Petroleum Reservoir Engineering Research Articles

Geoscience spillover: Gunnar Böðvarsson and the adoption of petroleum technologies in Iceland’s geothermal industry, 1940s–1970s

ABSTRACT During the twentieth century, Iceland became a leader in geothermal energy use, with hot water and steam providing for the heating of 9 out of 10 houses and almost one-third of the electricity supply. A crucial factor in the expansion of geothermal energy between the 1940s and 1970s were indirect ‘spillovers’ from the oil industry via the applied geosciences. While fundamentally different in end use, geothermal and hydrocarbon industries employ similar geoscientific methods for exploring and extracting fluids and gases. This article traces the spillovers from oil to geothermal by examining Iceland’s Geothermal Division and its founding director, Gunnar Böðvarsson. He saw the oil industry as a model and embraced its geoscientific exploration methods, oilwell rotary drilling and petroleum reservoir engineering. Adapted to the requirements of geothermal energy, petroleum technologies greatly improved the knowledge of geothermal reservoirs and the efficiency of well drilling and hot water and steam extraction. The geoscience spillover between oil and geothermal reveals an understudied dimension of geothermal history and the crucial role of the geosciences at the intersection of academia and energy industries, which also resulted in reverse spillovers from geothermal to oil and complicates the common dichotomization of fossil fuels vs. renewable alternatives.

Field-split preconditioned active-set reduced-space algorithm for complex black oil reservoir simulation at large-scale

Accurate black oil reservoir simulation is important for the understanding of underground resources in hydrology and petroleum reservoir engineering. The success of fast prediction relies on a robust and scalable black oil simulator, which can handle the complex subsurface fluid dynamics with coupling several different physical processes, and meanwhile run efficiently on distributed memory parallel computers. In this work, we introduce a highly parallel simulator to accurately compute the reservoir flow coupling with wells, including some adaptive fully implicit schemes for the temporal discretization, the improved active-set reduced-space algorithm for the nonlinear algebraic system, and several types of field-split methods for preconditioning. This parallel simulator is applied on the domain decomposition framework, which is designed to overcome the computational issues of traditional simulators implemented for personal computers or small workstations. High-resolution reservoir simulation results on the Society of Petroleum Engineers (SPE) comparative solution project or real-field cases are obtained and analyzed, and the parallel performance of the algorithm is studied on a supercomputer with scaling up to 27440 processor cores. The numerical experiments indicate that the proposed black oil simulator is capable of accurately predicting the highly complex physical processes and interactions between wells and the reservoir for full field scale simulation.

Advances in the pilot point inverse method: Où En Sommes-Nous maintenant?

At a conference some years ago, one of the attendees came up to Ghislain de Marsily and asked, “Excuse me, but aren’t you the de Marsily who developed the Pilot Point Method? It is an honor to meet you.” His response highlights one of Ghislain’s greatest qualities, his humility: “Yes I am, thank you, you are very kind, but that was a very long time ago.” Since Ghislain de Marsily first developed the Pilot Point Method (PPM) in 1978, its development and use has grown significantly in applied decision-support modeling settings including hydrogeology, as well as in other industries, e.g., petroleum reservoir engineering. A technique that was once confined to academic realms, the PPM is now widely accepted as one of the industry pillars of inversion and uncertainty quantification for predictive groundwater modeling. Herein, we provide an update to de Marsily’s paper entitled “Four Decades of Inverse Problems in Hydrogeology” [De Marsily et al., 2000], but with a particular focus on the incredible adoption and advancement of de Marsily’s PPM and related inverse techniques over the last twenty years in the field of predictive groundwater modeling.

History Matching of Reservoir Simulation Model: a Case Study from the Mishrif Reservoir, Buzurgan Oilfield, Iraq

In petroleum reservoir engineering, history matching refers to the calibration process in which a reservoir simulation model is validated through matching simulation outputs with the measurement of observed data. A traditional history matching technique is performed manually by engineering in which the most uncertain observed parameters are changed until a satisfactory match is obtained between the generated model and historical information. This study focuses on step by step and trial and error history matching of the Mishrif reservoir to constrain the appropriate simulated model. Up to 1 January 2021, Buzurgan Oilfield, which has eighty-five producers and sixteen injectors and has been under production for 45 years when it started in 1976. Reservoir exhibits heterogeneity in porosity and permeability throughout the field, therefore it’s a big challenge to control all reservoir properties during matching process. The historical matching process includes matching field and wells oil and water production rates, water injection rates, water cut, and reservoir static pressure. Finally, the results show that the good matching between simulated model and observed data; oil and water production rates, water injection rates, water cut, and static reservoir pressure which allow for implementing perfect future production forecasting strategies.

XFEM modeling of the effect of in-situ stresses on hydraulic fracture characteristics and comparison with KGD and PKN models

Increasing the permeability of hydrocarbon reservoirs by creating artificial cracks that are induced by injection of fluids under high pressure is called hydraulic fracturing (HF). This method is widely used in petroleum reservoir engineering. For design of Hydraulic Fracture operations, several analytical models have been developed. KGD and PKN are the first and most used analytical models in this area. Although number of advanced softwares are developed in recent years, KGD and PKN models are still popular and have even been used in a number of softwares. In both models the characteristics of the fracture namely: fracture length (L), fracture width (w), and fluid pressure at the crack mouth (p) are determined based on closed form relations using the reservoir rock shear stiffness, Poisson’s ratio, fluid injection rate, and injection time. Despite their ease of use, KGD and PKN models do not consider some important geo-mechanical and hydro-mechanical parameters and this shortcoming makes their results to be approximate. The aim of this study is evaluating the effects of in-situ stress on the fracture length, width, and fluid pressure employing XFEM method. In this study, tensile fracture mode and cohesive zone model are used for creation and propagation of cracks. In this paper, by conducting a series of numerical simulations using XFEM and after verification of the results, the accuracy of the analytical formulas of KGD and PKN models are examined. The results show that due to some simplifying assumptions used in KGD and PKN analytical models and neglecting some hydraulic and geomechanical parameters such as in-situ stresses, the length, width, and fluid pressure of the crack obtained from analytical formulas differ from the results of the numerical simulations. In this paper, the effects of in-situ stresses on hydraulic fracture characteristics (width, length, and crack mouth fluid pressure) are investigated and presented in the form of a number of correction (modification) factors that can be used for improvement of the results of KGD and PKN models. The findings of this study can help for more accurate design of hydraulic fracture process in oil industry for increasing the production of hydrocarbon reservoirs.

On the stability and phase behavior of Titan's subsurface liquid columns

On Titan, liquid hydrocarbon may stay in the subsurface porous permeable crust known as the alkanofer, analogous to water in Earth's aquifer. In addition to pressure gradient, the subsurface liquid in alkanofers is subject to vertical compositional grading due to the gravity and temperature gradient. The common wisdom is that the liquid would normally stay underground in a stability established by the pressure that increases with depth as observed in aquifers on Earth. However, Titan's liquids consist of nitrogen and hydrocarbons, mainly methane and ethane, the behavior of which is very sensitive to temperature and pressure. Consequently, the liquid density does not always increase with depth, thus may introduce a reverse density profile that leads to vertical convective instability of the liquid column. If reverse density profiles are present, capillary pressures arising from liquid trapped within small pores in the crust can help with the column stability. The liquid held in the capillaries can seal the space below it thus helping with the stability, unless the overpressure built from underneath becomes larger than the capillary pressure, which causes leakage to allow the liquids to seep upward from the deep. This situation is analogous to hydrocarbon seeps on Earth, where oil and natural gas escape the reservoir and flow slowly through network of cracks to the surface. An algorithm based on an extended Gibbs equation commonly used in petroleum reservoir engineering is employed in this work to produce pressure, density, and compositional profiles for evaluating the stability and phase behavior of Titan's subsurface fluids.

Machine learning and data mining assisted petroleum reservoir engineering: a comprehensive review

The oil and gas industry faces several challenges associated with managing massive datasets and extracting relevant information. The machine learning tools have proven to be significantly valuable for analysing complex, heterogeneous data and produce quicker and more reliable outcomes even on large-scales. Machine learning and data mining tools have been applied in several aspects of the upstream oil and gas industry, such as exploration, drilling, reservoir engineering, and production forecasting. This review has been explicitly focused on machine learning and data mining implementations in reservoir engineering, including reservoir characterisation and performance prediction, well test analysis, well logging and formation evaluation, and enhanced oil recovery operations. The commonly used statistical measures for classification and regression models have been discussed as well. The observations from the review have led to suitable suggestions that shall enrich the research in this area. [Received: July 29, 2021; Accepted: October 30, 2021]

Accelerated Bayesian inference-based history matching of petroleum reservoirs using polynomial chaos expansions

The forecast for oil production from an oil reservoir is made with the aid of reservoir simulations. The model parameters in reservoir simulations are uncertain whose values are estimated by matching the simulation predictions with production history. Bayesian inference (BI) provides a convenient way of estimating parameters of a mathematical model, starting from a probable distribution of parameter values and knowing the production history. BI techniques for history matching require Markov chain Monte Carlo (MCMC) sampling methods, which involve large number of reservoir simulations. This limits the application of BI for history matching in petroleum reservoir engineering, where each reservoir simulation can be computationally expensive. To overcome this limitation, we use polynomial chaos expansions (PCEs), which represent the uncertainty in production forecasts due to the uncertainty in model parameters, to construct proxy models for model predictions. As an application of the method, we present history matching in simulations based on the black-oil model to estimate model parameters such as porosity, permeability, and exponents of the relative permeability curves. Solutions to these history matching problems show that the PCE-based method enables accurate estimation of model parameters with two orders of magnitude less number of reservoir simulations compared with MCMC method.

Petrophysical and mechanical rock property database of the Los Humeros and Acoculco geothermal fields (Mexico)

Abstract. Petrophysical and mechanical rock properties are key parameters for the characterization of the deep subsurface in different disciplines such as geothermal heat extraction, petroleum reservoir engineering or mining. They are commonly used for the interpretation of geophysical data and the parameterization of numerical models and thus are the basis for economic reservoir assessment. However, detailed information regarding petrophysical and mechanical rock properties for each relevant target horizon is often scarce, inconsistent or distributed over multiple publications. Therefore, subsurface models are often populated with generalized or assumed values resulting in high uncertainties. Furthermore, diagenetic, metamorphic and hydrothermal processes significantly affect the physiochemical and mechanical properties often leading to high geological variability. A sound understanding of the controlling factors is needed to identify statistical and causal relationships between the properties as a basis for a profound reservoir assessment and modeling. Within the scope of the GEMex project (EU H2020, grant agreement no. 727550), which aims to develop new transferable exploration and exploitation approaches for enhanced and super-hot unconventional geothermal systems, a new workflow was applied to overcome the gap of knowledge of the reservoir properties. Two caldera complexes located in the northeastern Trans-Mexican Volcanic Belt – the Acoculco and Los Humeros caldera – were selected as demonstration sites. The workflow starts with outcrop analog and reservoir core sample studies in order to define and characterize the properties of all key units from the basement to the cap rock as well as their mineralogy and geochemistry. This allows the identification of geological heterogeneities on different scales (outcrop analysis, representative rock samples, thin sections and chemical analysis) enabling a profound reservoir property prediction. More than 300 rock samples were taken from representative outcrops inside the Los Humeros and Acoculco calderas and the surrounding areas and from exhumed “fossil systems” in Las Minas and Zacatlán. Additionally, 66 core samples from 16 wells of the Los Humeros geothermal field and 8 core samples from well EAC1 of the Acoculco geothermal field were collected. Samples were analyzed for particle and bulk density, porosity, permeability, thermal conductivity, thermal diffusivity, and heat capacity, as well as ultrasonic wave velocities, magnetic susceptibility and electric resistivity. Afterwards, destructive rock mechanical tests (point load tests, uniaxial and triaxial tests) were conducted to determine tensile strength, uniaxial compressive strength, Young's modulus, Poisson's ratio, the bulk modulus, the shear modulus, fracture toughness, cohesion and the friction angle. In addition, X-ray diffraction (XRD) and X-ray fluorescence (XRF) analyses were performed on 137 samples to provide information about the mineral assemblage, bulk geochemistry and the intensity of hydrothermal alteration. An extensive rock property database was created (Weydt et al., 2020; https://doi.org/10.25534/tudatalib-201.10), comprising 34 parameters determined on more than 2160 plugs. More than 31 000 data entries were compiled covering volcanic, sedimentary, metamorphic and igneous rocks from different ages (Jurassic to Holocene), thus facilitating a wide field of applications regarding resource assessment, modeling and statistical analyses.

Machine learning and data mining assisted petroleum reservoir engineering: a comprehensive review

Machine learning and data mining assisted petroleum reservoir engineering: a comprehensive review

Application of accelerated fixed-point algorithms to hydrodynamic well-fracture coupling

The coupled simulations of dynamic interactions between the well, hydraulic fractures and reservoir have significant importance in some areas of petroleum reservoir engineering. Several approaches to the problem of coupling between the numerical models of these parts of the full system have been developed in the industry in past years. One of the possible approaches allowing formulation of the problem as a fixed-point problem is studied in the present work. Accelerated Anderson’s and Aitken’s fixed-point algorithms are applied to the coupling problem. Accelerated algorithms are compared with traditional Picard iterations on the representative set of test cases including ones remarkably problematic for coupling. Relative performance is measured, and the robustness of the algorithms is tested. Accelerated algorithms enable a significant (up to two orders of magnitude) performance boost in some cases and convergent solutions in the cases where simple Picard iterations fail. Based on the analysis, we provide recommendations for the choice of the particular algorithm and tunable relaxation parameter depending on anticipated complexity of the problem.

All-Time Modeling of Co-Current Spontaneous Water Imbibition Into Gas-Saturated Rocks Using a Novel Transition Time

Abstract Spontaneous imbibition (SI) into a porous medium is an important transport phenomenon in petroleum reservoir engineering. The study of spontaneous water imbibition is critical to predict the production performance in these reservoirs developed by waterflooding, especially in the fractured gas reservoirs with active aquifers. While some studies have been reported to characterize spontaneous water imbibition into gas-saturated rocks, they are either limited or inaccurate due to the fact that the existing models have specific assumptions that cannot be applied in other time intervals. To this end, we proposed a novel transition imbibition time t* and developed an all-time (including both early- and later-time SI) model to match the experimental SI data. Furthermore, we proposed a novel model to estimate capillary pressures at different water saturations and to characterize the water saturation profile in capillary-dominated stage. Comparison with the existing capillary pressure estimation models was performed to test the differences. The results demonstrated that the all-time model could fit the experimental imbibition data of the entire SI process satisfactorily. The new saturation model established in this paper can be well fitted with the water saturation profile measured by the X-ray computer tomography (CT) scanners. The results and findings from this work may be of great significance in many areas related to SI, particularly in the development of naturally fractured gas reservoirs with active aquifers.

Revising the effectiveness of thermal method application for unconventional bitumen oil production stimulation

A theoretical model of petroleum reservoir engineering process with high viscosity oil using the technology of double horizontal wells is proposed. Numerical solutions of the problem in a two-dimensional formulation are obtained. With this method of producing high viscosity oil the efficiency of oil reservoir development can be increased by ensuring uniform heating of the developed zone of the field. The proposed model allows us to trace the two-dimensional picture of oil filtration in the reservoir and investigate the main regularities of the process. The costs for oil reservoir heating, flow rate development and changes in the mass of pumped oil in the initial period of well operation are determined. The obtained solutions for a long stretch of time were extrapolated.

An integrated procedure for reservoir connectivity study between neighboring fields

Reservoir connectivity has a considerable effect on reservoir characterization, plans for field developments and production forecasts. Reducing the uncertainties about the lateral and vertical extension of different pay zones is the main step in developing and managing the reservoirs. Nearly all the proposed methodologies for the verification of reservoir connectivity are limited to the study of the communication of different compartments in one field. In the presented paper, first a comprehensive procedure is proposed to study the reservoir connectivity between nearby fields. The steps in this procedure are not necessarily hierarchy, but all the considerations in each step are studied to cover all the uncertainties that affect the reservoir communication. This procedure mainly comprises the study of reservoir extension, pressure communication in the hydrocarbon column, fluid similarity, top seal efficiency and faults sealing. Then, to apply this procedure for proving the communication between nearby fields, a case study of Ilam Formation in southwest of Iran is presented. The results confirm the lateral connectivity of the three pre-explored distinctive oil fields in Ilam Formation. The established connectivity leads to an increase in the pre-estimated oil-in-place volumes. This incorporated case study demonstrates how different data including geophysics, structural and petroleum geology, production and reservoir engineering are integrated to prove the communication of Ilam reservoir between these fields. This manifested technique is a powerful road map for other cases worldwide and is extremely recommended to be performed before developing those fields that are suspicious to lateral connectivity.

Unconditionally stable, efficient and robust numerical simulation of isothermal compositional grading by gravity

The gravitational force has been considered as one of the most important factors leading to composition variation of multicomponent chemical species mixture in many industrial processes and natural phenomena. This has been largely studied through experimental and numerical modeling, especially in chemical processes and petroleum reservoir engineering. The modeling and simulation of dynamical process of composition variation under gravity is fundamentally important to understand the evolutionary process of petroleum reservoir formation and initial state. This work presents the dynamical modeling of composition variation in the framework of the modified Helmholtz free energy coupling with the realistic equations of state. An efficient, easy-to-implement, thermodyanmically consistent, and robust numerical scheme is proposed for the dynamical model. This scheme is rigorously proved to be unconditionally stable. The implementation is straightforward based on the single-component system and it is not required to choose a reference species for multicomponent fluids. For the multicomponent system of huge number of species, the proposed scheme allows to numerically compute the system of partial differential equations in a random order, which is called an “unbiased scheme” in this work. The current scheme is computationally efficient and saves computer memory. Several numerical examples are designed to verify the properties of the scheme.

Thermodynamically consistent modeling of two-phase incompressible flows in heterogeneous and fractured media

Numerical modeling of two-phase flows in heterogeneous and fractured media is of great interest in petroleum reservoir engineering. The classical model for two-phase flows in porous media is not completely thermodynamically consistent since the energy reconstructed from the capillary pressure does not involve the ideal fluid energy of both phases and attraction effect between two phases. On the other hand, the saturation may be discontinuous in heterogeneous and fractured media, and thus the saturation gradient may be not well defined. Consequently, the classical phase-field models can not be applied due to the use of diffuse interfaces. In this paper, we propose a new thermodynamically consistent energy-based model for two-phase flows in heterogeneous and fractured media, which is free of the gradient energy. Meanwhile, the model inherits the key features of the traditional models of two-phase flows in porous media, including relative permeability, volumetric phase velocity and capillarity effect. To characterize the capillarity effect, a logarithmic energy potential is proposed as the free energy function, which is more realistic than the commonly used double well potential. The model combines with the discrete fracture model to describe two-phase flows in fractured media. The popularly used implicit pressure explicit saturation method is used to simulate the model. Finally, the experimental verification of the model and numerical simulation results are provided.

Thermal characteristics of the X geothermal resources, and a recommendation on utilization possibility

Like in petroleum, geothermal has a high cost and risk in exploration, development including drilling and utilization. This needs a clear definition and understanding of the nature and characteristic of the system in question, so the increasing of investment cost and risk could be mitigated. Un-like in the petroleum industry, reservoir engineering and geoscience are intricately intertwined in geothermal. Considering this issue, in this study the author has integrated the results of reservoir engineering analysis with geoscience concept, to determine the up-flow zone, is a zone with high thermal potential and high permeability, so it can develop as geothermal field. It was conducted at a geothermal prospect in Indonesia located at the average altitudes of about 1000 meter above sea level (m.a.s.l), where 26 wells have been drilled. The research focus in characterising of the system, using wellbore temperatures and pressures measured. This will conclude the reservoir temperature and pressure as well as enthalpy, and up-flow zone by deploying several methods and approach: namely Horner temperature, BPD curve and Pivot concept, and thermal conductivity or heat transfer concept which applied in geoscience. The research includes a literature review on heat energy conversion to electricity based on reservoir temperature and or enthalpy approach, which is used to recommend the conversion system that can extract the heat efficiently. In addition, the question on location of the up-flow zone has been answered by this study, i.e. in the southern part of the field.

A continuous learning algorithm for history matching

History matching is a classical petroleum reservoir engineering data assimilation process whereby a reservoir model is calibrated to reproduce the behavior of a real reservoir yielding more reliable models for reservoir management, reservoir performance forecast and field development decisions. In this paper, we introduce a continuous learning-from-data algorithm for history-matching problems that generates solutions using the patterns of input attributes identified in the k-best solutions for each variable involved in the process. The proposed algorithm consists of a two-staged optimization strategy, in which each stage handles different types of reservoir uncertain attributes. The proposed learning approach continuously evaluates the data of all-available models and supports the strategic choice of input patterns that can be used in the generation of different and eventually better history-matched models. We apply the proposed algorithm to the UNISIM-I-H benchmark case, a complex synthetic reservoir model based on Namorado field, Campos basin, Brazil. The results outperform the ones from related work for the same benchmark, indicating the efficiency and effectiveness of the proposed strategy towards improving the history-matching quality of an initial set of solutions, with a lower simulation footprint.

Investigation radii in multi-zone composite reservoirs

In petroleum reservoir engineering, an investigation radius is a basic, practical and meaningful parameter to evaluate the controlled area of a well. The investigation radius in homogeneous reservoirs is usually calculated by an explicit function related to the square root of time. At present, no research on investigation radii in multi-zone composite reservoirs has been found in the literature. In this work, first, we presented an application problem for which the commercial software Saphir cannot interpret an investigation radius in multi-zone composite reservoirs. Then, based on the investigation radius in homogeneous reservoirs, we firstly derived a calculation formula for the investigation radius in a multi-zone composite reservoir by the assumption of homogeneous properties in each zone. Compared with the formula for homogeneous reservoirs, the formula for multi-zone composite reservoirs is more complicated and shows a nonlinear implicit function in time. By use of the newly derived formula of the investigation radius, given a group of reservoir parameters, we numerically calculated the dynamical investigation radii with the elapse of time for both 2-zone and 3-zone composite reservoirs. Accordingly, we plotted a series of relationship curves for the investigation radii with time affected by model parameters, such as permeability, porosity and total compressibility. The relationship curves obviously show the multi-zone properties of a reservoir. The relationship curves of N-zone composite reservoirs can reflect (N-1) inflection points and an inflection point represents a response of pressure wave to an interface between two neighboring zones. Finally, we used real reservoir parameters from an example well in a 2-zone composite reservoir to calculate the investigation radius. In summary, the newly derived formulas have been shown in this work to be a convenient and practical new tool to calculate the investigation radii in composite reservoirs.

Study of compositional multiphase flow formulation using complementarity conditions

In this article, two formulations of multiphase compositional Darcy flows taking into account phase transitions are compared. The first formulation is the so-called natural variable formulation commonly used in reservoir simulation, the second has been introduced by Lauseret al.and uses the phase pressures, saturations and component fugacities as main unknowns. We will discuss how the Coats and the Lauser approaches can be used to solve a compositional multiphase flow problem with cubic equations of state of Peng and Robinson. Then, we will study the results of several synthetic cases that are representative of petroleum reservoir engineering problems and we will compare their numerical behavior.