A Quick Look at Viscoplastic Stress Relaxation (VSR) Theory from the Upcoming Zoback/Petro.ai/Henry URTeC Presentation
Data Science & Analytics

A Quick Look at Viscoplastic Stress Relaxation (VSR) Theory from the Upcoming Zoback/Petro.ai/Henry URTeC Presentation

Rosemary Jackson  •  

Plan to join Dr. Mark Zoback, Professor of Geoscience Stanford University, and Petro.ai at the Houston URTeC Conference on Monday, June 20, 2022, 1:50 PM, Exhibition Hall, Station B for Zoback’s presentation of Lithologically-Controlled Variations of the Least Principal Stress with Depth and Resultant Frac Fingerprints During Multi-Stage Hydraulic Fracturing.

“The paper,” Dr. Brendon Hall, VP of Geoscience at Petro.ai and one of the paper’s authors, explains, “focuses on two important aspects of the science that Petro.ai uses in their Drilling Spacing Unit Design Service (DSUDS): Frac Fingerprint and Viscoplastic Stress Relaxation (VSR) Theory.

“In last week’s blog, we addressed the Frac Fingerprint side of the geoscience. Now let’s look at VSR Theory.

“VSR Theory addresses a couple of inconsistencies with the prevailing method of determining the minimum horizontal stress which is using the Eaton equations. The main thing VSR looks at is the amount of ductile or compliant material in the earth that can cause the rock to relax over time. When there are forces pushing on the rock with different levels in different directions, the stress can change. The maximum horizontal stress and the minimum horizontal stress are both such stresses in the earth. The minimum horizontal stress is important for how fractures can initiate and propagate.

Creep strain normalized by differential stress (creep compliance)

As that stress relaxes with more compliant materials, the stress values become closer to one another. This means that the minimum horizontal stress goes up and the maximum horizontal stress can come down. That minimum horizontal stress going up is what’s important for hydraulic fracturing. That’s something that the legacy theories miss and is predicted by the VSR theory.

“From a pragmatic point of view what Zoback has come up with is a way to determine what the stress profile is from a data driven approach using logs and measurements of the composition of the earth and then calibrating that with stress measurements that have been observed.

“Those observed stress measurements can be from DFIT tests or from completion shut-in pressures, the ISIP measurements. It’s a package that gives you a data driven way of determining stress that accounts for these factors.

Well trajectories and lithofacies

“The calibration points are direct measures of stress,” Kyle LaMotta, VP of Analytics adds. “There are different diagnostic tools that can be used to measure the stress. Those points are very sporadic so typically you’ll have a few of them and they don’t cover a very large depth range. You might have one interval or a couple in different intervals, but typically you’ll have a log sweep that doesn’t cover all the intervals that you’re interested in.

“The VSR prediction tool fills in the gaps between the measured stress and where you don’t have measurements.”

“Right, that’s very important, Kyle,” Hall continues. "Typically, we only have measurements in a few intervals and that gives us a framework for prediction away from where we have those measurements.

Some of the important data that Petro.ai uses to bring the VSR model in are logs that measure the compliant, ductile part of the rock, like a p-clay which is a measurement of the TOC, total organic carbon. Triple combo logs, a standard tool in logging measurements, are also good including gamma ray, neutron density, and porosity. Other compositional logs— volume of quartz, volume of limestone—give you more clues about the lithology of the rock.

You also need a measure of Young’s modulus, the stiffness of the rock. This is typically the hardest one to get. That’s based off a sonic log. If a sonic log is taken, which is the speed of sound in different directions in the rock, then the stress according to the Eaton equation can be evaluated which provides a comparison in the analysis.

“What VSR theory accounts for is the fact that these ductile rocks have a higher stress than you might think which is important when you’re trying to access the stress barrier.”

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