A Fully Coupled Three-Phase Model for Capillary Pressure and Relative Permeability for Implicit Compositional Reservoir Simulation

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1003-1019 ◽  
Author(s):  
Odd Steve Hustad ◽  
David John Browning
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Reservoir Simulation ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Capillary Pressures ◽  
And Performance ◽  
Model Features ◽  
2D And 3D

Summary A coupled formulation for three-phase capillary pressure and relative permeability for implicit compositional reservoir simulation is presented. The formulation incorporates primary, secondary, and tertiary saturation functions. Hysteresis and miscibility are applied simultaneously to both capillary pressure and relative permeability. Two alternative three-phase capillary pressure formulations are presented: the first as described by Hustad (2002) and the second that incorporates six representative two-phase capillary pressures in a saturation-weighting scheme. Consistency is ensured for all three two-phase boundary conditions through the application of two-phase data and normalized saturations. Simulation examples of water-alternating-gas (WAG) injection are presented for water-wet and mixed-wet saturation functions. 1D homogeneous and 2D and 3D heterogeneous examples are employed to demonstrate some model features and performance.

Three-Phase Relative Permeability and Capillary Pressure Models With Hysteresis and Compositional Consistency

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2394-2408 ◽  
Author(s):  
Sajjad S. Neshat ◽  
Gary A. Pope
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Numerical Stability ◽  
Physical Parameters ◽  
Gas Oil ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Minimum Number ◽  
Trapping Number ◽  
New Formulation

Summary New coupled three-phase hysteretic relative permeability and capillary pressure models have been developed and tested for use in compositional reservoir simulators. The new formulation incorporates hysteresis and compositional consistency for both capillary pressure and relative permeability. This approach is completely unaffected by phase flipping and misidentification, which commonly occur in compositional simulations. Instead of using phase labels (gas/oil/solvent/aqueous) to define hysteretic relative permeability and capillary pressure parameters, the parameters are continuously interpolated between reference values using the Gibbs free energy (GFE) of each phase at each timestep. Models that are independent of phase labels have many advantages in terms of both numerical stability and physical consistency. The models integrate and unify relevant physical parameters, including hysteresis and trapping number, into one rigorous algorithm with a minimum number of parameters for application in numerical reservoir simulators. The robustness of the new models is demonstrated with simulations of the miscible water-alternating-gas (WAG) process and solvent stimulation to remove condensate and/or water blocks in both conventional and unconventional formations.

Relative Permeability Characterization for Water-Alternating-Gas Injection in Oil Reservoirs

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0799-0808 ◽  
Author(s):  
H.. Shahverdi ◽  
M.. Sohrabi
Keyword(s):  
Relative Permeability ◽  
Gas Injection ◽  
Hysteresis Effect ◽  
Oil Reservoirs ◽  
Unsteady State ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Phase Water ◽  
Wag Injection

Summary Large quantities of oil usually remain in oil reservoirs after conventional waterfloods. A significant part of this remaining oil can still be economically recovered by water-alternating-gas (WAG) injection. WAG injection involves drainage and imbibition processes taking place sequentially; therefore, the numerical simulation of the WAG process requires reliable knowledge of three-phase relative permeability (kr) accounting for cyclic-hysteresis effects. In this study, the results of a series of unsteady-state two-phase displacements and WAG coreflood experiments were used to investigate the behavior of three-phase kr and hysteresis effects in the WAG process. The experiments were performed on two different cores with different characteristics and wettability conditions. An in-house coreflood simulator was developed to obtain three-phase relative permeability values directly from unsteady-state WAG experiments by history matching the measured recovery and differential-pressure profiles. The results show that three-phase gas relative permeability is reduced in consecutive gas-injection cycles and consequently the gas mobility and injectivity drop significantly with successive gas injections during the WAG process, under different rock conditions. The trend of hysteresis in the relative permeabilty of gas (krg) partly contradicts the existing hysteresis models available in the literature. The three-phase water relative permeability (krw) of the water-wet (WW) core does not exhibit considerable hysteresis effect during different water injections, whereas the mixed-wet (MW) core shows slight cyclic hysteresis. This may indicate a slight increase of the water injectivity in the subsequent water injections in the WAG process under MW conditions. Insignificant hysteresis is observed in the oil relative permeability (kro) during different gas-injection cycles for both WW and MW rocks. However, a considerable cyclic-hysteresis effect in kro is observed during water-injection cycles of WAG, which is attributed to the reduction of the residual oil saturation (ROS) during successive water injections. The kro of the WW core exhibits much-more cyclic-hysteresis effect than that of the MW core. No models currently exist in reservoir simulators that can capture the observed cyclic-hysteresis effect in oil relative permeability for the WAG process. Investigation of relative permeability data obtained from these displacement tests at different rock conditions revealed that there is a significant discrepancy between two-phase and three-phase relative permeability of all fluids. This highlights that not only the three-phase relative permeability of the intermediate phase (oil), but also the three-phase kr of the wetting phase (water) and nonwetting phase (gas) are functions of two independent saturations.

A Robust Methodology To Simulate Water-Alternating-Gas Experiments at Different Scenarios Under Near-Miscible Conditions

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1506-1518 ◽  
Author(s):  
Pedram Mahzari ◽  
Mehran Sohrabi
Keyword(s):  
Porous Media ◽  
History Matching ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Matching Process ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Three Phase Flow ◽  
Cycle Dependent

Summary Three-phase flow in porous media during water-alternating-gas (WAG) injections and the associated cycle-dependent hysteresis have been subject of studies experimentally and theoretically. In spite of attempts to develop models and simulation methods for WAG injections and three-phase flow, current lack of a solid approach to handle hysteresis effects in simulating WAG-injection scenarios has resulted in misinterpretations of simulation outcomes in laboratory and field scales. In this work, by use of our improved methodology, the first cycle of the WAG experiments (first waterflood and the subsequent gasflood) was history matched to estimate the two-phase krs (oil/water and gas/oil). For subsequent cycles, pertinent parameters of the WAG hysteresis model are included in the automatic-history-matching process to reproduce all WAG cycles together. The results indicate that history matching the whole WAG experiment would lead to a significantly improved simulation outcome, which highlights the importance of two elements in evaluating WAG experiments: inclusion of the full WAG experiments in history matching and use of a more-representative set of two-phase krs, which was originated from our new methodology to estimate two-phase krs from the first cycle of a WAG experiment. Because WAG-related parameters should be able to model any three-phase flow irrespective of WAG scenarios, in another exercise, the tuned parameters obtained from a WAG experiment (starting with water) were used in a similar coreflood test (WAG starting with gas) to assess predictive capability for simulating three-phase flow in porous media. After identifying shortcomings of existing models, an improved methodology was used to history match multiple coreflood experiments simultaneously to estimate parameters that can reasonably capture processes taking place in WAG at different scenarios—that is, starting with water or gas. The comprehensive simulation study performed here would shed some light on a consolidated methodology to estimate saturation functions that can simulate WAG injections at different scenarios.

Proxy models for evaluation of permeability, three-phase relative permeability, and capillary pressure curves from rate-transient data

SIMULATION ◽  
2019 ◽  
pp. 003754971985713 ◽  
Author(s):  
Zhenzihao Zhang ◽  
Turgay Ertekin
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Functional Relationship ◽  
Water Saturation ◽  
Petrophysical Properties ◽  
Laboratory Measurements ◽  
Connate Water ◽  
Three Phase ◽  
Transient Data ◽  
Critical Gas Saturation

This study developed a data-driven forecasting tool that predicts petrophysical properties from rate-transient data. Traditional estimations of petrophysical properties, such as relative permeability (RP) and capillary pressure (CP), strongly rely on coring and laboratory measurements. Coring and laboratory measurements are typically conducted only in a small fraction of wells. To contend with this constraint, in this study, we develop artificial neural network (ANN)-based tools that predict the three-phase RP relationship, CP relationship, and formation permeability in the horizontal and vertical directions using the production rate and pressure data for black-oil reservoirs. Petrophysical properties are related to rate-transient data as they govern the fluid flow in oil/gas reservoirs. An ANN has been proven capable of mimicking any functional relationship with a finite number of discontinuities. To generate an ANN representing the functional relationship between rate-transient data and petrophysical properties, an ANN structure pool is first generated and trained. Cases covering a wide spectrum of properties are then generated and put into training. Training of ANNs in the pool and comparisons among their performance yield the desired ANN structure that performs the most effectively among the ANNs in the pool. The developed tool is validated with blind tests and a synthetic field case. Reasonable predictions for the field cases are obtained. Within a fraction of second, the developed ANNs infer accurate characteristics of RP and CP for three phases as well as residual saturation, critical gas saturation, connate water saturation, and horizontal permeability with a small margin of error. The predicted RP and CP relationship can be generated and applied in history matching and reservoir modeling. Moreover, this tool can spare coring expenses and prolonged experiments in most of the field analysis. The developed ANNs predict the characteristics of three-phase RP and CP data, connate water saturation, residual oil saturation, and critical gas saturation using rate-transient data. For cases fulfilling the requirement of the tool, the proposed technique improves reservoir description while reducing expenses and time associated with coring and laboratory experiments at the same time.

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