Revisiting the Drainage Relative Permeability Measurement by Centrifuge Method Using a Forward-backward Modelling Scheme

Abstract Measurement of drainage relative permeability by the centrifuge method was first introduced by Hagoort1. It has been shown that capillary end effects can cause errors in the measurements if a minimum rotational speed is not honored2. To determine the ωmin, we propose maintaining the value of capillary-gravity number, N cg min, to be of the order of 10−2 or smaller, at which the capillary end effect becomes negligible. The above conclusions were determined by applying a forward numerical simulator developed for centrifuge experiments and applying Hagoort's method as a backward model. These forward and backward models form a forward-backward loop which is a powerful tool for error analysis such as determining the impact of capillary end effects. Introduction Measurement of drainage relative permeability using the centrifuge method was first introduced by Hagoort[1]. He viewed the gravity drainage process as a gravity stable Buckley- Leverett displacement with the same set of assumptions. In addition, he assumed constant centrifugal acceleration along the core length and infinite mobility for the gas phase. In the full version of this paper, it will be shown that these assumptions are reasonable. Nevertheless, error caused by capillary end effect is one of the issues in relative permeability measurements. In the centrifuge method, if the rotational speed, ω, of the experiment is not maintained above a critical minimum, the calculated relative permeability values will be underestimated[2]. Although Hagoort proposed a correction procedure for cases where the measurements are affected by capillary end effects, it has been shown that this procedure introduces some noise into the calculated relative permeability values. Further, it is not easy to perform Hagoort's correction procedure in core analysis laboratories; rather, it is much easier and preferable to avoid the problem entirely by designing the experiment with a proper rotational speed from the beginning. On the other hand, since the target of such measurements is usually in modelling gravity drainage processes, one would desire that the relative permeability measurements be obtained under a capillary dominated flow regime. That is to say, if the measurements are performed under severe rotational speeds, the de-saturation flow regime would not be a capillary dominated flow. The objective of this work is to introduce a criterion for designing relative permeability experiments so that the minimum rotational speed that minimizes capillary end effects is honoured. To find this criterion, a forward-backward modelling scheme is developed. The forward numerical model accepts arbitrary capillary pressure and relative permeability functions as inputs and simulates the centrifugal displacement process. The simulated centrifuge drainage results is then used as raw centrifuge data and processed by Hagoort's method as the backward model. The resulting relative permeability curve is then compared with the original input relative permeability to quantify the capillary end effect. Figure 1 shows the forward backward loop schematically.

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