In this installment of our VPPS Byte posts, is a discussion on the value of rock pore typing in a tight gas sand reservoir and the use of a rock pore type catalogue for your oil and gas reservoirs.

In March 2018, Scott Dodge presented at the New Zealand Petroleum Conference a workflow developed for pore typing a tight gas sand reservoir located in the NZ Taranaki basin shown below in figure 2.

The challenges in tight gas sand reservoirs are the identification of zones that will produce gas that is water free and at economic rates following a propped hydraulic fracture treatment.

We will introduce the use of **R**ock **P**ore **T**ypes as first discussed by Archie in 1950, figure 3.

In 1950 Gus Archie described “Type of Rock” as referred to in this illustration as a formation whose parts have been deposited under similar conditions and have undergone similar processes of later weathering, cementation or re-solution. The connecting lines are meant to portray that a specific formation or rock type will have certain effective pore-size distributions that will produce a particular family of capillary pressure curves. The pore-size distribution controls the porosity and is related to the permeability and water saturation.”

At Virtual Petrophysics we define **R**ock **P**ore **T**ypes as units of rock deposited under similar conditions with similar diagenetic processes resulting in a unique porosity-permeability and capillary pressure-water saturation relationship. Reservoir rock pore morphology determines the irreducible water saturation, connate water saturation and absolute permeability.

*In petrophysics we are attempting to describe the pore system which determines the porosity, permeability and capillary pressure saturation. If this can be done purely with capillary pressure as Archie foretold, then why shouldn’t we use it as the primary tool to group rocks with similar pore types or capillary pressure behaviour?*

This differs from other “Petrophysical Rock Type” models that use core described lithofacies and/or mineralogy electro-facies as a basis for grouping rocks to develop permeability and saturation height functions. These Petrophysical Rock Type models identify rocks of similar log response characteristics, but do not incorporate capillary pressure pore structure information that controls the saturation and flow properties in the rocks.

In 1949 (AIME), Purcell showed that permeability can be derived from capillary pressure measurements from Poiseuille’s law (1838) and the Washburn equation (1921) based on parallel non-communicating tubes or capillary bundle model. Recently in 2015 (SCA2012-28), Ruth and Lindsay applied Effective Medium Theory to show that the capillary bundle model presented by Purcell can be replaced using a representative element volume for complex porous media. The equation is nearly identical to Purcell’s but incorporates the electrical property formation factor and does not necessitate formation specific calibration factors. In other words, a theoretical permeability model using interfacial tension, capillary pressure and formation factor as inputs. We will refer to this as the Purcell-Ruth (PR) permeability.

The RPT workflow we have developed starts with the capillary pressure water saturation measurement shown on the left side of figure 4.

The incremental pore size distribution is derived from the derivative of the non-wetting phase saturation and effective pore radius computed using the Washburn equation (middle figure). The split between macro and micro porosity is determined by the maximum capillary pressure in the reservoir which limits the smallest pore that can be charged by hydrocarbons. In our reservoir example, this corresponds to an effective pore radius of 0.2 microns.

The Purcell-Ruth permeability is computed at each capillary pressure and is integrated to arrive at the absolute permeability. The normalised cumulative permeability is plotted against effective pore radius in the middle figure in red starting at low Pc (large pore radius). This shows that only the large pores in the rock contribute to the permeability, in this example effective pore radius in the 1 to 10 micron range. All effective pore radius smaller than 1 micron do not contribute to the absolute permeability.

The last figure on the right in figure 4 shows the incremental cumulative porosity distribution in black and the corresponding PR permeability in red. The initial RPT is determined using the Windland r35 method which determines the effective pore radius at 35 percent non-wetting phase saturation. This is refined later using the mean hydraulic radius from the PR permeability.

Rather than refer to the conventional pore-throat and pore-body model we invoke effective medium theory that pertains to analytical or theoretical modeling that describes the macroscopic properties of composite materials, or in this case, the pore system.

The pore system is a conduit like network having an effective mean hydraulic pore radius as represented in the Darcy equation. In tight gas pore systems containing significant pore altering diagenesis, the pore system is better represented as an interconnected network of planar voids, hence the effective medium theory and Ruth permeability model provides a method to determine permeability with capillary pressure.

Virtual Petrophysics has developed a reservoir **R**ock **P**ore **T**ype catalogue containing the significant petrophysical properties associated with each RPT. We have found great value in a RPT catalogue for use in reservoir models to define and constrain petrophysical properties. Additionally the RPT catalogue is used to evaluate new drill wells to assist in completion decisions that ultimately impact on the producibility.

An example is shown in figure 5 that shows the highest quality RPT in the reservoir. The data contained for each RPT are:

- RCA – cpor, kair, kinf, rhoma
- SCAL – frf, ri, Sw@100 psi, r35, RPT, Rel perm sw initial, sgr, kg@swi, kw@sgr
- Porosity vs Permeability of all measurements in the reservoir
- RPT air/brine drainage Pc vs Sw
- MICP PSD, Cumulative distribution and R35
- Type log example
- Petrography thin section descriptions, photo micro-graphs, xrd

The challenge is taking the core based petrophysical model and apply it to well log measurements for greater reservoir coverage in non cored wells. For this model to be successful, NMR log data is required to apply this pore morphology based model and Purcell-Ruth permeability.

Core plug NMR measurements are used to determine if the same information provided by capillary pressure is present in the T2 surface relaxation measurement. The lower left image in figure 6 is a core plug T2 pore size distribution along with it’s corresponding cumulative distribution. The next image is the MICP measured capillary pressure effective pore size distribution and cumulative which are nearly identical. The T2 distribution is converted from the time domain to length scale making use of the relationship of surface area to pore volume ratio with surface relaxivity. Now a comparison of the NMR and MICP are shown in the third image in microns. The last step shows that the Windland r35 derived from NMR is the same as that from MICP. We can now apply the model to NMR well log measurements.

For a more complete review of this topic, please send me an email if you would like to receive the New Zealand Petroleum Conference 2018 presentation.

Founder, Director and Principal of Virtual Petrophysics