Citation: Jin, L.; Wojtanowicz, A.K.;
Ge, J. Prediction of Pressure Increase
during Waste Water Injection to
Prevent Seismic Events. Energies 2022,
15, 2101. https://doi.org/10.3390/
en15062101
Academic Editors: Nediljka
Gaurina-Me ¯ dimurec and
Borivoje Paši´ c
Received: 31 December 2021
Accepted: 11 March 2022
Published: 13 March 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Prediction of Pressure Increase during Waste Water Injection to
Prevent Seismic Events
Lu Jin
1,
*, Andrew K. Wojtanowicz
1
and Jun Ge
2
1
Craft & Hawkins Department of Petroleum Engineering, Louisiana State University, Baton Rouge,
LA 70803, USA; awojtan@lsu.edu
2
Bureau of Economic Geology, The University of Texas at Austin, Austin, TX 78712, USA;
jun.ge@beg.utexas.edu
* Correspondence: lujin329@yahoo.com
Abstract: A considerable increase of seismicity has occurred in the USA in the last decade (2009–2020)
with an annual average of 345 M3+ earthquakes. Numerous field cases have shown that excessive
well pressure due to a high injection rate may have triggered seismic events. This study defines
conditions for inducing a seismic event by excessive injection in the well’s pressure that may cause
geomechanical damage to the rock. Introduced here is an analytical model and method for predicting
pressure increase during injection of produced water contaminated with oil. The model calculates
time-dependent advancement of the captured oil saturation causing the well’s injectivity damage and
pressure increase. Critical conditions for a seismic event are set by defining rock failure when well
pressure exceeds the fracturing pressure of the wellbore or when the increased pore pressure reduces
the effective normal stress at the “weak” interface inside the rock, computed with a geomechanical
model. This concept is demonstrated in three field case studies using data from geological formations
in areas of petroleum operations. The results confirm field observations of the initial rapid increase of
oil invasion and injection pressure that could only be controlled by reducing the rate of injection to
assure continuing long-time operation.
Keywords: injection wells; induced seismicity; produced water injection; injection pressure model;
rock slippage diagram
1. Introduction
In the United States, the estimated volume of water produced in oilfields is in the
range of 20 to 30 billion barrels (3.2–4.8 billion m
3
) per year [1,2]. The volume has increased
over the last decade due to maturing of conventional oil/gas fields and the development of
unconventional shale deposits [3–5]. In 2020, approximately 65% of the total oil production
in the US was from unconventional reservoirs as reported by the U.S. Energy Information
Administration (US EIA). Table 1 shows the effect of the “shale revolution” on US water
production [2].
Table 1. Comparison of oil, gas, and water production in the US before (2007) and after (2017) the
“shale revolution” [2].
Time
Category
Oil, Million bbl/yr
(Million m
3
/yr)
Gas, Million cf/yr
(Million m
3
/yr)
Water, Million bbl/yr
(Million m
3
/yr)
2007 1750 (278) 24,374,000 (69,016) 20,195 (3211)
2012 2264 (360) 29,730,220 (841,868) 21,181 (3368)
2017 3405 (541) 35,005,078 (991,235) 24,395 (3878)
Energies 2022, 15, 2101. https://doi.org/10.3390/en15062101 https://www.mdpi.com/journal/energies