Accurate determination of relative permeability hysteresis is needed to predict water-alternating-gas (WAG) injection reliably. Two series of gas/water relative permeability hysteresis curves were obtained from corefloods under mixed-wet conditions. The results revealed that none of the widely used hysteresis models (e.g., Carlson and Killough models) is able to predict the observed cyclic relative permeability hysteresis for alternating injection of gas and water. The results suggest that, for mixed-wet systems, it is necessary to consider irreversible hysteresis loops for modeling both the wetting and the nonwetting phase.
Introduction
Because of nonwetting-phase trapping, wetting-phase relative permeability for imbibition increased compared with the drainage case and nonwetting-phase imbibition relative permeability was less than that of the drainage case. Therefore, relative permeability to a fluid at a given saturation depends on whether that saturation was obtained by approaching it from a higher or lower value. This behavior in relative permeability is the hysteresis effect.
Much of the hysteresis data in the literature was obtained with saturations starting at endpoint values (i.e., irreducible-water saturation or residual-oil saturations for a water/oil system). These data usually deal with the differences between bounding relative permeabilities. Such data are more applicable to modeling reservoir processes in which phase saturations increase or decrease to an intermediate value, then change in the opposite direction. Examples include enhanced-oil-recovery methods such as WAG injection or cyclic-steam stimulation.
Most of the existing relative permeability hysteresis functions were developed for strongly water-wet porous media. However, it generally is accepted that many oil reservoirs are mixed-wet. In a mixed-wet system, the oil-wet pores correspond to the largest pores in the rock, while the small pores are water-wet. There are only a few relative permeability models developed for mixed-wet porous media, of which none are included in commercial simulators.
The purpose of this study was to further investigate the effect of cyclic hysteresis for water/gas systems under mixed-wet conditions. These two-phase relative permeability data are of interest for reliable simulation of processes involving cyclic changes between imbibition and drainage displacement, including WAG injection. The results of this study can be applied to underground hydrocarbon-gas storage, which usually involves cyclic pressurization (drainage) and depressurization (imbibition) on an annual basis. This is especially true if the underground formation has an active aquifer.
Two series of gas/water displacements were carried out to investigate and identify the cyclic hysteresis effect under mixed-wettability conditions. The measured data were used to estimate relative permeability values by use of a history-matching technique in a coreflood simulator. The experimentally derived relative permeability curves were used to investigate the performance of the Killough and Carlson hysteresis models available in commercial simulators. These models are used widely to include hysteresis effects in simulating the WAG process. The experimental data also were used to investigate different nonwetting-phase-trapping models.
Gas/Water Hysteresis Experiments
Drainage/Imbibition/Drainage/Imbibition/Drainage/Imbibition (DIDIDI). These tests started with gas injection (drainage) into a core saturated with 100% water, followed by a water-injection period (imbibition). The gas- and water-injection periods were repeated to simulate three injection cycles (i.e., DIDIDI).
Imbibition/Drainage/Imbibition/Drainage/Imbibition (IDIDI). Another series of gas/water displacements was carried out to further investigate and identify the hysteresis effects for a gas/water system under mixed-wettability conditions. First, the immobile-water saturation was established. This series of tests began with brine injection into a core saturated with 82% gas and 18% immobile water. This brine-injection (imbibition) period was followed by a gas-injection (drainage) period. The periods of water and gas injection were repeated for a total of three water injections and two gas injections with this series of fluid displacements, named IDIDI. Comparisons were made between the results of this IDIDI test and the DIDIDI test. The bounding curves (for both imbibition and drainage) were compared with scanning curves, and an investigation was made into the possible effects of saturation history on the gas-trapping and hysteresis behaviors of relative permeability to gas krg and to water krw.
Results
Hysteresis Effect. A black-oil coreflood simulator was used to history match the coreflood results and obtain relative permeability curves. A good match was obtained between the simulation and the experiment, which is important for reliable estimation of the relative permeability curves by this method. The capillary pressure values for the first imbibition curve were obtained by application of a J-function from data measured on Clashach sandstone (1,000 md). In the saturation range of the experiment, capillary pressure values were as low as 5 psia, and they did not affect the simulation results. Therefore, to reduce uncertainty (i.e., by decreasing the number of parameters that should be optimized during history matching), the effects of capillary pressure hysteresis were ignored in subsequent simulations and estimations.
Hysteresis-Model Assessments. DIDIDI Experiment. In the DIDIDI experiments, the wetting phase (water) showed little hysteresis between imbibition (water-injection) and drainage (gas-injection) cycles. However, the nonwetting-phase (gas) relative permeability showed significant hysteresis in both imbibition and drainage cycles. For wetting-phase (water) relative permeabilities, use of either the Carlson or the Killough model would work well because there was no significant hysteresis in the experimental results. For the nonwetting phase, theoretically, both models consider hysteresis for alternating between drainage and imbibition. The Carlson model predicted zero trapped-gas saturation for the first imbibition cycle. Therefore, in the Carlson model, gas relative permeabilities for the first imbibition cycle would be the same as those of the first drainage cycle. As a result, the Carlson model would not be able to capture any hysteresis for the first imbibition cycle and all subsequent cycles. The Killough model uses the Land formulation to predict trapped-gas saturation. The Land formulation still underestimates the trapped-gas saturation for the first imbibition cycle, yet the prediction is much better than that of the Carlson model. As a result of underestimating trapped gas, krg predictions from the Killough model are higher than those from experimental data (Fig. 1). The Killough model does not assume any hysteresis for the change of saturation direction from imbibition to drainage; as a result it would not predict any hysteresis for successive drainage cycles.
As imbibition and drainage cycles continue, the Killough model does not predict further hysteresis. There will be no hysteresis even for the successive imbibition cycles because the historical turning point is not passed in the successive drainage stages. For both Carlson and Killough hysteresis models, the deviation from the experimental data was larger during the later cycles of the experiments. The predicted pressure drop for the imbibition cycles of the experiment was underestimated significantly by both models. This was especially true for the Carlson model and led to significant overestimating of injectivity during imbibition cycles.
IDIDI Experiment. In the IDIDI experiment, both the wetting (water) and nonwetting (gas) phases showed hysteresis for a change of saturation direction between imbibition and drainage. The nonwetting-phase (gas) hysteresis was much lower compared with that observed in the DIDIDI experiments. However, the wetting-phase (water) relative permeability hysteresis was greater in this case compared with the DIDIDI experiment.
For wetting-phase relative permeabilities, neither the Carlson nor the Killough model predicted hysteresis and, for different cycles of the imbibition and drainage, the relative permeability values for both phases were the same as those of the first imbibition cycle. Therefore, the predictions by these two models would be the same. Fig. 2 highlights the differences between the predicted and experimental relative permeability values for the first drainage cycle for the Carlson model. The hysteresis models overestimated both the wetting- and nonwetting-phase relative permeability values during the entire IDIDI experiment.
Fig. 3 compares gas-saturation changes in the IDIDI experiment with the Carlson-model prediction. The hysteresis model overestimated the saturation changes during the experiment. Similar to the DIDIDI case, the deviation from the experimental data became larger for the later cycles of the experiments. The predicted pressure drop for the imbibition cycles of the experiment was underestimated significantly by hysteresis models. Generally, injectivity was better (higher) in the case of DIDIDI experiments compared with the IDIDI experiments (considering the much lower pressure drop across the core for the former case).
Conclusions
- For the nonwetting phase (gas), relative permeability of the scanning drainage cycles would not follow those of the former imbibitions, which is against the assumptions in the Carlson, Land, and Killough hysteresis models, showing the importance of including nonreversible-hysteresis-loop models in commercial simulators.
- Contrary to predictions of existing relative permeability hysteresis models, it was observed that although the same saturation as the former imbibition turning point was achieved in drainage cycles, endpoint relative permeability of gas would be less than that in the previous drainage cycle. Therefore, at the end of the second gas-injection cycle (i.e., at the same saturation as that of the end of the first gas-injection cycle), krg was less than that for the first gas injection. This observation was validated by calculating the endpoint krw value (steady-state point) from the Darcy equation. Current two-phase hysteresis models assume that these values are the same. For both wetting (water) and nonwetting (gas) phases, the cyclic hysteresis effect is less important as the later cycles are approached.
IDIDI Gas/Water System.
- Wetting-phase (water) relative permeability showed hysteresis in alternating imbibition and drainage cycles. The results showed that krw values dropped in successive change-of-saturation direction from imbibition to drainage and vice versa. The hysteresis in krw became less as the number of alternations increased (i.e., later cycles).
- As the alternation between imbibition and drainage cycles continued, krg for drainage and imbibition cycles continued decreasing. In the three-cycle WAG injection, krg was higher for the first water-injection cycle and was lowest for the third water-injection cycle. Generally, krg cyclic hysteresis for this series of experiments was not significant.
DIDIDI Gas/Water System.
- Generally, wetting-phase (water) relative permeability showed little hysteresis when alternating between imbibition and drainage cycles (especially at higher water saturations). For lower water saturations, krw showed some hysteresis (possibly because of slightly different trapped-gas saturation at the end of imbibition cycles, which itself was caused by slightly different initial gas saturations). Compared with the krw, cyclic hysteresis was more pronounced for krg.
This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 161827, “Experimental and Theoretical Investigation of Water/Gas Relative Permeability Hysteresis: Applicable to Water-Alternating-Gas (WAG) Injection and Gas-Storage Processes,” by S. Mobeen Fatemi, SPE, and Mehran Sohrabi, SPE, Heriot-Watt University, prepared for the 2012 Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, 11–14 November. The paper has not been peer reviewed.