Lynn D. Helms

Date of Award

January 2022

Document Type


Degree Name

Doctor of Philosophy (PhD)


Petroleum Engineering

First Advisor

Vamegh Rasouli

Second Advisor

Minou Rabiei


Rock Physics Based Velocity-Porosity Correlations Developed for Estimation of the Elastic Properties of the Bakken Formations of the Williston Basin, North DakotaABSTRACT Oil production from the Bakken Shale in North Dakota has benefitted from significant technological advancements since its beginning approximately two decades ago. Most of the advancements resulted from better characterization of shales, which are very heterogeneous and their properties vary at different scales. The need for costly operations such as drilling long laterals and multi-stage hydraulic fracturing for production from these unconventional reservoirs, signifies the importance of understanding the physical and mechanical properties of these formations in order to reduce the risk margins and improve project economics at diffetent phases of the life of the field. Rock physics is a relatively new discipline that has been used in shale reservoirs to integrate petrophysical, geomechanical and seismic measurements. Rock physics models are predictive tools used to estimate the velocity, or elastic properties of formations, based on strong theoretical foundations, as opposed to some of the simple empirical correlations that have been developed for specific regional formations. While the basic rock physics models use simplified asumptions and involve less input, more complex models, such as inclusion-based models, estimate velocity-porosity relation as function of different parameters including pore fluid saturation and type, cementation, confining pressure and diagenesis. The downside is that these models require performing tedious calculations and in some cases solving complex differential equations. These models may also differ depending on the type of formation, for example, in the Bakken, separate models may be used for the upper Bakken and lower Bakken shales (UBS, LBS) compared to the clastic or carbonate formations in the Middle Bakken (MB) member. In this research study, we developed velocity-porosity correlations for the Bakken formation. These models were developed based on large volume of data from simulaion of many cases using the differential equivalent medium (DEM) theory, a commonly used rock physics model. DEM models were developed for single mineral rocks, i.e. rocks composed of only one mineral, with different porosities. The pores were then modeled with three phase fluid (water, oil and gas) at different saturation levels and finally, different pore aspect ratios were assumed to simulate crack, interparticle, intergranular and moldic type pore geometries. The correlation constants were extracted for different key minerals in the Bakken, including quartz, calcite, dolomite, anhydrite, illite and kerogen. Having the volume fraction of minerals from lab-based XRD or Elemental Capture Spectroscopy (ECS) logs, linerar averaging was applied to estimate the velocity and elastic properties of the formations. The correlations were applied to several wells in the Bakken and also compared with the existing lab data, which showed a good agreement with the DEM model. The simplicity of using the correlations, that can be developed in an excel spreadsheet and using a single approach for different type of formations, offers a great advangtage for their applications.