Bubble Point Conditions Research Articles

A Bayesian Framework for Addressing the Uncertainty in Production Forecasts of Tight-Oil Reservoirs Using a Physics-Based Two-Phase Flow Model

Summary Extrapolation of history matched single-phase flow solutions is a common practice to forecast production from tight-oil reservoirs. Nonetheless, this approach (a) omits multiphase flow effects that exist below bubblepoint conditions and (b) has not included the quantification of the uncertainty of the estimated ultimate recovery (EUR). This work combines a new two-phase (oil and gas) flow solution within a Bayesian framework to address the uncertainty in the EUR. We illustrate the application of the procedure to tight-oil wells of west Texas. First, we combine the oil and the gas flow equations into a single dimensionless two-phase flow equation. The solution is a dimensionless flow rate model that can be easily scaled using two parameters: hydrocarbon pore volume and characteristic time. Second, this study generates the probabilistic production forecasts using a Bayesian approach in which the parameters of the model are treated as random variables. We construct parallel Markov chains of the parameters using an adaptative Metropolis-Hastings (M-H) Markov chain Monte Carlo (MCMC) for this purpose. Third, we evaluate the robustness of our inferences using posterior predictive checks (PPCs). Finally, we quantify the uncertainty in the EUR percentiles using the bootstrap method. The results of this research are as follows. First, this work shows that EUR estimates based on single-phase flow solutions will consistently underestimate the ultimate oil recovery factors in solution-gas drives where the reservoir pressure is less than the bubblepoint. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, the application of parallel Markov chains using an adaptative M-H MCMC scheme that addresses the correlation between the model’s parameters solves the issues of mixing and autocorrelation of Markov chains and, thus, it speeds up speeding up the convergence of the Markov chains. Third, we generate replicated data from our posterior distributions to assess the robustness of our inferences (PPCs). Finally, we use hindcasting to calibrate and strengthen our inferences. To our knowledge, all these approaches are novel in EUR forecasting. Using a Bayesian framework with a low-dimensional (two-parameter) physics-based model provides a fast and reliable technique to quantify the uncertainty in production forecasts. In addition, the use of parallel chains with an adaptative M-H MCMC accelerates the rate of convergence and increases the robustness of the method.

Investigating the impact of dissolved natural gas on the flow characteristics of multicomponent fluid in pipelines

Abstract The conventional equations for describing the flow characteristics of the mixtures merely consider fluid that is homogenic, if it is above the bubble point conditions but ignore that a system containing sub-micron sized gas or vapor bubbles distributed throughout the volume of the liquid, which can exhibit unexpected heterogenic and complex phase properties. In this paper, a new mathematical model for the flowing gas-liquid mixture is presented, which has been proposed considering the colloidal feature of the system above the saturation or bubble point pressure. This approach is more in line with the actual dynamic performance of the oil and gas mixture export pipeline. Experimental data, simulations and field case studies validate the new proposed mathematical model of flow characteristics in pipeline. The obtained results confirmed that the calculated data are in good agreement with the experimental data. Based on Azerbaijan oil-gas-condensate field “Guneshli” data, this new model was used for calculating the condition in which the transformation of the flow characteristics from stable into instable is occurred. It has been discovered that the flow becomes unstable at a pressure about 30% higher than Bubble Point Pressure, which causes pulsation effect in the pipeline structure. However, homogenic behavior should be observed in this hydrodynamic condition. Also, the model provides a guideline on how to optimize the flow rate by adjusting the pipeline parameters to minimize the flow resistance, liquid slugging and hydraulic hammering effects, which cause instable operation.

An Investigation of Recovery Mechanisms for Oil Field Optimization by Three-Phase Core Flood and Simulation Studies

Two potential recovery mechanisms are being considered for a major field which required laboratory measurements to investigate the efficiency of the two scenarios: gas flood followed by water flood and water flood followed by gas flood. Although simply stated, the recovery scenarios involved complex three-phase processes which had to be replicated in the laboratory at reservoir conditions to provide reliable data upon which reservoir development decisions could be made. The first sequence consisted of water displacing oil to residual oil saturation (Sorw), oil displacing water to residual water saturation (Swro) and gas displacing both oil and water to Sor3φ,g and Swr3φ,g. The second sequence consisted of gas displacing oil to residual oil saturation (Sorg), oil displacing gas to trapped gas saturation (Sgto) and water displacing both oil and gas to Sor3φ,w and Sgt3φ,w respectively. Composite cores of four well-matched plugs at Swi were used and all measurements were made at bubble point conditions. A vertical core holder was housed inside a reservoir condition facility equipped with gamma attenuation saturation monitoring (GASM). Temperature stability and the use of GASM were paramount for the accurate measurement of produced fluids, especially trapped gas saturation. Oil, gas and water produced volumes were also measured using a separator housed inside the core flood oven to provide optimum temperature stability. The laboratory results were modelled in a compositional simulator using an equation of state tuned to conventional PVT data and both swelling and multiple contact experiments. The objective was to build a three-phase predictive model from the constituent two-phase relative permeability data. The paper details the experimental methods and presents results for each section of the two sequences. The key conclusions are that Sorg>Sorw> Sor3φ,g> Sor3φ,w and Sgt3φ,w< Sgto.

A general finite volume based numerical algorithm for hydrocarbon reservoir simulation using blackoil model

Purpose – The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model. Design/methodology/approach – The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated. Findings – It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions. Research limitations/implications – While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured. Practical implications – The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable. Originality/value – A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

Vapor–Liquid Equilibrium Data for Carbon Dioxide + (R,S)-1,2-Isopropylidene Glycerol (Solketal) + Oleic Acid Systems at High Pressure

This paper reports experimental phase equilibrium data for the systems {CO2 (1) + solketal (2)} and {CO2 (1) + solketal (2) + oleic acid (3)}. The phase transition pressure measurements for ternary mixtures were carried out by injecting a known amount of carbon dioxide into a mixture with fixed molar ratios of the two other components (0.75 solketal + 0.25 oleic acid). A variable-volume cell with a front window was used for the measurements. The experimental data were measured over the temperature range from (308 to 338) K and at pressures of up to 20 MPa. Bubble point conditions were measured for the binary system {CO2 (1) + solketal (2)}, whereas bubble and dew point conditions were measured for the ternary system {CO2 (1) + solketal (2) + oleic acid (3)}. Phase equilibrium modeling with the Peng–Robinson equation of state was successful in describing the behavior of the investigated systems.

A modified rock physics model for analysis of seismic signatures of low gas-saturated rocks

In seismic applications, the bulk modulus of porous media saturated with liquid and gas phases is often estimated using Gassmann's fluid substitution formula, in which the effective bulk modulus of the two-phase fluid is the Reuss average of the gas and liquid bulk moduli. This averaging procedure, referred to as Wood's approximation, holds if the liquid and gas phases are homogeneously distributed within the pore space down to sizes well below the seismic wavelength and if the phase transfer processes between liquid and gas domains induced by the pressure variations of the seismic wave are negligible over the timescale of the wave period. Using existing theoretical results and low-frequency acoustic measurements in bubbly liquids, we argue that the latter assumption of “frozen” phases, valid for large enough frequencies, is likely to fail in the seismic frequency range where lower effective bulk modulus and velocity, together with dispersion and attenuation effects, are expected. We provide a simple method, which extends to reservoir fluids a classical result by Landau and Lifshitz valid for pure fluids, to compute the effective bulk modulus of thermodynamically equilibrated liquid and gas phases. For low gas saturation, this modulus is significantly lower than its Wood's counterpart, especially at the crossing of bubble point conditions. A seismic reflector associated to a phase transition between a monophasic and a two-phase fluid thus will appear. We discuss the consequences of these results for various seismic applications including fizz water discrimination and hydrocarbon reservoir depletion and CO2 geological storage monitoring.

A network flow model for the genesis and migration of gas phase

We present a network flow model to compute transport, through a pore network, of a compositional fluid consisting of water with a dissolved hydrocarbon gas. The model captures single-phase flow (below local bubble point conditions) as well as the genesis and migration of the gas phase when bubble point conditions are achieved locally. Constant temperature computational tests were run on simulated 2D and 3D micro-networks near bubble point pressure conditions. In the 2D simulations which employed a homogeneous network, negligible capillary pressure, and linear relative permeability relations, the observed concentration of CO2 dissolved in the liquid phase throughout the medium was linearly related to the liquid pressure. In the case of no gravity, the saturation of the gas phase throughout the medium was also linearly related to the liquid pressure; under gravity, the relationship became nonlinear in regions where buoyancy forces were significant. The 3D heterogeneous network model had nonnegligible capillary pressure and nonlinear relative permeability functions. While 100 % of the CO2 entered the 3D network dissolved in the liquid phase, 25 % of the void space was occupied by gas phase and 47 % of the CO2 exiting the outlet face did so via the gaseous phase after 500 s of simulation time.

Calculation of isentropic compressibility and sound velocity in two-phase fluids

Derivative properties from equations of state (EoS) are well defined for homogeneous fluid systems. However, some of these properties, such as isothermal and isentropic (or adiabatic) compressibilities and sound velocity need to be calculated at conditions for which a homogeneous fluid splits into two (or more) phases, liquid or vapor. The isentropic compressibility and sound velocity of thermodynamically equilibrated fluids exhibit important discontinuities at phase boundaries, as noticed long ago by Landau and Lifschitz in the case of pure fluids. In this work, the two-phase isentropic compressibility (or inverse bulk modulus) is expressed in terms of the two-phase isothermal compressibility, two-phase thermal expansivity and an apparent heat capacity, defined as the partial derivative of total enthalpy with respect to temperature at constant pressure and composition. The proposed method is simple (simpler than previous approaches), easy to implement and versatile; it is not EoS-dependent and it requires only a flash routine and the expression of total enthalpy at given pressure, temperature and composition. Our approach is applied to a variety of fluid systems representative of reservoir applications and geophysical situations, including petroleum fluids (oil and gas condensate) and mixtures of water and gas (methane or CO 2). For low gas content in the two-phase fluid, i.e., near bubble point conditions, we obtain significantly lower bulk moduli and sound velocities than predicted within Wood's conventional approach, in which the liquid and gas phases are considered to be “frozen” at the passage of the acoustic wave.

Solution theory model for thermophysical properties of refrigerant/lubricant mixtures

AbstractA general model for predicting the thermophysical properties of refrigerant/lubricant mixtures has been developed based on applicable theory for the excess Gibbs energy of nonideal solutions. In our approach, flexible thermodynamic forms are chosen to describe the properties of both the gas and liquid phases of refrigerant/lubricant mixtures. After an extensive study of models for describing nonideal liquid effects, the Wohl [3]‐suffix equations, which have been extensively used in the analysis of hydrocarbon mixtures, have been developed into a general form applicable to mixtures where one component is a polyolester or alkylbenzene lubricant. We have developed a nonideal solution computer code, based on the Wohl model that predicts dew point or bubble point conditions over a wide range of composition and temperature and includes the calculation of the enthalpy and entropy of refrigerant/lubricant mixtures. Our present analysis includes the thermodynamic properties of an ideal solution mixture and the corrections due to nonideal solution behavior. These nonideal solution corrections are based on analysis of the excess Gibbs energy of the mixture. We find that these nonideal solution corrections are small (<4%) for most refrigerant/lubricant mixtures, except at very low temperatures. © 2009 American Institute of Chemical Engineers AIChE J, 2009

A Spectroscopic and Computational Exploration of the Cybotactic Region of Gas-Expanded Liquids: Methanol and Acetone

Local compositions in supercritical and near-critial fluids may differ substantially from bulk compositions, and such differences have important effects on spectroscopic observations, phase equilibria, and chemical kinetics. Here, we compare such determinations around a solute probe dissolved in CO2-expanded methanol and acetone at 25 degrees C from solvatochromic experiments with molecular dynamics simulations. UV/vis and steady-state fluorescence measurements of the dye Coumarin 153 in the expanded liquid phase indicate preferential solvation in both the S0 and S1 states by the organic species. Simple dielectric continuum models are used to estimate local compositions from the spectroscopic data and are compared to molecular dynamics simulations of a single C153 molecule dissolved in the liquid phase at bubble point conditions. The simulations provide information about the local solvent structure around C153. They suggest the presence of large solvent clustering near the electron-withdrawing side of the probe. Preferential solvation exists in both the S0 and S1 states, but a large disagreement between simulation and experiment exists in the S1 state. Potential reasons for this disparity are discussed.

Continuous thermodynamic correlation and calculation of vapor pressure and vapor–liquid equilibrium constant of hydrocarbon fuel fractions

To quantitatively predict the vapor–liquid equilibrium characterization of hydrocarbon fuel fractions, continuous thermodynamics with the Gaussian distribution function to represent the composition of each fuel fraction is applied to correlate the experimental vapor pressure data. The vapor and liquid phase distribution functions, the vapor–liquid equilibrium constants of the component characterized by the normal boiling-point under different bubble-point conditions are calculated. It can be observed that the continuous thermodynamic method is a suitable tool for the correlation of vapor pressure data and the description of vapor–liquid equilibria of the multicomponent systems such as fuel fractions.

Measurement of Phase Boundaries of Hydrocarbon Mixtures Using Fiber Optical Detection Techniques

In this paper we present a novel technique for experimental determination of dew and bubble points of oils and gases under reservoir conditions. Extrinsic fiber optic sensors mounted on an 80-mL titanium equilibrium cell are part of the measurement setup. Formation of a new phase in the sample confined within the cell is sharply indicated by the creation of characteristic changes in the fiber optic signal. This allows for precise detection of dew and bubble point conditions. The entire apparatus is transportable and can easily be carried to field locations for quick and accurate studies of bottom hole samples. Phase behavior measurements (dew and bubble points) of three model systems and a real reservoir fluid are presented.

KB method in two phase flash calculations

A new algorithm has been developed for rigorous two phase flash calculations. It avoids the need to compute bubble points and dew points that are sometimes required to locate phase regions. Not having to extrapolate property models to extreme dew point or bubble point conditions, this method is faster and more stable than those currently in use.