Because of their heterogeneity, carbonate reservoirs are more difficult to model than clastic reservoirs. The main difficulty comes from the number of different pore types, compared with the typical interparticle pore type in clastics. By using saturation-height models (SHMs) in combination with conventional permeability measurements, a new approach attempts to extract the fundamental properties of individual pore systems. The key idea centers on identifying the governing pore systems from capillary pressure curves and permeability measurements. The approach results in the ability to predict permeability continuously as a function of pore-system mixing ratios.

## Introduction

Because of the presence of multiple pore types, carbonate rocks are difficult to model. To account for their heterogeneity, carbonate rocks are often modeled using rock-typing schemes. Two particularly challenging properties are permeability and saturation. Although these properties have been recognized as being closely connected, little information is available on how to handle them consistently.

Even when permeability and SHMs satisfactorily describe the core measurements, it is not trivial to ensure their consistency in 3D models. One possible situation is building SHMs that impose consistency through the governing parameters. Throughout this work, a Brooks-Corey function is used because it was found to describe unimodal mercury-injection capillary pressures (MICPs) satisfactorily.

For the examples discussed in this contribution **(Fig. 1),** microporosity (corresponding to the pore system accessible beyond pore throats of 2 μm or less) forms between 40 and 70% of the pore volume and is mostly located within the micritic grains. A significant difference between the two examples shown in Figs. 1a and 1d is the relative contribution of microporosity on average equaling 0.53 for Rock Type 1 (RT1) and 0.75 for Rock Type 2 (RT2). For RT2, microporosity can be located in the mud between the grains.

## Capillary Pressure Curve Data Analysis and Modeling

The MICP modeling strategy relies on treating the two pore systems as independent, fitting each one of the pore systems first then looking for the best correlation to predict the Brooks-Corey parameters.

On the basis of the measured individual-core-plug properties, the standard deviation for both plug porosity and the relative ratio of microporosity to total porosity was derived. By making the plots with the same fundamental inputs (SHM, porosity, permeability transform), the properties predicted by the models can be highlighted and contrasted.

## Permeability Modeling

The measured permeability as a function of porosity does not appear to follow a clear trend, making permeability prediction from porosity a challenging task.

Instead of looking at the total porosity, looking at the porosity connected by pore throats of at least 2 μm allows a clear trend to emerge for both rock types. The permeability appears to be correlated to the large pores irrespective of the rock type.

Following a binning exercise, two types of transforms can be fitted to the data. Both models describe the covered range satisfactorily. The difference between the two approaches becomes significant outside of the sampled porosity range.

A somewhat different approach can be taken to predict permeability. Earlier work proposed that an SHM can be converted into permeability for multimodal rocks. So, using the derived bimodal SHM, the permeability of the pore-systems microporosity and total-porosity mixture can be derived as a function of total porosity or ratio of microporosity. Using this method ensures that both pore systems add up to permeability contribution in contrast to the approach in which the microporosity is assumed to be insignificant irrespective of the mixture ratio. For the measured RT1 and RT2 ranges, the microporosity influence on permeability appears insignificant. So, at what point does microporosity begin to affect flow?

## Discussion

In the case of a bimodal rock as analyzed in this paper (RT1 and RT2), a small permeability effect from microporosity is assessed. This conclusion has a significant effect on the SHM modeling strategy where the larger pores are modeled as a function of total (plug) permeability, with the smaller pores following a porosity-only approach. The validity of the approach is confirmed by RT3 properties that are used as a blind test. The limit separating the two pore systems corresponds to 2 μm and is applied consistently between permeability prediction and SHM modeling.

At a fundamental level, this work suggests that, on the basis of MICPs and porosity/permeability data characterizing a bimodal rock,

- Fundamental pore-systems properties can be extracted.
- Permeability can be predicted on the basis of continuous pore-systems mixing independent of rock type.

An advantage of such an approach is that the permeability is calculated as a continuous function of constituents; it not only allows the two systems to have different porosities but also allows continuous variations in relative ratio of microporosity to total porosity beyond measured ranges. The relative ratio of microporosity to total porosity can be seen as a proxy for the connectivity of the total-porosity pore system; the connectivity of the pore system has already been recognized as the main permeability control factor. While the connectivity is the main controller, the pore sizes (as suggested by the thin-section images shown in Fig. 1) are not different enough to explain the contrasting properties of RT1 vs. RT2.

The modeling approach in this paper might be a convenient route to include in the model’s diagenetic overprints, such as leaching, for example. Although the effect of these diagenetic overprints on permeability enhancement is obvious, the effect on porosity is subtle. While the maximum porosity sampled in RT1 is 32%, the corresponding number for RT3 is 2.5% lower at 29.5%. This observation justifies the possible use of a permeability multiplier in order to mimic this diagenetic effect while the porosity is left basically unchanged.

## Conclusions

Extracting fundamental pore-systems properties can be achieved by combining capillary pressures and porosity/permeability data. Treating RT2 in isolation from RT1 is difficult to model given the fact that the two modes are not clearly separated. Bringing RT1 and RT2 into the same model produces a robust SHM and permeability model. The models will cover a wider range of sampled properties compared with individual rock types.

The traditional permeability vs. porosity transforms are vulnerable to limited porosity ranges and predefined rock types, for example; however, the permeability from SHMs allows a continuous modeling strategy without the artificial breaking down of the data cloud into rock types.

The key idea involves identifying the governing pore systems from MICP and permeability. This paper shows that a body of rock that required two SHMs for each pore system for each of the two rock types can be simplified to just one SHM per pore system (hence just two SHMs) in a consistent manner between permeability and the SHM. The fundamental control in the approach is relative ratio of microporosity to total porosity—the amount of microporosity. This provides the flexibility to model complex diagenetic effects in three dimensions.

Finally, this paper shows that, by decoupling the two pore systems’ porosities, the permeability heterogeneity can be explained as a function of both porosity and microporosity content.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper IPTC 18587, “Heterogeneous Carbonates: A Modeling Method Ensuring Consistency Between the Saturation-Height and Permeability Models for Bimodal Rocks,” by **Iulian N. Hulea, Harm Dijk, **SPE,** Danila Karnaukh,** and **Mirano Spalburg,** Shell, prepared for the 2016 International Petroleum Technology Conference, Bangkok, Thailand, 14–16 November. The paper has not been peer reviewed. Copyright 2016 International Petroleum Technology Conference. Reproduced by permission.