Estimation of Flow and Hysteresis Parameters Applicable to WAG Experiments

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Water-alternating-gas (WAG) injection has demonstrated encouraging results for improving oil recovery. However, numerical simulation of three-phase flow and the associated hysteresis effects are not well-understood. In the complete paper, a new assessment of the WAG-hysteresis model, which was developed originally for water-wet conditions, was carried out by automatic history matching of two coreflood experiments in water-wet and mixed-wet conditions. The results indicate that history matching the entire WAG experiment would lead to a significantly improved simulation outcome.


Using an optimization software, the authors have carried out a series of history-matching exercises on coreflood experiments to evaluate the performance of the WAG-hysteresis model and to simulate WAG experiments conducted on mixed-wet and water-wet cores at near-miscible conditions. The main difference here compared with previous work is the tuning of the parameters relevant to the WAG-hysteresis model on entire WAG experiments (rather than on individual cycles of one experiment) with a new methodology to estimate more-representative two-phase relative permeability curves from the WAG experiments.

Coreflood Experiments and History-Matching Method

There are numerous coreflood experiments in the literature that can be used for studying pure WAG-related interactions at near-miscible conditions. The unique advantages of this data set are gravity-segregation effect has been excluded by rotating the core while the ­fluids were being injected and all the fluids (water/oil/gas) were thermodynamically pre-equilibrated to minimize the effect of mass transfers at near-miscible conditions. Therefore, the processes taking place in the coreflood experiments can be attributed solely to multiphase flow and hysteresis effects. The following coreflood tests were selected from the data set to investigate the behavior of flow functions with respect to fluid saturation, injection scenario, and initial wettability:

  • Continuous gas injection in the water-wet core saturated with oil at irreducible water saturation, used to estimate two-phase gas/oil relative permeabilities
  • Continuous gas injection in the mixed-wet core saturated with oil at irreducible water saturation, used to estimate two-phase gas/oil relative permeabilities
  • WAG experiment performed at low-gas/oil-interfacial-tension (near-miscible) conditions in a mixed-wet core, with the starting water-injection displacement used to obtain water/oil-flow functions
  • WAG experiment performed at near-miscible conditions in a water-wet core, with the starting water-injection displacement used to obtain water/oil-flow functions

In these experiments, the first sequence of water injection, in which no gas existed in the core, was used for estimating two-phase oil/water relative permeability.

When considering the oil-recovery profile of the experiments used in this work, tests showed that WAG injection performed much better than continuous gas injection in these experiments. It should be pointed out that the value of irreducible water saturation was the same for both experiments.

In the current investigation, the process of history matching was carried out on the entire WAG experiment. Numerical simulation was used, and the core (total length of 0.605 m) was separated into 400 gridblocks. The first aim was to investigate whether the entire-WAG-simulation approach using unsteady-state relative permeability could reduce the errors involved in simulation. Therefore, three parameters (the gas-trapping coefficient, the reduction factor for residual oil, and the reduction factor for gas relative permeability) as well as a three-phase water relative permeability (in tabular format) were adjusted in an automated-history-matching process to minimize the error between simulation and experimental data.

First, the coreflood experiments with two-phase flow were used to estimate the two-phase oil/water and gas/oil relative permeabilities. After that, the estimated two-phase relative permeabilities were used together with the Stone I three-phase model, the entire WAG experiment was simulated, and the errors between the prediction of the simulation and the experimental values were calculated. Then, in the history-matching process, the parameters of the WAG-hysteresis model as well as Land’s trapping parameter were used as the tuning parameters while minimizing the error of estimation.

During the history-matching process, it was identified that the two-phase experiments could be history matched with different relative permeability functions and the resultant two-phase relative permeabilities would lead to different values for WAG-hysteresis parameters. Therefore, in a separate attempt, two-phase relative permeabilities were changed and then the WAG-hysteresis parameters were tuned to history match the experiment. The outcome of these simulations would shed some light on the performance of the WAG-hysteresis model, which would lead to the development of an improved methodology for simulating WAG coreflood experiments. It should be pointed out that the pressure values reported here are for the inlet of the core recorded during the experiment.

The WAG-hysteresis model was developed mainly to update relative permeabilities on the basis of cyclic invasion of gas and water; therefore, the basis for capturing the hysteresis effects is use of representative two-phase relative permeabilities. A set of relative permeability curves obtained solely from two-phase displacements was used with the WAG-hysteresis parameters to history match the full (all cycles) WAG experiment. However, it was found that, when a representative set of two-phase relative permeability values could not be estimated from unsteady-state water or gas injections, a sound evaluation of the WAG-hysteresis model could not be made.

A New Methodology for History Matching WAG Experiments

In any WAG injection scenario, there are regions under two-phase flow as well as the regions affected by three-phase-flow regimes. Any representative reservoir simulation should be able to capture the two- and the three-phase-flow behaviors simultaneously. Also, alternating injection of gas and water is associated with hysteresis effects observed in both pore- and core-scale experiments such as trapping of gas, reduction of water relative permeability, and reduction in residual oil saturation. The WAG-hysteresis model is predominantly based on updating the two-phase relative permeability functions (in other words, the foundation of the hysteresis model is a two-phase parameter system).

Having examined the impact of two-phase relative permeability, it became clear that the performance of the WAG-hysteresis model is affected significantly by the base two-phase relative permeabilities entered in simulation. The variations in the simulation outcomes stemmed from the different saturation ranges that are in play during two- and three-phase-flow experiments. Fig. 1 depicts two sets of relative permeabilities for oil/water and gas/oil tables that can match water- and gas-injection experiments. These curves were obtained through history matching the two-phase water- and gas-­injection experiments, which highlights the nonuniqueness issue in unsteady-state relative permeabilities. As can be seen from the active saturation ranges in two- and three-phase-flow regimes, in the left image (water/oil relative permeability), the simulation results of a two-phase unsteady-state experiment are controlled by the saturation range highlighted by the blue circle, whereas the active ­water-saturation range for a three-phase WAG experiment would vary between 0.8 and 0.6, as highlighted by the purple arrow. In the right-side image of Fig. 1 (oil/gas relative permeability), the two-phase unsteady-state experiment would cover the saturation ranges highlighted by the red arrow and the three-phase WAG experiment can be influenced with gas saturation of 0.0 to 0.3, as highlighted by the green arrow. It would be very cumbersome to obtain gas/oil relative permeability in this range by means of unsteady-state, or even steady-state, experiments. Therefore, there is an essential issue involved in the history matching of the WAG experiment; the saturation ranges of the two- and three-phase experiments would not overlap and, hence, discrepancies in simulation of the WAG experiment may occur because of a lack of reliability of the two-phase-flow functions (obtained from the unsteady-state experiment).

Fig. 1—Comparison of the active saturation ranges of two-phase and three-phase coreflood experiments. It can be seen that the active saturation ranges for unsteady-state two-phase flow cannot represent the three-phase-flow region.


In this section of the complete paper, the aim was to estimate a set of more-reliable two-phase relative permeability curves within the active saturation range with a lower degree of uncertainty. An algorithm was proposed to extend the active saturation range by history matching the first cycles of the WAG experiment. The authors examined the proposed methodology when applied to two WAG experiments; their findings are detailed in the complete paper.


The following conclusions can be drawn from the history matching of entire (full-cycle) WAG experiments in mixed- and water-wet conditions performed to assess hysteresis effects in WAG cycles:

  • The outcome of history matching is strongly dependent on the two-phase relative permeability curves. But, because most of the two-phase-flow functions estimated from unsteady-state experiments might suffer from nonuniqueness issues, it is concluded that different WAG-hysteresis parameters would be needed for different sets of two-phase relative permeabilities. Therefore, it is recommended to tune the WAG-hysteresis parameters on the complete cycles of the WAG experiment if the two-phase relative permeabilities are fixed.
  • A new methodology was proposed to obtain a representative set of two-phase relative permeability curves by use of the history matching of the first water- and first gas-injection sequences to cover the active saturation ranges of the three-phase-flow experiments. The new methodology would enable significant alleviation of the nonuniqueness issue.
  • Inclusion of the WAG-hysteresis parameters in history matching, rather than use of measured values of these parameters, can reduce the error of simulation significantly.
  • Under mixed-wet conditions, the WAG-hysteresis parameters were automatically tuned on water‑flow/gas-flow/water-flow cycles to match oil/water/gas productions and the core inlet pressure. Then, the remaining cycles of the WAG experiment were considered to examine whether the model could predict the experimental results accurately. The WAG-hysteresis model failed to predict the subsequent cycles reasonably.
  • In summary, because of inaccuracies involved in saturation models, it would be highly recommended to history match full WAG cycles altogether to be able to capture two- and three-phase-flow effects simultaneously, which would lead to more-representative flow functions for large scales where two- and three-phase flows coexist.
This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 183321, “An Improved Approach for Estimation of Flow and Hysteresis Parameters Applicable to WAG Experiments,” by Pedram Mahzari and Mehran Sohrabi, Heriot-Watt University, prepared for the 2016 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 7–10 November. The paper has not been peer reviewed.

Estimation of Flow and Hysteresis Parameters Applicable to WAG Experiments

01 January 2018

Volume: 70 | Issue: 1


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