Analytical Upgridding of Geocellular Mode in the Presence of Gravity-Dominated Displacement

SPE Journal ◽  
2011 ◽  
Vol 16 (04) ◽  
pp. 828-841 ◽  
Author(s):  
Ake Rittirong ◽  
Mohan Kelkar
Keyword(s):  
Oil Recovery ◽  
Flow Characteristics ◽  
Scale Model ◽  
Fine Scale ◽  
Computationally Efficient ◽  
Fractional Flow ◽  
Two Phase ◽  
Analytical Methodology ◽  
Three Phase ◽  
2D Flow

Summary In simulating enhanced-oil-recovery (EOR) processes, it is critical that all the flow behaviors be properly accounted for in the simulation. Because of computation limitations, long calculation time, and complexity of physics, geological models cannot be directly used for fieldwide simulations. Upgridding reduces the number of gridblocks in the simulation model and therefore makes the simulation more efficient. An appropriate upgridding process needs to preserve the dynamic behavior of the fine-scale model. We propose such an analytical methodology. Our new technique is based on preserving the characteristics, which are based on the fractional-flow concept specifically modified for vertical flow between the layers. We develop our method with a specific application to gravity-dominated displacement. In upgridding the fine-scale model, we have developed a criterion by which the sequence in which the fine-scale layers are combined is proposed such that fractional-flow characteristics based on the fine-scale model are honored. Using this methodology, we can determine not only the sequence in which layers are combined, but also to what extent we can upgrid the fine-scale model. The proposed methodology is developed for two-phase, 2D flow under the effect of gravity-segregated displacement. However, it is also tested for three-phase, 3D flow in gravity-dominated displacement with moderate effect of viscous and capillary forces. The proposed solution is analytical; therefore, it is computationally efficient. We have validated the methodology with both synthetic and field examples and demonstrate that the proposed methodology is superior to conventional proportional layering and variance-based methodologies.

Fast Upscaling of Polymer Flood Simulations Using Fractional Flow and Scaled Mobilities

2021 ◽  
Author(s):  
Hasan Al-Ibadi ◽  
Karl Stephen ◽  
Eric Mackay
Keyword(s):  
Relative Permeability ◽  
Control Method ◽  
Pressure Profile ◽  
Polymer Flooding ◽  
Mobility Control ◽  
Scale Model ◽  
Fine Scale ◽  
Fractional Flow ◽  
Water Viscosity ◽  
Flow Mobility

Abstract We introduce a pseudoisation method to upscale polymer flooding in order to capture the flow behaviour of fine scale models. This method is also designed to improve the predictability of pressure profiles during this process. This method controls the numerical dispersion of coarse grid models so that we are able to reproduce the flow behaviour of the fine scale model. To upscale polymer flooding, three levels of analysis are required such that we need to honour (a) the fractional flow solution, (b) the water and oil mobility and (c) appropriate upscaling of single phase flow. The outcome from this analysis is that a single pseudo relative permeability set that honours the modification that polymer applies to water viscosity modification without explicitly changing it. The shape of relative permeability can be chosen to honour the fractional flow solution of the fine scale using the analytical solution. This can result in a monotonic pseudo relative permeability set and we call it the Fractional-Flow method. To capture the pressure profile as well, individual relative permeability curves must be chosen appropriately for each phase to ensure the correct total mobility. For polymer flooding, changes to the water relative permeability included the changes to water viscosity implicitly thus avoiding the need for inclusion of a polymer solute. We call this type of upscaling as Fractional-Flow-Mobility control method. Numerical solution of the upscaled models, obtained using this method, were validated against fine scale models for 1D homogenous model and as well as 3D models with randomly distributed permeability for various geological realisations. The recovery factor and water cut matched the fine scale model very well. The pressure profile was reasonably predictable using the Fractional-Flow-Mobility control method. Both Fractional-Flow and Fractional-flow-Mobility control methods can be calculated in advance without running a fine scale model where the analysis is based on analytical solution even though produced a non-monotonic pseudo relative permeability curve. It simplified the polymer model so that it is much easier and faster to simulate. It offers the opportunity to quickly predict oil and water phase behaviour.

Cuttings Characteristics and Mechanics Behavior in Horizontal Wells of Liaohe Oil Field

2013 ◽  
Vol 316-317 ◽  
pp. 842-845
Author(s):  
Xian Zhong Yi ◽  
Jun Feng Zhang ◽  
Sheng Zong Jiang
Keyword(s):  
Flow Characteristics ◽  
Oil Field ◽  
Cuttings Transport ◽  
Two Phase ◽  
Fluid Medium ◽  
Washing Process ◽  
Three Phase ◽  
Flow Phenomena ◽  
Phase Liquid ◽  
Cuttings Bed

Cuttings transport of drilling and washing process in horizontal well is a typical two-phase (liquid-solid) or three-phase (gas-liquid-solid) flow phenomena. In this paper, it analyzes the flow characteristics of Huan 127-Lian H2 horizontal wellbore , then uses experimental method to study the behavior of the particle size distribution and the mechanics. This study provides an important way to master cuttings settling in fluid medium, it can explain how the cuttings bed is generated and cleared, and why the procession of cuttings of migration is stopped. In addition, measurement and analysis of drill cuttings is the basis erosion and abrasion analysis of BHA.

An Experimental Investigation of Viscous-Oil Recovery Efficiency as a Function of Voidage-Replacement Ratio

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1236-1253 ◽  
Author(s):  
Tae Wook Kim ◽  
E.. Vittoratos ◽  
A. R. Kovscek
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Crude Oils ◽  
Replacement Ratio ◽  
Two Phase ◽  
Foamy Oil ◽  
Three Phase ◽  
Solution Gas Drive ◽  
Gas Drive ◽  
Solution Gas

Summary Recovery processes with a voidage-replacement ratio (VRR) (VRR = injected volume/produced volume) of unity rely solely on viscous forces to displace oil, whereas a VRR of zero relies on solution-gas drive. Activating a solution-gas-drive mechanism in combination with waterflooding with periods of VRR less than unity (VRR < 1) may be optimal for recovery. Laboratory evidence suggests that recovery for VRR < 1 is enhanced by emulsion flow and foamy (i.e., bubbly) crude oil at pressures under bubblepoint for some crude oils. This paper investigates the effect of VRR for two crude oils referred to as A1 (88 cp and 6.2 wt% asphaltene) and A2 (600 cp and 2.5 wt% asphaltene) in a sandpack system (18-in. length and 2-in. diameter). The crude oils are characterized with viscosity, asphaltene fraction, and acid/base numbers. A high-pressure experimental sandpack system (1 darcy and Swi = 0) was used to conduct experiments with VRRs of 1.0, 0.7, and 0 for both oils. During waterflood experiments, we controlled and monitored the rate of fluid injection and production to obtain well-characterized VRR. On the basis of the production ratio of fluids, the gas/oil and /water relative permeabilities were estimated under two-phase-flow conditions. For a VRR of zero, the gas relative permeability of both oils exhibited extremely low values (10−6−10−4) caused by internal gas drive. Waterfloods with VRR < 1 displayed encouraging recovery results. In particular, the final oil recovery with VRR = 0.7 [66.2% original oil in place (OOIP)] is more than 15% greater than that with VRR = 1 (55.6% OOIP) with A1 crude oil. Recovery for A2 with VRR = 0.7 (60.5% OOIP) was identical to the sum of oil recovery for solution-gas drive (19.1% OOIP) plus waterflooding (40.1% OOIP). An in-line viewing cell permitted inspection of produced fluid morphology. For A1 and VRR = 0.7, produced oil was emulsified, and gas was dispersed as bubbles, as expected for a foamy oil. For A2 and VRR < 1, foamy oil was not clearly observed in the viewing cell. In all cases, the water cut of VRR = 1 is clearly greater than that of VRR = 0.7. Finally, three-phase relative permeability was explored on the basis of the experimentally determined two-phase oil/water and liquid/gas relative permeability curves. Well-known algorithms for three-phase relative permeability, however, did not result in good history matches to the experimental data. Numerical simulations matched the experimental recovery vs. production time acceptably after modification of the measured krg and krow relationships. A concave shape for oil relative permeability that is suggestive of emulsified oil in situ was noted for both systems. The degree of agreement with experimental data is sensitive to the details of gas (gas/oil system) and oil (oil/water system) mobility.

Scaling Up Low-Salinity Waterflooding in Heterogenous Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-22
Author(s):  
Hasan Al-Ibadi ◽  
Karl Stephen ◽  
Eric Mackay
Keyword(s):  
Relative Permeability ◽  
Coarse Grid ◽  
Numerical Dispersion ◽  
Absolute Permeability ◽  
Scale Model ◽  
Salinity Range ◽  
Fine Scale ◽  
Fractional Flow ◽  
Low Salinity ◽  
Low Salinity Waterflooding

SummaryModeling the dynamic fluid behavior of low-salinity waterflooding (LSWF) at the reservoir scale is a challenge that requires a coarse-grid simulation to enable prediction in a feasible time scale. However, evidence shows that using low-resolution models will result in a considerable mismatch compared with an equivalent fine-scale model with the potential of strong, numerically induced pulses and other dispersion-related effects. This work examines two new upscaling methods that have been applied to improve the accuracy of predictions in a heterogeneous reservoir where viscous crossflow takes place.We apply two approaches to upscaling to bring the flow prediction closer to being exact. In the first method, we shift the effective-salinity range for the coarse model using algorithms that we have developed to correct for numerical dispersion and associated effects. The second upscaling method uses appropriately derived pseudorelative permeability curves. The shape of these new curves is designed using a modified fractional-flow analysis of LSWF that captures the relationship between dispersion and the waterfront velocities. This second approach removes the need for explicit simulation of salinity transport to model oil displacement. We applied these approaches in layered models and for permeability distributed as a correlated random field.Upscaling by shifting the effective-salinity range of the coarse-grid model gave a good match to the fine-scale scenario, while considerable mismatch was observed for upscaling of the absolute permeability alone. For highly coarsened models, this method of upscaling reduced the appearance of numerically induced pulses. On the other hand, upscaling by using a single (pseudo)relative permeability produced more robust results with a very promising match to the fine-scale scenario. These methods of upscaling showed promising results when they were used to scale up fully communicating and noncommunicating layers as well as models with randomly correlated permeability.Unlike documented methods in the literature, these newly derived methods take into account the substantial effects of numerical dispersion and effective concentration on fluid dynamics using mathematical tools. The methods could be applied for other models where the phase mobilities change as a result of an injected solute, such as surfactant flooding and alkaline flooding. Usually these models use two sets of relative permeability and switch from one to another as a function of the concentration of the solute.

Hysteresis in Flow in Porous Media With Phase Transitions

1999 ◽  
Author(s):  
Pavel Bedrikovetsky ◽  
Dan Marchesin ◽  
Paulo Roberto Ballin
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Initial Boundary ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Fractional Flow ◽  
Two Phase ◽  
Initial Boundary Problem ◽  
Gas Drive

Abstract Two-phase flow with hysteresis in porous media is described by the Buckley-Leverett model with three types of fractional flow functions: imbibition, drainage and scanning. The mathematical theory for the Riemann problem and for non-self-similar initial-boundary problem is developed. The structure of the solutions is presented and the physical interpretation of the phenomena is discussed. We obtain the analytical solution for the injection of water slug with gas drive into oil reservoirs. The solutions show that the effect of hysteresis is to decrease gas flux (in the case where the drainage relative permeability lies below the imbibition relative permeability). This effect increases oil recovery for Water-Alternate-Gas injection in oil reservoirs.

RIEMANN SOLUTIONS FOR VERTICAL FLOW OF THREE PHASES IN POROUS MEDIA: SIMPLE CASES

2013 ◽  
Vol 10 (02) ◽  
pp. 335-370 ◽  
Author(s):  
PANTERS RODRÍGUEZ-BERMÚDEZ ◽  
DAN MARCHESIN
Keyword(s):  
Conservation Laws ◽  
Spatial Dimension ◽  
Immiscible Fluids ◽  
Fractional Flow ◽  
Two Phase ◽  
Riemann Solutions ◽  
Two Fluids ◽  
Three Phase ◽  
Three Phase Flow ◽  
Curve Method

We study Riemann solutions for a system of two nonlinear conservation laws that models buoyancy-driven flow of three immiscible fluids in a porous medium, which do not exchange mass. We also assume that the fluids are incompressible and the flow occurs in the vertical spatial dimension. We consider the simplified case in which two of the three fluids have equal densities, obtaining the Riemann solutions by the wave curve method. As expected, the solutions contain waves traveling both upwards and downwards. The sequences of waves contain rarefactions, shocks (sometimes traveling with characteristic speed), and constant states. The shocks found in this work are proper or generalized Lax shock waves. The solutions we found are L1-continuous with respect to the initial data. Waves involving only two fluids often take part in three-phase flow Riemann solutions; this is the basis of a useful tool (the wedge construction) to obtain shocks separating states in distinct two-phase regimes having a common fluid. This tool is similar to fractional flow theory, or Oleinik's convex construction. In this investigation, the wave curve method from the theory of conservation laws is combined with numerical calculations.

A Robust Three-Phase Isenthalpic Flash Algorithm Based on Free-Water Assumption

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Ruixue Li ◽  
Huazhou Andy Li
Keyword(s):  
Energy Conservation ◽  
Oil Recovery ◽  
Pure Water ◽  
Free Water ◽  
Conservation Equation ◽  
Feasible Region ◽  
Feed Mixture ◽  
Two Phase ◽  
Energy Conservation Equation ◽  
Three Phase

Isenthalpic flash is a type of flash calculation conducted at a given pressure and enthalpy for a feed mixture. Multiphase isenthalpic flash calculations are often required in compositional simulations of steam-based enhanced oil recovery methods. Based on a free-water assumption that the aqueous phase is pure water, a robust and efficient algorithm is developed to perform isenthalpic three-phase flashes. Assuming that the feed is stable, we first determine the temperature by solving the energy conservation equation. Then, the stability test on the feed mixture is conducted at the calculated temperature and the given pressure. If the mixture is found unstable, two-phase and three-phase vapor–liquid–aqueous isenthalpic flash can be simultaneously initiated without resorting to stability tests. The outer loop is used to update the temperature by solving the energy conservation equation. The inner loop determines the phase fractions and compositions through a three-phase free-water isothermal flash. A two-phase isothermal flash will be initiated if an open feasible region in the phase fractions appears in any iteration during the three-phase flash or any of the ultimately calculated phase fractions from the three-phase flash do not belong to [0,1]. A number of example calculations for water/hydrocarbon mixtures are carried out, demonstrating that the proposed algorithm is accurate, efficient, and robust.

Bubble Behaviour in Three Phase Capillary Microreactors

2003 ◽  
Vol 1 (1) ◽  
Author(s):  
Mark J Simmons ◽  
David C Y Wong ◽  
Paul J Travers ◽  
James S Rothwell
Keyword(s):  
High Speed ◽  
Flow Characteristics ◽  
Flow Regimes ◽  
Two Phase ◽  
Microchannel Reactors ◽  
Flow Maps ◽  
Three Phase ◽  
Monolith Reactors ◽  
Produce Flow ◽  
Churn Flow

Two-phase flow characteristics in vertical capillary downflow were investigated in order to obtain understanding of the behaviour of three-phase monolith reactors. Experiments were conducted using air and dyed water in round and square capillary tubes of 2 mm and 3 mm diameter. The flow regimes and transitions observed were recorded using high speed videography and this data was used to produce flow maps for each tube. The gas and liquid superficial velocities used ranged from 0.001 to 10 m/s and 0.0001 to 1 m/s respectively. The flow regimes and their transitions were found to be a strong function of tube geometry and surface tension effects, and some differences were observed between capillaries of round and square section. This has significant implications for the design of microchannel reactors. Annular, slug-annular, slug, bubbly and churn flow regimes were observed in the round tubes; channelling/irregular flow was observed in the square tubes in place of annular and slug-annular flow.

Two-Stage Upscaling of Two-Phase Flow: From Core to Simulation Scale

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 304-316 ◽  
Author(s):  
Arild Lohne ◽  
George A. Virnovsky ◽  
Louis J. Durlofsky
Keyword(s):  
Capillary Pressure ◽  
Effective Properties ◽  
Absolute Permeability ◽  
Scale Model ◽  
Phase Flow ◽  
Fine Scale ◽  
Coarse Scale ◽  
Two Stage ◽  
Two Phase ◽  
Rate Dependent

Summary In the coarse-scale simulation of heterogeneous reservoirs, effective or upscaled flow functions (e.g., oil and water relative permeability and capillary pressure) can be used to represent heterogeneities at subgrid scales. The effective relative permeability is typically upscaled along with absolute permeability from a geocellular model. However, if no subgeocellular-scale information is included, the potentially important effects of smaller-scale heterogeneities (on the centimeter to meter scale) in both capillarity and absolute permeability will not be captured by this approach. In this paper, we present a two-stage upscaling procedure for two-phase flow. In the first stage, we upscale from the core (fine) scale to the geocellular (intermediate) scale, while in the second stage we upscale from the geocellular scale to the simulation (coarse) scale. The computational procedure includes numerical solution of the finite-difference equations describing steady-state flow over the local region to be upscaled, using either constant pressure or periodic boundary conditions. In contrast to most of the earlier investigations in this area, we first apply an iterative rate-dependent upscaling (iteration ensures that the properties are computed at the appropriate pressure gradient) rather than assume viscous or capillary dominance and, second, assess the accuracy of the two-stage upscaling procedure through comparison of flow results for the coarsened models against those of the finest-scale model. The two-stage method is applied to synthetic 2D reservoir models with strong variation in capillarity on the fine scale. Accurate reproduction of the fine-grid solutions (simulated on 500'500 grids) is achieved on coarse grids of 10'10 for different flow scenarios. It is shown that, although capillary forces are important on the fine scale, the assumption of capillary dominance in the first stage of upscaling is not always appropriate, and that the computation of rate-dependent effective properties in the upscaling can significantly improve the accuracy of the coarse-scale model. The assumption of viscous dominance in the second upscaling stage is found to be appropriate in all of the cases considered. Introduction Because of computational costs, field-simulation models may have very coarse cells with sizes up to 100 to 200 m in horizontal directions. The cells are typically populated with effective properties (porosity, absolute permeability, relative permeabilities, and capillary pressure) upscaled from a geocellular (or geostatistical) model. In this way, the effects of heterogeneity on the geocellular scale will be included in the large-scale flow calculations. The cell sizes in geocellular models may be on the order of 20 to 50 m in horizontal directions. However, heterogeneities on much smaller scales (cm- to m- scale) may have a significant influence on the reservoir flow (Coll et al. 2001; Honarpour et al. 1994), and this potential effect cannot be captured if the upscaling starts at the geocellular scale.

Multiple-Mixing-Cell Method for Three-Hydrocarbon-Phase Displacements

SPE Journal ◽  
2015 ◽  
Vol 20 (06) ◽  
pp. 1339-1349 ◽  
Author(s):  
Liwei Li ◽  
Saeid Khorsandi ◽  
Russell T. Johns ◽  
Kaveh Ahmadi
Keyword(s):  
Relative Permeability ◽  
Cell Model ◽  
Phase Identification ◽  
Displacement Efficiency ◽  
Compositional Simulation ◽  
Fractional Flow ◽  
Two Phase ◽  
Cell Method ◽  
Multiple Mixing ◽  
Three Phase

Summary Low-temperature oil displacements by carbon dioxide involve complex phase behavior, in which three hydrocarbon phases can coexist. Reliable design of miscible gasflooding requires knowledge of the minimum miscibility pressure (MMP), which is the pressure required for 100% recovery in the absence of dispersion or as defined by slimtube experiments as the “knee” in the recovery curve with pressure in which displacement efficiency is greater than 90%. There are currently no analytical methods to estimate the MMP for multicomponent mixtures exhibiting three hydrocarbon phases. Also, the use of compositional simulators to estimate MMP is not always reliable. These challenges include robustness issues of three-phase equilibrium calculations, inaccurate three-phase relative permeability models, and phase identification and labeling problems that can cause significant discontinuities and failures in the simulation results. How miscibility is developed, or not developed, for a three-phase displacement is not well-known. We developed a new three-phase multiple-mixing-cell method that gives a relatively easy and robust way to determine the pressure for miscibility or, more importantly, the pressure for high-displacement efficiency. The procedure that moves fluid from cell to cell is robust because it is independent of phase labeling (i.e., vapor or liquid), has a robust way to provide good initial guesses for three-phase flash calculations, and is also not dependent on three-phase relative permeability (fractional flow). These three aspects give the mixing-cell approach significant advantages over the use of compositional simulation to estimate MMP or to understand miscibility development. One can integrate the approach with previously developed two-phase multiple-mixing-cell models because it uses the tie-line lengths from the boundaries of tie triangles to recognize when the MMP or pressure for high-displacement efficiency is obtained. Application of the mixing-cell algorithm shows that, unlike most two-phase displacements, the dispersion-free MMP may not exist for three-phase displacements, but rather a pressure is reached in which the dispersion-free displacement efficiency is maximized. The authors believe that this is the first paper to examine a multiple-mixing-cell model in which two- and three-hydrocarbon phases occur and to calculate the MMP and/or pressure required for high displacement efficiency for such systems.

Sign in / Sign up

Export Citation Format

Share Document