Water saturation models greatly affect reserves calculations

Among the challenges in water saturation and hence oil saturation calculations are the accuracy of the applied model and the accuracy of its input parameters. Even in the most simplistic reservoirs where the Archie model is applicable, these parameters affect the accuracy of the calculated saturation.

Many in the petroleum industry focus on one parameter, namely R_t or true formation resistivity, thinking that it is the most important factor in all applications.

Sometimes companies spend thousands of dollars trying to perfect this parameter, although an erroneous R_t might not generate the largest errors.

This article discusses all the saturation input parameters, namely: formation water resistivity, true formation resistivity, the saturation exponent, and the cementation exponent. In addition, it also covers the effects of these parameters on the accuracy of the saturation model.

Water saturation models

Hydrocarbon reserves calculations represent an ongoing challenge to the industry because of its impact on the required spending on facilities and field development. The calculations require continuous updates and careful selection of parameters and various methodologies.

The analysis in this article calculates reserves based on reservoir parameters, mainly the porosity and water saturation. With regard to porosity, the industry has many tools available that measure accurate values within reasonable error margins. Therefore, the article will not discuss porosity and will consider it as a controllable parameter.

But the industry has no direct method for measuring water saturation. Water saturation is an interpreted parameter that is affected greatly by the accuracy of the components of the model used in the calculations. The industry has many saturation models and the selection of the one that best fits a certain reservoir depends on the geology and rock properties of that reservoir.

For example, in a simple sandstone reservoir with almost no shale, the Archie saturation parameter is adequate. When the sandstone contains more shale, the Archie equation will not fit. In this case, another model may be more appropriate.

When the shale content becomes more complex, the calculations will require more complicated saturation models to accommodate the effect of shale mineralogy and claycation-exchange capacity on rock resistivity. The Waxman-Smits and the Dual Water are two models that can handle this complexity.

Although the proper choice of the saturation model represents a challenge, a greater challenge is the selection of the parameters. Selection of the proper cementation and saturation exponents is critical.

Because tools for measuring these parameters downhole are unavailable, some rely on limited laboratory core analysis to provide averaged values for the entire field.

Saturation models

As mentioned previously, saturation models range between very simple, such as the Archie model, to very complex such as the Waxman-Smits model. The model selection is based on the rock and geology of the reservoir.

The Archie equation, Equation 1 (see equation box), is accurate for simple sandstone rock with a minimum shale component. In the equation, R_w is the formation water resistivity, Rt is the true formation resistivity, Φ is formation porosity, n is the saturation exponent, m is the cementation exponent, and S_w is the water saturation.

On the other hand, rocks with a high shale component require a more complex model such as the Waxman-Smits (Equation 2). This model provides greater accuracy compared to other saturation models.

The Waxman-Smits equation contains the BQv parameter, which is related to the cation-exchange capacity of the rock. This parameter represents the effect of shale on the resistivity measurements and corrects for this effect.

The Archie and Waxman-Smits models share four important parameters. These are R_w, R_t, m, and n. The R_t is measured on a foot-by-foot basis with resistivity logs. On the other hand, the industry does not have a tool to measure the other three parameters on a foot-by-foot basis but uses an average value based on laboratory core analyses.

Equation 3 is the basic equation for calculating the original hydrocarbon in place (OHIP). In the equation, F is porosity, S_w is water saturation, H is the reservoir thickness, and A is the reservoir area.

Porosity is measured with an understandable accuracy and hence will not be included in the error analysis discussed in this article.

For simplicity, this article will only use the Archie equation to discuss the extent of potential errors in reserves calculations. The methodology here analyzes each component separately and assumes that all other components are accurate.

True formation resistivity

Resistivity tools measure formation resistivity on a foot-by-foot basis. Many in industry are concerned that this resistivity measurement may be inaccurate because of the effect of formation bedding, tool centralization, mud type, mud invasion, etc. For these reasons, some companies spend much money and expend considerable effort in correcting the measured resistivity to obtain a true formation resistivity

To obtain what is called true formation resistivity, R_t, companies have developed many simulators to correct the measured resistivity. But our research has found that the accuracy of R_t is important but not the major factor that propagates errors in reserves calculations. We believe that the amount of effort and money spent to obtain the true formation resistivity would be better spent on other saturation parameters that have more effect on water saturation calculations and hence hydrocarbon reserves.

Also, obtaining the true formation resistivity requires many assumptions in the simulators, thus raising questions about the validity of the calculated values.

True formation resistivity