scholarly journals Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling

2021 ◽  
Vol 26 (3) ◽  
pp. 60
Author(s):  
Ahmad Abushaikha ◽  
Dominique Guérillot ◽  
Mostafa Kadiri ◽  
Saber Trabelsi

This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of view, the extension consists of the addition to each phase equation of a term depending on the gradient of the pressure of the other phase, leading to a coupled system of differential equations. The obtained system is much more involved than the classical Darcy system since it involves the Forchheimer equation in addition to the Darcy one. This model is more appropriate when there is a substantial difference between the phases’ velocities, for instance in the case of gas/water phases, and applications in oil recovery using gas flooding. Based on the Buckley–Leverett theory, including capillary pressure, we derive an explicit expression of the phases’ velocities and fractional water flows in terms of the gradient of the capillary pressure, and the total constant velocity. Various scenarios are considered, and the respective numerical simulations are presented. In particular, comparisons with the classical models (without phase coupling) are provided in terms of breakthrough time among others. Eventually, we provide a post-processing method for the derivation of the solution of the new coupled system using the classical non-coupled system. This method is of interest for industry since it allows for including the phase coupling approach in existing numerical codes and software (designed for solving classical models) without major technical changes.

2001 ◽  
Vol 4 (06) ◽  
pp. 455-466 ◽  
Author(s):  
A. Graue ◽  
T. Bognø ◽  
B.A. Baldwin ◽  
E.A. Spinler

Summary Iterative comparison between experimental work and numerical simulations has been used to predict oil-recovery mechanisms in fractured chalk as a function of wettability. Selective and reproducible alteration of wettability by aging in crude oil at an elevated temperature produced chalk blocks that were strongly water-wet and moderately water-wet, but with identical mineralogy and pore geometry. Large scale, nuclear-tracer, 2D-imaging experiments monitored the waterflooding of these blocks of chalk, first whole, then fractured. This data provided in-situ fluid saturations for validating numerical simulations and evaluating capillary pressure- and relative permeability-input data used in the simulations. Capillary pressure and relative permeabilities at each wettability condition were measured experimentally and used as input for the simulations. Optimization of either Pc-data or kr-curves gave indications of the validity of these input data. History matching both the production profile and the in-situ saturation distribution development gave higher confidence in the simulations than matching production profiles only. Introduction Laboratory waterflood experiments, with larger blocks of fractured chalk where the advancing waterfront has been imaged by a nuclear tracer technique, showed that changing the wettability conditions from strongly water-wet to moderately water-wet had minor impact on the the oil-production profiles.1–3 The in-situ saturation development, however, was significantly different, indicating differences in oil-recovery mechanisms.4 The main objective for the current experiments was to determine the oil-recovery mechanisms at different wettability conditions. We have reported earlier on a technique that reproducibly alters wettability in outcrop chalk by aging the rock material in stock-tank crude oil at an elevated temperature for a selected period of time.5 After applying this aging technique to several blocks of chalk, we imaged waterfloods on blocks of outcrop chalk at different wettability conditions, first as a whole block, then when the blocks were fractured and reassembled. Earlier work reported experiments using an embedded fracture network,4,6,7 while this work also studied an interconnected fracture network. A secondary objective of these experiments was to validate a full-field numerical simulator for prediction of the oil production and the in-situ saturation dynamics for the waterfloods. In this process, the validity of the experimentally measured capillary pressure and relative permeability data, used as input for the simulator, has been tested at strongly water-wet and moderately water-wet conditions. Optimization of either Pc data or kr curves for the chalk matrix in the numerical simulations of the whole blocks at different wettabilities gave indications of the data's validity. History matching both the production profile and the in-situ saturation distribution development gave higher confidence in the simulations of the fractured blocks, in which only the fracture representation was a variable. Experimental Rock Material and Preparation. Two chalk blocks, CHP8 and CHP9, approximately 20×12×5 cm thick, were obtained from large pieces of Rørdal outcrop chalk from the Portland quarry near Ålborg, Denmark. The blocks were cut to size with a band saw and used without cleaning. Local air permeability was measured at each intersection of a 1×1-cm grid on both sides of the blocks with a minipermeameter. The measurements indicated homogeneous blocks on a centimeter scale. This chalk material had never been contacted by oil and was strongly water-wet. The blocks were dried in a 90°C oven for 3 days. End pieces were mounted on each block, and the whole assembly was epoxy coated. Each end piece contained three fittings so that entering and exiting fluids were evenly distributed with respect to height. The blocks were vacuum evacuated and saturated with brine containing 5 wt% NaCl+3.8 wt% CaCl2. Fluid data are found in Table 1. Porosity was determined from weight measurements, and the permeability was measured across the epoxy-coated blocks, at 2×10–3 µm2 and 4×10–3 µm2, for CHP8 and CHP9, respectively (see block data in Table 2). Immobile water saturations of 27 to 35% pore volume (PV) were established for both blocks by oilflooding. To obtain uniform initial water saturation, Swi, oil was injected alternately at both ends. Oilfloods of the epoxy-coated block, CHP8, were carried out with stock-tank crude oil in a heated pressure vessel at 90°C with a maximum differential pressure of 135 kPa/cm. CHP9 was oilflooded with decane at room temperature. Wettability Alteration. Selective and reproducible alteration of wettability, by aging in crude oil at elevated temperatures, produced a moderately water-wet chalk block, CHP8, with similar mineralogy and pore geometry to the untreated strongly water-wet chalk block CHP9. Block CHP8 was aged in crude oil at 90°C for 83 days at an immobile water saturation of 28% PV. A North Sea crude oil, filtered at 90°C through a chalk core, was used to oilflood the block and to determine the aging process. Two twin samples drilled from the same chunk of chalk as the cut block were treated similar to the block. An Amott-Harvey test was performed on these samples to indicate the wettability conditions after aging.8 After the waterfloods were terminated, four core plugs were drilled out of each block, and wettability measurements were conducted with the Amott-Harvey test. Because of possible wax problems with the North Sea crude oil used for aging, decane was used as the oil phase during the waterfloods, which were performed at room temperature. After the aging was completed for CHP8, the crude oil was flushed out with decahydronaphthalene (decalin), which again was flushed out with n-decane, all at 90°C. Decalin was used as a buffer between the decane and the crude oil to avoid asphalthene precipitation, which may occur when decane contacts the crude oil.


2014 ◽  
Vol 695 ◽  
pp. 499-502 ◽  
Author(s):  
Mohamad Faizul Mat Ali ◽  
Radzuan Junin ◽  
Nor Hidayah Md Aziz ◽  
Adibah Salleh

Malaysia oilfield especially in Malay basin has currently show sign of maturity phase which involving high water-cut and also pressure declining. In recent event, Malaysia through Petroliam Nasional Berhad (PETRONAS) will be first implemented an enhanced oil recovery (EOR) project at the Tapis oilfield and is scheduled to start operations in 2014. In this project, techniques utilizing water-alternating-gas (WAG) injection which is a type of gas flooding method in EOR are expected to improve oil recovery to the field. However, application of gas flooding in EOR process has a few flaws which including poor sweep efficiency due to high mobility ratio of oil and gas that promotes an early breakthrough. Therefore, a concept of carbonated water injection (CWI) in which utilizing CO2, has ability to dissolve in water prior to injection was applied. This study is carried out to assess the suitability of CWI to be implemented in improving oil recovery in simulated sandstone reservoir. A series of displacement test to investigate the range of recovery improvement at different CO2 concentrations was carried out with different recovery mode stages. Wettability alteration properties of CWI also become one of the focuses of the study. The outcome of this study has shown a promising result in recovered residual oil by alternating the wettability characteristic of porous media becomes more water-wet.


1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.


2021 ◽  
Author(s):  
Omar Chaabi ◽  
Emad W. Al-Shalabi ◽  
Waleed Alameri

Abstract Low salinity polymer (LSP) flooding is getting more attention due to its potential of enhancing both displacement and sweep efficiencies. Modeling LSP flooding is challenging due to the complicated physical processes and the sensitivity of polymers to brine salinity. In this study, a coupled numerical model has been implemented to allow investigating the polymer-brine-rock geochemical interactions associated with LSP flooding along with the flow dynamics. MRST was coupled with the geochemical software IPhreeqc. The effects of polymer were captured by considering Todd-Longstaff mixing model, inaccessible pore volume, permeability reduction, polymer adsorption as well as salinity and shear rate effects on polymer viscosity. Regarding geochemistry, the presence of polymer in the aqueous phase was considered by adding a new solution specie and related chemical reactions to PHREEQC database files. Thus, allowing for modeling the geochemical interactions related to the presence of polymer. Coupling the two simulators was successfully performed, verified, and validated through several case studies. The coupled MRST-IPhreeqc simulator allows for modeling a wide variety of geochemical reactions including aqueous, mineral precipitation/dissolution, and ion exchange reactions. Capturing these reactions allows for real time tracking of the aqueous phase salinity and its effect on polymer rheological properties. The coupled simulator was verified against PHREEQC for a realistic reactive transport scenario. Furthermore, the coupled simulator was validated through history matching a single-phase LSP coreflood from the literature. This paper provides an insight into the geochemical interactions between partially hydrolyzed polyacrylamide (HPAM) and aqueous solution chemistry (salinity and hardness), and their related effect on polymer viscosity. This work is also considered as a base for future two-phase polymer solution and oil interactions, and their related effect on oil recovery.


Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wang Chengjun ◽  
Li Xiaorui

The determination of miscible characteristic is one of the key technologies for enhancing oil recovery of gas flooding. If the miscible characteristic at each development period of gas flooding can be known in real time, it will be helpful to guide gas flooding development scheme. The minimum miscible pressure (MMP) is mostly used to describe miscible characteristic. Currently, the MMP forecasting methods can be classified into two categories—the empirical method and theoretical calculation method. In this paper, the main controlling factors affecting MMP are analyzed combined with reservoir engineering method, phase equilibrium theory, reservoir numerical simulation technology, and so on. Based on this, new empirical and theoretical MMP forecasting model was built. Meanwhile, new ideas for improving forecasting accuracy through modifying miscible criterion were proposed. The calculation accuracies of the two MMP forecasting models can be improved to over 90% that is more accurate and adapted than other methods. This research result can supply new ideas for gas flooding MMP forecasting.


Author(s):  
Jennifer Niessner ◽  
S. Majid Hassanizadeh ◽  
Dustin Crandall

We present a new numerical model for macro-scale two-phase flow in porous media which is based on a physically consistent theory of multi-phase flow. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy’s law as well as constitutive relationships for relative permeability and capillary pressure. This approach is known to have a number of important shortcomings and, in particular, it does not account for the presence and role of fluid–fluid interfaces. An alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. In addition to the standard equations, the model uses a balance equation for specific interfacial area. The constitutive relationship for capillary pressure involves not only saturation, but also specific interfacial area. We show how parameters can be obtained for the alternative model using experimental data from a new kind of flow cell and present results of a numerical modeling study.


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