blocks. This chapter describes the construction of a block-centered grid for a reservoir and the relationships between block sizes, block boundaries, and distances between points representing blocks. The resulting gridblocks can be classified into interior and boundary gridblocks. Chapter 2 also derived the flow equations for interior gridblocks. However, the boundary gridblocks are subject to boundary conditions and thus require special treatment. This chapter presents the treatment of various boundary conditions and introduces a general flow equation that is applicable for interior blocks and boundary blocks. This chapter also presents the equations for directional transmissibilities in both Cartesian and radial-cylindrical coordinate systems and discusses the use of symmetry in reservoir simulation.

Analyzing and predicting the production behavior of CBM reservoirs is complex and challenging. The complex storage and transport mechanisms involved in CBM production can be best represented by the numerical models. Numerical models can accurately and simultaneously account for gas desorption, relative permeability, permeability, and porosity change caused by the coal compressibility, permeability changes due to matrix shrinkage, well-to-well interference, and operating procedures. However, because of extreme complication of physical and thermodynamic phenomena that occur during CBM/ECBM recovery process, the existing models do not adequately model the mechanism of gas recovery from coal. Reservoir simulation is also a cost-effective way to assess the sensitivity of the reservoir performance to uncertainties in measured data.

Phase equilibrium calculation, also known as flash calculation, has been extensively applied in petroleum engineering, not only as a standalone application for a separation process but also as an integral component of compositional reservoir simulation. Previous research devoted numerous efforts to improve the accuracy of phase equilibrium calculations, which place more importance on safety than speed. However, the equation-of-state-based flash calculation consumes an enormous amount of computational time in compositional simulation and thus becomes a bottleneck to the broad application of compositional simulators. Therefore it is of vital importance to accelerate flash calculation without much compromise in accuracy and reliability, turning it into an active research topic in the past two decades. With the rapid development of computational techniques, machine learning brings another wave of technology innovation. As a subfield of machine learning the deep neural network becomes a promising computational technique due to its great capacity to deal with complicated nonlinear functions, and it thus attracts increasing attention from academia and industry. In this chapter the acceleration of flash calculation is investigated. Starting from using experimental data as input, we establish a fully connected deep neural network to represent the underneath thermodynamic correlations between the selected input and output parameters. Due to the limitation of collecting experimental data especially due to the high cost, we are turning to establish a deep neural network model to approximate the iterative flash calculation at given moles, volume, and temperature, known as the flash at given moles, volume and temperature (NVT flash). A dynamic model designed for NVT flash problems is iteratively solved to generate data for training the neural network. In order to test the model’s capacity to handle complex fluid mixtures, three real reservoir fluids are investigated, including one Bakken oil and two Eagle Ford oils. Compared to previous studies that follow the conventional flash framework in which stability testing precedes phase splitting calculation, we incorporate stability test and phase split calculation together and accomplish two steps by a single deep learning model. The trained model is able to identify the single vapor, single liquid, and vapor–liquid states under the subcritical region of the hydrocarbon mixtures. A number of examples are presented to show the accuracy and efficiency of the proposed deep neural network. It is found that the trained model makes predictions much faster than the iterative NVT flash calculation for the given cases and meanwhile preserves high accuracy. Network optimization is performed by investigating the performance of different input and output parameters, as well as tuning of hyperparameters.

This chapter discusses the viability of air injection for conventional reservoirs as an enhanced oil recovery (EOR) technology by discussing its EOR mechanisms, major impact factors, and successful projects. Then, the viability and feasibility of its application for EOR in unconventional reservoirs are presented. Some reservoir simulation study results are presented to validate the observations. This discussion of viability is only from a technical perspective and does not consider economics.

Wells in reservoir simulation are the most astute form of discontinuity. As such, the difficulties encountered due to boundary conditions are accentuated by the presence of wells. Yet, wells are paramount to reservoir evaluation because of the fact that engineering is all about optimizing well performance. In general, the contribution of any reservoir block penetrated by a well to the well flow rate is independent of the flow equation for that block. Such contribution has to be estimated separately from and then substituted into the flow equation for the wellblock. Fluid flow toward a well in a wellblock is radial regardless of the dimensionality of the flow problem. A well is modeled as a line source/sink term. In this chapter, the emphasis in 1-D and 2-D flow problems is on the estimation of the well geometric factor, while in 3-D flow problems, the focus is on the distribution of the well rate among the different blocks that are penetrated by the well. The estimation of the wellblock geometric factor is presented for a well hosted by one block and falling inside block boundaries and a well hosted by one block and falling on one or two of block boundaries (in 1-D and 2-D flow) that are reservoir boundaries. We present the production rate equation for a wellblock and the equations necessary for the estimation of the production rate or flowing bottom-hole pressure (FBHP) for wells operating under different conditions, which include (1) a shut-in well, (2) a specified well production rate, (3) a specified well pressure gradient, and (4) a specified well FBHP.

Discretization process creates inherent challenges involving proper representation of natural processes. The problem is accentuated by boundaries, which create discontinuities—an absurd condition for natural systems. Historically, the petroleum engineers have identified these problems and have attempted to address many problems that emerge from discretization and boundary conditions, which must be addressed separately. Few, however, have recognized that the engineering approach keeps the process transparent and enables modelers to remedy with physically realistic solutions. This chapter presents discretization of 1-D, 2-D, and 3-D reservoirs using point-distributed grids in Cartesian and radial-cylindrical coordinate systems. This chapter describes the construction of a point-distributed grid for a reservoir and the relationships between the distances separating gridpoints, block boundaries, and sizes of the blocks represented by the gridpoints. The resulting gridpoints can be classified into interior and boundary gridpoints. While Chapter 2 derives the flow equations for interior gridpoints, the boundary gridpoints are subject to boundary conditions and thus require special treatment. This chapter presents the treatment of various boundary conditions and introduces a general flow equation that is applicable to interior gridpoints and boundary gridpoints. This chapter also presents the equations for directional transmissibilities in both Cartesian and radial-cylindrical coordinate systems and discusses the use of symmetry in reservoir simulation.

Physical phenomena can be modeled at varying degrees of complexity and at different scales. Multiscale modeling and computation provides a framework for constructing mathematical and computational models of such phenomena, by examining the connection between models at different scales, based on fundamental principles, and based on mathematical theory of approximation. Recently, mesoscopic algorithms have been proposed and widely accepted in petroleum industry and lattice Boltzmann method (LBM) is the most famous one. The word mesoscopic is used to describe the flow property with regarding to certain Knudsen number range and the capability of capturing both macroscopic phenomena and microscopic interactions. LBM is proved to have super parallelization property and easy to implement using fully explicit scheme. Complex boundary can be treated well in LBM and numerous mechanisms can be coupled easily. Meanwhile, generalized multiscale finite element method has also been developed with the usage of certain upscaling technique such as proper orthogonal decomposition. In this chapter, we will start from the concepts and properties of upscaling techniques and then step into the application on discretized numerical methods. Multipoint flux approximation methods are also an option to conclude multiscale properties in one scheme. Finally, LBM is presented with rigorous derivations and modified schemes for specific engineering cases are presented to show the coupling with various mechanisms.

Low-salinity or controlled salinity waterflooding (LSWF) is a promising enhanced oil recovery (EOR) technique. In simulations of this process, numerical dispersion smears saturation fronts, causing errors in the results. The objective of this work is to control these effects in LSWF simulation. We examine the impact of numerical dispersion on simulated LSWF performance. The low-salinity (LS) front is smeared even at unfeasibly fine grids. The velocities of the water fronts are altered. A numerical mixed zone forms around the interface between the injected and resident brines. This mimics a typical physical mixing effect. In reservoir simulation, threshold salinities are defined where the low salinity effect (LSE) is first encountered. It has been suggested that numerical dispersion effects can be corrected by imposing effective thresholds. We demonstrate that existing methods to evaluate these effective salinities do not accurately predict the salt front movement especially when dispersion is significant. We propose a simple simulation-based approach to evaluate the effective salinities based on the conservation of volumes of the resident and injected brines in the reference and upscaled solutions. After comparing analytical and corrected coarse-grid solutions in one-dimension, the effectiveness of the approach is demonstrated in multi-dimensional systems. A method is proposed to control the numerical mixed zone to replicate a physical longitudinal mixing effect. This method is demonstrated in one-dimension and does not require a fine-grid numerical solution as a benchmark. We investigate the effects of effective thresholds on the modeled transverse mixing or dispersion. A method to model transverse dispersion in simulations with an effective longitudinal component is suggested. This method is extended to the explicit modeling of physical dispersion in systems with transverse flows. We can now simply evaluate the effective salinities for a simulation grid; and control its numerical dispersion effects to representative physical mixing or dispersion.

Using the In Salah CO2 storage case study, this study demonstrates how reservoir simulation history-matching and pressure analysis can be used to improve conformance assurance. By adopting a holistic approach to reservoir simulation and history matching, in conjunction with the injection pressure analysis and use of microseismic monitoring data, an improved understanding of the injection processes at the In Salah storage site was gained, revealing distinctively different responses to CO2 injection at each of the three injection wells. It has been shown that injection well performance at wells KB-501 and KB-503 was characterised by periods of matrix and fracture flow, the latter being due to shear reactivation of existing fractures in the vicinity of the wellbore. In contrast, the analysis at KB-502 revealed that CO2 injection has resulted in fracture reactivation in both shear and tensile modes with propagation both laterally and vertically. The findings of this study have shown that the injection-induced microseismic events recorded close to the KB-502 well is mainly caused by injecting CO2 into a 4-kilometer long fracture-zone intersecting the borehole. This fracture zone experienced tensile opening of fractures during injection and then subsequent partial closure after the injection was suspended. It is furthermore clear that the rather unique combination of microseismic and InSAR monitoring data and reservoir history matching around the injection well KB-502 provide highly valuable insights into injection-induced seismicity and fracture flow behaviour for CO2 storage projects. Episodes of flow in natural fractures can be separated from flow in induced fractures and the need for a dynamic, stress-dependent, permeability variable have been demonstrated.

Publisher Summary This chapter deals with the multiphase fluid flow equations. This chapter presents a brief discussion of the literature that contains many derivations of the equations describing fluid flow in porous media. It begins by introducing the continuity equation, and then presents some important sets of fluid flow equations that are commonly used to model hydrocarbon reservoirs. Subsequently, the continuity equation can be derived by considering the flow of fluid into and out of a single reservoir gridblock. Moreover, the basic conservation laws of reservoir simulation are the conservation of mass, energy, and momentum. Mass balance in a representative elementary volume (REV) or gridblock is achieved by equating the accumulation of mass in the gridblock with the difference between the mass leaving the gridblock and the mass entering the gridblock. Furthermore, momentum conservation is modeled using Darcy's Law. This assumption means that the model cannot accurately represent turbulent flow in a reservoir or near the wellbore. Finally, some well models allow the user to model turbulent flow, especially for high flow rate gas wells. Turbulent flow models relate pressure change to a linear flow term, as in Darcy's Law, plus a term that is quadratic in flow rate.

We illustrate elements of a traditional model study to demonstrate how to prepare input data for the reservoir simulation process, and to give the reader experience applying a simulator to a realistic model study. A deterministic reservoir forecasting process is used in a traditional model study. It is an iterative process that makes it possible to integrate reservoir geoscience and engineering data. The deterministic reservoir forecasting process includes history matching, forecasting, and sensitivity analysis. The process is illustrated by studying aquifer influx into a dipping, undersaturated oil reservoir.

Hydraulic fracturing has become the most important technology in the development of shale gas and tight gas/oil reservoirs. The application of hydraulic fracturing is also essential for hot dry rock geothermal systems. It is important to understand how hydraulic fractures propagate in the formation and the effects of reservoirs heterogeneities on fracture propagation. In this chapter, a fully hydromechanical coupled model of hydraulic fracture propagation is presented, based on the extended finite-element method. Furthermore, its extension to reservoir simulation coupling with embedded discrete fracture model has also been developed and discussed.

Natural fractures and their interactions with the induced hydraulic fractures play a critical role in the final induced fracture path as the created combined natural fracture–hydraulic fracture network is complex and will represent more realistically the production forecasting through reservoir simulation in shale reservoirs that correspondingly affects stimulated reservoir volume and the production efficiency. Most current commercial reservoir simulators incorporate predetermined predicted propagation path and fracture network created in these reservoirs making the production forecasting unreliable as they will not reflect any of the complexities of the tight reservoirs resulting in misleading production forecasting, recovery factors, and development plans. In this chapter, a coupled model accounting for several factors in the fracturing of shale reservoirs is presented. The fracture modeling results obtained were used in a case study conducted in the oil window of a well pad in the Eagle Ford reservoir. After the field case is implemented for fracturing, reservoir simulation has been conducted to perform a history match using the first 4 years' production data with the introduced new model. Due to the significant drop in the production rates during the first 2 years, a refracturing operation has also been simulated to determine how much more oil and gas can be produced from this well pad if the wells are refractured. The coupled model has then been compared with a commercial reservoir simulator incorporating a predetermined fracturing path to emphasize the differences of incorporating complex fracture network. The results of our comparative study indicated that the modified zipper pattern has provided the optimum recovery in the study well pad and using predefined fractures underestimates oil production, whereas the coupled approach introduced in this chapter provides more accurate production prediction for both fractured and refractured wells.

National techno-economic pathways to reduce carbon emissions are required for the United Kingdom to meet its decarbonisation obligations as mandated by the Paris Agreement. Analysis using energy systems models indicate that carbon capture and storage is a key technology for the UK to achieve its mitigation targets at lowest cost. There is potential to significantly improve upon the representation of the CO2 storage systems used in these models, but sensitivities of a given reservoir system to future development pathways must be evaluated. To investigate this we generate a range of numerical simulations of CO2 injection into the Bunter Sandstone of the UK Southern North Sea, considered to be one of the most important regional aquifers for CO2 storage. The scenarios investigate the sensitivity of CO2 storage to characteristics of regional development including number of injection sites and target rates of CO2 injection. This enables an evaluation of the impact of a range of deployment possibilities reflecting the range of scenarios that may be explored in an energy system analysis. The results show that limitations in achieving target injection rates are encountered at rates greater than 2 MtCO2/year-site due to local pressure buildup. The areal location of injection sites has minimal impact on the results because the Bunter Sandstone model has good regional connectivity. Rather, the depth of the site is the most important factor controlling limits on CO2 injection due to the relationship between the limiting pressure and the lithostatic pressure gradient. The potential for model simplification is explored by comparison of reservoir simulation with analytical models of average reservoir pressure and near-site pressure. The numerical simulations match average pressure buildup estimated with the “closed-box” analytical model of Zhou et al. (2008) over a 50 year injection period. The pressure buildup at individual sites is estimated using the Mathias et al. (2011) formulation and compared to the simulation response. Discrepancies in the match are mostly due to the interaction of signals from multiple injection sites and heterogeneous permeability in the numerical simulations. These issues should be the focus of further development of simplified models for CO2 storage in an energy systems analysis framework.

Finite difference methods are developed to model lineal and cylindrical displacements of fluid in cores, with and without transient mudcake buildup. The importance of matching conditions between different flow regions is emphasized as is the manner they are implemented numerically. Detailed finite difference equations and illustrative calculations are given.

The appearance of geological patterns bearing somewhat random features, or complicated, but periodic, well-defined physical structures, very often raises questions among flow modelers regarding possibilities for quantitative flow simulation. The reservoir description process—the ability to describe geological structures accurately—is certainly not useful unless the ability to simulate flows is equally well developed. This chapter presents analytical methods drawing on the literature from other areas of continuum mechanics. The best known attempts at simple continuum models are the dual porosity approaches for naturally fractured reservoirs. Mathematical geostatisticians often develop their reservoir models by minimizing suitably defined error functions that are consistent with measured statistics, subject to auxiliary boundary constraints. These functions are typically positive definite, so that a solution to the minimization process exists. The differential equation methods used in modeling and the optimization approaches used in geostatistics are closely related. The similarities are explored in variational calculus, a well-known mathematical specialty that relates differential equations to global minimization problems.

To study the complex characteristics of fracture-vug carbonate reservoirs of various types and scales, the representative elementary volume (REV) has been researched for the first time, during which three principles (REV existence, correlation of occurrence environment, and technical feasibility) for medium selection and the concept of “multiple REV” were proposed, the types of fracture-vug reservoir were divided, the idea that such a reservoir is composed of equivalent continuum and discrete medium was put forward and equivalent continuum and discrete medium systems were established. Fluid flow patterns and features were studied in reservoirs with vugs, fractures, and solution pores as reservoir space, respectively. A numerical coupling model of reservoir simulation was established, which focuses on two-phase flow in caves, coupling calculation between caves and porous medium and finite volume numerical simulation, and provides a theoretical basis for numerical simulation of fluid flow law in different fracture-vug systems, and based on which the core simulator program has been developed. Using dual-medium numerical simulation theory, and considering the flow features in various media and calculation accuracy, simulation methods for caverns, collapsed caves, network fractures, and solution pores, etc. have been developed, and the adaptive implicit numerical calculation method has been formed. Based on previous studies on the Tahe fracture-vug reservoir and its development using the numerical simulation technology, the waterflooding mechanism and residual oil distribution in fracture-vug reservoirs at single-well and multiwell scales have been simulated. Based on these simulations, waterflooding practice has been performed and has delivered good economic benefits.

This chapter introduces the ideas underlying quantitative formation invasion modeling but restricted to isotropic Darcy flows dealing with piston-like, slug, or plug-like displacements. Miscible and immiscible multiphase flows are developed, and their limitations are explained in the chapter. The chapter presents single-phase flow invasion into rocks, assuming that the influence of mudcake is negligible. The formulations for such problems are simple. They highlight the basic differences between the reservoir flow problems covered in undergraduate curricula and the Lagrangian models needed to track moving fronts. The flows with nontrivial external and internal moving boundaries are discussed. The lineal cake buildup on the filter paper is considered and then the plug flow of two dissimilar liquids in a linear core without mudcake is examined. The chapter also introduces dynamic filtration analytically and numerically, using recently developed methods in borehole and pipeline flow modeling.

This chapter discusses the mechanics of formation invasion and various physical mechanisms that occur simultaneously, with a view toward quantitatively modeling these phenomena. The chapter emphasizes the fact that all of the gross fluid motions within the formation pore spaces, whether they are miscible, immiscible, compressible, or simple, single-phase, incompressible flows, acting individually or in combination, are unaffected by electrical or nuclear properties. Measured electrical, electromagnetic, and nuclear properties obtained by logging tools depend on the exact distribution of fluids, whereas their time-dependent changes depend on different space and time scales that characterize each fluid component. A detailed fluid dynamics analysis takes precedence in simulation because good electrical modeling is premised on the use of correct fluid distributions. True reservoir planning and economic modeling cannot take place until the uncertainty in the measured parameters can be understood. Thus reservoir flow modeling plays crucial roles at two scales—the production level, which is traditionally the domain of reservoir engineers, and the logging tool level. Petroleum engineers use partial differential equation models to simulate reservoir flows, interpret well tests, characterize formation heterogeneities, and assist in infill drilling planning and secondary recovery. Many hierarchies for fluid flow modeling exist, ranging from simple single-phase oil alone or gas only flows to multiphase descriptions, encompassing both miscible and immiscible limits, to black oil and compositional models.

Carbon capture and storage (CCS) in subsurface reservoirs has been identified as a potentially cost-effective way to reduce CO 2 emissions to the atmosphere. Global emissions reductions on the gigatonne scale using CCS will require regional or basin-scale deployment of CO 2 storage in saline aquifers. Thus the evaluation of both the dynamic and ultimate CO 2 storage capacity of formations is important for policy makers to determine the viability of CCS as a pillar of the greenhouse gas mitigation strategy in a particular region. We use a reservoir simulation model representing the large-scale Bunter Sandstone in the UK Southern North Sea to evaluate the dynamics and sensitivities of regional CO 2 plume transport and storage. At the basin-scale, we predict hydrogeological changes in the storage reservoir in response to multiple regional carbon sequestration development scenarios. We test the sensitivity of injection capacity to a range of target CO 2 injection rates and fluctuations in CO 2 supply. Model sensitivities varying the target injection rates indicate that in the absence of pressure management up to 3.7 Gt of CO 2 can be stored in the Bunter region over 50 years given the pressure constraints set to avoid fracturing the formation. Long-term (approx. 1000 years), our results show that up to 16 Gt of CO 2 can be stored in the Bunter region without pressure management. With pressure management, the estimate rises to 32 Gt. However, consideration must be given to the additional operational and economic requirements of pressure management using brine production.

This paper presents an integrated techno-economic framework for the optimal design and operation of a shale gas supply chain network. A 3D coupled compositional reservoir model is constructed utilizing CMG’s software suites to simulate realistic drilling, completion, stimulation (DCS) and well-pad production processes, for a specified supply chain network. Several well pad design configurations and operations are selected for shale well development, and re-stimulation and/or stimulation operations are compared for implementation in different well pad designs. Reservoir simulation output data are incorporated into a mixed integer linear programming (MILP) model developed in GAMS optimization software. The Strategic MILP model recommends an optimal drilling strategy, schedule for product transportation, and supply chain network configuration that optimizes after-tax profit. Additionally, the management of freshwater and the recycle of wastewater is developed incorporating the spatial variation of total dissolved solids (TDS) composition from multi-well shale pads. The results show the significant influence of reservoir heterogeneity and implemented DCS strategies, on the profitability of the case study shale gas assets.

Injecting CO 2 in to the subsurface for safe storage of CO 2 the pressure propagates far away from the injection point and this can be a potential problem if the overpressure extents to neighbouring subsurface activities or potential leakage pathways. For structural closure trap configurations the CO 2 plume is captured within the local structural closure but the pressure footprint is on a more regional scale. This rise the question on, how large the storage complex needs to be for any individual storage operations and how large an area monitoring activities have to cover. The EC CCS guidance document addresses the issues with statements on competitions between subsurface operations but returns no absolute values. Pressure modelling of CO 2 injection process with state of the art reservoir simulation tools is challenges by use of realistic model boundary conditions in order to model a realistic pressure level. Combined use of models on a site scale and on a regional scale can instruct how boundary conditions are set-up for a site scale model. Pressure management through pressure release wells could be an option to mitigate undesirable over-pressure developments. For local structural closures the pressure release wells can be placed outside the closure hereby mitigate the overpressure without introducing a potential leakage by drilling inside the trap. The paper addresses the issue of selecting model boundary conditions and modelling mitigation of pressure development by use of a large regional model with local structural traps in the Bunter Sandstone Formation in the UK Southern North Sea.

This completely revised chapter (to the first edition) develops the general equations needed to model single-phase liquid and gas flows from anisotropic, heterogeneous, layered reservoirs produced by systems of vertical, deviated, horizontal and multilateral wells. A new flow simulator is described via menus and detailed calculations for several complicated flow scenarios, plus three-dimensional color graphics for calculated pressure fields, are offered. Effects include changing the roles of pressure and rate constraints during simulation, shutting laterals during simulation, extending laterals and drilling new wells during simulation, effects of neighboring wells, effects of drive mechanisms, and so on.

Transient compressible numerical flow simulation is introduced and methods are developed to integrate the three-dimensional equations (in general curvilinear coordinates). Pressure and streamfunction solutions are discussed. Examples are given, e.g., pressure drawdown and buildup, wells in “Texas shaped reservoir,” application of “alternating-direction-implicit (ADI) methods,” and so on. An example approximation factorization method, popular in the literature, is summarized.

In this investigation, the Warren and Root model proposed for the simulation of naturally fractured reservoir was improved. A reservoir simulation approach was used to develop a 2D model of a synthetic oil reservoir. Main rock properties of each gridblock were defined for two different types of gridblocks called matrix and fracture gridblocks. These two gridblocks were different in porosity and permeability values which were higher for fracture gridblocks compared to the matrix gridblocks. This model was solved using the implicit finite difference method. Results showed an improvement in the Warren and Root model especially in region 2 of the semilog plot of pressure drop versus time, which indicated a linear transition zone with no inflection point as predicted by other investigators. Effects of fracture spacing, fracture permeability, fracture porosity, matrix permeability and matrix porosity on the behavior of a typical naturally fractured reservoir were also presented.

An important part of the work of a reservoir engineer is in the monitoring and management of producing fields. In this chapter we outline the key elements of this. The three elements in which the reservoir engineer is involved are reservoir monitoring, history matching, and consideration and implementation of further development and operating conditions. Monitoring of flow rates, reservoir pressure, and phase saturations including the use of tracers and four-dimensional (4D) seismic are discussed. History matching of reservoir simulation models to new data is examined.