The data from a SCAL (Special Core Analysis) experiment comes from a rock sample, or core plug, that's just a few inches long. A reservoir simulator, however, thinks in terms of grid blocks that can be hundreds of feet across. You can't just plug the lab data directly into the model. The properties of that tiny plug—its porosity and permeability—are different from the bulk properties of the massive grid block it's supposed to represent.

Normalization is the process of stripping out the specific properties of the core plug to get at the underlying fluid-rock behavior. This creates a more universal curve that can then be reapplied, or scaled, to the properties of a larger reservoir grid block. It’s the essential translation step that makes lab data useful for large-scale simulation.

Capillary pressure curves measured on different core plugs, even from the same formation, can look wildly different. This is because the pressure required to push a non-wetting fluid into the pores depends heavily on the size and geometry of those pores, which is reflected in permeability ($k$) and porosity ($\phi$). To compare these curves on an equal footing, we use the Leverett J-function.

This function removes the influence of specific rock and fluid properties, creating a dimensionless, universal capillary pressure curve for a given rock type.

By calculating $J(S_w)$ for multiple core samples of the same rock type, you can plot them all together. Ideally, they collapse into a single, well-defined trend. This average J-function curve represents the fundamental capillary behavior of that specific lithofacies. To use it in a simulation, you reverse the process. For any given grid block, you plug in its specific $k$ and $\phi$ values, along with the reservoir fluid properties, to generate a custom capillary pressure curve valid for that block.

Relative permeability ($k_r$) curves also need normalization. While the shape of the curves is governed by pore geometry, the saturation endpoints—like irreducible water saturation ($S_{wi}$) and residual oil saturation ($S_{or}$)—can vary significantly. The goal is to normalize the saturation scale so that curves from similar rock types can be averaged effectively.

A common method uses a normalized water saturation, $S_w^*$:

This equation transforms the saturation scale to run from 0 to 1. At $S_{wi}$, the normalized saturation $S_w^*$ is 0. At the maximum water saturation ($1 - S_{or}$), the normalized saturation is 1.

Once the saturation axis is normalized, the relative permeability values ($k_{rw}$ and $k_{ro}$) are plotted against $S_w^*$. This allows for the averaging of curves from multiple core plugs of the same rock type. The resulting average curves can then be de-normalized using the specific $S_{wi}$ and $S_{or}$ values for a particular reservoir grid block.

The full workflow connects these steps. First, geologists and petrophysicists group core samples into distinct rock types based on their geological characteristics and basic properties. Within each group, capillary pressure curves are normalized using the Leverett J-function to generate an average trend.

Simultaneously, relative permeability curves for that same rock type are normalized using the saturation scaling method. The endpoints themselves, like $S_{wi}$, are often correlated with properties like porosity or permeability for that rock type. This creates a complete, self-consistent package of saturation functions for each rock type in the reservoir model.

This meticulous process ensures that the fluid flow behavior seen in tiny lab samples is faithfully upscaled to predict the performance of the entire reservoir.

This careful normalization ensures that simulations are based on physically meaningful data, providing a much more reliable forecast of reservoir performance.