Fracture development during disposal of hazardous drilling cuttings by deep underground injection:A review

Shuai Zhang,Yongun Feng,*,Bin Li,Jingen Deng,Tie Geng,Jinai Zhang

a College of Petroleum Engineering,China University of Petroleum,Bejing,102249,China

b State Key Laboratory of Petroleum Resources and and Prospecting,China University of Petroleum,Beijing,102200,China

c Oilflied Chemicals Division,China Oilfield Services Limited,Langfang,065201,China

d Sinopec Tech Houston,Houston,TX,USA

Keywords:Hazardous drilling cuttings Cuttings disposal Cuttings re-injection Fracture development Multiple fractures

A B S T R A C T Drilling fluids with complicated compositions are becoming more common as the oil and gas industry develops.The production of hazardous cuttings is increasing,which not only stifles the oil and gas industry’s development but also poses a severe environmental threat.Deep underground re-injection is a cost-effective and efficient method for dealing with hazardous cuttings.Numerous experiments and numerical studies on cuttings re-injection have been conducted in the past thirty years.However,there is still a divergence of views on the fracture development in the process of cuttings re-injection.A comprehensive review of existing studies is necessary to help researchers advance this technology.This paper provides a review of the fundamental studies on fracture behaviors during the deep underground re-injection of drilling cuttings.The limitations of the existing studies are also discussed to inspire new research endeavors.

1.Introduction

The exploration and development process in the oil and gas industry generates a large number of different types of waste,including drilling,completion,workover and fracturing to increase the production,transportation and storage of hydrocarbons.The amount of waste generated from drilling activities is second only to that of oilfield water(Shokanov et al.,2008;Onwukwe and Nwakaudu,2012;Feng et al.,2016;Robertson and Chilingar,2017;Kholy et al.,2019).Drilling waste mostly consists of drilling fluids and cuttings,with the major components listed in Table 1.Drilling wastes comprise a variety of components that are harmful to the environment and humans,such as heavy metals,radioactive compounds,organic salts,and other contaminants.It should also be noted that the total amount of waste generated during drilling is several times greater than the borehole’s volume(Getliff et al.,1998).More countries are requiring zero discharge of drilling waste due to stricter environmental restrictions.As a result,studies have focused in recent years on how to achieve zero discharge of drilling waste by a cost-effective and efficient method.

Table 1Composition of waste of drilling activities(Onwukwe and Nwakaudu,2012).

Curing,biological treatment and heat treatment are the most commonly applied surface treatment methods for hazardous cuttings.These technologies have several drawbacks,including high costs,ease of contamination,and the need to occupy significant land areas or disposal space(Gaurina-Me?imurec,2002;Arfie et al.,2005;Gaurina-Me?imurec et al.,2005).The deep underground reinjection of hazardous cuttings is an effective way to deal with this problem.This method can accomplish zero drilling waste discharge,reduce transportation and surface accumulation expenses,and,most crucially,no location restrictions(Sipple-Srinivasan et al.,1997;Bruno et al.,2000;Reddoch,2000;Reed et al.,2002;Guo and Abou-Sayed,2003;Guo et al.,2004;Bruno,2008).

Small volume injection of drilling waste through well annulus was successfully implemented in the Gulf of Mexico in the 1980s.Deep underground re-injection of drilling cuttings was widely used in the Gulf of Mexico,the North Sea,Alaska,and other fields in the 1990s,mostly for the treatment of offshore drilling waste(Marinello et al.,2001;Keck,2002;Abou-Sayed et al.,2003;Gumarov et al.,2009;Newman et al.,2009;Gaurina-Medjimurec,2015).Millions of barrels of drilling waste have been safely injected around the world as a result of continuous technical efforts.In response to low oil prices and severe environmental requirements,cuttings re-injection has become the preferred method of treating drilling waste in offshore oil and gas fields around the world and has begun to be applied in onshore fields(Keck,2002;Fragachan et al.,2006;Gumarov et al.,2009).While most cases of cuttings re-injection are successful,there are several failures according to a review of historical cases(Marinello et al.,1996;Gumarov et al.,2018;Gaurina-Me?imurec et al.,2020).For example,at least four leakage incidents occurred during re-injection operations in the ?sgard,Norway,and all of these were observed on the surface(Saasen et al.,2001).According to statistics,the proportion of waste re-injection in Norway dropped from 50%in 2006 to 40%in 2009.It is due to a variety of reasons.Notably,in 2010,the proportion dropped rapidly to under 20%due to leakage caused by fractures in the formation and decreased to under 8%in 2011(NPD,2011;Sigra Group,2013).The Prudhoe Bay cuttings re-injection project,which began in 1995 and lasted three years,pumped nearly 8 million barrels of mud.However,it had to be stopped and the injection well was abandoned because the mud was transported to the nonbonded cement of the adjacent well which caused leakage.

According to the overview of unsuccessful cases,the following are the major factors of failure:

(1)Poor quality of cement leads to mud leakage;

(2)Induced fractures in unconstrained formations extend too long in the vertical direction causing leakage;

(3)Construction failure due to lack of good design;and

(4)Poor understanding of mud transportation.

Thus,two key issues that must be answered for cuttings reinjection applications are(i)where does the waste goes and(ii)how much waste can be injected into the target formation safely?The essence of these issues is the extension and geometry of the induced fractures during the cuttings re-injection process(Peterson et al.,2001;Shokanov et al.,2008;Ji et al.,2009).The fracture expectations for hydraulic fracturing and cuttings re-injection are not the same.Hydraulic fracturing aims to create a wide range of fractures(typically a single fracture)in a single operation to improve the formation’s permeability,and the risks of hydraulic fracturing are fault activation,induced seismicity and contamination of the reservoir(Wisen et al.,2019;Cremen et al.,2020;Zhang et al.,2020).Cuttings re-injection,on the other hand,tends to generate a multi-fractures area with a small range to avoid leaking caused by long fracture extensions.Many studies have been published on the induced fractures of cuttings re-injection.The intermittent injection is commonly accepted in the cuttings re-injection process.The initial fracture behaves similarly to hydraulic fractures because it extends in the direction of the maximum horizontal principal stress.Then,The stress near the wellbore increases during the shut-in period as a result of fluid leaching from the slurry and solid-phase depositing on the fracture surface,which may prevent the fracture from fully closing.A multi-fractures disposal domain can be formed by intermittent injection(Abou-Sayed et al.,2003,2005;Zaki et al.,2005;Bai et al.,2006;Guo et al.,2007;Shokanov et al.,2011;Gumarov et al.,2012).However,there is no consensus on whether the re-injection process will open the existing fractures or create new fracture branches,and the shape of the final multifractures disposal domain.

The fundamental studies on induced fractures of cuttings reinjection that have been published are summarized in this paper.The most recent experimental,theoretical and numerical studies on cuttings re-injection fracture extension are reviewed.The applicability and limitations of the published studies are investigated.The paper also discusses the challenges of cuttings reinjection and makes some suggestions for further research.

2.A brief background on deep re-injection of drilling cuttings

2.1.The basic process of cuttings re-injection

The ground configuration of the cuttings re-injection system is shown in Fig.1.The red,green and blue arrows represent the cuttings transport,large cuttings transport and mixed slurry transport,respectively.The main workflow is as follows(Xia et al.,2014;Benelkadi et al.,2019;Mahrous et al.,2019):

(1)Collecting drilling waste;

(2)Mixing drilling waste with liquid waste or water and adding chemical reagents to make the slurry meet the requirements for deep underground re-injection;and

(3)Pumping slurry into the target formation using a highpressure pump.

As shown in Fig.2 there are two main methods of cuttings reinjection.One is the annular injection and the other is the dedicated(abandoned)well injection(Shokanov et al.,2011).

The annular re-injection is to inject the mixed slurry along with the annular space between the two casings,usually injected in the annulus of the intermediate casing.Meanwhile,drilling or extraction can be handled with production casing or tubing.Typically,each well receives waste from only one subsequent well and injects it into the subsurface through the high-quality annulus.The operational duration for injection from the annulus is normally a few months,whereas it might take up to several years for dedicated wells.The limitation of annular re-injection is that it can only be applied successfully if the annular space is open to a suitable formation and meets a set of requirements,such as casing pressurebearing capacity and corrosion resistance(Fristoe,1990;Abou-Sayed and Guo,2001).

Fig.1.Ground configuration of cuttings re-injection system(Mahrous et al.,2019).

2.2.Risk of cuttings re-injection

Although annular injection provides the opportunity for immediate disposal of drilling waste,engineers prefer to use separate wells for cuttings re-injection in 80% cases.Because annular reinjection requires accurate pre-designed injection locations and severe requirements for cementing quality and wellbore integrity.The dedicated wells,on the other hand,are highly adaptable and can inject a wide variety of wastes with a much higher injection volume(Sipple-Srinivasan et al.,1997;Alba Rodriguez et al.,2007;Fragachan et al.,2007;Maliardi et al.,2014).For dedicated well reinjection operations,the location of the re-injection point must be considered.First and foremost,the re-injection point should be located below 200 m of the aquifer(Veil and Dusseault,2003).Secondly,the re-injection location should be at least 1000 m from the adjacent well and 400 m from the fault,according to the US National Petroleum Office.Meeting these requirements can greatly reduce the risk of leakage during cuttings re-injection and storage(Tsang and Apps,2005).Furthermore,the re-injection of cuttings is fraught with dangers,the most serious of which are(Abou-Sayed and Guo,2001;Abou-Sayed et al.,2002;Fragachan et al.,2006;Nagel and McLennan,2010;Al-Dossary et al.,2011;Gaurina-Me?imurec et al.,2020):

(1)Causing contamination due to fracture extension to the surface or into the underground drinking aquifer;

(2)Communicating with existing wells and causing reservoir contamination;

(3)Causing contaminant leakage due to poor wellbore integrity;

(4)Causing contaminant leakage due to fault reactivation;and

(5)Project failure due to an inaccurate estimate of formation storage capacity.

One of the main factors for the above-mentioned risks is that the geometry and propagation of the fracture during the re-injection procedure are not clearly interpreted.As a result,the ability to precisely estimate fracture geometry and extension is one of the most essential factors in the success of cuttings re-injection.

In this paper,the fundamental studies on cuttings re-injection fractures are reviewed and discussed from experimental investigations,physical models,mathematical models,and numerical simulation studies,respectively.

3.Experimental studies of cuttings re-injection fractures

The cuttings re-injection experiment is similar to the hydraulic fracturing experiment,which intends to understand the propagation of fractures in the formation.A single fracture is created by a continuous injection until the fracture opens in a hydraulic fracturing experiment.However,a considerably different fracture geometry can be created by intermittent injection of cuttings compared with hydraulic fracturing(Nagel and McLennan,2010).At present,experimental studies of hydraulic fracture are extremely extensive but less for cuttings re-injection.

3.1.The earliest experiment of waste underground re-injection

Some oil companies considered injecting waste into the subsurface for disposal as early as the 1980s.But there is insufficient evidence on whether the injected waste will be constrained in the subsurface for a long time.ARCO Oil Company conducted experiments exploring waste re-injection under permafrost in the Prudhoe Bay Field in 1989.The experiments were to verify whether the waste previously injected had penetrated the permafrost formation or not,and then to determine the optimal injection parameters and safe injection pressure.Field experiments were carried out with intermittent injection in interbedded sandstone and shale at a depth of about 610 m.Each injection well had 6-18 m long injected sections,and the injected slurry consisted mainly of wastewater.The high permeability and the stress state of the target formation indicated that the horizontal fractures rather than vertical fractures will be created,and the ground deformation and fracture geometry were recorded using a surface tiltmeter.The experimental results revealed that during the injection process,several horizontal fractures were generated,and vertical transport of waste was constrained due to the non-homogeneous stress state and rock mechanical characteristics of the permafrost formation.It is of no risk when injecting at 0.01 m3/s with a surface pressure of up to 9.6 MPa in this formation(Abou-Sayed et al.,1989).The feasibility of the waste re-injection and the multiple fractures created by intermittent re-injection were first demonstrated in the field experimental studies.However,it was only a verification of the possibility of subsurface re-injection of oilfield waste,and no applicable waste re-injection theory was presented.

3.2.Typical laboratory experiments for cuttings re-injection

A joint industrial project named“Drilling Waste Disposal by Injection Into a Hydraulic Fracture”,project number DEA-81,was launched in 1999,with member companies including AMOCO,BP,Shell,and other petroleum companies to further investigate the differences between cuttings re-injection and hydraulic fracturing.The project also aimed to identify the fracture boundary and to improve the theoretical knowledge of cuttings re-injection.

The DEA-81 group carried out laboratory experiments in shale,hard sandstone,soft sandstone and artificial sandstone,using small-size rock samples of 0.28 m×0.28 m×0.4 m,with an injection hole of 0.02 m in diameter and 0.28 m in depth drilled in the center of the sample.The slurry in the experiment consisted of 20%solids,76%brine and 4%oil(all by volume).The density of the slurry is 1.29 g/cm3.The solids in the slurry consist of Pierre I Shale and‘RevDust’(calcium montmorillonite clay).Each experiment was conducted under three directional confining pressure,and multiple batches of re-injection experiments were conducted to simulate field operations.The major observations from the DEA-81 project are as follows:

(1)With cuttings re-injection in the low permeability zone,fractures tend to be confined in the low permeability zone when the difference of in situ stress between the high and low permeability zone is not particularly great,as shown in Fig.3a.

(2)Multiple fractures will be created by intermittent reinjection,and multiple subparallel fractures will initiate from the borehole in the well-consolidated rock samples,as shown in Fig.3b.

(3)The in situ stress is changed and multiple fractures are generated in shale formation because of the clay swelling with water during the re-injection process.

(4)The mechanism of fracture generation in high permeability formations is significantly different from that in low permeability formations,as the entry of particles into the formation and the permanent deformation of the formation near the fracture increase the storage capacity of the formation(Fig.3c).

(5)Under the same injection volume,the fracture size of the intermittent re-injection is smaller than that of the continuous re-injection.

The DEA-81 experiments also explored the fracture barrier mechanism of cuttings re-injection and proposed the disposal domain concept(Moschovidis et al.,1994).However,the limitation of the DEA-81 experiments is only qualitatively analyzing the fractures in different formations and does not quantitatively describe the characteristics of fractures,such as azimuth,length and width(Willson et al.,1999).

To date,the DEA-81 experiments are the most typical and famous laboratory studies.Because laboratory experiments,which can only briefly illustrate the phenomena of waste re-injection induced fractures and cannot obtain key parameters like the total volume of waste and the fracture region,are difficult to conduct.Most of the subsequent studies have focused on field experiments.

3.3.Field experiments

Despite the presence of a disposal domain and many fractures during cuttings re-injection in the DEA-81 laboratory,there are still substantial disparities between the laboratory and field operations.

In field experiments,fiber optics,tiltmeters,microseismic monitoring,and other diagnostic instruments are widely utilized to monitor fracture distribution and geometry.Table 2 lists the adaptations of different diagnostic techniques that can be applied for hydraulic fracturing,waste re-injection,fault identification,and other engineering applications.Using diagnostic procedures in cuttings re-injection field experiments,the fracture zone and project safety can be evaluated,and more crucially,the parameters of the induced fractures can be obtained(Mahmoud et al.,2021).

Table 2Application of fracture diagnostics for characterizing fracture parameters.

Table 3Influence factors of cuttings re-injection.

In 1998,the Joint Industry Group performed field experiments at the Baker Hughes Proving Ground in Oklahoma,USA,to corroborate the results of the laboratory studies and to further understand the storage mechanism and geometry of the fractures created during cuttings re-injection.Field tests are conducted away from other operations areas to eliminate interference from other operations.Three vertical wells were used in the field experiment,comprising one injection well and two monitoring wells.Cuttings were injected into the Atoka Shale at the depth of approximately 594 m and the Wilcox Sandstone between 792 and 853 m,respectively.Microseismic monitoring device and tiltmeter were used to monitor fracture orientation and geometry during the reinjection.The deeper Wilcox injections were done first in the open hole,and then the injection in the Atoka Shale was done through the perforations in this project.The injection rate is 0.01 m3/s,the injection period is 10-20 min,and the shut-in period between two injections selected for adequate fracture closure is 80-100 min.Each formation was injected for 3 d,with a total of 17 batches in the Wilcox Sandstone and 20 batches in the Atoka Shale.Lateral cores were obtained at the end of the experiment and the development of injection fractures was analyzed by combining the monitoring results.

Fig.3.(a)DEA 81 Test#17,plaster(simulating shale)bounded by high permeability(artificial)sandstone,4 injection cycles;(b)Up to 5 fractures(pointed by the arrows)appear to have been initiated from the wellbore during the first 5 injections in DEA81 Test#18;(c)DEA 81 Test#13,multiple fractures created during intermittent injection of simulated drillcuttings slurry into high permeability sandstone(reproduced from Willson et al.,1999).

Multiple fractures were observed in the Atoka Shale and Wilcox Sandstone(Figs.4 and 5).The Wilcox Sandstone core captured 21 fractures with the azimuth ranging from 0°to 33°(from 92°to 125°),two adjacent fractures were filled with cuttings slurry,11 induced fractures were created without slurry,and eight natural fractures were created with no slurry but which were activated by the re-injection process.The Atoka Shale core revealed nine fractures with the azimuth ranging from 0°to 26°(from 99°to 125°).Thus,field experiments also demonstrated that intermittent injection can cause multiple fractures.Reproducible and stable injection pressure behavior with an increasing trend has been observed for the same volume of injection,indicating the presence of fractures in a limited area.But,for a larger injection volume,the injection pressure drops slightly and remains stable,indicating that the fracture extends beyond the existing disposal zone.In addition,the results of surface and downhole tiltmeters,as well as microseismic monitoring,were consistent with the reported fractures in the core and were able to map the relatively tiny injection volumes efficiently.Although the field experiments were successful,they only described the number and orientation of fractures without the height and width.The effects of opening and closing pressures of fractures and construction parameters on cuttings re-injection were not revealed in this field experiment(Moschovidis et al.,1998,2000).

Peterson et al.(2001)conducted an in-depth evaluation of the fracture system created in the DEA-81 field experiment.The goal was to assess the appropriateness of multiple injections in establishing a“disposal domain”.In-depth analysis based on observations from core and Formation Micro Image borehole image logs illustrates the concept of disposal domain and multiple fractures created by the Wilcox and Atoka test intervals.However,the Wilcox diagram illustrates that remarkable aperture fractures have a far narrower striking range than induced fractures.In the Wilcox sandstone,the range of remarkable aperture fractures is 119°-125°(6°range at approximately 18.3 m from the point of injection),while the total strike range is 92°-125°.Similarly,the“large aperture”fractures in the Atoka Shale range from 119°to 125°(6°,approximately 18.6 m from the injection point),while the total strike range is 99°-125°.The results indicate that the majority of the injected slurry was deposited in just a few fractures.These fractures are similar to the hydraulic fractures in the core observed in several other experiments and were found at a distance of several feet(Warpinski et al.,1993;Fast et al.,1994).These fractures indicate that the extensive disposal domain seen in the DEA-81 field experiments did not occur.The injected slurry is only deposited along with a few fractures and extends over a relatively short distance.The small-scale fractures where the slurry was deposited looked to be related to the slurry injection process,whereas the complicated fractures seemed to be caused by the presence of complex natural fractures in the formation,according to the analysis of the slurry injection results.However,these findings do not mean that if the injection continues,no disposal domain will be established(Peterson et al.,2001;Shokanov et al.,2011).

Another typical monitoring experiment was conducted by Abou-Sayed et al.(2005)on the world’s largest cuttings re-injection project in 2005.The project began in 1998 and the re-injection area is located in Prudhoe Bay,northern Alaska,USA.Continuous reinjection of drilling waste from three injection wells at the depth of approximately 1981 m,and total injection interval is 122 m thick.The standard operation consists of injecting slurry into one well continuously for 10-14 d and then switching to another well for continuing injection.It means that only one well is working at the same time,while the other two are shut-in.The average shut-in time per well is 24 d,and the average injection rate is 0.035-0.05 m3/s.The monitoring experiment obtained the results as follows:(1)Step rate tests(SRTs)and fall-off tests can determine the propagation pressure,length and height of the fracture.The pressure increase is due to the growth of fracture size and the deposition of solid phase on the fracture surface.(2)Fracture sizes determined by well testing and temperature logging are smaller than those predicted by simulation.Despite the increase in fracture closure pressure,there is no significant rise in reservoir pressure,reflecting the good pressure dissipation performance of the disposal area.Similarly,to evaluate the feasibility of cuttings reinjection and reduce potential risks,Pierce et al.(2010)and Gumarov et al.(2012)conducted field monitoring experiments by formation breakdown tests,SRT,leak-off tests,and extended falloff tests in the Caspian Sea and Peru.

Although field monitoring provided useful data,the commonly used monitoring methods do not guarantee a high level of accuracy.More advanced monitoring methods,such as microseismic,downhole tiltmeter,and real-time monitoring technology from nearby wells,are required to obtain more accurate disposal areas and fracture geometry(Fragachan et al.,2006).

The hydraulic fracture is typically described as a two-wing planar fracture with the wellbore in the center.However,almost all experiments to date have shown that this description isoversimplified.Fisher et al.(2002)suggested that fractures can be classified as simple(typical description),complex,or very complex,as shown in Fig.6.Based on this conjecture,a large-scale hydraulic fracturing field experiment was conducted using a microseismograph and a surface tiltmeter.The experiments were carried out with different types of slurry and different injection methods to confirm the complex fracture behavior of the Barnett Shale of North Texas shale.The experimental results show that a complex fracture network was created in the hydraulic fracturing area(Fig.7),and the height and length of the fractures are variable.Fracturing fluids without gel solids contribute to creating longer,more complex fractures while leaving no gel residue or filter cake that could damage the fracture conductivity.Although this experiment was not conducted specifically for the cuttings re-injection project,it can be inferred from the experimental results that intermittent injection may create a more complex fracture network,while the increase of solids phase content may lead to changes in fracture size.

Fig.4.Microseismic events and fracture mapping based on downhole and surface tiltmeter data for the Wilcox injections(plan view)(reproduced from Moschovidis et al.,2000).

Fig.5.Microseismic events and fracture mapping based on downhole and surface tiltmeter data for the Atoka injections(plan view)(reproduced from Moschovidis et al.,2000).

In 2018,multidisciplinary technology was integrated into the cuttings re-injection project in the Abu Dhabi offshore field,providing real-time data to the analysis center through downhole sensors and visualization services to achieve real-time monitoring of fractures and reduce the risk of re-injection(Gumarov et al.,2018).

3.4.Specific formation experiments

Cuttings re-injection operations have been proven to work in both sandstone and shale layers,according to the previous assessment.However,most of the cases are carried out in high permeability sandstone formations,which can ensure a large treatment volume and effectively control the extension of fractures and avoid leakage(Dvorkin et al.,2001;Keck,2002;Mehtar et al.,2016).Therefore,it is necessary to conduct an in-depth study of re-injection fractures in sandstone formations,especially in weakly consolidated sandstone formations.

Fig.6.Schematic illustration of fracture complexity(Fisher et al.,2002).

Fig.7.Plan view of fracture structure plot(reproduced from Fisher et al.,2002).

Khodaverdian and McElfresh(2000)suggested that the mechanism of fracture in poorly consolidated sandstones is significantly different from that of linear elastic fracture mechanics in shales.Numerous hydraulic fracturing injection tests were conducted on unconsolidated sands in a radial flow cell(RFC)to illustrate the fundamental mechanisms of confining fracture propagation.The experimental apparatus,as shown in Fig.8,was designed to simulate a 0.3 m thick unconsolidated sand formation in a 180°sector and a 0.9 m radial distance from the wellbore.A series of experiments was performed on 3000 mD sand samples injected with cross-linked guar and visco-elastic surfactants at different overburden stresses.In each test,one or more injection cycles were performed at different overburden stresses in the range of 2.76-6.89 MPa.To form a single fracture,only one perforation was used per injection,and the remaining perforations were isolated.In each cycle,5.7-11.4 L of fluid are injected at a rate of 0.19 m3/s.Subsequently,the injection was stopped and the pressure drop data were recorded.At the end of the experiment,the RFC device was disassembled to dissect and photograph the samples.The experimental results show that fracture-like breakup does occur in unconsolidated sandstone formations(Fig.9a).However,since the cohesion and tensile strength of the formation are absent or small,the tip propagation mechanisms are not consistent with linear elastic fracture mechanics.Propagation of fracture tips in unconsolidated sandstones is mainly due to fluid intrusion and shear damage within a process zone in front of the tip.Besides,as Fig.9b shown,multiple subparallel fractures were induced by repeated cyclic injections of inefficient borate cross-linked guar.

Fig.8.Overall view of the RFC(Khodaverdian and McElfresh,2000).

Notably,there are few laboratory experiments on cuttings reinjection.Few researchers did more experiments after the DEA-81 experiment.Because of poor visualization and difficult variable control,field experiments can only monitor the approximate orientation of the fractures and evaluate the effect of cuttings re-injection implementation.As a result,the experiments can only assess the geometry and extension of cuttings re-injection fractures qualitatively,whereas the essence of fracture generation and propagation are functions of operational parameters and rock mechanical characteristics.

To conclude,it is hard to conduct laboratory experiments when critical information is lacking.Laboratory experiments can only qualitatively characterize the propagation of re-injection-induced fractures and cannot be used to predict fractures on a field scale.Therefore,few laboratory experiments on cuttings re-injection have been conducted.The application of monitoring techniques such as tiltmeter and microseismic in the field experiments enabled the researchers to obtain parameters related to re-injectioninduced fractures and proved the existence of a multi-fractures disposal domain.The combined application of multiple monitoring technologies increases the accuracy of monitoring and reduces the risk of leakage.The geometric characteristics of fractures are quantitatively described by field experimental research.However,because of the high cost and difficulty in obtaining the fracture initiation and extension patterns,as well as computing the fractures,there are few field experiments.

Both field and laboratory experiments have confirmed the feasibility of hazardous cuttings re-injection and the existence of a multi-fractures disposal domain.Theoretical research on reinjection fractures needs to be further studied.

4.Physical models of cuttings re-injection fractures

Many studies have attempted to develop physical models to describe the fractures that are caused during cuttings injection,but there has yet to be a consensus.

4.1.Wagon-wheel model

Periodic re-injection of cuttings is believed to increase the formation’s in situ stress,resulting in increased fracture width or the creation of new fractures.A sufficient shut-in time between injections allows the slurry fluid to dissipate in the formation,putting the cuttings on the fracture surface,preventing the fracture from fully closing,and increasing local stress.The thermal poroelastic effect generates local stress changes as well,but because of its rapid dissipation,it can be neglected.The change in fracture closure stress that results when cuttings are deposited on the fracture surface is expected to be permanent.

Fig.9.Fracture tip zones for Test #1:(a)Invasion zone around the fracture tip,and(b)Shear failure and subparallel fracturing during tip propagation(reproduced from Khodaverdian and McElfresh,2000).

According to this,Moschovidis et al.(1994)proposed the concept of fracture disposal domain as shown in Fig.10.The minimum horizontal stress rises as the number of injections accumulates,and the wellbore circumferential stress ultimately equalizes,at which time there is no preferred fracture orientation.Thus,a subsequent injection may induce a very complex vertical fracture with different orientations that may be non-planar,bifurcated,and connected with previously generated fractures in the near-well zone.All fractures are similar in size under the same injection conditions,and as more batches of cuttings are injected,the horizontal stress gradually increases until it equals the overburden stress,and after that fractures may be created in any direction.This is the earliest physical model of cuttings re-injection fractures and the prototype of the wagon-wheel model.

Moschovidis et al.(2000)published a paper describing in detail the complex fracture disposal domain model in shale based on previous studies(Fig.11).The model is a disposal domain formed by multiple fractures,which are uniformly distributed over 360°,similar to a wagon-wheel.However,the fractures are not generated in a certain order or angle during the generation of the disposal domain.The fracture can be generated in any direction since the horizontal stress is changed and gradually equalized due to solid phase deposition and hydration.It should be emphasized that the optimal condition for achieving the wagon-wheel disposal domain is a nearly isotropic horizontal stress.Ji et al.(2009)also presented a new wagon-wheel model and classified it into two types:uniform strain and uniform width models(Fig.12).The wagon-wheel concept,however,was eventually proven impractical,and we will discuss the reasons in-depth in the next section.

4.2.Other models

The wagon-wheel model is based on shale or well-consolidated sandstone formations,whereas Schmidt et al.(1995)indicated that cuttings re-injection in soft formations would make it impossible to generate wagon-wheel or clear multi-fractures disposal domains.Because the soft formation’s strength is so weak,each injection will induce enough shear force to overcome the cementing force between particles,resulting in larger pores in the near-well zone,increased waste storage capacity,and forming a complex crossseam network domain,as shown in Fig.13.This model is called a disaggregation or liquefaction model(Schmidt et al.,1995;Baker et al.,1999;Willson et al.,1999).

Fig.10.Schematic diagram of the disposal domain concept(reproduced from Moschovidis et al.,1994).

The direction of maximum in situ stress is always the same as the overburden stress mentioned in the preceding models.In formations with weak anisotropy,the horizontal stress is gradually increased with more batches of injection.Another model will be created,i.e.the T-shape model(Fig.14),when the horizontal stress is greater than the overburden stress.The model first generated a vertical fracture,which would be followed by a T-shaped fracture when further injection batches are supplied(Gulrajani and Nolte,2000;Shokanov et al.,2008).

In conclusion,although there are several fracture models,experts agree that multi-batches injection will increase in situ stress and result in multiple fractures in the near-well zone.The major reason that causes the fractures to reopen or switch is a change in the in situ stress.The basic mechanisms of in situ stress change are summarized below(Moschovidis et al.,1994;Hagan et al.,2002;Abou-Sayed et al.,2003;Gumarov et al.,2009;Ovalle et al.,2009;Mura,2013):

Fig.11.Schematic diagram of the“wagon-wheel”disposal domain concept(Moschovidis et al.,2000).

Fig.12.Uniform width and uniform strain multi-fracture models(reproduced from Ji et al.,2009).

Fig.13.Disaggregation model of cuttings injection fractures(Schmidt et al.,1995).

(1)Deposition of solids on the fracture surface increases in situ stress.The injection volume,fracture shape and anisotropy of the initial stress state may all be used to compute it.

(2)In prolonged cold slurry injection,thermal stress changes can cause the near-wellbore area to transition from compression to tension.The fluctuation in temperature,elasticity and thermal characteristics of the formation may be utilized to compute the change in local total stress generated by cooling.

(3)Because of the pore elasticity effect,pore pressure accumulation resulting during slurry injection changes in situ stress.Similar formulae for determining thermal stress may be used to determine the increase in local stress generated by pore pressure accumulation.

Fig.14.Horizontal fracture initiation when the vertical stress is less than the horizontal stress(reproduced from Gulrajani and Nolte,2000).

In short,the researchers have proposed various physical models of cuttings re-injection fractures.However,most of them are based on experience and there is insufficient theoretical evidence to prove the models’correctness,which is the key issue causing the ongoing controversy of fracture geometry.For the past 20 years,researchers have used mathematical models and numerical simulations to try to quantify the fracture geometry and propagation principle during cuttings re-injection.In the following sections,we will concentrate on these.

5.Mathematical models of cuttings re-injection fractures

Cuttings re-injection and hydraulic fracturing are quite similar.However,unlike hydraulic fracturing,there is a lack of basic theoretical study on cuttings re-injection(Nagel and McLennan,2010).The researchers used fundamental mechanical theory to try to derive analytical solutions for fracture geometry during cuttings reinjection,with the purpose of resolving a long-standing debate and,more significantly,providing a theoretical foundation for numerical simulation investigations.

5.1.Mathematical models of fracture with a single injection

Since the 1980s,researchers have proposed several mathematical models for hydraulic fracturing.The Khristinaovic-GeertsmadeKlerk(KGD),Perkins-Kern-Nordgren(PKN),and Penny-shape(radial fracture)models are the most often used two-dimensional(2D)models,which assume constant fracture height and increasing fracture width and length during fracture extension(Khristianovic and Zheltov,1955;Carter,1957;Geertsma and De Klerk,1969;Williams,1970;Nordgren,1972;Daneshy,1973).For true three-dimensional(3D)models,Clifton’s and Cleary’s models are the most representative.The model assumes that the flow state of the fracturing fluid and the elastic deformation of the formation have the greatest impact on the geometry of the hydraulic fracture,whereas the fracture mechanism only impacts the laminar flow(Clifton and Abou-Sayed,1979;Cleary et al.,1983).Although these models mainly focus on the single fracture created by hydraulic fracturing and do not consider the effect of multiple injections,they provide a theoretical basis for the study of multiple fractures in cuttings re-injection.

Deloge and Bouteca(2001)derived an analytical solution for vertical propagation of fractures in shales to better diagnose the stability or instability of the fracture propagation.The derivation process starts from the well-known solution of the circular fracture,introducing the linear variation of the stress and analyzing the effect of the stress gradient.Then,the derived results were applied to the elliptical fractures,and the effect of Young’s modulus variation on fractures was also considered.It was found that the fractures tend to propagate upward depending on the stress gradient,and the ratio(width/length)is about 0.71 for elliptical fractures.

Ji et al.(2009)used mathematical model calculations to determine if the cuttings re-injection generated a wheel or a multibranches model.The 3D fracture in the formation was simplified to a 2D PKN model and a penny-shape model in the plane.Then,the stress changes around the existing fractures were analyzed according to the pressure calculation methods proposed in Sneddon and Elliott(1946)and Sneddon(1946).The ratios of stress changes to net fracture pressure are used in the research process to demonstrate the variation of the three principal stresses.As shown in Fig.15,in the PKN model,the fracture height is fixed and both the maximum and minimum horizontal principal stresses decrease rapidly with increasing distance to the fracture(in thex-coordinate).It also decreases with increasing vertical distance from the fracture center.The stress variation is most obvious near the fracture.Negative stresses are observed around the top and bottom of the fracture.This indicates that subsequent injections will cause the fractures to be more easily initiated and propagated in height,affecting the re-fracture location.Similarly,Fig.16 shows the variation of the maximum and minimum horizontal principal stresses(inz-andr-directions,respectively)in the radial(penny)model.The trend of the variation of the maximum and minimum principal stresses in this model is similar to that of the PKN with significant changes occurring only in the vicinity of the fracture.Negative stresses were also observed in the region near the vertical tip of the fracture.

In addition,the variation of stress depends on the fracture geometry and the Poisson’s ratio of the rock,which was found by the calculation results.The near-well area is where the in situ stress changes.The maximum and minimum horizontal stresses near the fracture have the same changing pattern,whereas the far-field stress is mostly unaffected.As a result,the fracture can only turn when the minimum and maximum horizontal principal stress are very close,otherwise,due to the simultaneous increase of them,the fracture will reopen in the original direction.

Fig.15.(a)2D PKN fracture geometry,(b)Normalized stress change in minimum horizontal stress(x-direction,PKN fracture),and(c)Normalized stress change in maximum horizontal stress(z-direction,PKN fracture)(reproduced from Ji et al.,2009).

Fig.16.(a)Radial fracture geometry,(b)Normalized stress change in minimum horizontal stress(z-direction,radial fracture),and(c)Normalized stress change in maximum horizontal stress(r-direction,radial fracture)(reproduced from Ji et al.,2009).

Ji et al.(2009)reduced the ideal disposal domain concept to a model with uniform width or uniform strain,according to earlier discussions(Fig.12).A simple calculation demonstrates how impractical high wellbore pressure is for creating multiple fractures in a uniform width model.For instance,the wellbore pressure is up to 100 MPa if six 2-wing,0.03 m-wide,and 61 m-long fractures are formed along the 0.12 m-diameter wellbore in the wagon-wheel disposal zone.Obviously,such unreasonably high wellbore pressures do not occur during most injection operations.Therefore,a uniform width wagon-wheel disposal domain during cuttings reinjection is extremely difficult to achieve.Similarly,for the uniform strain wheel model,if the same fractures as the uniform width were created,the total tangent stress increment would be 21 MPa which will exceed the original minimum horizontal stress.Also,the calculation results show that the total fracture width is inversely proportional to the radius in the uniform strain model,and the fracture width at the borehole is only 0.01 mm,which is also unrealistic.In summary,the wagon-wheel ideal disposal domain should not occur in real operations.

5.2.Mathematical models of fracture with multiple injections

After the confirmation that the wagon-wheel disposal domain was unable to be generated,a new model for the potential position of the cuttings injection fracture was provided,and its accuracy was assessed using the PKN theory.The model suggests four possible cases for new fracture generation during cuttings re-injection as shown in Fig.17,including Case 1-reopening existing fracture,Case 2-generating new orthogonal fracture,Case 3-generating new oblique fracture at wellbore,and Case 4-branching fracture at the distance of the originally packed fracture(Ji et al.,2009).

Case 1 is possible because for reopening the existing fracture the wellbore pressure just needs to overcome the minimum horizontal stress in the vicinity of the wellbore.However,if a new fracture can be created which is perpendicular to the existing fracture,the wellbore pressure must exceed the stress concentration in the nearwell zone(Case 2)(Gulrajani and Nolte,2000).At this point,the stress increment needs to satisfy the following equation:

whereΔσhdenotes the minimum horizontal stress change,σHdenotes the original maximum horizontal stress,σhdenotes the original minimum horizontal stress,ν denotes the Poisson’s ratio of rock,andpiis the net fracture pressure.

It can be observed from Fig.15b thatΔσhis always less than or equal to the original net fracture pressurepo,andpois always less than σhor net fracture pressurepi.Therefore,it is difficult to meet this condition in most cuttings re-injection projects.Compared to Case 2,Case 1 is more likely to occur.

Fig.17.Competing locations to initiate subsequent multiple fractures(reproduced from Ji et al.,2009).

Case 3 is to create a new oblique fracture near the wellbore,and the angle between the new fracture and the existing fracture is θ.In this case,the wellbore pressure is required to exceed the stress concentration in the near-well zone,and the following equation must be satisfied:

In reality,the minimum horizontal stress around the fracture is always increasing(Δσhis positive)and the above equation cannot be satisfied,thus it is not possible to create a new oblique fracture compared to reopening of the existing fracture.

Case 4 is to reopen the existing fracture first and then a new branch fracture is created away from the wellbore.In this case,the minimum horizontal stress change should satisfy the following equation:

When the formation’s original maximum and minimum horizontal stress values are close and the Poisson’s ratio is minimal,the equation can be satisfied.In reality,most sandstone formations meet this requirement.

This evaluation indicates that multiple fractures are most likely to occur during cuttings injection by reopening an existing fracture and subsequently branching from the initial fracture,based on the examination of the four instances.The second fracture,in particular,seems unlikely to be originated in the wellbore.It has also been proven that the wagon-wheel concept is impossible(Ji et al.,2009).

Shokanov et al.(2011)further discussed the increase of in situ stress in the near-well zone and the mechanism of multi-fractures generation based on Ji et al.(2009).They created a near-well stress concentration model(Fig.18)and proposed that the stress concentration due to the transfer of stresses distributed in the drilledout formation to the edge of the wellbore.The stress concentration value is about 50%larger than the actual fracture closure pressure.As a result,the wellbore pressure required to generate a new fracture near the wellbore during the injection process is significantly higher than that required to reopen an existing fracture.Then the relationship between the ratio increase of the maximum and minimum horizontal stresses and Poisson’s ratio in the PKN,penny-shaped and KGD fracture models were proposed(Shokanov et al.,2011):

whereLdenotes the fracture half-length,Rdenotes the wellbore radius,andfΔv denotes the ratio increase between the minimum and maximum horizontal stresses.For example,in a formation with Poisson’s ratio of 0.2-0.4,the stress increases between the maximum and minimum horizontal stresses in the PKN,pennyshaped and KGD models are 0.4-0.8,0.6-0.9 and 1,respectively.

Fig.18.Drilling-induced stress concentration at the wellbore(reproduced from Shokanov et al.,2011).

A more in-depth evaluation of the four models(Fig.17)of secondary fracture was then performed based on the relationship between the stress increase ratio and Poisson’s ratio.The results of the studies were generally consistent with those obtained by Ji et al.(2009).Cuttings re-injection is most likely to reopen existing fractures first,followed by a new fracture branch distant from the wellbore.The fracture extension is symmetrical,meaning that under identical conditions,four branching fractures will form in each of the four directions surrounding the wellbore.The decrease in fluid pressure away from the wellbore,as well as the specific orientation of the branching fracture,is unclear in this investigation,making it impossible to predict whether branching will continue at the distal end of the branching fractures(Shokanov et al.,2011).

Different mathematical models explain the fracture initiation location and extension direction during the first and subsequent injections and demonstrate the feasibility of re-injection of hazardous cuttings and the multi-fractures disposal domain from a theoretical point of view.However,field experiments have shown that re-injection-induced fractures are influenced by a variety of factors.The previous studies only considered the physical properties of the formation and analyzed the opening state of the fracture from the perspective of fracture mechanics.However,the generation of fractures during cuttings re-injection is not only related to the physical properties of the formation,but the performance of the injected slurry will also have a great effect on the fractures.The theoretical analysis is difficult to consider both formation properties and slurry properties,thus there is a great difference between the theoretical studies and the real operations.In recent years,numerical simulation techniques have been increasingly used to investigate the law of fracture generation under multiple factors during the cuttings re-injection process,and we will focus on this technique in the next section.

6.Numerical studies of cuttings re-injection fractures

The theoretical analysis depends on various assumptions,and the study’s findings may differ significantly from the real scenario,making it hard to predict fracture behavior and geometry accurately.Thus,numerical simulation techniques are applied to analyzing fracture development,which may give important references for the design of field projects,to more accurately forecasting fracture extension during cuttings re-injection,and to producing more realistic research findings.Similarly,several studies on numerical simulation of fractures during hydraulic fracturing have been conducted,but a few on cuttings re-injection.

6.1.Disposal domain numerical simulation studies

Buller(1996)mentioned that a company in the North Sea used numerical simulations to investigate cuttings re-injection fractures,including pseudo-3D models(Gopher,FracPro and STIMPLAN),real 3D models(TerraFrac and Gyfrac)and the company’s models,but did not go into details about the models.

Abou-Sayed et al.(2003)created a 3D model to simulate the injection of multiple batches of cuttings.The intensity of in situ stress anisotropy was varied in the model as a way to observe the fracture opening and extension rules of multiple injections under different in situ stress conditions.The simulation results show that multi-batches injection in formations with strong stress anisotropy will create a limited range of multiple fractures in the lower stress region firstly.More solid phases were deposited in the fracture surface as the number of injection batches increased,and local stress rapidly rose.The increasing injection pressure weakens the vertical fracture propagation barrier at some point during the reinjection.As a result,the fracture will extend into the intermediate disposal layer.In the end,the fracture broke the second barrier and formed a top disposal layer,as shown in Fig.19a.It is noted that the extent of fracture became larger for the same volume of each injection due to leak-off damage from previous injections.Multiple injection batches,on the other hand,can create a wide range of multiple fractures in formations with weak stress anisotropy,and the fracture size increases as the number of injection batches increases,with no obvious occurrence of multiple disposal layers(Fig.19b).Furthermore,new fractures could be formed from a new batch injection only if the shut-in period between injection batches was long enough for existing fractures to close enough.But researchers did not clarify the specific type of model and parameter settings,nor did they take into consideration the features of the slurry or the transit of the cuttings particles,even though the 3D model is used.Therefore,this study can only quantify the shape of the disposal domain that may be formed by multi-batch injections,but it cannot obtain the influence of formation properties or construction parameters on the disposal domain and fractures.

6.2.Fracture barrier methods

Because fractures tend to extend upward,there is a risk of contaminant leakage caused by an excessive extension,therefore understanding the mechanism of the fracture barrier is critical.Guo et al.(2004)investigated the fracture barrier mechanism during cuttings re-injection using a true 3D hydraulic fracturing simulator-TerraFracTM.The model is based on 3D linear elastic and non-Newtonian fluids to simulate the movement of fluid in fractures and the change of fracture geometry.There are three primary fracture barrier mechanisms observed.The first is the stress barrier where the overburden fracture pressure is significantly greater than the fracture pressure of the targeted formation to prevent the fractures from extending upward(Fig.20a).The second is the permeability barrier.When the fractures extend to the higher permeability formation,the liquid leak-off rate is accelerated and the solid phase will be deposited on the fracture surface at a faster rate,forming a filter cake,thus preventing the fracture from continuing to grow upward(Fig.20b).The last one is the Young’s modulus barrier.The formation with a higher Young’s modulus has a higher stiffness,which generates less fracture width,thus increasing the friction between the fluid and the fracture,preventing the continued upward growth of the fracture(Fig.20c).The limitation of this model is that it does not consider the effect of multiple factors simultaneously(Abou-Sayed et al.,2000;Guo et al.,2000,2004,2006).

Fig.19.Fracture extent and geometry change(a)with strong stress anisotropy and(b)without stress anisotropy(Abou-Sayed et al.,2003).

6.3.Impacts of construction factors on fractures

Many factors impact the development of hazardous cuttings reinjection-induced fractures,including construction parameters such as re-injection rate and slurry composition.The majority of previous cuttings re-injection numerical simulation results indicated that the most of studies focus on fracture initiation and extension under various construction factors.

Yamamoto and Nakama(2004)developed a model that can simulate particle movement in the fluid by introducing solid-phase transport in the hydraulic fracturing model to investigate the influences of solid-phase concentration in the slurry on fracture extension during cuttings re-injection.In the model,the fracture opening,the interaction between solid particles,and the influence of solid concentration on viscosity are all taken into account.The displacement discontinuity method is used to calculate the coupled solution of fluid pressure and fracture opening,and the finite element method is used to calculate the coupled solution of Newtonian fluid and non-Newtonian fluid.Besides,it is assumed in the model that only fluids will filter through the fracture surface,while all solids will deposit on the fracture surface.According to the simulation results,the solid phase concentration has a substantial impact on fracture extension and final geometry.The deposition of solid particles and the increase in viscosity contributed to a greater tendency for fractures to propagate upward(Fig.21)when the high concentrated slurry is injected.However,the high solids concentration slurry requires a higher injection pressure,which increases the danger of injection.Although this model considered the phenomenon of mixed fluid flow,the solid particles in the slurry are uniform,which is far from the real situation.

For evaluating the performance of cuttings re-injection in low permeability shale formations,Gil et al.(2010)proposed a method that combined 2D discrete elements and a particle model that can simulate asymmetric free propagation of fractures.The failure between rocks was expressed as the failure of bonds between particles,which makes it easier to evaluate the types of rock failure.The simulation results show that the pressure drop during shut-in has a significant impact on the direction of secondary fractures during cuttings re-injection.The secondary fracture will initially occur at an angle to the existing fracture when the well is injected again with little pressure drop during shut-in(i.e.the fracture cannot be entirely closed),but will soon be parallel to the existing fracture.When re-injected with a considerable pressure decrease during shut-in,the secondary fractures are more likely to branch and turn dramatically.Additionally,the maximum horizontal stress has almost no effect on the initial fracture pressure,and only shows a significant effect on the fracture turning.The larger the stress difference,the faster the secondary fracture will be parallel to the existing fracture,and conversely,the easier it is for the secondary fractures to propagate in other directions.But the increase of the minimum stress will significantly increase the fracture pressure,which has a greater effect on the injection pressure.However,this model is a 2D model,which does not consider the effect of the slurry properties on the fractures,and cannot reflect the real situation of the formation and the fracture generation under the whole life cycle.

Ji et al.(2010)developed a true 3D boundary element model based on the properties of the re-injection slurry and the formation.The effect of different properties of slurry on fractures was simulated by varying the rheological properties of the slurry in the model,solid particle size,concentration,leak-off coefficient,and formation parameters.The results indicated that the solid particle concentration and size were the key parameters controlling the fracture propagation.A premature solid screen-out will occur when the injected particle size is 500-600 μm,with a high concentration of solids on the fracture tip.This will cause the injection pressure to increase rapidly,and the fracture height and the risk of slurry leakoff will increase accordingly.However,under the same conditions,no solids were highly concentrated in the fracture during injection with smaller solid particles(250-300 μm)(Fig.22a).Similarly,both high slurry concentration(Fig.22b and c)and high leak-off coefficient during cuttings re-injection can lead to premature solids screen-out and a rapid increase in injection pressure.The simulation results of different Young’s moduli are the same as the study by Guo et al.(2004)(Fig.22d).That is,the fracture will be narrower if the formation’s Young’s modulus is higher.As a result,the slurry will have more resistance in entering the fracture,preventing the fracture from continuing to extend.The model’s limitation is that only the effects of the slurry performance and the formation properties on single fractures were investigated,but the case of intermittent re-injection creating multiple fractures was not considered.

Fig.20.Fracture containment due to(a)stress barrier,(b)high permeability barrier,and(c)modulus barrier(Guo et al.,2004).

Fig.21.Final geometry of the fracture with different solid concentrations:(a)5%,(b)10%,and(c)20%(Yamamoto and Nakama,2004).

The cohesive element method has been used to simulate the brittle failure of rocks.It is also a powerful method for simulating the effect of operational parameters on fractures during cuttings reinjection(Chen et al.,2009;Carrier and Granet,2012;Guo et al.,2017;Feng and Gray,2018;Taleghani et al.,2018).Shen and Standifird(2015)established a simplified 3D finite element model using the cohesive element method to determine the optimal injection pressure and rate during cuttings re-injection and used the pore elasticity damage rule to simulate the extension of the fractures in the vertical and horizontal directions,respectively.It was observed that higher stable net pressure could be obtained at higher injection rates.The anisotropy of the formation is not taken into account in this simulation,and the cohesive element fracture simulation requires the fracture position and extension direction to be specified in advance,thus the simulated results may differ from the actual ones.

Most slurries during cuttings re-injection are non-Newtonian fluids,mainly plastic and pseudoplastic fluids,with complex rheological properties,which are difficult to characterize with one model.Guo et al.(2020)developed a model to characterize Bingham-type slurry flow behavior using an effective potential gradient and implemented the method using the module of TOUGH2.They discretized the continuity equation by the integral finite difference method and proposed an analytical solution for numerical model verification.Besides,a hypothetical model was developed to evaluate the effects of the slurry density,injection depth,injection pattern,and other engineering parameters on the slurry transport behavior,storage capacity,and formation breakup time.The model is in general agreement with the field experimental results.It is proved that the model can simulate the complex slurry flow process of the formation and can be used for cuttings re-injection design and formation storage capacity evaluation to reduce operational risks.

In summary,numerical simulation studies provided stronger evidence for the creation of multi-fractures disposal domains.Meanwhile,three barrier mechanisms for re-injection-induced fractures have been proposed.The fracture propagation patterns under various construction conditions were also obtained.

However,most fracture models are based on the theory of linear elastic fracture mechanics,which cannot be applied to plastic formations.The majority of numerical simulation studies focus on shale or sandstone formations,while the basic theoretical study of cuttings re-injection under soft rock formations is still lacking.Furthermore,rather than modeling multiple factors(particularly slurry temperature),most numerical simulations only simulate one or few of them,resulting in inconsistencies between simulation findings and actual situations.The more serious problem is that most studies only focus on a single fracture,while numerical simulation studies for multiple fractures are uncommon.

7.Summary

This paper first summarizes the fundamental studies on the development of cuttings re-injection fractures in the published sources in the past 30 years.Then,the strengths and limitations of the existing studies are discussed.From this literature review,the following summary is drawn.

Experimental studies,mathematical model analysis and numerical simulation studies have all demonstrated that a multifractures disposal domain can be formed in the near-well zone during cuttings re-injection.

Fig.22.(a)Fracture width and particle size,(b)Solids distribution in fracture with injection slurry of 50%solids,(c)Solids distribution in fracture with injection slurry of 30%solids,and(d)Fracture width with different Young’s moduli(reproduced from Ji et al.,2010).

The feasibility of deep waste re-injection and the existence of a multi-fractures disposal domain were verified for the first time through re-injection experiments.Cuttings re-injection projects can be carried out in shale or sandstone formations.The fractures created by re-injection in shale formations are narrower and longer than those in sandstone formations.This means that shale formations are not conducive to large waste re-injection projects.

According to the researchers,cuttings re-injection required intermittent construction to ensure that more waste can be injected into the formation.The solid phase deposits on the fracture surface as the fluid leaks off during the shut-in period,preventing the fracture from entirely closing.The in situ stress near the fracture will be altered.Based on this,a variety of physical models for re-injection disposal domains are proposed,including complex vertical fracture models,ideal wheel models,disaggregation models in soft formation,and T-shaped models.

More mathematical model studies have been conducted based on experimental and physical model studies.The disposal domain model for cuttings re-injection is expected to be explained and developed using mathematical formulations.At first,individualfracture models were studied based on classical models(KGD,PKN and penny).The maximum and minimum horizontal principal stresses at the same position near the fracture have the same trend and normally grow under a single fracture condition,but at the tip of the fracture,negative stresses appear,indicating that the stresses are reducing.The far-field stresses are almost unaffected.Then,the stress and the fracture’s radius near the wellbore of the wheel model were calculated,and it was found that the results were unrealistic,proving a wheel model is impossible to occur in realistic situations.

The key to studying multiple fractures is determining where secondary fractures begin,and four types of secondary fracture initiating locations have been proposed:reopening existing fracture,generating new orthogonal fracture,generating new oblique fracture at wellbore,and branching fracture at the distance of the originally packed fracture.Following calculations,it was observed that when cuttings are injected again,existing fractures are first reopened,and new oblique branching fractures are created alongside existing fractures away from the wellbore,with the angle varying depending on the in situ stress condition.

However,as shown in Table 3,numerous factors influence the fracture disposal domain of cuttings re-injection.Many assumptions and simplifications are made in experimental and theoretical studies,making it impossible to establish the fracture extension pattern when multiple factors are taken into account.Numerical simulation techniques have considerably decreased research costs while also bringing study conditions closer to reality.The geometry of the multi-fracture disposal domain depends on the anisotropy of formation stress,according to numerical simulation studies.In the formation with weak anisotropy,a disposal domain with a larger circumferential zone that can receive a large amount of waste will be formed.Furthermore,“stress barrier,permeability barrier,and Young’s modulus barrier”are three barrier mechanisms for reinjection-induced fractures.A caprock with high stress,high permeability,and high Young’s modulus can prevent excessive extension of the fracture in the vertical direction,thus reducing the risk of leakage.In the numerical simulation results for different construction parameters,it was found that high solid content slurry,high injection rate,and high viscosity cause a rapid increase in injection pressure,excessive fracture height,and reduced formation disposal capacity.

To summarize,deep underground re-injection is an effective solution for dealing with hazardous cuttings.A multi-fractures disposal domain is formed during re-injection construction,and its shape depends on the formation conditions and construction parameters.Many researchers have studied the cuttings reinjection,but there is no clear conclusion and corresponding calculation formulae for the re-injection-induced fractures.Because all of the fracture characterization methods are based on hydraulic fracturing theory,research on re-injection-induced fractures has remained stationary.

Based on the issues of the fundamental studies of cuttings reinjection fractures,the following recommendations are made for future works:

(1)Most studies of cuttings injection projects have been conducted in vertical wells,and studies of deviated or horizontal wells are recommended.

(2)It is strongly recommended to consider the effect of the existing natural fractures in the formation during the cuttings re-injection so that the study results are closer to the real process.

(3)It is suggested to strengthen laboratory experiments,improve existing experimental devices,and consider using transparent cores and colored slurry for visualization experiments to observe particle transport,concentration,deposition and fracture initiation laws during cuttings reinjection.

(4)It is recommended to derive the functional equations between fracture geometry,construction parameters and formation parameters from the fundamental theory,which can not only describe the fractures more accurately but also promote the development of numerical simulation technology.

(5)The temperature of the injected slurry can have a significant effect on the in situ stress in the near-well zone,but few studies have been published on the temperature of the injected slurry.

(6)The majority of the studies on cuttings re-injection are for shale or sandstone formations,and it is recommended that more studies should be done for weakly cemented sandstone formations.However,it should be noted that the fractures formed by hydraulic fracturing or cuttings re-injection in weakly consolidated formations are more likely to be erosion fractures and may not be able to be well characterized by elastic-plastic fracture mechanics.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The work was financially supported by National Natural Science Foundation of China(Grant Nos.52074312 and 52004298).

List of symbols

σHMaximum horizontal principal stress

σhMinimum horizontal principal stress

WFracture width of uniform-width model

WRFracture width at radius position of uniform-strain model

pwNet pressure in fracture

x，yCoordinates

cHalf height of fracture in PKN model

Δσx，Δσz，ΔσrThe change of principal stress inx,z,rdirections

RHalf height of fracture in radial model

σ Original in situ stress

r／rwbThe ratio of the distance from a position to the center of the wellbore to the radius of the wellbore