The objective of this paper is to present a detailed workflow for developing a field-wide (or basin-wide) “common” equation of state (EOS) model to describe PVT properties1 of all reservoir fluids and wellstream mixtures at all relevant conditions of pressure and temperature. The presented workflow is a result of having developed many field-wide EOS models in conventional reservoirs around the world, and more recently several basin-wide EOS models for North American unconventionals (Eagle Ford, Montney, Bakken, Permian and Scoop/Stack). We address several important considerations in developing a common EOS, as well as when and why a common EOS is needed.
The starting point for developing a common EOS is the use of
Measured PVT data must be scrutinized for quality using a series of consistency checks that include component and phase material balances, cross plots, and continual comparison with EOS results. Using all PVT data from all samples gives a substantial, statistically significant data set that allows trend analysis and outlier identification.
One key to developing a common EOS model is using a sufficient number of components, and proper characterization of heavy fractions that contain varying proportions of the three hydrocarbon groups (paraffin, naphthene and aromatic compounds – PNA). The heavy fractions single carbon numbers C7, C8, C9… and the remaining “residue”, e.g. C36+ are often given average properties that reflect the relative proportions of PNA compounds – i.e. relative paraffinicity (or relative aromaticity). The determination of single carbon number (SCN) and residue properties is what we refer to as heptanes-plus characterization, and it is this characterization that will differ from field to field, or basin to basin.
Sometimes within a given field or basin, the relative paraffinicity may vary so much that a single, common EOS using SCN description is not possible. Two options remain: developing multiple EOS models, or creating a single EOS with some/all heavy fractions having two subfractions – paraffinic and aromatic (e.g. C7P and C7A, C36+P and C36+A). In this latter approach, the P-A split must be estimated, correlated or measured for each fluid mixture, making the approach complicated and less common, but necessary in some fluid systems2.
Developing a common EOS for a field/basin is necessary because in-situ reservoir fluids may vary spatially, change in composition during depletion and gas injection, and because of fluid mixing throughout the production system – within reservoirs, wells, and topside facilities.
For unconventional basins, only a small number of the thousands of wells have laboratory PVT data available, despite significant well-to-well fluid variations – e.g. gas oil ratio (GOR) ranging from 300 to 300,000 scf/STB in the Eagle Ford and Montney basins. Simple PVT correlations are not applicable over the entire range of fluid compositions. Many wells produce complex retrograde condensates, near-critical fluids, and volatile oils that require an accurate and consistent EOS model for estimating PVT properties required by geologic, engineering, and marketing professionals.
Cui, Xiaona (Northeast Petroleum University and Texas A&M University) | Yang, Erlong (Northeast Petroleum University) | Song, Kaoping (Northeast Petroleum University) | Huang, Jingwei (Texas A&M University) | Killough, John (Texas A&M University) | Dong, Chi (Northeast Petroleum University) | Liu, Yikun (Northeast Petroleum University) | Wang, Keliang (Northeast Petroleum University)
Phase behavior of hydrocarbons in confined nanopores is quite different from that of the bulk. In confined space, the high capillary pressure between vapor phase and liquid phase, and depressed critical properties under confinement will all affect the in-situ phase behavior. According to the theory of adsorption-induced structural phase transformation in nanopores, we modify the molar volume term of the Peng-Robinson equation of state (PR-EOS) by considering the reduced mole number of fluids caused by absorption to describe the phase behavior of fluids under confinement. Then capillary pressure is coupled with phase equilibrium equations, and the resulting system of nonlinear fugacity equations based on the modified PR-EOS is solved to present a comprehensive examination of the effect of capillary pressure and confinement on saturation pressures. Binary mixtures of methane with heavier hydrocarbons and a real reservoir fluid from the Eagle Ford confined at different pore sizes are considered. The effect of capillary pressure and confinement on the phase envelop shifts are compared.
The modified PR-EOS show that there exists a linear relationship between critical temperature shift and pore size reductions, a quadratic relationship between critical pressure shift and pore size reductions which are consistent with the experimental and molecular simulation results. The shift in the phase envelop of binary mixtures and Eagle Ford fluids show that both the capillary pressure and confinement decrease the bubble point pressures, while they oppositely influence dew point pressures. It is worthy to be noted that the effect of capillary pressure on phase envelop shifts will be suppressed when taking the critical point shifts caused by confinement into consideration. For Eagle Ford fluids, the effect of confinement on phase envelop shift is dominant compared with that of capillary pressure, and the capillary pressure cannot be overlooked when pore radius decreases to 50 nm. While the confinement begins to play an important role on the saturation pressures when pore radius decreases to 100 nm.
In addition, the methodology presented in this study can be extended to the phase equilibrium calculations of multiple pores since the modified PR-EOS can provide a consistent phase behavior description of fluid molecules over the whole range of pore sizes.
Mud filtrate invasion occurs in the immediate vicinity of the well as a result of the overbalance pressure of the mud column in the well. Oil-based muds (OBM), unlike water-based muds (WBM), are miscible with reservoir fluid, and OBM contamination alters the properties of the original formation fluid. The bubblepoint of contaminated fluid is usually lower than clean fluid. While fluid is pumped out of the formation, it becomes cleaner and the bubblepoint increases; the upper limit of the increase is the clean formation fluid. While increasing the pumping rate can shorten cleanup time, pumping below the bubblepoint can modify the fluid phase behavior and cause asphaltene content in the formation fluid to precipitate out and sensor data to become erratic and noisy. Therefore, it is important not to pump below the bubblepoint, knowing the clean fluid bubblepoint in real time provides a guideline for the field engineer. The purpose of fluid sampling is to collect a representative formation fluid—samples with an acceptably low contamination. The clean fluid bubblepoint provides a lower limit on pumping pressure, which helps ensure pumping does not go below the bubblepoint and the sample is in single phase.
This paper describes how clean fluid compositions are determined from the asymptote of the principal component analysis (PCA) reconstructed scores and then used as input for the equation of state (EOS) program to compute fluid properties such as bubblepoint and gas/oil ratio (GOR). The optical spectral data from the optical fluid analyzer is first despiked, and outliers from the despiked data are removed using the robust ordinary least squares regression (ROLSR) method and robust PCA (RPCA). After removing outliers, clean fluid spectra data are reconstructed using asymptotic PCA scores and PCA loadings. Using a neural network model, clean fluid compositions are determined from reconstructed fluid spectral data, and fluid compositions are used as input for the EOS program to determine fluid properties.
Results confirm that the clean fluid bubblepoint and GOR do not change significantly after a few tens of liters of fluid pumpout. Analysis of the first principal component (PC1) confirms that most of the variations occur during the first few tens of liters of pumpout, indicating the predicted clean fluid compositions and properties are somewhat stable. This approach can help determine the clean fluid properties, even while pumping before taking the sample, helping ensure a monophasic fluid sample. When pumpout accumulated volume reaches 40 to 50 L—within 15 to 20 min of pumping out contaminated fluid—clean fluid compositions and properties can be estimated and used to determine reservoir continuity. Additionally, knowing the clean reservoir GOR and API gravity can help determine the type of reservoir fluid in real time.
Different from the conventional reservoirs, the liquid-rich shale reservoirs are known to possess a broad pore size distribution. In macropores and fractures, the porous geometries are in the size of micrometers. However, in organic matter, a significant amount of porosity consists of nanopores. In the nanopores, the fluid phase behavior deviates from the bulk-scale phase behavior due to the nano-confinement effect. The deviated phase behavior results in significant challenges in evaluating oil and gas in-place and understanding reservoir fluid depletion mechanism.
In this paper, the nano-confinement effect on hydrocarbon phase behavior in shale reservoirs is studied in three steps. Firstly, the bubble point temperatures of hydrocarbons in multiple sizes of nanopores are measured using the laboratory approach of differential scanning calorimetry (DSC). Secondly, a pore-size-dependent equation of state (PR-C EOS) extended from Peng-Robinson equation of state is completed with the experimental data. The PR-C EOS models the phase diagram with an extra dimension of pore size and the modeling results agree well with the experimental data. Thirdly, a multi-scale PVT simulator is developed to calculate the PVT of reservoir fluids in the shale pore size distribution systems. The whole pore size distribution is discretized into specific sizes of pores and PR-C EOS is used to describe the fluid per pore. The simulated multi-scale PVT provides a realistic picture of fluid phase behavior in liquid-rich shale reservoirs with macro-to nano-scale porous geometries and sheds light upon GOR behavior during production history.
The paper highlights the limitations in the use of cubic equations of state (CEOS), for modelling reservoir behavior of liquid phase (black and volatile oil), in highly undersaturated reservoirs. This is important in high shrinkage volatile oils for which complex dependence of fluid behavior with composition is found.
Vaca Muerta formation fluids run from medium black oils to very dry gas, according to source rock maturity. High shrinkage volatile oil and very rich gas condensate are found and compositional variation is areally continuous. Despite this huge difference in fluid nature, where saturation pressures are present, more than 200 kg/cm2 undersaturation are reported.
Due to the complex dependence of fluid behavior with composition for near critical gas condensate and volatile oil, the use of compositional modelling is mandatory.
Reservoir pressure evolution with production and recovery calculations rely largely on compressibility, which itself is not a fitting parameter for usual CEOS. A very good fit for liquid volumes in CEOS, i.e. less than 5 % maximum error in volume, leads to unacceptable differences in compressibility (over 30 %).
To compare the consequences in production of this difference, a black oil model was run with different fluid scenarios: one with experimental compressibility and other two with compressibility obtained from CEOS. In the model, all formation, fracture and other fluid properties are the same, as well as the BHP imposed.
The results from numerical simulation show that rates and cumulative production from CEOS compressibility scenarios are half of those obtained with experimental compressibility. Part of this difference may be explained from fluid behavior alone, and the remaining is due to poral compressibility and fracture conductivities related to the different trends in pressure.
The CEOS are the only ones implemented up to now in the commercially available compositional numerical simulators. In this paper we show the limitation of these CEOS for the description of highly undersaturated volatile oil reservoirs.
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 23-25 July 2018. The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by anyone other than the author without the written consent of URTeC is prohibited.
According to Energy Information Administration (EIA), production of shale gas and associated gas from tight oil plays will be the largest contributor to natural gas production growth, accounting for nearly two-thirds of the total U.S. production by 2040 (EIA, 2017). Therefore, much effort has been made to investigate the development mechanisms of unconventional reservoirs. However, it is a great challenge to fully understand the phase-and flow-behavior of shale oil and gas due to the dominance of nano-sized pores and the heterogeneity of the porous geometries.
Khodaparast, Pooya (Department of Energy and Mineral Engineering and EMS Energy Institute, The Pennsylvania State University, University Park) | Johns, Russell T. (Department of Energy and Mineral Engineering and EMS Energy Institute, The Pennsylvania State University, University Park)
Surfactant floods can attain high oil recovery if optimum conditions with ultra-low interfacial tensions (IFT) are achieved in the reservoir. A new equation-of-state (EoS) phase behavior model based on the hydrophilic-lipophilic difference (HLD-NAC) has been shown to fit and predict phase behavior data continuously throughout the Winsor I, II, III, and IV regions. The state-of-the-art for viscosity estimation, however, uses empirical non-predictive models based on fits to salinity scans, even though other parameters change, such as the phase number and compositions. In this paper, we develop the first-of-its-kind microemulsion viscosity model that gives continuous viscosity estimates in composition space. This model is coupled to our existing HLD-NAC phase behavior EoS.
The results show that experimentally measured viscosities in all Winsor regions (two and three-phase) are a function of phase composition, temperature, pressure, salinity, and
The improved oil recovery of unconventional shale reservoirs has attracted much interest in recent years. Gas injection, such as CO2 and natural gas, is one of the most considered techniques for its sweep efficiency and effectiveness in low permeability reservoirs. However, the uncertainties of fluid phase behavior in shale reservoirs pose a great challenge in evaluating the performance of gas injection operation. Shale reservoirs are featured with macro-scale to nano-scale pore size distribution in the porous space. In fractures and macropores, the fluid shows bulk behavior, but in nanopores the phase behavior is significantly altered by the confinement effect. The integrated behavior of reservoir fluids in this complex environment remains uncertain.
In this study, we investigate the nano-scale pore size distribution effect on the phase behavior of reservoir fluids in gas injection for shale reservoirs using a multi-scale equation of state modeling. A case of Anadarko Basin shale oil is used. The pore size distribution is discretized as a multi-scale system with pores of specific diameters. The phase equilibria of methane injection into the multi-scale system are calculated. The constant composition expansions are simulated for oil mixed with various fractions of injected gas. Bubble point, swelling factor, criticality and fluid volumetrics are studied in comparison to the behavior of the bulk fluid. It is found that fluid in nanopores becomes supercritical with injected gas, but lowering the pressure below bubble point will turn it into the subcritical state. The swelling factor is slightly higher with nanopores, and bubble point is lower than the bulk. The degree of deviation depends on the amount of injected gas.
Two algorithms are proposed for isothermal multiphase flash. These are referred to as modified RAND and vol-RAND. The former uses the chemical potentials and molar-phase amounts as the iteration variables, while the latter uses chemical potentials and phase volumes to cosolve a pressure-explicit equation of state (EOS) with the equilibrium equations. Compared with the conventional secondorder approach using Gibbs-energy minimization, these methods are more structured, with all components in all phases treated in the same way. Both have been derived to include chemical reactions for any number of phases along with the possible simplifications for only phase equilibria. The simple structured implementation of these methods is demonstrated for modified RAND and vol-RAND. The rate of convergence of the methods presented is shown to be the same as the conventional second-order method for isothermal flash. It is demonstrated that the use of an association term [cubic plus association (CPA)] adds little additional computational cost when using vol-RAND compared with a simple cubic Soave-Redlich-Kwong (SRK) without association. The RAND methods scale better in terms of the O(n3) operations as more phases are introduced, and are computationally less expensive than the conventional Gibbs minimization method for more than three phases.