Petroleum Reservoir Engineering Research Articles

Discontinuous approximation of flow in porous media with adsorption

AbstractPolymer flooding in petroleum reservoir engineering can be described by a Brinkman‐based model of flow in porous media coupled to a non‐strictly hyperbolic system of conservation laws for multiple components that form the aqueous phase. The coupled flow‐transport problem is discretized by coupling an H(div)‐conforming discontinuous Galerkin (DG) method for the Brinkman flow problem with a classical DG method for the transport equations.

Stochastic hydrogeology's biggest hurdles analyzed and its big blind spot

Abstract. This paper considers questions related to the adoption of stochastic methods in hydrogeology. It looks at factors affecting the adoption of stochastic methods including environmental regulations, financial incentives, higher education, and the collective feedback loop involving these factors. We begin by evaluating two previous paper series appearing in the stochastic hydrogeology literature, one in 2004 and one in 2016, and identifying the current thinking on the topic, including the perceived data needs of stochastic methods, the attitude in regulations and the court system regarding stochastic methods, education of the workforce, and the availability of software tools needed for implementing stochastic methods in practice. Comparing the state of adoption in hydrogeology to petroleum reservoir engineering allowed us to identify quantitative metrics on which to base our analysis. For impediments to the adoption of stochastic hydrology, we identified external factors as well as self-inflicted wounds. What emerges is a picture much broader than current views. Financial incentives and regulations play a major role in stalling adoption. Stochastic hydrology's blind spot is in confusing between uncertainty with risk and ignoring uncertainty. We show that stochastic hydrogeology comfortably focused on risk while ignoring uncertainty, to its own detriment and to the detriment of its potential clients. The imbalance between the treatment on risk on one hand and uncertainty on the other is shown to be common to multiple disciplines in hydrology that interface with risk and uncertainty.

Coupling of Discontinuous Galerkin Schemes for Viscous Flow in Porous Media with Adsorption

Polymer flooding is an important stage of enhanced oil recovery in petroleum reservoir engineering. A model of this process is based on the study of multicomponent viscous flow in porous media with adsorption. This model can be expressed as a Brinkman-based model of flow in porous media coupled to a nonstrictly hyperbolic system of conservation laws for multiple components (water and polymers) that form the aqueous phase. The discretization proposed for this coupled flow-transport problem combines an ${H}({div})$-conforming discontinuous Galerkin (DG) method for the Brinkman flow problem with a classical DG method for the transport equations. The DG formulation of the transport problem is based on discontinuous numerical fluxes. An invariant region property is proved under the (mild) assumption that the underlying mesh is a B-triangulation [B. Cockburn, S. Hou, and C.-W. Shu, Math. Comp., 54 (1990), pp. 545--581]. This property states that only physically relevant (bounded and nonnegative) saturation and ...

Upscaling relative phase permeability for superelement modeling of petroleum reservoir engineering

A technique for locally rescaling (upscaling) the functions of the relative phase permeability (RPP) has been developed, which minimizes the error in the approximating the phase filtration rates for the superelement modeling of waterflooding a layered heterogeneous oil reservoir. The RPP is locally upscaled for each superelement based on the solution of two-dimensional two-phase filtration problems on a refined computational grid. Modified RPP functions (MFRPPs) are represented in the parametric form; i.e., the values of the parameters are sought when solving the problem of minimizing the deviations of the averaged and approximated phase velocities at the sites corresponding to the faces of the superelement. The efficiency of applying MFRPP to superelement modeling is illustrated by an example of a model reservoir region where oil is extracted using injection and production wells and by an example of waterflooding at a real oilfield.

Simulation of incompressible two-phase flow in porous media with large timesteps

Multiphase flow in porous media occurs in several disciplines including petroleum reservoir engineering, petroleum systems' analysis, and CO2 sequestration. While simulations often use a fully implicit discretization to increase the time step size, restrictions on the time step often exist due to non-convergence of the nonlinear solver (e.g. Newton's method). Here this problem is addressed for the Buckley–Leverett equations, which model incompressible, immiscible, two-phase flow with no capillary potential. The equations are recast as a gradient flow using the phase-field method, and a convex energy splitting scheme is applied to enable large timesteps, even for high degrees of heterogeneity in permeability and viscosity. By using the phase-field formulation as a homotopy map, the underlying hyperbolic flow equations can be solved with large timesteps. For a heterogeneous test problem, the new homotopy method allows the timestep to be increased by more than six orders of magnitude relative to the unmodified equations while maintaining convergence.

Constructing a discrete fracture network constrained by seismic inversion data

ABSTRACTRock fractures are of great practical importance to petroleum reservoir engineering because they provide pathways for fluid flow, especially in reservoirs with low matrix permeability, where they constitute the primary flow conduits. Understanding the spatial distribution of natural fracture networks is thus key to optimising production. The impact of fracture systems on fluid flow patterns can be predicted using discrete fracture network models, which allow not only the 6 independent components of the second‐rank permeability tensor to be estimated, but also the 21 independent components of the fully anisotropic fourth‐rank elastic stiffness tensor, from which the elastic and seismic properties of the fractured rock medium can be predicted. As they are stochastically generated, discrete fracture network realisations are inherently non‐unique. It is thus important to constrain their construction, so as to reduce their range of variability and, hence, the uncertainty of fractured rock properties derived from them. This paper presents the underlying theory and implementation of a method for constructing a geologically realistic discrete fracture network, constrained by seismic amplitude variation with offset and azimuth data. Several different formulations are described, depending on the type of seismic data and prior geologic information available, and the relative strengths and weaknesses of each approach are compared. Potential applications of the method are numerous, including the prediction of fluid flow, elastic and seismic properties of fractured reservoirs, model‐based inversion of seismic amplitude variation with offset and azimuth data, and the optimal placement and orientation of infill wells to maximise production.

About this title ‐ Geomechanics and Geology

Geomechanics investigates the origin, magnitude and deformational consequences of stresses in the crust. In recent years awareness of geomechanical processes has been heightened by societal debates on fracking, human-induced seismicity, natural geohazards and safety issues with respect to petroleum exploration drilling, carbon sequestration and radioactive waste disposal. This volume explores the common ground linking geomechanics with inter alia economic and petroleum geology, structural geology, petrophysics, seismology, geotechnics, reservoir engineering and production technology. Geomechanics is a rapidly developing field that brings together a broad range of subsurface professionals seeking to use their expertise to solve current challenges in applied and fundamental geoscience. A rich diversity of case studies herein showcase applications of geomechanics to hydrocarbon exploration and field development, natural and artificial geohazards, reservoir stimulation, contemporary tectonics and subsurface fluid flow. These papers provide a representative snapshot of the exciting state of geomechanics and establish it firmly as a flourishing subdiscipline of geology that merits broadest exposure across the academic and corporate geosciences.

Correlative multiple porosimetries for reservoir sandstones with adoption of a new reference-sample-guided computed-tomographic method

One of the main interests in petroleum geology and reservoir engineering is to quantify the porosity of reservoir beds as accurately as possible. A variety of direct measurements, including methods of mercury intrusion, helium injection and petrographic image analysis, have been developed; however, their application frequently yields equivocal results because these methods are different in theoretical bases, means of measurement, and causes of measurement errors. Here, we present a set of porosities measured in Berea Sandstone samples by the multiple methods, in particular with adoption of a new method using computed tomography and reference samples. The multiple porosimetric data show a marked correlativeness among different methods, suggesting that these methods are compatible with each other. The new method of reference-sample-guided computed tomography is more effective than the previous methods when the accompanied merits such as experimental conveniences are taken into account.

EOR-For-Shale Ideas to Boost Output Gain Traction

Low oil prices may not be the biggest threat to the long-term sustainability of the North American shale business. Some are more concerned about the low recovery rates of horizontal shale wells, estimated to be about 7% on average— far short of the 40% achieved through primary and secondary (waterflooding) production in conventional reservoirs. Refracturing has been touted as the next big thing to improve ultimate recovery, but such operations remain relatively expensive and may only temporarily reset production to initial rates once or twice in a well’s life. To see long-term results and a doubling or tripling of current recovery rates, a number of experts say enhanced oil recovery (EOR) technologies must be developed to work in tight shale reservoirs. And due to persistently low natural gas prices, current efforts appear to be exclusively focused on oil and condensate producing wells. It is early days for this area of EOR research. There is no consensus on which approaches will work best, how much they may cost, what the most pressing challenges are, or exactly when an EOR operation should begin. “Our understanding is really small,” said Todd Hoffman, an assistant professor of petroleum engineering at Montana Tech University. “We’re coming from the conventional world where ‘this’ is how we did EOR and we may just have to throw all that out.” Hoffman is one of several researchers trying to figure out how EOR methodologies can be adapted or reinvented for the oil-rich shale fields of North Dakota, Texas, and Canada. One of the most popular ideas being studied is a huff-and-puff approach that uses a single horizontal well to alternate between producing oil and injecting natural gas or CO2 to re-pressurize the reservoir and displace oil. Another idea is to apply continuous injections into one well and use an offset well as the producer. Others are looking into flooding the wells with surfactants and possibly acid to stimulate production. In May, EOG Resources laid claim to the first economic demonstration of an injection-based EOR technology for tight oil in the US. The company said the development may have long-term production benefits and is competitive with drilling new wells. But other than making it clear that the process has been successful and uses dry gas produced in the same field, EOG is withholding key operational details such as whether it involves the huff-and-puff technique or continuous injections. A number of other innovative shale producers including Statoil, Nexen Energy, Continental Resources, and Marathon Oil have also either funded research or are known to be running pilots, but have not made their results public. As most shale producers remain silent about their EOR efforts, there are a growing number of technical papers being published by university petroleum departments and reservoir engineering consultants. They are using computer models and corefloods to test their theories and have produced promising numbers that suggest there may be several practical ways to implement EOR strategies for shale.

A meshless solution of two dimensional multiphase flow in porous media

Multiphase fluid flow problems are of importance in many disciplines including hydrology and petroleum reservoir engineering. Standard methods such as the finite differences, finite volumes and expanded mixed finite elements methods use very general unstructured grids and need different grid adaptation strategies to ensure optimal solution of this non-linear problem. The meshless methods seem to be quite a good alternative to these classical mesh-based methods. In our work we used the meshless Petrov–Galerkin local method based on the pressure-saturation formulation.

Change-of-Support Models on Irregular Grids for Geostatistical Simulation

In many domains, numerical models are initialized with inputs defined on irregular grids. In petroleum reservoir engineering, they consist of a great variety of grid cells of different size and shape to enable fine-scale modeling in the vicinity of the wells and coarse modeling in less important regions. Geostatistical simulation algorithms, which are used to populate the cells of unstructured grids, often have to address the problem of transition from the small-scale statistical data stemming from laboratory cores analysis and seismic processing to the multiple larger scale geological supports. The reasonable generalization of the above-mentioned problem is integrating the point-support data to simulations on irregular supports. Classical geostatistical simulation methods for generating realizations of a stationary Gaussian random function cannot be applied to unstructured grids directly, because of the uneven supports. This article provides a critical review of existing geostatistical simulation methodologies for unstructured grids, including fine-scale simulations with upscaling and direct sequential simulation algorithms, and presents two different generalizations of the discrete Gaussian model for this purpose, thereby discussing the theoretical assumptions and the accuracy when implementing these models.

The Study of the Relationship between the Thickness Combination of the Well and Liquid Production per Unit Thickness

Liquid production per unit thickness is the important indicator which reflect production capacity, and it is magnitude is the radio of well’s daily fluid production rate and sandstone thickness. It is an important job for petroleum reservoir engineering to study the effect of different sandstone thickness type combination to liquid production per unit thickness. Each sandstone thickness type has different size of reservoir thickness, porosity, permeability, etc.so the different sandstone thickness type will produce different degrees of influence to the size of liquid production per unit thickness. The relationship between each sandstone thickness radio and liquid production per unit thickness is obtained by studying all kinds of sandstone thickness radio under different liquid production per unit thickness.

Fracture characterization by fusion of geophysical and geomechanical data: a case study from the Asmari reservoir, the Central Zagros fold-thrust belt

Fractured reservoirs contain a large proportion of hydrocarbon reserves in the Middle East. In these types of reservoirs, a variety of fracture types and networks provide the required permeability for hydrocarbon storage and flow. Fractured reservoir characterization has been challenging to petroleum geoscientists and reservoir engineers in terms of developing new approaches in this direction. A variety of techniques have been developed in the literature to study the distribution and the impact of fracture pore types on reservoir characterization. However, such techniques are not suitable for subsurface cases where prediction of fractures become troublesome and each of the developed techniques has its own advantages and limitations. In this study, an integrated approach is proposed for fracture characterization by employing different sources of data including 3D seismic attributes, geomechanical parameters, unconventional logs (image log and nuclear magnetic response (NMR) log), velocity-deviation log (VDL), conventional well logs, and routine core analysis data. Based on the azimuths of horizontal principal stresses and natural fractures, location of the wells over the structure hanging wall is determined. Interpretation of the seismic profiles from the study area indicated a fault-related fold structure style with fault throws controlling the magnitude of curvature. Moreover, fracture distribution of the Asmari reservoir is predicted by using curvature attribute, geomechanical parameters and horizontal slices of VDL. It seems that fractures probably have a much higher distribution at zone 1 and zone 3 of the Asmari formation.

Modeling a distributed environment for a petroleum reservoir engineering application with software product line

Petroleum reservoir engineering is a complex and interesting field that requires large amount of computational facilities to achieve successful results. Usually, software environments for this field are developed without taking care out of possible interactions and extensibilities required by reservoir engineers. In this paper, we present a research work which it is characterized by the design and implementation based on a software product line model for a real distributed reservoir engineering environment. Experimental results indicate successfully the utilization of this approach for the design of distributed software architecture. In addition, all components from the proposal provided greater visibility of the organization and processes for the reservoir engineers.

Innovative Geosteering Technology in Multilateral Wells

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 24002, ’Innovative Geosteering Technology Used in Drilling Smart Multilateral Wells, Kuwait,’ by T. El Gezeery, A. Aziz Ismael, K. Al-Anezi, G.S. Padhy, Fawaz Al Saqran, A. Abdul-Latif, and J. Silambuchelvan, Kuwait Oil Company, and J. Estarabadi and G. Ferroni, Geolog International, prepared for the 2013 Offshore Technology Conference, Houston, 6-9 May. The paper has not been peer reviewed. Copyright 2013 Offshore Technology Conference. Reproduced by permission. The Burgan reservoir in Kuwait has the potential for premature water breakthrough, leaving behind bypassed zones of oil. The placement and completion of horizontal wells in such reservoirs is a challenge necessitating a collaborative approach from petroleum geoscience, reservoir engineering, and petroleum engineering. This paper describes placement of horizontal wells in this kind of heterogeneous reservoir through an integrated approach. Introduction The Minagish field was discovered in 1959 and is located in the southwestern part of Kuwait. It contains several reservoir intervals in its stratigraphic column, varying from Early Jurassic to Late Cretaceous. The field is situated 12 km northwest from the West Umm Gudair field (Fig. 1). The field has been penetrated by more than 180 wells. The field structure of the Burgan formation is a closed elongated asymmetrical anticline oriented in a north/south direction. The top of the Burgan structure is located at approximately 5,500-ft true vertical depth (TVD) minus the elevation above mean sea level of the depth reference point of the well. Regional Geology. The Burgan formation consists of a lower braided river system with stacked sand bodies. The sediment ranges from fine to medium grain sizes, and the porosities are high enough for lateral migration. On top of the upper Burgan channels, the sediments are generally finer but still retain a fluvial character. The amount of shale is higher. The marsh and tidal sediments, which consist of fine sands, silty sands, and sandy silts, seem to be of lower connectivity for vertical migration. The porosity is relatively low (between 15 and 18%), and the minimum of the measured permeability is close to 1 md for these layers. It seems that these shaly sediments can act as permeability barriers for vertical migration, but oil is observed in all channels and has been able to reach the reservoirs. This complex channel geometry makes these reservoirs the most challenging clastic reservoirs in the Minagish field.

Convergence of an iterative method for solving a class of nonlinear equations

In this paper, we consider the semilocal convergence of one popular iterative method for solving the nonlinear equations arising from the discretization of two-phase flow in porous media. This method is very important in petroleum reservoir engineering. The semilocal convergence of the method is proved under the proper assumptions coinciding with physical properties, which can provide the theoretical foundation for its applications. Numerical results of two-phase flow are also given.

Volume-translated cubic EoS and PC-SAFT density models and a free volume-based viscosity model for hydrocarbons at extreme temperature and pressure conditions

This research focuses on providing the petroleum reservoir engineering community with robust models of hydrocarbon density and viscosity at the extreme temperature and pressure conditions (up to 533K and 276MPa, respectively) characteristic of ultra-deep reservoirs, such as those associated with the deepwater wells in the Gulf of Mexico. Our strategy is to base the volume-translated (VT) Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) cubic equations of state (EoSs) and perturbed-chain, statistical associating fluid theory (PC-SAFT) on an extensive data base of high temperature (278–533K), high pressure (6.9–276MPa) density rather than fitting the models to low pressure saturated liquid density data. This high-temperature, high-pressure (HTHP) data base consists of literature data for hydrocarbons ranging from methane to C40. The three new models developed in this work, HTHP VT-PR EoS, HTHP VT-SRK EoS, and hybrid PC-SAFT, yield mean absolute percent deviation values (MAPD) for HTHP hydrocarbon density of ∼2.0%, ∼1.5%, and <1.0%, respectively.An effort was also made to provide accurate hydrocarbon viscosity models based on literature data. Viscosity values are estimated with the frictional theory (f-theory) and free volume (FV) theory of viscosity. The best results were obtained when the PC-SAFT equation was used to obtain both the attractive and repulsive pressure inputs to f-theory, and the density input to FV theory. Both viscosity models provide accurate results at pressures to 100MPa but experimental and model results can deviate by more than 25% at pressures above 200MPa.

Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media

Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.

Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes

The paper investigates a nonparametric regression method based on smoothing spline analysis of variance (ANOVA) approach to address the problem of global sensitivity analysis (GSA) of complex and computationally demanding computer codes. The two steps algorithm of this method involves an estimation procedure and a variable selection. The latter can become computationally demanding when dealing with high dimensional problems. Thus, we proposed a new algorithm based on Landweber iterations. Using the fact that the considered regression method is based on ANOVA decomposition, we introduced a new direct method for computing sensitivity indices. Numerical tests performed on several analytical examples and on an application from petroleum reservoir engineering showed that the method gives competitive results compared to a more standard Gaussian process approach.

Numerical Modeling of Degenerate Equations in Porous Media Flow

In this paper is introduced a new numerical formulation for solving degenerate nonlinear coupled convection dominated parabolic systems in problems of flow and transport in porous media by means of a mixed finite element and an operator splitting technique, which, in turn, is capable of simulating the flow of a distinct number of fluid phases in different porous media regions. This situation naturally occurs in practical applications, such as those in petroleum reservoir engineering and groundwater transport. To illustrate the modelling problem at hand, we consider a nonlinear three-phase porous media flow model in one- and two-space dimensions, which may lead to the existence of a simultaneous one-, two- and three-phase flow regions and therefore to a degenerate convection dominated parabolic system. Our numerical formulation can also be extended for the case of three space dimensions. As a consequence of the standard mixed finite element approach for this flow problem the resulting linear algebraic system is singular. By using an operator splitting combined with mixed finite element, and a decomposition of the domain into different flow regions, compatibility conditions are obtained to bypass the degeneracy in order to the degenerate convection dominated parabolic system of equations be numerically tractable without any mathematical trick to remove the singularity, i.e., no use of a parabolic regularization. Thus, by using this procedure, we were able to write the full nonlinear system in an appropriate way in order to obtain a nonsingular system for its numerical solution. The robustness of the proposed method is verified through a large set of high-resolution numerical experiments of nonlinear transport flow problems with degenerating diffusion conditions and by means of a numerical convergence study.