Value of negative pressure sealing drainage on wound healing of Gustilo IIIB and IIIC open fractures

BACKGROUND Gustilo III fractures have a high incidence and are difficult to treat.Patients often experience difficulty in wound healing.Negative pressure drainage technology can help shorten wound healing time and has positive value in improving patient prognosis.AIM To explore the clinical value of the negative pressure sealing drainage technique in wound healing of Gustilo IIIB and IIIC open fractures.METHODS Eighty patients with Gustilo IIIB and IIIC open fractures with skin and soft tissue injuries who were treated in the Second People’s Hospital of Dalian from March 2019 to December 2021 were selected as the research subjects.They were divided into a study group(n=40,healed with negative pressure closed drainage)and a control group(n=40,healed with conventional dressing changes)according to the variation in the healing they received.The efficacy of the clinical interventions,the variations in the regression indicators(time to wound healing,time to fracture healing,time to hospitalization),and the conversion and healing of bacterial wounds were compared 1-3 mo after the intervention.RESULTS The total effective rate of patients among the study group was 95.00%(38/40),which was notably higher than 75.00%(30/40)among the control group(P<0.05).The wound healing time,fracture healing time,and hospital stay of the patients in the study group was shorter than the control group(P<0.05).After the intervention,the negative bacterial culture at the wound site rate and wound healing rate of the patients among the study group increased compared to the control group(P<0.05).CONCLUSION Negative pressure sealing and drainage technology has a good therapeutic effect on patients with Gustilo IIIB and IIIC open fracture wounds with skin and soft tissue injury.It can notably enhance the wound healing rate and the negative rate of bacteria on the wound surface and help to speed up the recovery process of patients.

Outcomes of early versus late irrigation and debridement of pediatric open long bone fractures

BACKGROUND Open long bone fractures are a major concern for pediatric patients due to the risk of surgical site infection(SSI).Early studies have recommended irrigation and debridement of open fractures within 6 hours-8 hours for the prevention of SSI.According to the American College of Surgeons(ACS)Best Practice Guidelines,in 2015,irrigation and debridement should be done within 24 hours.AIM To identify whether early irrigation and debridement,within 8 hours,vs late,between 8 hours and 24 hours,for pediatric open long bone fractures impacts rate of SSI.METHODS Using retrospective data review from the National Trauma Data Bank,Trauma Quality Improvement Project(TQIP)of 2019.TQIP database is own by the ACS and it is the largest database for trauma quality program in the world.Propensity matching analysis was performed for the study.RESULTS There were 390 pediatric patients with open long bone fractures who were incl-uded in the study.After completing propensity score matching,we had 176 patients in each category,irrigation and debridement within 8 hours and irrigation and debridement between 8 hours and 24 hours.We found no significant differences between each group for the rate of deep SSI which was 0.6%for patients who received surgical irrigation and debridement within 8 hours and 1.1%for those who received it after 8 hours[adjusted odd ratio(AOR):0.5,95%CI:0.268-30.909,P>0.99].For the secondary outcomes studied,in terms of length of hospital stay,patients who received irrigation and debridement within 8 hours stayed for an average of 3.5 days,and those who received it after 8 hours stayed for an average of 3 days,with no significant difference found,and there were also no sig-nificant differences found between the discharge dispositions of the patients.CONCLUSION Our findings support the recommendation for managing open long bone fractures from the ACS:Complete surgical irrigation and debridement within 24 hours.

Clinical outcome of open ankle fractures in patients above 70 years of age

BACKGROUND Open fractures of the ankle are complex injuries requiring multidisciplinary input and are associated with significant morbidity and mortality.However,data on the clinical outcomes of open ankle fracture management in patients older than 70 is minimal.AIM To evaluate the clinical outcomes following open ankle fracture management in patients older than 70.Our secondary aim is to look at predictors of poor outcomes.METHODS Following local research and audit department registration,22 years of prospectively collated data from an electronic database in a district general hospital were assessed.All patients older than 70 years of age with an open ankle fracture requiring surgical intervention were identified.Demographic information,the nature,and the number of surgical interventions were collated.Complications,including surgical site infection(SSI),venous thromboembolic events(VTEs)during hospital stay,and mortality rate,were reviewed.RESULTS A total of 37 patients were identified(median age:84 years,range:70-98);n=30 females median age:84 years,range:70-97);n=7 males median age:74 years,range:71-98))who underwent surgical intervention after an open ankle fracture.Sixteen patients developed SSIs(43%).Superficial SSIs(n=8)were managed without surgical intervention and treated with antibiotics and regular dressing changes.Deep SSIs(n=8;20%)required a median of 3(range:2-9)surgical interventions,with four patients requiring multiple washouts and one patient having metalwork removed.VTE incidence was 5%during the hospital stay.Eight patients died within 30 d,and mortality at one year was 19%.The 10-year mortality rate was 57%.The presence of a history of stroke,cancer,or prolonged inpatient stay was found to be predictive of lower survivorship in this population(log-rank test:cancer P=0.008,stroke P=0.001,length of stay>33 d P=0.015).The presence of a cardiac history was predictive of wound complications(logistic regression,P=0.045).Age,number of operations,and diabetic history were found to be predictive of an increase in the length of stay(general linear model;age P<0.001,number of operations P<0.001,diabetes P=0.041).CONCLUSION An open ankle fracture in a patient older than 70 years has at least a 20%chance of requiring repeated surgical intervention due to deep SSIs.The presence of a cardiac history appears to be the main predictor for wound complications.

Proppant transport law in multi-branched fractures induced by volume fracturing

To further clarify the proppant transport and placement law in multi-branched fractures induced by volume fracturing, proppant transport simulation experiments were performed with different fracture shapes, sand ratios, branched fracture opening time and injection sequence of proppants in varied particle sizes. The results show that the settled proppant height increases and the placement length decreases in main fractures as the fracturing fluid diverts gradually to the branched fractures at different positions. The flow rate in branched fractures is the main factor affecting their filling. The diverion to branched fractures leads to low flow rate and poor filling of far-wellbore branched fractures. The inclined fracture wall exerts a frictional force on the proppant to slow its settlement, thus enhancing the vertical proppant distribution in the fracture. The increase of sand ratio can improve the filling of near-wellbore main fracture and far-wellbore branched fracture and also increase the settled proppant height in main fracture. Due to the limitation of fracture height, when the sand ratio increases to a certain level, the increment of fracture filling decreases. When branched fracture is always open(or extends continuously), the supporting effect on the branched fractures is the best, but the proppant placement length within the main fractures is shorter. The fractures support effect is better when it is first closed and then opened(or extends in late stage) than when it is first opened and then closed(or extends in early stage). Injecting proppants with different particle sizes in a specific sequence can improve the placement lengths of main fracture and branched fracture. Injection of proppants in an ascending order of particle size improves the near-wellbore fracture filling, to a better extent than that in a descending order of particle size.

Therapeutic Strategies and Evolution in the Short Term: Fractures by Firearms in Civilian Practice about 35 Operated Lesions

Fracture by firearms is a surgical emergency. The aim of our study was to report our experience in the management of open fractures by firearms and monitoring with a decline of 6 months the lesions observed in peacetime. This retrospective study over 3 years (January 2007-November 2010), supplemented by a prospective (December 2010-November 2011) is based on an analysis of operative reports and clinical records of patients admitted to the Yaoundé Central Hospital. 29 cases were selected, including 35 lesions were observed. Our series consists of 27 men and 2 women, mean age 30 years. 40% of our patients were initially supported (debridement) before the 6th hour and 51.42% between the 6th and 24th hours. In terms of internal fixation, these figures were 66% between the 25th and 96th hours. The type of material was used as the external fixate (64.9%). Conversion processing by the establishment of an internal hardware, after 3 - 6 weeks and control NFS (numeration of blood count or blood count), VS (rate of sedimentation), CRP (C reactive protein). Unfortunately this has been possible only in two cases because of financial means. In 40% of cases, surgical outcome was simple, and complications to a type of osteomyelitis, shortening, suppuration in 42.7% of cases.

Exclusive Fibula Osteosynthesis for Treating Open Fractures Gustillo I-III B of the Distal Half of the Leg Bones in a Resources-Limited Setting

Introduction: Management of open leg bones fractures is a challenging health issue for the surgeon, particularly true in resource-limited settings. In this study, we evaluate exclusive fibular osteosynthesis in the treatment of open fractures of the distal half of the leg bones as a therapeutic option in our context. Methods: This is a prospective, experimental, multicenter study of 30 open fractures of the distal half of the leg bones treated with exclusive fibula osteosynthesis, conducted in 3 hospitals in the DRC from January 1, 2013 to September 30, 2016. Results: The age range of 20 to 40 years grouped 22 (73.4%) patients, the sex ratio was 1:1 and the unemployed were the most involved with 16 (53.3%) cases. The Gustilo II, I, III B and III A types represented 40%, 33.3%, 20% and 6.7%, respectively. The fractures were located in the distal third in 12 (40%) cases, in the middle third in 11 (36.7%) cases, and in both malleoli in 7 cases (23.3%). Osteosynthesis of the fibula by screw plate was applied in 22 (73.3%) patients and pinning in 8 (26.7%). Satisfactory reduction of the tibial fracture site was achieved in 29 (96.7%) cases and 100% bone healing was achieved within an average of 10 weeks. Four (13.3%) loss of alignment, 1 (3.3%) infection, 1 (3.3%) skin necrosis and 2 (6.7%) ankle stiffness complicated our fractures. Conclusion: Exclusive osteosynthesis of the fibula as a common technique for fractures of the distal half of the leg bones allowed us to reduce, immobilize and consolidate the tibial fracture in the required time and to preserve the mobility of the ankle.

Pedicled abdominal flap using deep inferior epigastric artery perforators for forearm reconstruction: A case report

BACKGROUND Pedicled abdominal flaps are a widely used surgical technique for forearm reconstruction in patients with soft tissue defects.However,some drawbacks include restricted flap size,partial flap loss,and donor-site morbidity.To address these concerns,we present a case of a pedicled abdominal flap using the deep inferior epigastric artery perforators(DIEP)for forearm reconstruction in a patient with a large soft tissue defect.CASE SUMMARY A 46-year-old male patient was admitted to our hospital with forearm injury caused by a pressing machine.A 15 cm×10 cm soft tissue defect with complete rupture of the ulnar side structures of the forearm was found.One week after orthopedic management of the neurovascular injury and fractures using the first stage of Masquelet technique,the patient was referred to the plastic and recon-structive surgery department for wound coverage.Surgical debridement and negative-pressure wound therapy revealed a 20 cm×15 cm soft tissue defect.A pedicle abdominal flap with the DIEP was used to cover the defect.Three weeks later,the flap was detached from the abdomen,and the abdominal defect was directly closed.Subsequently,the second stage of Masquelet technique was performed at the fracture site at week 10.Finally,all donor and recipient sites healed without complications,such as flap dehiscence,infection,hematoma,or necrosis.Fracture site osteosynthesis was achieved without complications.CONCLUSION Pedicled abdominal flap using the DIEP provides a reliable option for forearm reconstruction in patients with large soft tissue defects.

Surgical Site Infections in Trauma and Orthopaedics at Bouaké Teaching Hospital (Côte d’Ivoire)

Background: Surgical site infections are serious healthcare problems. The aim was to describe the epidemiological, diagnostic, therapeutic, and prognostic aspects of surgical site infections in Trauma and Orthopaedics at Bouaké Teaching Hospital. Method: This retrospective, descriptive, and analytical study was conducted from January 2019 to December 31, 2021. The data studied included prevalence, initial lesions, type of surgical intervention, type of SSI, bacteria involved, treatment, and outcomes. Results: Forty-four (11%) of the 399 patients included in the study developed a surgical site infection. The mean age was 27 years, with 36 male and 8 female. Initial lesions were predominantly open fractures (n = 31;70%), with a mean delay of 48 hours for surgical management. Emergency interventions accounted for 70% (n = 31) of cases. The NNISS infection risk score was 1 in 80% (n = 35) of cases. Superficial infections (n = 34;77%) appeared early, on a mean 6 days postoperatively. Bacteriological analysis primarily identified Pseudomonas aeruginosa (n = 10;23%), sensitive to Imipenem and Chloramphenicol but resistant to Amoxicillin-clavulanic acid, Ceftriaxone, Gentamicin, and Ciprofloxacin. Multidrug-resistant bacteria were found in 89% (n = 8) of cases, with all bacteria resistant to Ceftriaxone. Surgical revision was performed in 10 patients (23%), primarily involving debridement with hardware retention (n = 7;70%). Chloramphenicol was the most commonly used antibiotic post-antibiogram (61%). Outcomes were favourable in 98% of cases. Identified risk factors included the type of lesion according to NRC classification, the delay in managing open fractures, and the NNISS score. Conclusion: The prevalence of surgical site infection was 11%, favoured by the delayed operation of open fractures.

Contaminated open fracture and crush injury: a murine model

Modern warfare has caused a large number of severe extremity injuries, many of which become infected. In more recent conflicts, a pattern of co-infection with Acinetobacter baumannii and methicillin-resistant Staphylococcus aureus has emerged. We attempted to recreate this pattern in an animal model to evaluate the role of vascularity in contaminated open fractures. Historically, it has been observed that infected bones frequently appear hypovascular, but vascularity in association with bone infection has not been examined in animal models. Adult rats underwent femur fracture and muscle crush injury followed by stabilization and bacterial contamination with A. baumannii complex and methicillin-resistant Staphylococcus aureus.Vascularity and perfusion were assessed by micro CT angiography and SPECT scanning, respectively, at 1, 2 and 4 weeks after injury. Quantitative bacterial cultures were also obtained. Multi-bacterial infections were successfully created, with methicillin-resistant S. aureus predominating. There was overall increase in blood flow to injured limbs that was markedly greater in bacteria-inoculated limbs. Vessel volume was greater in the infected group. Quadriceps atrophy was seen in both groups, but was greater in the infected group. In this animal model, infected open fractures had greater perfusion and vascularity than non-infected limbs.

IRRIGATION AND TRACTION THERAPY FOR OPEN FRACTURE WITH LARGE－SIZED FULL－THICKNESS SKIN－DEFICIT AND SEVERELY INFECTED WOUND

In this paper the results of skeletal traction and irrigation therapy (STIT) used for open fracture complicated with large-sized full-thickness skin-deficit and infection wounds (OFIW) were presented. Fourteen patients of OFIW were treated by the plaster cast and wound dressing (PCWD), and 30 patients of OFIW were treated by STIT. The results indicated that after one week of treatment, the white blood cell count in the STIT group, compared to 17. 6±l. 0×109/L from before treatment, returned to 8. 8±0. 8×109/L,and in contrast, the cell count of the PCWD group was about 13. 0±1. 4×109/L. All of wound exudate culture in the STIT group was negative, and those of 7 cases (7/14) in PCWD group were positive (P<0. 0l). The symptoms and signs such as pain, fever and septic exudate on the wound in the STIT group were much milder than those in the PCWD group. There were 5 cases (35. 7%) of toxicemia and septicemia, 2 cases (14. 3%) of osteomyelitis, 2 cases (14. 3 %) of amputation, 1 case (7. 1%) of delayed union and 3 cases (21. 4 %) of malunion in the PCWD group, and no complications in the STIT group.

Diagnosis,treatment and complications of radial head and neck fractures in the pediatric patient

Radial head and neck fractures represent up to 14%of all pediatric elbow fractures and can be a difficult challenge in the pediatric patient.In up to 39%of proximal radius fractures,there is a concomitant fracture,which can easily be overlooked on the initial standard radiographs.The treatment options for proximal radius fractures in children range from non-surgical treatment,such as immobilization alone and closed reduction followed by immobilization,to more invasive options,including closed reduction with percutaneous pinning and open reduction with internal fixation.The choice of treatment depends on the degree of angulation and displacement of the fracture and the age of the patient;an angulation of less than 30 degrees and translation of less than 50%is generally accepted,whereas a higher degree of displacement is considered an indication for surgical intervention.Fractures with limited displacement and non-surgical treatment generally result in superior outcomes in terms of patient-reported outcome measures,range of motion and complications compared to severely displaced fractures requiring surgical intervention.With proper management,good to excellent results are achieved in most cases,and long-term sequelae are rare.However,severe complications do occur,including radio-ulnar synostosis,osteonecrosis,rotational impairment,and premature physeal closure with a malformation of the radial head as a result,especially after more invasive procedures.Adequate follow-up is therefore warranted.

Scoring system for poor limb perfusion after limb fracture in children

BACKGROUND Assessment of the vascular status following limb fracture in children is important to evaluate the risk of compartment syndrome,which is an emergency condition.AIM To establish a simple and efficient grading scale of limb perfusion in children undergoing surgery for limb fracture.METHODS This retrospective study included pediatric patients with a limb fracture and postoperative plaster fixation who were admitted at The Department of Pediatric Orthopedics of Xinhua Hospital between February 2017 and August 2017.The outcome was poor limb perfusion,which is defined as the postoperative use of mannitol.The children were divided into two groups:The normal perfusion group and the poor perfusion group.Key risk factors have been selected by univariable analyses to establish the Grading Scale for Vascular Status.RESULTS A total of 161 patients were included in the study:85 in the normal perfusion group and 76 in the poor perfusion group.There were no significant differences in age,sex,body mass index,ethnicity,cause of fracture,fixation,or site of fracture between the two groups.After surgery,the skin temperature(P=0.048)and skin color(P<0.001)of the affected limb were significantly different between the two groups.The relative risk and 95%confidence interval for skin temperature of the affected limb,skin color,and range of motion of the affected limb are 2.18(1.84-2.59),2.89(2.28-3.66),and 2.16(1.83-2.56),respectively.The grading scale was established based on those three factors(score range:0-3 points).Forty-one patients(32.5%)with score 0 had poor limb perfusion;all patients with scores 1(n=32)and 2(n=3)had poor limb perfusion(both 100%).CONCLUSION In children undergoing surgery for limb fracture,a higher Grading Scale for Vascular Status score is associated with a higher occurrence of poor limb perfusion.A prospective study is required for validation.

Strategies and outcomes in severe open tibial shaft fractures at a major trauma center: A large retrospective case-series

BACKGROUND Severe open tibia fractures are challenging to treat with a lack of published clear management strategies.Our aim was to provide an overview of the largest singlecenter experience in the literature,with minimum 1-year follow-up,of adult type 3 open tibial shaft fractures at Cambridge University Hospitals(a United Kingdom major trauma center).We sought to define patient characteristics and our main outcome measures were infection,union and re-fracture.AIM To retrospectively define patient and injury characteristics,present our surgical methods and analyze our outcomes–namely infection,union and re-fracture rates.METHODS Consecutive series of 74 patients with 75 open tibial fractures treated between 2014 and 2020(26 classified as Gustilo-Anderson 3A,47 were 3B and two were 3C).Nine patients underwent intramedullary nailing(IMN),61 underwent Taylor spatial frame(TSF)fixation and 5 were treated with Masquelet technique(IMN and subsequent bone grafting).RESULTS Mean follow-up was 16 mo(IMN)and 25 mo(TSF).We had an infection rate of 6.7%(5),non-union rate of 4%(3)and re-fracture rate of 2.7%(2).Average time to union was 22 wk for IMN and 38.6 wk for TSF.Thirty-three cases had a bone defect with a mean of 5.4 cm(2-11).Patient age,sex,diabetes,smoking status or injury severity did not have a significant effect on union time with either fixation method.Our limb salvage rate was 98.7%.CONCLUSION Grade 1 to 3A injuries can effectively be treated with reamed or unreamed IMN.Grade 3B/C injuries are best treated by circular external fixators as they provide good,reproducible outcomes and allow large bone defects to be addressed via distraction osteogenesis.

Outcome of application of primary versus secondary Illizarov＇s fixator in open tibial shaft fractures

BACKGROUND: The present study aimed to compare outcome of primary and secondary Illizarov's fi xator application as a treatment method for type III open tibial fractures in terms of nonunion and wound infection.METHODS: This prospective study was done in a tertiary care center. Forty-eight type III tibial fractures were treated with Illizarov's apparatus between 2008 and 2011. The patients were divided into two groups depending on the treatment protocol, timing of wound closure and Illizarov's application, primary(n=28) and secondary(n=20).RESULTS: In the primary group, healing was achieved in all 28 patients. The median time to recovery was 24 weeks, and the median number of operations was 3. There were 6 patients with a bone defect. In the secondary group, complete recovery was achieved in 18 out of 20 patients. The median time to recovery was 30 weeks, and the median number of operations 5. There were 9 patients with a bone defect. The median time to recovery and the number of operations were signifi cantly smaller in patients undergoing primary operation. Union was 100% in the primary group and more than 95% in the secondary group. Chronic osteomyelitis persisted in one patient and below amputation was done in one patient in the secondary group.CONCLUSION: Primary wound closure and Illizarov's fixation required a smaller number of operations and shorter time to recovery than secondary wound closure and Illizarov's fi xation, mostly due to a signifi cantly less number of patients with a bone defect in the primary group.

Open Patellar Fracture in a 2-Year-Old Child: A Rare Case Report

We present this unusual fracture in order to stress the importance of being aware of the existence of open fractures of patella in 2-year-old child. Fractures of the patella are rare in children, as the patella is largely cartilaginous and has great mobility. Normally in this age closed patellar fractures cannot be diagnosed radiologically as the ossification starts only after 3 years of age. Our case is an open transverse patellar fracture in a two-year-old girl which is treated with transcartilagenous absorbable sutures, which is not found reported in the literature.

Open pelvic fractures associated with anorectal injuries:emergency management strategies and risk factors for mortality

Objective To investigate emergency management strategies and risk factors for mortality of open pelvic fractures associated with anorectal injuries.Methods Between April 2001 to April 2010,25 patients of openpelvic fractures

Floating elbow combining ipsilateral distal multiple segmental forearm fractures: A case report

BACKGROUND Floating elbow along with ipsilateral multiple segmental forearm fracture is a rare and high-energy injury,although elbow dislocation or fracture of the ulna and radius may occur separately.CASE SUMMARY We report the case of a 37-year-old woman with open(IIIA)fracture of the right distal humerus with multiple shaft fractures of the ipsilateral radius and ulna with a history of falling from a height of almost 20 m from a balcony.After providing advanced trauma life support,damage control surgery was performed to debride the arm wound and temporarily stabilize the right upper limb with external fixators in the emergency operating room.Subsequently,one-stage internal fixation of multiple fractures was performed with normal values of biochemical indicators and reduction in limb swelling.The patient achieved good outcome at the 7 mo follow-up.CONCLUSION One-or two-stage treatment must be performed according to the type of injury;we efficiently used the“damage control principle.”

Physics of Open Fractures: Reconsidering Tissue Viability, Contamination Risk and Importance of Wound Debridement

Understanding basic physics behind open fractures leads to a better understanding of mechanism of injury, open fractures pathophysiology and management. Explaining local changes in viability of open fracture involved tissues, importance of debridement and reconsidering contamination risks will be ultimate objectives after going through this review. The controversy is still there between minimal/conservative debridement of open fracture wounds in favour of direct closure of soft tissue on the same session against generous debridement and delayed closure by more complicated choices on the reconstructive ladder to avoid infection, delayed healing, wound chronicity, limb loss and prolonged hospital stay. In the article, basic physics behind open fractures is highlighted to gain a deeper understanding of tissue viability changes and contamination risks after injury.

Emergency Intramedullary Nailing in Open Leg Fractures: What Results?

Introduction: Leg fractures are the prerogative of violent trauma, which lead to pluritissular lesions, including the opening of the focus, thus worsening the prognosis. The indication of centromedullary nailing (CMN) is subject to time and trained team requirements. The aim of this work is to evaluate the results of CMN in emergency cases of open leg fractures in adults. Patients and Methods: This was a retrospective, descriptive and analytical study from January 1, 2014 to December 31, 2018. It concerned adult patients with an open leg fracture treated by CMN in emergency at the Orthopedics-Traumatology Department of the Yalgado Ouedraogo University Hospital. During five years, 91 patients were registered. Their average age was 34.1 years with a sex ratio of 2.2. The average admission time was 1 hour 41 minutes. Cauchoix and Duparc type I open fractures predominated (64.8%). Antibiotic therapy was instituted as soon as the patient arrived. The functional results of osteosynthesis were evaluated according to the Lysholm score after an average follow-up of 48 months. Results: The majority of our patients (51.3%) were operated on between the 6th and 18th hour. After careful trimming of the open fracture, CMN was performed in all our patients. The average hospital stay was six days. The mean Lysholm score was 87.23 ± 11.06 with a satisfactory functional result in 81.3% of cases. Discussion: The satisfactory results observed in 81.3% of our study testify to the reliability of the indication of CMN as specified by Dakouré et al. [4] in their series. Conclusion: Open leg fractures are very frequent injuries and have a considerable socio-economic impact. Centromedullary nailing is a suitable solution for adequate and rapid socio-professional reintegration of the patient.

Mathematical Model of a Hyperbolic Hydraulic Fracture with Tortuosity

The aim of the research is to study the propagation of a hydraulic fracture with tortuosity due to contact areas between touching asperities on opposite crack walls. The tortuous fracture is replaced by a model symmetric partially open fracture with a hyperbolic crack law and a modified Reynolds flow law. The normal stress at the crack walls is assumed to be proportional to the half-width of the model fracture. The Lie point symmetry of the nonlinear diffusion equation for the fracture half-width is derived and the general form of the group invariant solution is obtained. It was found that the fluid flux at the fracture entry cannot be prescribed arbitrarily, because it is determined by the group invariant solution and that the exponent n in the modified Reynolds flow power law must lie in the range 2 < n < 5. The boundary value problem is solved numerically using a backward shooting method from the fracture tip, offset by 0 < δ ≪ 1 to avoid singularities, to the fracture entry. The numerical results showed that the tortuosity and the pressure due to the contact regions both have the effect of increasing the fracture length. The spatial gradient of the half-width was found to be singular at the fracture tip for 3 < n < 5, to be finite for the Reynolds flow law n = 3 and to be zero for 2 < n < 3. The thin fluid film approximation breaks down at the fracture tip for 3 < n < 5 while it remains valid for increasingly tortuous fractures with 2 < n < 3. The effect of the touching asperities is to decrease the width averaged fluid velocity. An approximate analytical solution for the half-width, which was found to agree well with the numerical solution, is derived by making the approximation that the width averaged fluid velocity increases linearly with distance along the fracture.