Research ArticleStudy of the Penetration and Diffusion Characteristics ofInorganic Solidified Foam in Rock Fractures

Yi Lu123 TaoWang3 and Qing Ye3

1Work Safety Key Lab on Prevention and Control of Gas and Roof Disasters for Southern Coal MinesHunan University of Science and Technology Xiangtan Hunan 411201 China2Hunan Province Key Laboratory of Safe Mining Techniques of Coal Mines Hunan University of Science and TechnologyXiangtan Hunan 411201 China3School of Resource Environment and Safety Engineering Hunan University of Science and TechnologyXiangtan Hunan 411201 China

Correspondence should be addressed to Yi Lu luyijx163com

Received 5 July 2017 Revised 12 August 2017 Accepted 22 August 2017 Published 28 September 2017

Academic Editor Marco Rossi

Copyright copy 2017 Yi Lu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To explore the penetration and diffusion law in coal and rock fractures when inorganic solidified foam (ISF) is used to prevent coalfire the penetration experiment was conducted the results showed that the penetration pressure fluctuates within a certain rangeand decreases with the diffusion distance In the119883119884 plane the diffusion pattern presents an ellipsoid shape and the diffusion areabecomes increasingly large over time in the 119883119885 plane the foam fluid penetration changes from dense to loose in the 119883 directionand it does not undergo downward penetration and diffuses via its own weight in the 119885 direction in the 119884119885 plane it is loose onthe left and dense on the right The viscosity of ISF was tested and then the time-varying formula was fitted The formula of theeffective diffusion radius for foam fluid diffusing in the fracture channel was determined theoretically The permeability coefficientand other related parameters were calculated in terms of the penetration pressure and diffusion time of two monitoring points Atlast the prediction formula of effective diffusion distance of foam fluid was verified with the remaining seven monitoring pointsand all the relative error of monitoring is within 10

1 Introduction

Continuous oxygen is one of the essential conditions forspontaneous combustion of a coal seam [1 2] Mine fireor coal fires are induced by the air leakage passages thatprovide oxygen for loose coal [3] However the fracturechannels of the fire area are often complex and crisscrosseach other even extending to the high places In recent yearsincreasing numbers of scholars began to study foam sealingmaterials both at home and abroad because such materialscan diffuse and accumulate in the high fractures and providestereoscopic covering The materials of inert gas bubble [4]inhibitor foam [5 6] gel foam [7ndash10] three-phase foam [11ndash13] and foamed grout [14ndash16] are the primary foammaterialsused for a coal fire Each of the above-mentioned materialshas its own advantages and disadvantages

To address the disadvantages of the above-mentionedmaterials we performed research on ISF fire-fighting tech-nology [17] ISF can solve the problems of cooling plugginginsulation and compressive strength The fresh state of ISF(foamfluid) can accumulate to a high position as well as coverand cool high temperature coal Simultaneously ISF has goodinsulating ability thermal stability and adjustable coagula-tion time [18] When it is solidified ISF has high porosityand compressive strength The injection of ISF is a verycomplicated process To ensure that the foam fluid effectivelyreaches the coal fire area and seals the fractures it is necessaryto conduct research on the penetration and diffusion laws ofthe injection process However because the injection of ISF isa processwith strong concealment it is difficult to obtain fluidmechanics parameters and collect internal migration imagesof the foamfluid itself inside the loose coal and rock fractures

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 3781560 10 pageshttpsdoiorg10115520173781560

2 Advances in Materials Science and Engineering

Computer Computer

Cam

era

CCD

CameraCCD

Fractured rockmodel

e static strain gauge

High speed motionanalyzer

Elevating perfusionapparatus

Monitoring points (tiny earth pressure gauge)Perfusion inlet

0 X

z y

Gop

Coal pillar

Center line

12

345

67

8

910

Figure 1 The test system

In previous studies a similar complex model workedout by Gustafson and Stille for predicting grout penetrationin real rock was examined by Fujita et al considering 1Dcondition [19 20] The latter also reviewed various othergrout penetration models developed and used in Japan andelsewhere Yang et al investigated the rheological propertiesof cement grouts with different water cement ratios and theirflow in fractures [21] The present study deals with some ofthese issues anddescribes and discusses theoretical grout flowmodels for predicting flow into plane-parallel fractures ofcandidate cement grout materials that behave as Binghamfluids under static pressure and as Newton liquids underoscillatory pressure However little attention has been paidto the penetration characteristics of foam fluid in the rockfractures [22]Therefore its flowing diffusion range stackingheight and influence factors have not been well understoodwhich causes its blind application in fire controlling Todeal with this problem and provide basis for the designparameters of ISF this paper puts forward a perfusionexperiment of ISF in a fractured rock model that was builtaccording to the site application conditions in Luwa coalminethrough actually detecting some of the key parameters of thehydrodynamics of a foam fluid in the fractures identifyingthe relationship of various factors in the process of injectionand then summarizing the penetration and diffusion laws of afoam fluid inside the fractures Combined with the diffusionmorphological image of the foam fluid in different directionsthe diffusion regularity of the foam fluid is deduced

2 Experimental Procedures

21 The Test System The whole test system (Figure 1) isdivided into three parts elevating perfusion apparatus frac-tured rockmodel andmonitoring systemThe fractured rock

model consists of a loose coal pillar with the porosity of 015and the surrounding gob with the porosity of 035 The ISFwas prepared by the system composed of a foam generatorand a self-made mixer The prepared foam fluid was lifted inan elevating perfusion apparatus which can cause the foamto flow with a certain pressure head thereby enabling thefracture rock model to be infused The main steps of modeltest are as follows First build the similarity model accordingto the design requirements of filling mediums and then burythe tiny earth pressure gauges in the process of layeringSecond connect the monitoring equipment debug the high-speedmotion analyser and the static strain gaugeThird pourthe prepared ISF fluid into the fractured rock model using adesigned outlet pressure based on the regulating lifting heightof the elevating perfusion apparatus Four record the real-time diffusion image and the pressure data from the detectorand then analyse and determine the penetration and diffusionlaws combined with the viscosity parameters of the ISF fluidThe interfacemicrostructure was investigated using scanningelectron microscopy (SEM) (FEI Quanta TM 250 SEMsystem) with the size of the test specimen being a 10mm times10mm times 10mm prism

22 Arrangement of the Testing Points for Penetration PressureMonitoring There are ten tiny earth pressure gauges buriedin the fractured rock model The coordinates of the testingpoints are listed in Table 1

In the injection process of ISF the penetration pressureof the foam fluid in the fracture channels can be monitoredby the tiny earth pressure gauges embedded in the fracturedrock model The data collection interval is two secondsThe penetration test ends after all the penetration pressuremonitoring data have been collected the whole experimenttakes approximately 15 minutes to complete The size of the

Advances in Materials Science and Engineering 3

Table 1 Coordinates of the monitoring points

Number of the tinyearth pressure gauges

119883 coordinate(mm)

119884 coordinate(mm)

119885 coordinate(mm)

1 0 0 3002 232 93 2503 250 0 2504 232 minus93 2505 464 186 2006 500 0 2007 464 minus186 2008 696 279 1009 750 0 10010 696 minus279 100

Table 2 Offered parameters of the 01MPa tiny earth pressuregauges

Number of the tinyearth pressure gauges

Offered parameters119886 119887

1 minus080875 0068732 minus158700 0050423 minus144946 0056914 minus122361 0059345 minus092195 0065406 minus143612 0062607 minus102616 0066768 minus034060 0083509 minus111560 00658710 minus102340 006231

tiny earth pressure gauge is 15mm (diameter) times 64mm(thickness)maximummeasurement value is 01Mpa and theaccuracy isplusmn10FSThe computation formula betweenfluidpenetration pressure and dependent variable is as follows

119875 = 119886 + 119887120576 (1)

In formula (1) 119875 is the value of penetration pressure kPa120576 is the dependent variable times10minus6120576 119886 and 119887 are the offeredparameters After calibrating the foam fluid the determinedoffered parameters are listed in Table 2

3 The Test Result Analysis

31 The Penetration Pressure Analysis According to theoffered parameters of the 01MPa tiny earth pressure gaugesshown in Table 2 the penetration pressure of foam fluid canbe calculated The pressure values over time are shown inFigures 2 and 3

From Figures 2 and 3 overall the 1sim10 monitoringpoint data fluctuates up and down within a certain range

12

3

4

5

t1 = 0 s

t3 = 120 s

t2 = 160 s

t4 = 144 s

t5 = 382 s

0 200 800100 500 600 700300 900400

Time (s)

8

9

10

11

12

13

14

15

16

17

18

19

20

Pene

trat

ion

pres

sure

(Kpa

)Figure 2 The change of penetration pressure over time frommonitoring points 1ndash5

6

7

8

9

10

t6 = 324 s

t7 = 364 s

t9 = 644 s

t10 = 712 s

t8 = 734 s

420 480 720600 780 900540 840660360

Time (s)

5

6

7

8

9

10

11

12

13

14

15

Pene

trat

ion

pres

sure

(Kpa

)

Figure 3 The change of penetration pressure over time frommonitoring points 6ndash10

In addition to the 1 monitoring point (the injection inlet)overall the monitoring points are divided into three groupsthe first group contains the 2 3 and 4 monitoring pointsthe second group consists of the 5 6 and 7 monitoringpoints and the third group is composed of the 8 9and 10 monitoring points With the increase of diffusiondistance the penetration pressure decreases in agreementwith the traditional grouting penetration diffusion law Thepenetration pressure of the 1 monitoring point fluctuates

4 Advances in Materials Science and Engineering

with the value of 1637 kPa which was obtained from thebeginningThe first group of 2 3 and 4monitoring pointswas buried separately within the loose coal pillar the centreline and the surrounding gob The penetration diffusiondistance of the 2 3 and 4 monitoring points is 255mm250mm and 255mm respectively The 3 monitoring pointfirst collects the penetration pressure at the moment of 120 sand the 2 monitoring point and 4 monitoring point collectthe penetration pressure at the moment of 160 s and 144 srespectively This phenomenon occurs primarily because theporosity of loose coal pillar is smaller than the surroundinggob and the frictional resistance loss in the fracture channelis high As a result under the condition of the same 255mmdiffusion distance it takes a longer time for the foam fluid todiffuse to the 2 monitoring point In addition the averagepenetration pressure of the 2 monitoring point is 1313 kPawhich is smaller than the average penetration pressure of the3 monitoring point (1497 kPa) and the average penetrationpressure of the 4 monitoring point (1436 kPa) The set of5 6 and 7 monitoring points is buried in the samemanner as the first group of 2 3 and 4 monitoringpointsThe 5 6 and 7monitoring points are located alongthe centre line the loose coal pillar and the surroundinggob and the corresponding diffusion distance is 510mm500mm and 510mm respectively As the first group of datathe 6 monitoring point in the centre line first collectedthe penetration pressure at the moment of 324 s with theaverage penetration pressure value of 1194 kPa Next is the7 monitoring point arranged in the goaf at 364 s with theaverage penetration pressure value of 1072 kPa Finally the5 monitoring point in the loose coal pillar collects thepenetration pressure at the time of 382 s the average valueof penetration pressure is 1005 kPa

The penetration diffusion time and the penetration pres-sure relationship of the third group of monitoring points8 9 and 10 are similar to those of the first two groupsThe 8 9 and 10 monitoring pointsrsquo penetration diffusiondistances are 776mm 750mm and 776mm respectivelyThe 9 monitoring point in the centre line first detected thepenetration pressure with the value of 763 kPa at themomentof 644 s Subsequently the 10 monitoring point arranged inthe goaf detected the penetration pressure at 712 s the averagepenetration pressure value is 598 kPa Finally the 5 moni-toring points in the loose coal pillar detected the penetrationpressure at 734 s the average value is 552 kPa Although thepenetration diffusion distance difference of the three groupsis approximately 250mm the penetration diffusion time andthe penetration pressure average value difference of the threegroups are increasing because the foam fluid diffuses in loosecoal and rock fracture channel with energy loss therebycausing the speed to be increasingly lowTherefore under thesame penetration diffusion distance the time required for thelatter half of the distance becomes increasingly long and thepressure difference becomes increasingly high

32 PenetrationDiffusion ImageAnalysis Here the data fromthe monitoring points buried within the model is analysedTo more vividly illustrate the diffusion form of the foamfluid a high-speedmotion analyser was adopted in the whole

experiment the 119883-119884 plane of the foam fluid penetrationdiffusion pattern is shown in Figure 4

From Figure 4 with the increase of diffusion time thediffusion form of the foam fluid in the 119883-119884 plane becomesellipsoidal The diffusion velocity in the loose coal pillarand the surrounding gob is not the same as the diffusionarea of the foam fluid in the surrounding gob is larger thanthat of the loose coal pillar This difference is primarilybecause the fracture porosity of the loose coal pillar is smallcausing the foam fluid to experience greater free diffusionresistance From the diffusion area size at different momentsthe diffusion area is increasing with time but the diffusionarea of growth becomes smaller This behaviour occursprimarily because the foam fluid is a time-varying Binghamfluid resulting in the viscosity increasing from 4360MPasdotsat 60 s to 4451MPasdots at 360 s causing the foam fluid flows toslow Simultaneously with the increase of the diffusion rangethe penetration pressure drop of the foamfluid in the complexfracture network is gradually reduced and the front diffusionof foam fluid slows In addition the base material in the porewall of the foam fluid undergoes hydration and condensationreactions [23 24] thus causing the stability of the bubble toenhance that in turn makes it difficult to change the shapeof the structure In the SEM image obtained from the bubblewall (Figure 5) we can observe that the rod-shaped ettringitecrystals fill the capillary pores Surface products such as C-S-H gel can be observed as the major ISF microstructurecomponent CH as a pore product with a polycrystallineshape is another dominant cement hydration product Thephenomenon results in a large quantity of bubbles unitinginto a group The bubbles in the group flow as a wholeand block each other The fluidity of the foam fluid reducesgradually Figure 6 shows the condensation effect of foamfluid in a coal and rock fracture surface after 3 hours Thefigure reveals that the foam fluid can commendably diffuseand cover the fracture surface and the foam can form a layerof a certain thickness effectively isolating the coal and oxygencompounds

To perform in-depth analysis of the internal penetrationdiffusion of the ISF in the fractured rock model the 119883119885 and119884119885 sections were recorded by the CCD camera as shown inFigures 7 and 8 respectively

From Figure 7 in the 119883119885 penetration section with theincrease of the penetration diffusion distance the foam fluidpenetration in the fracture channel changes from dense toloose in the 119883 direction mainly because the penetrationpressure and the velocity of the foam fluid are high near theperfusion inlet thereby enabling the foam to diffuse fullyHowever the penetration pressure loss of the foam fluid ishigher when the position is further away from the perfusioninlet From the 119885 direction the fracture penetration is fullerat the same 119885 height of the perfusion inlet the next place isabove the plane of the perfusion inlet and the penetrationdiffusion effect is the worst in the sections under the height ofthe perfusion inlet It indicates that the penetration diffusionability of the foam fluid is stronger in its initial direction ofvelocity vector than the direction of the vector upward ordownward Upward penetration is fuller than the downwardpenetration because the peripheral interface cracks in the

Advances in Materials Science and Engineering 5

T = 60 s T = 120 s

Goaf Coal pillar

T = 180 s T = 240 s

T = 300 s T = 360 s

Figure 4 The penetration and diffusion form of the foam fluid in the119883-119884 plane

process of planar penetration channels are open and the crackchannel resistance is low indicating that the foam fluid doesnot act in the same manner as normal cement slurry Thisdifference in downward penetration mainly occurs becausethe density of foam fluid is smaller than that of ordinarycement with the value being approximately 15 the densityof a common slurry As a result the gravitational effect onthe foam fluid is not obvious Another primary factor is thatthe foam fluid is composed of bubbles as a result adhesionof cement and fly ash particles occurs in the bubble hole wallor the particles exist in a foam liquid membrane to form askeleton thereby preventing gravity settling of the particlesThe size of a single bubble is approximately 400 microns andeach bubble links together thereby causing the bubble size tobe greater than a single general cement or fly ash particle inthe slurry

Form the penetration and diffusion in the 119884119885 sectionshown in Figure 8 the left is loose and the right is dense inthe 119884 direction largely because the left part is the loose coalpillar model with the porosity of 015 and the right part is

the surrounding gob model with the porosity of 035 As theperfusion inlet is in the cross section the foam fluid will bemore easily diffuse into the right side with large porosity Inthe 119885 direction the distribution of penetration and diffusionis uniform except the top with the surface penetrationmainly because perfusion inlet of foam fluid is in the 119883direction which is vertical to the119884119885 sectionThe penetrationand diffusion of foam fluid in this 119884119885 section occurred whenthe fracture has been blocked by the119883 direction penetrationThe up and down diffusion process wasmainly affected by thewidth of fracture in the 119885 direction Thus in the 119884119885 planethe penetration and diffusion results show that the left part isloose and right part is dense

33 Penetration andDiffusion Law In the grouting engineer-ing field there is a large difference for different flow patternsof slurry diffuse in the geotechnical engineering [25ndash27] Tomeet the requirements of engineering reasonable groutingparameters for different slurrymust be determinedHoweverthe determination of the grouting parameters definitely

6 Advances in Materials Science and Engineering

Calcium silicate hydrate

Calcium hydroxide

Ettringite

Figure 5 SEM image obtained from the bubble wall

Figure 6 Condensation effect of a fluid penetration diffusion frontin the coal and rock surface after 3 hours

requires guidance fromgrouting theoryThe relativelymaturediffusion grouting theory is based on the spherical cylin-drical and sleeve valve pipe models [28ndash31] The effectivediffusion radius formula is only applicable to a Newtonianfluid However the inorganic solidified foam is a Binghamfluid which is a non-Newtonian fluid as a result such foamcannot be modelled by the above formulas Therefore inthis paper the diffusion theory of the ISF in porous mediawith fracture channels is derived As the ISF fluid diffusescompletely into the fractures channel we assume that it is awhole unit mass of foam fluid that reaches a certain positionalong a fracture channelTherefore we can draw lessons fromthe model of a Bingham fluid in pipe penetration [32] asshown in Figure 9

Assuming that the fracture radius is 1199030 a foamfluid unit istaken from the centre line position of the fracture channel itslength is 119889119897 and its radius is 119903The pressure of the left and rightends of the foam fluid unit 119889119897 is 119901 + 119889119901 and 119901 respectivelyThe differential pressure is 119889119901 The shear stress around thefoam fluid unit surface by the left direction (in the oppositedirection of flow velocity) is 120591 Thus we obtain the balance

Dense Loose

Figure 7 Penetration and diffusion form of the foam fluid in the119883-119885 section

DenseLoose

Figure 8 Penetration and diffusion form of the foam fluid in the119884-119885 section

equation for flow stress of a foam fluid unit as follows

1205871199032119889119901 = minus2120587119903120591119889119897 (2)

In the region of 0 le 119903 le 119903119901 the foam fluid column isstationary relative to the adjacent layer fluid The foam fluidmoves in a piston as a whole and the movement velocity isV = V119901 In the region of 119903119901 le 119903 le 1199030 the foam fluid columnis moving relative to the adjacent layer fluid So the followingequation can be obtained

119903119901 = minus2120591119904 sdot 119889119897119889119901 (3)

The basic rheological equation of a Bingham fluid slurry[33] can be expressed as

120591 = 120591119904 + 120578119901120574 (4)

Based on (2) and (4) the following can be obtained

120574 = minus119889V119889119903 = (120591 minus 120591119904)120578119901 = minus 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904) (5)

Consider boundary conditions 119903 = 1199030 V = 0 and thencalculate integral for both sides of (5)

intV0

V119889V = int1199030

119903[ 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904)] sdot 119889119903 997904rArr

V = minus 1120578119901 [

14119889119901119889119897 (11990320 minus 1199032) + 120591119904 (1199030 minus 119903)]

(6)

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

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Biomaterials

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Advances in Materials Science and Engineering 3

Table 1 Coordinates of the monitoring points

Number of the tinyearth pressure gauges

119883 coordinate(mm)

119884 coordinate(mm)

119885 coordinate(mm)

1 0 0 3002 232 93 2503 250 0 2504 232 minus93 2505 464 186 2006 500 0 2007 464 minus186 2008 696 279 1009 750 0 10010 696 minus279 100

Table 2 Offered parameters of the 01MPa tiny earth pressuregauges

Number of the tinyearth pressure gauges

Offered parameters119886 119887

1 minus080875 0068732 minus158700 0050423 minus144946 0056914 minus122361 0059345 minus092195 0065406 minus143612 0062607 minus102616 0066768 minus034060 0083509 minus111560 00658710 minus102340 006231

tiny earth pressure gauge is 15mm (diameter) times 64mm(thickness)maximummeasurement value is 01Mpa and theaccuracy isplusmn10FSThe computation formula betweenfluidpenetration pressure and dependent variable is as follows

119875 = 119886 + 119887120576 (1)

In formula (1) 119875 is the value of penetration pressure kPa120576 is the dependent variable times10minus6120576 119886 and 119887 are the offeredparameters After calibrating the foam fluid the determinedoffered parameters are listed in Table 2

3 The Test Result Analysis

31 The Penetration Pressure Analysis According to theoffered parameters of the 01MPa tiny earth pressure gaugesshown in Table 2 the penetration pressure of foam fluid canbe calculated The pressure values over time are shown inFigures 2 and 3

From Figures 2 and 3 overall the 1sim10 monitoringpoint data fluctuates up and down within a certain range

12

3

4

5

t1 = 0 s

t3 = 120 s

t2 = 160 s

t4 = 144 s

t5 = 382 s

0 200 800100 500 600 700300 900400

Time (s)

8

9

10

11

12

13

14

15

16

17

18

19

20

Pene

trat

ion

pres

sure

(Kpa

)Figure 2 The change of penetration pressure over time frommonitoring points 1ndash5

6

7

8

9

10

t6 = 324 s

t7 = 364 s

t9 = 644 s

t10 = 712 s

t8 = 734 s

420 480 720600 780 900540 840660360

Time (s)

5

6

7

8

9

10

11

12

13

14

15

Pene

trat

ion

pres

sure

(Kpa

)

Figure 3 The change of penetration pressure over time frommonitoring points 6ndash10

In addition to the 1 monitoring point (the injection inlet)overall the monitoring points are divided into three groupsthe first group contains the 2 3 and 4 monitoring pointsthe second group consists of the 5 6 and 7 monitoringpoints and the third group is composed of the 8 9and 10 monitoring points With the increase of diffusiondistance the penetration pressure decreases in agreementwith the traditional grouting penetration diffusion law Thepenetration pressure of the 1 monitoring point fluctuates

4 Advances in Materials Science and Engineering

with the value of 1637 kPa which was obtained from thebeginningThe first group of 2 3 and 4monitoring pointswas buried separately within the loose coal pillar the centreline and the surrounding gob The penetration diffusiondistance of the 2 3 and 4 monitoring points is 255mm250mm and 255mm respectively The 3 monitoring pointfirst collects the penetration pressure at the moment of 120 sand the 2 monitoring point and 4 monitoring point collectthe penetration pressure at the moment of 160 s and 144 srespectively This phenomenon occurs primarily because theporosity of loose coal pillar is smaller than the surroundinggob and the frictional resistance loss in the fracture channelis high As a result under the condition of the same 255mmdiffusion distance it takes a longer time for the foam fluid todiffuse to the 2 monitoring point In addition the averagepenetration pressure of the 2 monitoring point is 1313 kPawhich is smaller than the average penetration pressure of the3 monitoring point (1497 kPa) and the average penetrationpressure of the 4 monitoring point (1436 kPa) The set of5 6 and 7 monitoring points is buried in the samemanner as the first group of 2 3 and 4 monitoringpointsThe 5 6 and 7monitoring points are located alongthe centre line the loose coal pillar and the surroundinggob and the corresponding diffusion distance is 510mm500mm and 510mm respectively As the first group of datathe 6 monitoring point in the centre line first collectedthe penetration pressure at the moment of 324 s with theaverage penetration pressure value of 1194 kPa Next is the7 monitoring point arranged in the goaf at 364 s with theaverage penetration pressure value of 1072 kPa Finally the5 monitoring point in the loose coal pillar collects thepenetration pressure at the time of 382 s the average valueof penetration pressure is 1005 kPa

The penetration diffusion time and the penetration pres-sure relationship of the third group of monitoring points8 9 and 10 are similar to those of the first two groupsThe 8 9 and 10 monitoring pointsrsquo penetration diffusiondistances are 776mm 750mm and 776mm respectivelyThe 9 monitoring point in the centre line first detected thepenetration pressure with the value of 763 kPa at themomentof 644 s Subsequently the 10 monitoring point arranged inthe goaf detected the penetration pressure at 712 s the averagepenetration pressure value is 598 kPa Finally the 5 moni-toring points in the loose coal pillar detected the penetrationpressure at 734 s the average value is 552 kPa Although thepenetration diffusion distance difference of the three groupsis approximately 250mm the penetration diffusion time andthe penetration pressure average value difference of the threegroups are increasing because the foam fluid diffuses in loosecoal and rock fracture channel with energy loss therebycausing the speed to be increasingly lowTherefore under thesame penetration diffusion distance the time required for thelatter half of the distance becomes increasingly long and thepressure difference becomes increasingly high

32 PenetrationDiffusion ImageAnalysis Here the data fromthe monitoring points buried within the model is analysedTo more vividly illustrate the diffusion form of the foamfluid a high-speedmotion analyser was adopted in the whole

experiment the 119883-119884 plane of the foam fluid penetrationdiffusion pattern is shown in Figure 4

From Figure 4 with the increase of diffusion time thediffusion form of the foam fluid in the 119883-119884 plane becomesellipsoidal The diffusion velocity in the loose coal pillarand the surrounding gob is not the same as the diffusionarea of the foam fluid in the surrounding gob is larger thanthat of the loose coal pillar This difference is primarilybecause the fracture porosity of the loose coal pillar is smallcausing the foam fluid to experience greater free diffusionresistance From the diffusion area size at different momentsthe diffusion area is increasing with time but the diffusionarea of growth becomes smaller This behaviour occursprimarily because the foam fluid is a time-varying Binghamfluid resulting in the viscosity increasing from 4360MPasdotsat 60 s to 4451MPasdots at 360 s causing the foam fluid flows toslow Simultaneously with the increase of the diffusion rangethe penetration pressure drop of the foamfluid in the complexfracture network is gradually reduced and the front diffusionof foam fluid slows In addition the base material in the porewall of the foam fluid undergoes hydration and condensationreactions [23 24] thus causing the stability of the bubble toenhance that in turn makes it difficult to change the shapeof the structure In the SEM image obtained from the bubblewall (Figure 5) we can observe that the rod-shaped ettringitecrystals fill the capillary pores Surface products such as C-S-H gel can be observed as the major ISF microstructurecomponent CH as a pore product with a polycrystallineshape is another dominant cement hydration product Thephenomenon results in a large quantity of bubbles unitinginto a group The bubbles in the group flow as a wholeand block each other The fluidity of the foam fluid reducesgradually Figure 6 shows the condensation effect of foamfluid in a coal and rock fracture surface after 3 hours Thefigure reveals that the foam fluid can commendably diffuseand cover the fracture surface and the foam can form a layerof a certain thickness effectively isolating the coal and oxygencompounds

To perform in-depth analysis of the internal penetrationdiffusion of the ISF in the fractured rock model the 119883119885 and119884119885 sections were recorded by the CCD camera as shown inFigures 7 and 8 respectively

From Figure 7 in the 119883119885 penetration section with theincrease of the penetration diffusion distance the foam fluidpenetration in the fracture channel changes from dense toloose in the 119883 direction mainly because the penetrationpressure and the velocity of the foam fluid are high near theperfusion inlet thereby enabling the foam to diffuse fullyHowever the penetration pressure loss of the foam fluid ishigher when the position is further away from the perfusioninlet From the 119885 direction the fracture penetration is fullerat the same 119885 height of the perfusion inlet the next place isabove the plane of the perfusion inlet and the penetrationdiffusion effect is the worst in the sections under the height ofthe perfusion inlet It indicates that the penetration diffusionability of the foam fluid is stronger in its initial direction ofvelocity vector than the direction of the vector upward ordownward Upward penetration is fuller than the downwardpenetration because the peripheral interface cracks in the

Advances in Materials Science and Engineering 5

T = 60 s T = 120 s

Goaf Coal pillar

T = 180 s T = 240 s

T = 300 s T = 360 s

Figure 4 The penetration and diffusion form of the foam fluid in the119883-119884 plane

process of planar penetration channels are open and the crackchannel resistance is low indicating that the foam fluid doesnot act in the same manner as normal cement slurry Thisdifference in downward penetration mainly occurs becausethe density of foam fluid is smaller than that of ordinarycement with the value being approximately 15 the densityof a common slurry As a result the gravitational effect onthe foam fluid is not obvious Another primary factor is thatthe foam fluid is composed of bubbles as a result adhesionof cement and fly ash particles occurs in the bubble hole wallor the particles exist in a foam liquid membrane to form askeleton thereby preventing gravity settling of the particlesThe size of a single bubble is approximately 400 microns andeach bubble links together thereby causing the bubble size tobe greater than a single general cement or fly ash particle inthe slurry

Form the penetration and diffusion in the 119884119885 sectionshown in Figure 8 the left is loose and the right is dense inthe 119884 direction largely because the left part is the loose coalpillar model with the porosity of 015 and the right part is

the surrounding gob model with the porosity of 035 As theperfusion inlet is in the cross section the foam fluid will bemore easily diffuse into the right side with large porosity Inthe 119885 direction the distribution of penetration and diffusionis uniform except the top with the surface penetrationmainly because perfusion inlet of foam fluid is in the 119883direction which is vertical to the119884119885 sectionThe penetrationand diffusion of foam fluid in this 119884119885 section occurred whenthe fracture has been blocked by the119883 direction penetrationThe up and down diffusion process wasmainly affected by thewidth of fracture in the 119885 direction Thus in the 119884119885 planethe penetration and diffusion results show that the left part isloose and right part is dense

33 Penetration andDiffusion Law In the grouting engineer-ing field there is a large difference for different flow patternsof slurry diffuse in the geotechnical engineering [25ndash27] Tomeet the requirements of engineering reasonable groutingparameters for different slurrymust be determinedHoweverthe determination of the grouting parameters definitely

6 Advances in Materials Science and Engineering

Calcium silicate hydrate

Calcium hydroxide

Ettringite

Figure 5 SEM image obtained from the bubble wall

Figure 6 Condensation effect of a fluid penetration diffusion frontin the coal and rock surface after 3 hours

requires guidance fromgrouting theoryThe relativelymaturediffusion grouting theory is based on the spherical cylin-drical and sleeve valve pipe models [28ndash31] The effectivediffusion radius formula is only applicable to a Newtonianfluid However the inorganic solidified foam is a Binghamfluid which is a non-Newtonian fluid as a result such foamcannot be modelled by the above formulas Therefore inthis paper the diffusion theory of the ISF in porous mediawith fracture channels is derived As the ISF fluid diffusescompletely into the fractures channel we assume that it is awhole unit mass of foam fluid that reaches a certain positionalong a fracture channelTherefore we can draw lessons fromthe model of a Bingham fluid in pipe penetration [32] asshown in Figure 9

Assuming that the fracture radius is 1199030 a foamfluid unit istaken from the centre line position of the fracture channel itslength is 119889119897 and its radius is 119903The pressure of the left and rightends of the foam fluid unit 119889119897 is 119901 + 119889119901 and 119901 respectivelyThe differential pressure is 119889119901 The shear stress around thefoam fluid unit surface by the left direction (in the oppositedirection of flow velocity) is 120591 Thus we obtain the balance

Dense Loose

Figure 7 Penetration and diffusion form of the foam fluid in the119883-119885 section

DenseLoose

Figure 8 Penetration and diffusion form of the foam fluid in the119884-119885 section

equation for flow stress of a foam fluid unit as follows

1205871199032119889119901 = minus2120587119903120591119889119897 (2)

In the region of 0 le 119903 le 119903119901 the foam fluid column isstationary relative to the adjacent layer fluid The foam fluidmoves in a piston as a whole and the movement velocity isV = V119901 In the region of 119903119901 le 119903 le 1199030 the foam fluid columnis moving relative to the adjacent layer fluid So the followingequation can be obtained

119903119901 = minus2120591119904 sdot 119889119897119889119901 (3)

The basic rheological equation of a Bingham fluid slurry[33] can be expressed as

120591 = 120591119904 + 120578119901120574 (4)

Based on (2) and (4) the following can be obtained

120574 = minus119889V119889119903 = (120591 minus 120591119904)120578119901 = minus 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904) (5)

Consider boundary conditions 119903 = 1199030 V = 0 and thencalculate integral for both sides of (5)

intV0

V119889V = int1199030

119903[ 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904)] sdot 119889119903 997904rArr

V = minus 1120578119901 [

14119889119901119889119897 (11990320 minus 1199032) + 120591119904 (1199030 minus 119903)]

(6)

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MetallurgyJournal of

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BioMed Research International

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4 Advances in Materials Science and Engineering

with the value of 1637 kPa which was obtained from thebeginningThe first group of 2 3 and 4monitoring pointswas buried separately within the loose coal pillar the centreline and the surrounding gob The penetration diffusiondistance of the 2 3 and 4 monitoring points is 255mm250mm and 255mm respectively The 3 monitoring pointfirst collects the penetration pressure at the moment of 120 sand the 2 monitoring point and 4 monitoring point collectthe penetration pressure at the moment of 160 s and 144 srespectively This phenomenon occurs primarily because theporosity of loose coal pillar is smaller than the surroundinggob and the frictional resistance loss in the fracture channelis high As a result under the condition of the same 255mmdiffusion distance it takes a longer time for the foam fluid todiffuse to the 2 monitoring point In addition the averagepenetration pressure of the 2 monitoring point is 1313 kPawhich is smaller than the average penetration pressure of the3 monitoring point (1497 kPa) and the average penetrationpressure of the 4 monitoring point (1436 kPa) The set of5 6 and 7 monitoring points is buried in the samemanner as the first group of 2 3 and 4 monitoringpointsThe 5 6 and 7monitoring points are located alongthe centre line the loose coal pillar and the surroundinggob and the corresponding diffusion distance is 510mm500mm and 510mm respectively As the first group of datathe 6 monitoring point in the centre line first collectedthe penetration pressure at the moment of 324 s with theaverage penetration pressure value of 1194 kPa Next is the7 monitoring point arranged in the goaf at 364 s with theaverage penetration pressure value of 1072 kPa Finally the5 monitoring point in the loose coal pillar collects thepenetration pressure at the time of 382 s the average valueof penetration pressure is 1005 kPa

The penetration diffusion time and the penetration pres-sure relationship of the third group of monitoring points8 9 and 10 are similar to those of the first two groupsThe 8 9 and 10 monitoring pointsrsquo penetration diffusiondistances are 776mm 750mm and 776mm respectivelyThe 9 monitoring point in the centre line first detected thepenetration pressure with the value of 763 kPa at themomentof 644 s Subsequently the 10 monitoring point arranged inthe goaf detected the penetration pressure at 712 s the averagepenetration pressure value is 598 kPa Finally the 5 moni-toring points in the loose coal pillar detected the penetrationpressure at 734 s the average value is 552 kPa Although thepenetration diffusion distance difference of the three groupsis approximately 250mm the penetration diffusion time andthe penetration pressure average value difference of the threegroups are increasing because the foam fluid diffuses in loosecoal and rock fracture channel with energy loss therebycausing the speed to be increasingly lowTherefore under thesame penetration diffusion distance the time required for thelatter half of the distance becomes increasingly long and thepressure difference becomes increasingly high

32 PenetrationDiffusion ImageAnalysis Here the data fromthe monitoring points buried within the model is analysedTo more vividly illustrate the diffusion form of the foamfluid a high-speedmotion analyser was adopted in the whole

experiment the 119883-119884 plane of the foam fluid penetrationdiffusion pattern is shown in Figure 4

From Figure 4 with the increase of diffusion time thediffusion form of the foam fluid in the 119883-119884 plane becomesellipsoidal The diffusion velocity in the loose coal pillarand the surrounding gob is not the same as the diffusionarea of the foam fluid in the surrounding gob is larger thanthat of the loose coal pillar This difference is primarilybecause the fracture porosity of the loose coal pillar is smallcausing the foam fluid to experience greater free diffusionresistance From the diffusion area size at different momentsthe diffusion area is increasing with time but the diffusionarea of growth becomes smaller This behaviour occursprimarily because the foam fluid is a time-varying Binghamfluid resulting in the viscosity increasing from 4360MPasdotsat 60 s to 4451MPasdots at 360 s causing the foam fluid flows toslow Simultaneously with the increase of the diffusion rangethe penetration pressure drop of the foamfluid in the complexfracture network is gradually reduced and the front diffusionof foam fluid slows In addition the base material in the porewall of the foam fluid undergoes hydration and condensationreactions [23 24] thus causing the stability of the bubble toenhance that in turn makes it difficult to change the shapeof the structure In the SEM image obtained from the bubblewall (Figure 5) we can observe that the rod-shaped ettringitecrystals fill the capillary pores Surface products such as C-S-H gel can be observed as the major ISF microstructurecomponent CH as a pore product with a polycrystallineshape is another dominant cement hydration product Thephenomenon results in a large quantity of bubbles unitinginto a group The bubbles in the group flow as a wholeand block each other The fluidity of the foam fluid reducesgradually Figure 6 shows the condensation effect of foamfluid in a coal and rock fracture surface after 3 hours Thefigure reveals that the foam fluid can commendably diffuseand cover the fracture surface and the foam can form a layerof a certain thickness effectively isolating the coal and oxygencompounds

To perform in-depth analysis of the internal penetrationdiffusion of the ISF in the fractured rock model the 119883119885 and119884119885 sections were recorded by the CCD camera as shown inFigures 7 and 8 respectively

From Figure 7 in the 119883119885 penetration section with theincrease of the penetration diffusion distance the foam fluidpenetration in the fracture channel changes from dense toloose in the 119883 direction mainly because the penetrationpressure and the velocity of the foam fluid are high near theperfusion inlet thereby enabling the foam to diffuse fullyHowever the penetration pressure loss of the foam fluid ishigher when the position is further away from the perfusioninlet From the 119885 direction the fracture penetration is fullerat the same 119885 height of the perfusion inlet the next place isabove the plane of the perfusion inlet and the penetrationdiffusion effect is the worst in the sections under the height ofthe perfusion inlet It indicates that the penetration diffusionability of the foam fluid is stronger in its initial direction ofvelocity vector than the direction of the vector upward ordownward Upward penetration is fuller than the downwardpenetration because the peripheral interface cracks in the

Advances in Materials Science and Engineering 5

T = 60 s T = 120 s

Goaf Coal pillar

T = 180 s T = 240 s

T = 300 s T = 360 s

Figure 4 The penetration and diffusion form of the foam fluid in the119883-119884 plane

process of planar penetration channels are open and the crackchannel resistance is low indicating that the foam fluid doesnot act in the same manner as normal cement slurry Thisdifference in downward penetration mainly occurs becausethe density of foam fluid is smaller than that of ordinarycement with the value being approximately 15 the densityof a common slurry As a result the gravitational effect onthe foam fluid is not obvious Another primary factor is thatthe foam fluid is composed of bubbles as a result adhesionof cement and fly ash particles occurs in the bubble hole wallor the particles exist in a foam liquid membrane to form askeleton thereby preventing gravity settling of the particlesThe size of a single bubble is approximately 400 microns andeach bubble links together thereby causing the bubble size tobe greater than a single general cement or fly ash particle inthe slurry

Form the penetration and diffusion in the 119884119885 sectionshown in Figure 8 the left is loose and the right is dense inthe 119884 direction largely because the left part is the loose coalpillar model with the porosity of 015 and the right part is

the surrounding gob model with the porosity of 035 As theperfusion inlet is in the cross section the foam fluid will bemore easily diffuse into the right side with large porosity Inthe 119885 direction the distribution of penetration and diffusionis uniform except the top with the surface penetrationmainly because perfusion inlet of foam fluid is in the 119883direction which is vertical to the119884119885 sectionThe penetrationand diffusion of foam fluid in this 119884119885 section occurred whenthe fracture has been blocked by the119883 direction penetrationThe up and down diffusion process wasmainly affected by thewidth of fracture in the 119885 direction Thus in the 119884119885 planethe penetration and diffusion results show that the left part isloose and right part is dense

33 Penetration andDiffusion Law In the grouting engineer-ing field there is a large difference for different flow patternsof slurry diffuse in the geotechnical engineering [25ndash27] Tomeet the requirements of engineering reasonable groutingparameters for different slurrymust be determinedHoweverthe determination of the grouting parameters definitely

6 Advances in Materials Science and Engineering

Calcium silicate hydrate

Calcium hydroxide

Ettringite

Figure 5 SEM image obtained from the bubble wall

Figure 6 Condensation effect of a fluid penetration diffusion frontin the coal and rock surface after 3 hours

requires guidance fromgrouting theoryThe relativelymaturediffusion grouting theory is based on the spherical cylin-drical and sleeve valve pipe models [28ndash31] The effectivediffusion radius formula is only applicable to a Newtonianfluid However the inorganic solidified foam is a Binghamfluid which is a non-Newtonian fluid as a result such foamcannot be modelled by the above formulas Therefore inthis paper the diffusion theory of the ISF in porous mediawith fracture channels is derived As the ISF fluid diffusescompletely into the fractures channel we assume that it is awhole unit mass of foam fluid that reaches a certain positionalong a fracture channelTherefore we can draw lessons fromthe model of a Bingham fluid in pipe penetration [32] asshown in Figure 9

Assuming that the fracture radius is 1199030 a foamfluid unit istaken from the centre line position of the fracture channel itslength is 119889119897 and its radius is 119903The pressure of the left and rightends of the foam fluid unit 119889119897 is 119901 + 119889119901 and 119901 respectivelyThe differential pressure is 119889119901 The shear stress around thefoam fluid unit surface by the left direction (in the oppositedirection of flow velocity) is 120591 Thus we obtain the balance

Dense Loose

Figure 7 Penetration and diffusion form of the foam fluid in the119883-119885 section

DenseLoose

Figure 8 Penetration and diffusion form of the foam fluid in the119884-119885 section

equation for flow stress of a foam fluid unit as follows

1205871199032119889119901 = minus2120587119903120591119889119897 (2)

In the region of 0 le 119903 le 119903119901 the foam fluid column isstationary relative to the adjacent layer fluid The foam fluidmoves in a piston as a whole and the movement velocity isV = V119901 In the region of 119903119901 le 119903 le 1199030 the foam fluid columnis moving relative to the adjacent layer fluid So the followingequation can be obtained

119903119901 = minus2120591119904 sdot 119889119897119889119901 (3)

The basic rheological equation of a Bingham fluid slurry[33] can be expressed as

120591 = 120591119904 + 120578119901120574 (4)

Based on (2) and (4) the following can be obtained

120574 = minus119889V119889119903 = (120591 minus 120591119904)120578119901 = minus 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904) (5)

Consider boundary conditions 119903 = 1199030 V = 0 and thencalculate integral for both sides of (5)

intV0

V119889V = int1199030

119903[ 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904)] sdot 119889119903 997904rArr

V = minus 1120578119901 [

14119889119901119889119897 (11990320 minus 1199032) + 120591119904 (1199030 minus 119903)]

(6)

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 5

T = 60 s T = 120 s

Goaf Coal pillar

T = 180 s T = 240 s

T = 300 s T = 360 s

Figure 4 The penetration and diffusion form of the foam fluid in the119883-119884 plane

process of planar penetration channels are open and the crackchannel resistance is low indicating that the foam fluid doesnot act in the same manner as normal cement slurry Thisdifference in downward penetration mainly occurs becausethe density of foam fluid is smaller than that of ordinarycement with the value being approximately 15 the densityof a common slurry As a result the gravitational effect onthe foam fluid is not obvious Another primary factor is thatthe foam fluid is composed of bubbles as a result adhesionof cement and fly ash particles occurs in the bubble hole wallor the particles exist in a foam liquid membrane to form askeleton thereby preventing gravity settling of the particlesThe size of a single bubble is approximately 400 microns andeach bubble links together thereby causing the bubble size tobe greater than a single general cement or fly ash particle inthe slurry

Form the penetration and diffusion in the 119884119885 sectionshown in Figure 8 the left is loose and the right is dense inthe 119884 direction largely because the left part is the loose coalpillar model with the porosity of 015 and the right part is

the surrounding gob model with the porosity of 035 As theperfusion inlet is in the cross section the foam fluid will bemore easily diffuse into the right side with large porosity Inthe 119885 direction the distribution of penetration and diffusionis uniform except the top with the surface penetrationmainly because perfusion inlet of foam fluid is in the 119883direction which is vertical to the119884119885 sectionThe penetrationand diffusion of foam fluid in this 119884119885 section occurred whenthe fracture has been blocked by the119883 direction penetrationThe up and down diffusion process wasmainly affected by thewidth of fracture in the 119885 direction Thus in the 119884119885 planethe penetration and diffusion results show that the left part isloose and right part is dense

33 Penetration andDiffusion Law In the grouting engineer-ing field there is a large difference for different flow patternsof slurry diffuse in the geotechnical engineering [25ndash27] Tomeet the requirements of engineering reasonable groutingparameters for different slurrymust be determinedHoweverthe determination of the grouting parameters definitely

6 Advances in Materials Science and Engineering

Calcium silicate hydrate

Calcium hydroxide

Ettringite

Figure 5 SEM image obtained from the bubble wall

Figure 6 Condensation effect of a fluid penetration diffusion frontin the coal and rock surface after 3 hours

requires guidance fromgrouting theoryThe relativelymaturediffusion grouting theory is based on the spherical cylin-drical and sleeve valve pipe models [28ndash31] The effectivediffusion radius formula is only applicable to a Newtonianfluid However the inorganic solidified foam is a Binghamfluid which is a non-Newtonian fluid as a result such foamcannot be modelled by the above formulas Therefore inthis paper the diffusion theory of the ISF in porous mediawith fracture channels is derived As the ISF fluid diffusescompletely into the fractures channel we assume that it is awhole unit mass of foam fluid that reaches a certain positionalong a fracture channelTherefore we can draw lessons fromthe model of a Bingham fluid in pipe penetration [32] asshown in Figure 9

Assuming that the fracture radius is 1199030 a foamfluid unit istaken from the centre line position of the fracture channel itslength is 119889119897 and its radius is 119903The pressure of the left and rightends of the foam fluid unit 119889119897 is 119901 + 119889119901 and 119901 respectivelyThe differential pressure is 119889119901 The shear stress around thefoam fluid unit surface by the left direction (in the oppositedirection of flow velocity) is 120591 Thus we obtain the balance

Dense Loose

Figure 7 Penetration and diffusion form of the foam fluid in the119883-119885 section

DenseLoose

Figure 8 Penetration and diffusion form of the foam fluid in the119884-119885 section

equation for flow stress of a foam fluid unit as follows

1205871199032119889119901 = minus2120587119903120591119889119897 (2)

In the region of 0 le 119903 le 119903119901 the foam fluid column isstationary relative to the adjacent layer fluid The foam fluidmoves in a piston as a whole and the movement velocity isV = V119901 In the region of 119903119901 le 119903 le 1199030 the foam fluid columnis moving relative to the adjacent layer fluid So the followingequation can be obtained

119903119901 = minus2120591119904 sdot 119889119897119889119901 (3)

The basic rheological equation of a Bingham fluid slurry[33] can be expressed as

120591 = 120591119904 + 120578119901120574 (4)

Based on (2) and (4) the following can be obtained

120574 = minus119889V119889119903 = (120591 minus 120591119904)120578119901 = minus 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904) (5)

Consider boundary conditions 119903 = 1199030 V = 0 and thencalculate integral for both sides of (5)

intV0

V119889V = int1199030

119903[ 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904)] sdot 119889119903 997904rArr

V = minus 1120578119901 [

14119889119901119889119897 (11990320 minus 1199032) + 120591119904 (1199030 minus 119903)]

(6)

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Advances in Materials Science and Engineering

Calcium silicate hydrate

Calcium hydroxide

Ettringite

Figure 5 SEM image obtained from the bubble wall

Figure 6 Condensation effect of a fluid penetration diffusion frontin the coal and rock surface after 3 hours

requires guidance fromgrouting theoryThe relativelymaturediffusion grouting theory is based on the spherical cylin-drical and sleeve valve pipe models [28ndash31] The effectivediffusion radius formula is only applicable to a Newtonianfluid However the inorganic solidified foam is a Binghamfluid which is a non-Newtonian fluid as a result such foamcannot be modelled by the above formulas Therefore inthis paper the diffusion theory of the ISF in porous mediawith fracture channels is derived As the ISF fluid diffusescompletely into the fractures channel we assume that it is awhole unit mass of foam fluid that reaches a certain positionalong a fracture channelTherefore we can draw lessons fromthe model of a Bingham fluid in pipe penetration [32] asshown in Figure 9

Assuming that the fracture radius is 1199030 a foamfluid unit istaken from the centre line position of the fracture channel itslength is 119889119897 and its radius is 119903The pressure of the left and rightends of the foam fluid unit 119889119897 is 119901 + 119889119901 and 119901 respectivelyThe differential pressure is 119889119901 The shear stress around thefoam fluid unit surface by the left direction (in the oppositedirection of flow velocity) is 120591 Thus we obtain the balance

Dense Loose

Figure 7 Penetration and diffusion form of the foam fluid in the119883-119885 section

DenseLoose

Figure 8 Penetration and diffusion form of the foam fluid in the119884-119885 section

equation for flow stress of a foam fluid unit as follows

1205871199032119889119901 = minus2120587119903120591119889119897 (2)

In the region of 0 le 119903 le 119903119901 the foam fluid column isstationary relative to the adjacent layer fluid The foam fluidmoves in a piston as a whole and the movement velocity isV = V119901 In the region of 119903119901 le 119903 le 1199030 the foam fluid columnis moving relative to the adjacent layer fluid So the followingequation can be obtained

119903119901 = minus2120591119904 sdot 119889119897119889119901 (3)

The basic rheological equation of a Bingham fluid slurry[33] can be expressed as

120591 = 120591119904 + 120578119901120574 (4)

Based on (2) and (4) the following can be obtained

120574 = minus119889V119889119903 = (120591 minus 120591119904)120578119901 = minus 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904) (5)

Consider boundary conditions 119903 = 1199030 V = 0 and thencalculate integral for both sides of (5)

intV0

V119889V = int1199030

119903[ 1120578119901 sdot (

1199032 sdot 119889119901119889119897 + 120591119904)] sdot 119889119903 997904rArr

V = minus 1120578119901 [

14119889119901119889119897 (11990320 minus 1199032) + 120591119904 (1199030 minus 119903)]

(6)

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 7

Loose coaland rock

Fracturechannel

p + dp

dl

p

r

rVp

V

rp

r0

P0 inlet

P1

Foam fluid column unit

Foam fluid

Figure 9 Schematic of the column flow of a unit of foam fluid in a fracture channel

For 0 le 119903 le 119903119901V119901 = minus 1

120578119901 [14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)] (7)

Therefore the flow of fracture channel per unit time is thesum of the shear zone and the piston area namely

1198761 = 1205871199032119901V119901 + int1199030119903119901

2120587119903V 119889V

= minus 41205871205912119904(119889119901119889119897)2 sdot

1120578119901 sdot [

14119889119901119889119897 (11990320 minus 1199032119901) + 120591119904 (1199030 minus 119903119901)]

+ int1199030119903119901

2120587 sdot 119903120578119901

sdot [14119889119901119889119897 11990320 + 1205911199041199030 minus 1

4119889119901119889119897 1199032119901 minus 120591119904119903119901] 119889119903

= 23

1205871205914119904120578119901 (119889119901119889119897) minus120587120591119904119903303120578119901 minus 120587120591119904119903408120578119901 sdot 119889119901119889119897

(8)

The average flow velocity of the section of fracturechannel can be expressed as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897) + 1

3 (120582

minus119889119901119889119897)4] (9)

We make three assumptions for the penetration anddiffusion of foam fluid in the fracture channel (1) the coalpillar and circumferential crack area are all homogeneous andisotropic (2) the foam fluid is a Bingham fluid and (3) thespreading form of the foam fluid is spherical diffusion In theinjection process of a foam fluid the injection content 119876satisfies

119876 = 119881119860119905 (10)

In (10) 119860 is a sphere when the foam fluid diffuses in thefracture channel 119860 = 41205871198972 119905 is the grouting time minus119889119901119889119897 ismuch larger than 120582 in the injection process Thus (9) can besimplified as

119881 = 119870120573 (minus119889119901119889119897 ) [1 minus

43 (

120582minus119889119901119889119897)] (11)

Combining (2) and (4) and then calculating the integralfor both sides of the equation the following is obtained

119901 = 1198761205734120587119905119870119897 minus

43120582119897 + 119862 (12)

Considering the boundary conditions of injecting foamfluid (ie for 119901 = 1199010 119897 = 1198970 and for 119901 = 1199011 119897 = 1198971) thefollowing is obtained

Δ119901 = 12060112057331199051198701198970 119897

31 minus 120601120573

311990511987011989721 + 431205821198971 minus

431205821198970 (13)

Equation (13) is the calculation formula of the effectivediffusion radius for foam fluid diffusing in the fracturechannel where Δ119901 is the penetration pressure differencebetween two monitoring points in the fracture channel 120601 isthe porosity the porosity of coal pillar in the test model is015 and the porosity of the goaf is 035 120573 is the viscosityratio of foam fluid and water 119905 is the grouting time 119870 is thepermeability coefficient 120582 is the ratio of two times the staticshear force and the fracture channel radius 1198970 is the radius ofinjection inlet with the value of 15mm 1198971 is the penetrationand diffusion distance

Penetration time is a major issue in the grouting of rockfractures The foam fluid state will be calculated as a timefunction making a distinction between flow rate controland pressure control The indoor environment temperature

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Advances in Materials Science and Engineering

Table 3 Penetration pressure and diffusion time of the monitoring points

Monitoring points 1 2 3 4 5 6 7 8 9 10Average penetrationpressure (kPa) 1647 1313 1497 1436 1005 1194 1072 552 763 598

Diffusion time (s) 0 160 120 144 382 324 364 734 644 712Differential pressurewith 1 (kPa) 0 324 15 201 632 453 565 1085 874 1039

Viscosity of ISF fluid(Pasdots) 4360 4370 4360 4365 4451 4448 4454 4557 4523 4548

Diffusion distance (mm) 0 255 250 255 510 500 510 776 750 776Porosity 035 015 035 035 015 035 035 015 035 035

Fitting curve

u = 0033e0166t + 4335 (R2 = 098)

2 4 6 80 12 14 16 18 20 2210

Time (min)

43

44

45

46

47

48

49

50

51

52

53

54

Visc

osity

(pamiddot

s)

Figure 10 Foam fluid viscosity varies over time

is 10∘C and the viscosity of the water is 13077MPasdots basedon the viscosity of the water table The viscosity of the ISFfluid was measured using a NDJ-5s rotary viscometer settingthe rotor number to 2 and the rotor speed to 6 The viscosityvaries with time as shown in Figure 10

The change of viscosity over time was fitted in Figure 10the fitting function obtained is given by

119906 = 119886119890119887119905 + 119888 (14)

where 119886 = 0033 119887 = 0166 and 119888 = 4335 the correlationcoefficient is1198772 = 098 As a result we can obtain the viscosityratio of foam fluid and water using

120573 = 119906ISF119906119882 = 119886119890119887119905 + 119888119906119882 = 00331198900166119905 + 4335

13077 times 10minus3 (15)

From Figures 2 and 3 the average penetration pressureand the diffuse time of monitoring points 1ndash10 are listed inTable 3

Based on (13) the relationship among the differentialpressure of the 1 monitoring point the diffusion time andthe diffusion distance can be expressed as

Δ11990113 = 12060131205733311990531198701198970 119897313 minus 1206013120573331199053119870119897213 + 4

312058211989713 minus431205821198970

Δ11990116 = 12060161205736311990561198701198970 119897316 minus 1206016120573631199056119870119897216 + 4

312058211989716 minus431205821198970

(16)

We substituted the related parameters in the Table 3 into(16) to obtain

1500 = 13665119870 + 03133120582

4530 = 98377119870 + 06467120582

dArr119870 = 4894 times 10minus3 (ms) 120582 = 3897 times 103 (Pam)

(17)

To further amend the formula of effective diffusiondistance of foam fluid the diffusion time and diffusiondistance of the remaining monitoring points 2 4 5 78 9 and 10 were substituted into the formula and thenthe predictive values were calculated The comparison of thepredicted values and the test values is provided in Table 4

From Table 4 the predicted values were overall in accordwith the experimental results The predicted values wereall less than the experimental results this difference occursmainly because the foam fluid impacts the tiny earth pressuregauges and causes it to be slightly mobile As a resultthe follow-up monitoring data may contain some errorsHowever because all the relative error ofmonitoring is within10 the prediction formula is reasonable Thus we canobtain the relations of the diffusion distance penetrationpressure difference and diffusion time given by (18) Based onit it can be obtained that the penetration pressure differencebetween two monitoring points (Δ119901) was affected by theporosity (120601) and the penetration and diffusion distance (1198971)In Figure 7 the porosity of the model is the same With

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in Materials Science and Engineering 9

Table 4 Comparison of the predicted values and the test values

Monitoring point 2 4 5 7 8 9 10Predicted value (kPa) 294 192 605 529 993 796 951Test value (kPa) 324 201 632 565 1085 874 1039Relative error () 925 448 427 637 847 892 846

the increase of the penetration and diffusion distance thepenetration pressure near the perfusion inlet is higher thanthe position which is further away from the perfusion inletFor the same penetration and diffusion distance the greaterthe porosity is the smaller the seepage pressure difference isand the greater the seepage pressure is which can prove thediffusion morphology in Figure 8

Δ119901 = 120601 ((119886119890119887119905 + 119888) 119906119882)31199051198701198970 1198973 minus 120601 ((119886119890119887119905 + 119888) 119906119882)

3119905119870 1198972

+ 43120582119897 minus

431205821198970

(18)

4 Conclusions

A similar fractured rock model was built according to thecoal pillar and the surrounding gobThepenetration pressureimage and law in the complex fracture were investigatedSome conclusions can be drawn as follows

(1) The pressure fluctuated up and down within a certainrange overallWith the increase of diffusion distance the pen-etration pressure decreased consistent with the traditionalgrouting penetration diffusion law Affected by the porosityof filling medium a longer time is required to monitor thepenetration pressure for the loose coal pillar than the gob andthe value of penetration pressure in loose coal pillar was lowerthan that of the gob at the same diffusion distance

(2) The diffusion form of the foam fluid in the 119883-119884plane is ellipsoidal with the diffusion area increasing withtime although the diffusion area of growth becomes smallerwith time in the 119883119885 section the foam fluid diffusion in thefracture channel is from dense to loose in the 119883 directionand from the119885 direction the fracture penetration is fuller atthe same119885 height of the injection inlet in the119884119885 section theleft part is loose and the right part is dense in the 119884 directionand the distribution of penetration and diffusion is uniformexcept the top with surface penetration

(3) The viscosity of the ISF fluid was measured by a NDJ-5s rotary viscometer The change of viscosity over time wasfitted to obtain the fitting function Based on the formulaof Bingham fluid penetration in a pipe the formula of thediffusion radius of the ISF was determined theoretically andthen compared and verified in terms of the pressure data fromthe monitoring point

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (51604110 51774135 51504093 and51374003) Provincial Natural Science of Hunan (2017JJ3074)China Postdoctoral Science Foundation (2017M612558) andResearch Project of Hunan Provincial EducationDepartment(17C0641)

References

[1] Y Tang ldquoInhibition of low-temperature oxidation of bitumi-nous coal using a novel phase-transition aerosolrdquo Energy ampFuels vol 30 pp 9303ndash9309 2016

[2] J Pandey N K Mohalik R K Mishra A Khalkho D Kumarand V K Singh ldquoInvestigation of the Role of Fire Retardants inPreventing Spontaneous Heating of Coal and Controlling CoalMine Firesrdquo Fire Technology vol 51 no 2 pp 227ndash245 2015

[3] T Xia XWang F Zhou J Kang J Liu andFGao ldquoEvolution ofcoal self-heating processes in longwall gob areasrdquo InternationalJournal of Heat and Mass Transfer vol 86 pp 861ndash868 2015

[4] H-Z Yu R Kasiski and M Daelhousen ldquoCharacterizationof Twin-Fluid (Water Mist and Inert Gas) Fire ExtinguishingSystems by Testing and Modelingrdquo Fire Technology vol 51 no4 pp 923ndash950 2014

[5] W Lu ldquoThe high inhibitor bubble for prevention and controlof coal spontaneous combustionrdquo Coal Science and Technologyvol 46 pp 41ndash44 2008

[6] J Deng Y Xiao Q Li J Lu and HWen ldquoExperimental studiesof spontaneous combustion and anaerobic cooling of coalrdquo Fuelvol 157 pp 261ndash269 2015

[7] X W Ren F Z Wang Q Guo Z B Zuo and Q S FangldquoApplication of Foam-gel Technique to Control CO ExposureGenerated during Spontaneous Combustion of Coal in CoalMinesrdquo Journal of Occupational and Environmental Hygienevol 12 no 11 pp D239ndashD245 2015

[8] Y Lu ldquoLaboratory study on the rising temperature of sponta-neous combustion in coal stockpiles and a paste foam suppres-sion techniquerdquo Energy amp Fuels vol 31 pp 7290ndash7298 2017

[9] X Qi DWang H Xin and X Zhong ldquoEnvironmental hazardsof coal fire and their prevention in Chinardquo EnvironmentalEngineering and Management Journal vol 12 no 10 pp 1915ndash1919 2013

[10] L Zhang B Qin B Shi and K Wen ldquoFormation mechanismof foamed gel for controlling the coal spontaneous combustionrdquoCombustion Science and Technology vol 188 no 1 pp 132ndash1432016

[11] B Qin Y Lu Y Li and D Wang ldquoAqueous three-phasefoam supported by fly ash for coal spontaneous combustionprevention and controlrdquo Advanced Powder Technology vol 25no 5 pp 1527ndash1533 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Advances in Materials Science and Engineering

[12] Z Shao D Wang Y Wang X Zhong X Tang and X HuldquoControlling coal fires using the three-phase foam and watermist techniques in theAnjialingOpenPitMine ChinardquoNaturalHazards vol 75 no 2 pp 1833ndash1852 2015

[13] F Zhou W Ren D Wang T Song X Li and Y ZhangldquoApplication of three-phase foam to fight an extraordinarilyserious coal mine firerdquo International Journal of Coal Geologyvol 67 no 1-2 pp 95ndash100 2006

[14] J J Feiler G J Colaizzi and C Carder ldquoFoamed grout controlsunderground coal-mine firerdquo Mining Engineering vol 52 pp58ndash62 2000

[15] G J Colaizzi ldquoPrevention control andor extinguishment ofcoal seam fires using cellular groutrdquo International Journal ofCoal Geology vol 59 no 1-2 pp 75ndash81 2004

[16] X LuDWang C ZhuW Shen SDong andMChen ldquoExper-imental investigation of fire extinguishment using expansionfoam in the underground goafrdquo Arabian Journal of Geosciencesvol 8 no 11 pp 9055ndash9063 2015

[17] Y Lu and B Qin ldquoMechanical properties of inorganic solidifiedfoam for mining rock fracture fillingrdquoMaterials Express vol 5no 4 pp 291ndash299 2015

[18] Y Lu B Qin Y Jia Q Shi and F Li ldquoThermal insulationand setting property of inorganic solidified foamrdquo Advances inCement Research vol 27 no 6 pp 352ndash363 2015

[19] G Gustafson and H Stille ldquoPrediction of groutability fromgrout properties and hydrogeological datardquo Tunnelling andUnderground Space Technology vol 11 no 3 pp 325ndash332 1996

[20] T Fujita F Shinkai and J Nobuto ldquoFundamental study ona grout penetration model for a HLW repositoryrdquo Journal ofEnergy and Power Engineering vol 6 pp 1191ndash1203 2012

[21] Z Yang K Hou and T Guo ldquoStudy on the effects of differentwater-cement ratios on the flow pattern properties of cementgroutsrdquo Applied Mechanics and Materials vol 71-78 pp 1264ndash1267 2011

[22] G Shi M Liu J Kong and D Wang ldquoFlow characteristics ofthree-phase foam inmine gob and its applicationrdquo InternationalJournal ofMining Science and Technology vol 25 no 5 pp 773ndash778 2015

[23] L Korat and V Ducman ldquoThe influence of the stabilizing agentSDS on porosity development in alkali-activated fly-ash basedfoamsrdquo Cement and Concrete Composites vol 80 pp 168ndash1742017

[24] D Lootens andD P Bentz ldquoOn the relation of setting and early-age strength development to porosity and hydration in cement-based materialsrdquo Cement and Concrete Composites vol 68 pp9ndash14 2016

[25] S Jacobsen L Haugan T A Hammer and E KalogiannidisldquoFlow conditions of fresh mortar and concrete in differentpipesrdquo Cement and Concrete Research vol 39 no 11 pp 997ndash1006 2009

[26] T Hirochi Y Maeda S YamadaM Shirakashi M Hattori andA Saito ldquoFlow patterns of icewater slurry in horizontal pipesrdquoJournal of Fluids Engineering vol 126 pp 935ndash940 2004

[27] M-H Wang C Huang K Nandakumar P Minev J Luoand S Chiovelli ldquoComputational fluid dynamics modelling andexperimental study of erosion in slurry jet flowsrdquo InternationalJournal of Computational Fluid Dynamics vol 23 no 2 pp 155ndash172 2009

[28] S-J Li L-G Wang Y-L Lu and B Zhang ldquoSlurry diffusionwithin cracked wall rock during the bolt-grouting processrdquoZhongguo Kuangye Daxue XuebaoJournal of China Universityof Mining and Technology vol 40 pp 874ndash880 2011

[29] Y Li Y Shen and X Huang ldquoTest study on diffusion lawsof foundation grouting in submarine immersed tube tunnelrdquoChina Journal of Underground Space Technology vol 8 pp1244ndash1249 2012

[30] X Z Yang X H Wang and J S Lei ldquoStudy on grouting diffu-sion radius of Binghamfluidsrdquo Journal of Hydraulic Engineeringvol 6 pp 75ndash79 2004

[31] D Wang and W Sui ldquoGrout diffusion characteristics duringchemical grouting in a deep water-bearing sand layerrdquo Interna-tional Journal of Mining Science and Technology vol 22 no 4pp 589ndash593 2012

[32] D V Georgievskii ldquoStability of Binghamflows from the earliestworks of A A Ilrsquoyushin to the presentrdquo Journal of EngineeringMathematics vol 78 pp 9ndash17 2013

[33] Z Q Yang K P Hou T T Guo and M A Qiu ldquoStudy ofcolumn-hemispherical penetration grouting mechanism basedon binghamfluid of time-dependent behavior of viscosityrdquoRockamp Soil Mechanics vol 32 pp 2697ndash2703 2011

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpswwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014