Ellis Ekhator,Boyun Guo

University of Louisiana at Lafayette,United States

The exploitation of natural gas from NGH can be conducted using either depressurization[12,13],thermal stimulation[12],chemical injection of inhibitors[1],CH4-CO2replacement[14]or a combination of these existing methods to efficiently dissociate gas from the Hydrate bearing layer[8,15].The depressurization method involves reducing NGH wellbore pressure below its hydration pressure within the prevailing reservoir temperature.Reducing pressure below the hydration pressure leads to gas hydrate dissociation[16];The thermal stimulation technique requires the injection of hot water,steam,or heated brine to increase the MH reservoir temperature above its hydrate stability temperature[4,17];The objective of chemical injection of inhibitors is to distort the hydrate stability conditions towards the dissociation region.This method uses chemical inhibitors like glycol,salts,and alcohol to move the 3-phase equilibrium conditions to the high pressure and low-temperature side;CH4-CO2replacement technique exploits methane gas from an NGH bearing layer without causing geo-mechanical failure concerns for the hydrate-bearing section[18-21].CH4-CO2method is conducted by injecting carbon dioxide(CO2)into an injection well located in an NGH environment to displace methane and subsequently sequester carbon dioxide[22-27].According to Hancock et al.[2],the combination of depressurization,thermal stimulation,and chemical stimulation method enhances the ability of the well to produce fluid in NGH environments.

Several field trials have been conducted all over the world to recover gas from the methane hydrate-bearing layer.The first onshore methane hydrate field trial was conducted using the depressurization method at the Mallik site in the Mackenzie delta area,Canada,in 2002.Then,a second trial was conducted at the same site between 2007 and 2008 via depressurization and thermal stimulation methods[12].The depressurization technique was applied in an NGH reservoir located in Mount Elbert,North Slope of Alaska,USA,in 2007[28]and again in the same site between 2011 and 2012 to assess the feasibility of this method[29].Other NGH test locations include the Messoyakha gas field in the artic[30];the marine hydrate located in the Eastern Nankai Trough,Japan[13];the methane hydrate in the Qilian Mountain permafrost,Qinghai,Northwest China[31],and the marine gas hydrates in Shenhu area,South China sea,China[32,33].

All NGH field trials conducted have not attained a commercial scale of production due to sand production challenge during gas hydrate dissociation and low well productivity[34].For example,after six days flow test period from the first marine methane hydrate in the Eastern Nankai Trough area of Japan,an average of 706 293 ft3/d of methane gas was produced,and up to 1059 ft3of sand was produced to surface equipment,thus resulting in termination of the flow test[35].A second and third production tests were also conducted in the Eastern Nankai Trough area,Japan,using a preexpanded Geo-form screen and an expandable screen,respectively[36].The second trial lasted for 12 days(cumulative volume of about 1.24×106ft3of methane),and the operation was brought to a halt owing to sand production.The third trial only lasted for 24 days with a cumulative volume of about 8.48 × 106ft3,and then,the operation was terminated due to severe weather concerns[36].The most extended field test was conducted in the Shenhu Area of South China Sea,China,for 60 days with a total of 1.06×107ft3of methane gas extracted(an average of about 1.77 × 105ft3/d).However,the operation was terminated owing to sand production and low well productivity[33].All field tests conducted so far seem to have the same issues of sand production and low well productivity during hydrate dissociation despite the use of open-hole gravel packing or cased-hole gravel pack completion design to mitigate sand production[13].A report given by Hou et al.[34]suggests that the high drawdown required to effect dissociation may be responsible for the excessive sand production and wellbore collapse;however,this could be just one of many related factors since sand production is ubiquitous in the dissociation of NGH[37,38].

Frac-packing has been applied successfully to address sand production challenges in most conventional oil and gas reservoirs with unconsolidated sediments[39];however,there are no documented experimental records or field studies involving the use of frac-packed wells to exploit methane gas from NGH reservoirs.To the best of our knowledge,only two publicly available studies analyze the technical feasibility of using frac-packed wells to exploit methane gas from offshore gas hydrate resources[34,40].Shan et al.[40]derived a well productivity model to estimate the long-term productivity of frac-packed NGH wells under pseudosteady state flow conditions.However,the analytical model presented by Shan et al.[40]only considered flow in the fractured section of the NGH reservoirs.

This paper assesses the effect of well completion types on gas well productivity in a class 1G(free gas and hydrate in the hydratebearing layer)subsea gas hydrate reservoir that has decomposed into gas and water.It is assumed that the free gas in the hydratebearing layer from the Class 1G hydrate reservoir will be produced first,and then the dissociated gas from the hydrate-bearing section.Three well completion systems are considered for the well completion type assessment study while assuming pseudo-steady state condition of flow,and they include:

(1)A frac-pack NGH well with a vertical hydraulic fracture and using the concept of the Unified Fracture Design proposed by Economides et al.[41]to predict the optimal fracture geometry(fracture width and half-length).

(2)A frac-packed vertical well with a horizontal hydraulic fracture to produce methane gas from a sub sea NGH resource.

(3)A vertical well with a cased hole gravel pack system in an NGH reservoir.

Fracture width estimation for the case of a frac pack NGH well with a vertical fracture is conducted using the Economides et al.’s[41]model(Unified Fracture Design approach).Next,estimation of fracture geometry for the frac-packed well with a horizontal fracture is conducted using the fracture hydraulics model developed by Hou et al.[34].Lastly,the fracture and proppant permeability estimation is conducted using Berg's equation[42].Furthermore,sensitivity analysis is conducted to identify critical factors influencing the productivity of frac-packed gas wells while using the natural gas hydrates parameters of the Shenhu area,South China Sea,China.Also,a productivity ratio will be used as a criterion to provide well selection types.

2.Mathematical models

This section presents three models for assessing well productivity and a proppant selection model used to estimate fracture or proppant permeability.The well productivity models considered include frac-packed gas hydrate wells with vertical fractures,fracpacked gas hydrate wells with a horizontal hydraulic fracture,and a cased hole gravel-packed well.The following assumptions are made in this investigation:

(1)The gas hydrate reservoir is homogenous and isotropic in the horizontal direction.

(2)Natural gas production will be contributed from the free gas in the Class 1G hydrate reservoir.

(3)Single-phase gas flow prevails in the Class 1G hydrate reservoir owing to free gas present in the hydrate-bearing zone,which is also in contact with an underlying free gas layer,providing gas flow even before hydrate dissociation pressure is reached.

(4)Darcys law is valid,and the turbulent flow effect is negligible owing to the low flow velocity of gas during gas hydrate dissociation.

(5)The NGH reservoir is depleted under pseudo-steady state conditions during gas production in the depressurization process.

2.1.Frac-packed well with a vertical fracture

Subsea gas hydrate reservoirs are primarily in shallow environments[34].Because the minimum formation stress is vertical,horizontal fractures are created[43].However,for a frac-pack vertical well in an NGH environment where the least formation stress is horizontal,a vertical hydraulic fracture is generally created during fracture propagation.Economides et al.[41]introduced the idea of Unified Fracture Design to optimize hydraulic fracturing treatment based on given proppant volume,reservoir thickness,reservoir permeability,and fracture drainage area parameters.They pointed out that an optimal fracture geometry(fracture width and fracture half-length)can be determined,giving a corresponding maximum productivity index,JD.Also,they introduced the idea of the Proppant Number,Np,which is a ratio of fracture conductivity(kfVf)and the product of fracture half-length and formation permeability.When the Proppant Number,Np,is known,it becomes relatively easy to estimate the optimum dimensionless fracture conductivity(CfD,opt),the maximum pseudo-steady state dimensionless productivity index,JDmax,and the fracture geometry(width and length).The Unified Fracture Design method has been applied in the oil and gas industry to estimate optimal fracture geometries[44,45].However,it has not been applied in an NGH reservoir to predict fracture geometry.This section will consider using a frac-pack well with a vertical hydraulic fracture.First,the optimal fracture geometry will be estimated using the Unified Fracture Design methodology.Next,the well productivity will be assessed using a conventional gas well productivity model.Based on the Unified Fracture Design,for a given treatment size(proppant volume in ft3),reservoir thickness(ft),reservoir permeability(md),the Proppant Number,Npis estimated using Equation(1)as:

kfrefers to the fracture permeability in millidarcy,and it is dependent on the proppant type and size and will be estimated using Berg's[42]empirical equation.Vpis the propped volume in cubic feet,and K is the reservoir permeability in millidarcy.The authors first proposed correlations to estimate the optimum dimensionless fracture conductivity based on the range of Proppant Number Npcalculated to evaluate the optimal fracture geometry.The equation to estimate the optimum dimensionless fracture conductivity(CfD,optis dependent on Proppant Number,Np)is given as[46]:

When the optimum dimensionless fracture conductivity is known,the optimum fracture geometry:fracture half-length,xf,and width,w can be estimated from Equation(3)and Equation(4)as:

where Vfrefers to the volume of the fracture for one propped wing,and it is defined as:

and the propped volume,Vp,can be calculated as

Where hfrefers to the height of the fracture in feet,ρprefers to proppant specific gravity,and φprefers to the proppant pack porosity.Furthermore,h/hfwill be equal to 1 if the pay zone thickness,h,is equivalent to the height of the created fracture,hf.According to Economides et al.[41],once the Proppant Number,Np,is determined,the maximum corresponding dimensionless productivity index under pseudo-steady state can be estimated based on the range of the Proppant Number,Np as:

Next,with the maximum dimensionless productivity index at pseudo-steady state estimated,the long-term productivity of the frac-pack well with a vertical hydraulic fracture in an NGH environment can be estimated using conventional gas well productivity model under pseudo-steady state flow condition as:

Where Qgrepresents the well productivity in Mscf/d,Khrepresents the horizontal permeability in millidarcy,h refers to the hydratebearing layer thickness in feet,refers to the average reservoir pressure in psia,Pwf represents the bottom hole flowing pressure in psia,used to effect dissociation of methane gas from the NGH resource,μgrepresents the gas viscosity in Centipoise and evaluated at average pressure,Z is the gas compressibility factor evaluated at average pressure,and T represents the gas hydrate reservoir temperature in Rankine.

2.2.Frac-packed well with a horizontal fracture

Since most methane gas found in NGH reservoirs is in shallow sediments,the minimum formation stress is often in the vertical direction,and as a result,horizontal fractures are generally created during well stimulation[34].Hou et al.[34]developed fracture hydraulics models to predict bottom hole fracturing pressure by assuming that.

(1)The treatment fluid is a Newtonian fluid.

(2)The created fracture assumes a circular shape with a constant width.

(3)The treatment fluid leak-off is negligible during frac-packing due to frozen pore spaces in the NGH zone.

According to Hou et al.[34],the bottom hole fracturing pressure can be estimated as:

where pFrefers to the bottom hole fracturing pressure in psi;ptrefers to the fracture tip pressure in psi,fFis the Fanning friction factor;ρLrefers to the fluid density in;qIis the injection rate in bpm,rwrefers to wellbore radius in feet,R is the fracture radius in feet,and w is the average fracture width in inch.Equation(9)can be modified to estimate the average fracture width as

Equation(10)assumes that 1/R is negligible when compared to 1／rw.However,if the following parameters are available:poison's ratio,υ;fracturing treatment fluid viscosity,μ;Young's modulus,E(psi),and the radius of fracture,Rf(ft),then,the average fracture width can be quickly estimated using the equation derived by Geertsma and de Klerk[47]as:

where the propped width of the fracture,wp,is given by

where Cprefers to the total or overall proppant concentration in the treatment slurry.

Next,if the volume of proppant in ft3,Vpis known based on the mass of proppant(Ibm)pumped during the treatment operation,then the radius of the fracture in feet,can be determined using the following equation:

2.2.1.Well productivity model

The Shan et al.[40]model was modified to account for flow across all the NGH reservoir(frac and un-frac section),and it is strictly based on a technical feasibility study.The assumptions for the model formulation are:

(1)The gas hydrate reservoir is homogeneous and isotropic in the horizontal direction.

(2)Pseudo-steady-state flow condition prevails within the well drainage area.That is,the pressure in the NGH reservoir has dropped below its hydration pressure.

(3)The minimum formation stress is in the vertical direction based on the shallow nature of the NGH sediment,thus,hydraulic fracture with a circular shape in the horizontal plane at the mid-depth of the hydrate zone is created during well stimulation treatment operation.

(4)The horizontal fracture drains gas from the reservoir volumes overlaying and undelaying the fracture(Linear vertical flow)in the fractured zone,while radial horizontal flow prevails from the non-fractured region to the fractured region.

(5)Darcy's law dominates the fluid flow in the matrix and fracture due to the gas phase's relatively low flow velocity causedbythehigh-watersaturationduring depressurization.

(6)Single gas-phase flow prevails in the Class 1G NGH reservoir owing to free gas presence in the hydrate-bearing zone and the underlying free gas zone.

For a vertical non fractured well under pseudo-steady state condition of flow,horizontal radial flow regime prevails.Under pseudo-steady state flow conditions,the gas flow rate in the nonfractured region can be estimated as[48]:

where Qgrefers to gas production rate in Mscf/d,kHrefers to effective horizontal reservoir matrix permeability to gas flow in md,h refers to the thickness of gas hydrate reservoir in ft,refers to the average reservoir pressure in psia,pRrefers to the pressure at the fracture tip in psia,μgrefers to gas viscosity in cp at the average reservoir pressure,z refers to the average gas compressibility factor estimated at the average reservoir pressure,T is the NGH formation temperature inoR,reis the radius of the drainage area in ft,and R is the radius of fracture in ft.

Shan et al.[40]model account for vertical flow from the gas hydrate zone to the fracture,and it is estimated using the following equation:

where kvrefers to the effective reservoir vertical permeability in md,pwrefers to the wellbore pressure in psia,and rwrefers to the wellbore radius in ft.

The parameter C in Equation(15)is estimated using the relation in Equation(16)as:

where wpis the propped fracture width,and kfis the fracture permeability.

A combination of Equation(14)and Equation(15)links the two regions(the fractured region and the non-fractured region)by assuming a series flow of fluid and this ensures a full flow path from the drainage boundary to the wellbore.The modified Shan et al.[40]model for gas flow rate estimation in a frac-pack NGH well with a horizontal fracture is given in the U.S field unit as:

2.3.Cased-hole well with internal gravel pack

The conventional gravel pack method used in the oil industry can be employed to mitigate sand production in an NGH well[49].Previous field trials have applied the use of sand control design systems such as open-hole gravel pack system,expandable screens,standalone screens,and pre-packed screen to control sand production during gas hydrate dissociation[49-51].However,little or no success has been achieved to control sand production and sustain the long-term productivity from wells in an NGH environment despite using numerical simulation methods and conventional gravel sizing procedures[52,53].A possible reason for past failures could be based on design objectives that were purely focused on sand bridging or sand prevention without considering excluding the fines fraction from the formation[49].

This section presents a conventional model used in the oil and gas industry to estimate productivity for a vertical well with a cased hole gravel pack system located in the Shenhu NGH environment and under pseudo-steady state condition.Equation(37)to Equation(39)in the subsequent section is used to select the maximum allowable proppant size,DmaxP,the minimum allowable proppant size,DminP,and the median diameter size of the proppant,D50,respectively.Also,Berg's[42]empirical equation as defined in Equation(42)in the subsequent section estimates the proppant pack permeability(Also,fracture permeability).Lastly,skin effect due to perforation and a cased hole gravel pack is estimated using Karakas and Tariq[54]and Furui[55]models.The assumptions made in this section are as follows:

(1)The gas hydrate reservoir is homogenous and isotropic in the horizontal direction.

(2)Free gas in the hydrate-bearing zone will be produced using the depressurization technique.

(3)Only a single gas phase flow prevails during hydrate dissociation in the Class 1G gas hydrate reservoir.

(4)Darcy's law is valid,and the non-turbulent flow effect can be ignored because of the relatively low flow velocity of the gas phase on dissociation.

(5)The NGH reservoir is under pseudo-steady state condition.

2.3.1.Perforation skin effect estimation

Locke[56]was one of the proponents to investigate the performance of perforated well systems.Locke produced an easy-touse nomograph to estimate the skin factor for perforated wells;however,the method only applies to standard phasing angles(00,900,1200,and 1800),and specific perforation diameters[57].Later,Karakas and Tariq[54]derived a famous semi-analytical equation to estimate the perforation skin effect,which has been used as a standard in computer simulations and broader coverage than Locke's method[56].This study adopted the Karakas and Tariq[54]model to estimate skin factors due to perforation for a cased-hole gravel pack well in the Shenhu NGH reservoir located in the South China Sea,China.From Karakas and Tariq’s report,the total skin effect due to perforation,SP,is given as:

The plane flow effect,Sh,is estimated using the following equation:

The parameter ∝is estimated from a reference table given by Karakas and Tariq[54],and it is based on standard phasing angles.The vertical pseudo skin effect,Svis given as:

Where the following represent dimensionless parameters:

with h representing reservoir thickness in ft,lpis the length of perforation in inch,Khand Kv are the Horizontal and vertical permeabilities in md,and rpis the radius of perforation in inch.The wellbore skin effect,Swb,is estimated as:

Where rwdis a dimensionless parameter given by:

The parameters,C1 and C2,can be estimated from a reference table given by Karakas and Tariq[54].

2.3.2.Cased-hole gravel pack skin factor estimation

A study conducted by Furui[55]proposed that conventional models like Golan and Whitson[58]used in estimating skin factor in a gravel pack-filled perforation might give erroneous results when the tunnel permeability approaches the formation permeability.Furui[55]cited that a transition from linear to spherical flow near the perforation through the casing could be the main reason.He developed a new model for the estimation of skin factors,which has become an industry standard.In this study,it is assumed that:

(1)The pressure drop through the gravel is negligible,and the migration of fines has not reduced the gravel's permeability.

(2)The turbulence effect is negligible owing to the relatively low flow velocity of methane gas during hydrate dissociation.

(3)Skin factor due to formation damage is negligible,and an optimal perforation design strategy is adopted to minimize the perforation skin effect.

An estimate of skin factor,Scg,for cased hole gravel packed wells in an NGH environment is presented as follows based on Furui's model[55]:

The dimensionless variables in Equation(28)can be obtained as follows[55]:

Where Spis estimated using Equation(19)and refers to perforation skin factor,also,Splin Equation(33)is defined by:

Furthermore,the parameter,v is estimated based on the perforation phasing angle as:

2.3.3.Well productivity model for cased hole gravel pack

For a vertical well located in a natural gas hydrate(NGH)environment with a cased hole gravel pack system,the well productivity is estimated using the conventional gas well productivity equation under the assumption that the NGH reservoir is under pseudo-steady state condition of flow.That is,the NGH reservoir pressure has dropped below its dissociation pressure.Also,it is assumed that the gas hydrate reservoir is homogenous and isotropic in the horizontal direction.The gas flow rate in the U.S field unit is defined as:

Where Qgrefers to the gas production rate in Mscf/d,refers to effective horizontal reservoir matrix permeability to gas flow in md,h refers to the thickness of gas hydrate reservoir in ft,refers to the average reservoir pressure in psia,refers to the bottom hole flowing pressure in psia,μgrefers to gas viscosity in cp at the average reservoir pressure,z refers to the average gas compressibility factor estimated at the average reservoir pressure,T is the NGH formation temperature inoR,is the radius of the drainage area in ft,and rwis the radius of the wellbore in ft,and SCGrefers to gravel pack skin factor.

2.4.Proppant selection/sizing model

The dissociation of methane gas from NGH reservoirs results in grain detachment and migration toward the sand-control media's outer boundary,and with some fines and clay content penetrating through the sand-control media[49].Consequently,sand control techniques adopted in conventional oil and gas reservoirs(open hole gravel packing,internal gravel packing and frac packing)can be employed in an NGH reservoir with unconsolidated sands[49,59].Both gravel packing and frac-packing techniques require proper sizing and proppant selection based on particle size distribution characteristics[34,60].Using large proppant sizes will enhance gas productivity and reduce skin effect,but could result in massive sand production,erosion of wellbore,and total loss of well.On the other hand,using small proppant/gravel sizes would lower sanding risk in the wellbore.However,it may in-crease the likelihood of plugging by formation fines or clay and reducing productivity in an NGH well.Therefore,it is crucial to optimize the design objective to meet sand exclusion requirements and allow the free flow of formation fines[49].

Coberly and Wagner[60]proposed that for uniform sands,the gravel or proppant should have a D10size that is less than 10-13 times the d10of the formation particle size.However,this approach resulted in permeability impairment due to large gravel sizes,which could not pre-vent the invasion of formation fines.Efforts to remedy field failures from applying Coberly and Wagner approach were made by several researchers[61-63].Hill[61]recommended reducing the ratio(D10/d10)to 8;however,there was no improvement.Later,Buzarde et al.[62]recommended that the pack to formation sand ratio(D50/d50),based on the 50-percentile points,be ≤8,and(D90/d90)based on the 90-percentile points,be ≤12.Later,investigators realized that formation fines were critical in designing sand control[63,64].Schwartz[64]proposed a gravel sizing procedure based on a uniformity coefficient that is at most 1.5.He suggested the following rules:D10=6d10for uniform sands(UC ＜3);D40= 6d40for non-uniform sands(5 ＜UC ＜10);and D70= 6d70for severe nonuniform sands(UC ＞10).Next,Saucier[65]proposed a rule used as an industry standard to select proppant sizes.He recommended that the diameter of the median size of the gravel pack D50be five to six times the diameter of the median size in the formation sand(D50= 5 - 6d50).Saucier's criterion retains formation fines at the boundary of the proppant pack,resulting in the reduction of permeability at this interface,and subsequently,loss of productivity[34].Later,Jennings[66]raised the multiplier by 6-8 times(D50=6 to 8 times d50)to allow some invasion of formation fines rather than retaining the sand at the proppant/sand interface.

A recent study was conducted by Li et al.[49]to select unique proppant sizes with a focus on retaining coarse formation particles and eliminating formation fines through the sand control media for clayey hydrate-bearing formations in the Shenhu area,South China Sea,owing to its characteristics high clay content which could result in screen plugging.Their work divided the formation sand into two components based on particle size distribution:coarse component and fine component.Then,they determined the gravel sizes required to retain coarse components and eliminate fine components,respectively.Next,they found the proper gravel size by intersecting the two components(coarse and fine).Although this is a novel method for sand control in an NGH environment with a high clay content,it is based on a technical feasibility study,and it is yet to be applied in field trials.In this study,we propose the following procedure to select proppant sizes to retain coarse particles while allowing the invasion of formation fines to some extent into the proppant pack based on the formation particle size distribution:

(1)The maximum allowable proppant sizeDMaxPis equal to 6.5 times the 10-weight percentile of formation particles so that large particles(top 10%)are retained outside of fracture and can be defined as

(2)The minimum allowable proppant size DMinPis equal 6.5 times the 90-weight percentile of formation sand particles,this enables retaining of least 90% of formation particles in the proppant pack,and it is defined as

(3)The 50-weight percentile points of the proppant/gravel(D50)

is designed based on the constant uniformity coefficient as

(4)D10and D90of the proppant/gravel can be determined by Equation(40)and Equation(41),respectively as

2.4.1.Fracture or proppant permeability

Fracture or proppant permeability can be estimated using empirical correlations that are based on the size distribution of proppant particles(mainly D50)and as well as their fractional porosity(Ø)according to studies conducted by some authors[42,67-70].Krumbein and Monk[67]estimated the permeability of sand packs(in Darcy)of constant 40%porosity for specified size and sorting ranges.They developed a correlation that relates the permeability to the geometric mean of grain diameter(in millimeters)and the standard deviation of grain diameter(in phi units).Although the Krumbein and Monk equation does not include porosity as a factor,however,Beard and Weyl[68]adopted their experimental technique and later found that Krumbein and Monk's correlation fit their experimental data reasonably for sample porosity ranging from 23%to 43%.Both researchers:Krumbein and Monk[67]and Beard and Weyl[68],used sieved sands from a common source,and grain properties like angularity,sphericity,and surface texture did not differ much.Also,sorting was intentionally controlled to be log-normal.In another study,Morrow et al.[71]proposed that permeability correlated best with the log of grain size times sorting for fines fraction less than 44 and this was based on statistical data from Gulf Coast sands.Later,Berg[42]developed a model that linked grain size,shape,and sorting to estimate permeability.Berg considered“rectilinear pores”and defined them as pores that penetrated the solid without a change in shape or direction in various packings of spheres and derived a simple relation as:

where kf,gis fracture or proppant permeability in md,D is particle diameter in micrometers(μm),φ is fractional porosity.P is the sorting term,usually expressed in the phi unit(phi=-Log2D)and accounts for the spread in grain size.The sorting term,P,is defined by the simple relation as:

In this study,Berg’s[42]equation was used to estimate fracture and proppant permeability since the correlation was derived by assuming that the smaller grain fractions primarily control permeability(in md).Berg[42]model was developed to determine the permeability of unconsolidated sediments with relatively clean consolidated quartz rocks,giving a good result for sand packs with fractional porosity less than 30%.

3.Workflow diagram for well completion selection type in marine class IG NGH reservoir

Fig.1 represents the workflow diagram for selecting well completion types in a typical Class 1G marine gas hydrate reservoir with clayey silt lithology,which is used for this study.Here,the least vertical stress orientation determines which model to be used to design for frac-packing:Economides et al.[41]or the modified Shan et al.[40]model.Also,the decision to design for frac-packing or cased-hole gravel pack well system will depend on the frac-packed wells' productivity ratio to the casedhole gravel pack well.

4.Field case studies

This segment presents well productivity estimations based on the three productivity models(Frac-Pack vertical well with a vertical hydraulic fracture,a Frac-pack NGH with horizontal fracture,and a cased hole gravel pack well)considered in this study.The NGH reservoirs in Shenhu area,Northern South China Sea,is used as a field case study.Based on Su et al.’s[72]report,the NGH in the Shenhu area,South China Sea,is located about 3870 ft below the mud line.The NGH bearing layer extends from 510 ft to 580 ft below the mud line.The seawater has a pressure gradient of 0.465 psi/ft.The NGH average reservoir pressure is approximately 2053 psia based on 0.465 psi/ft normal pressure gradient and a depth of 4415 ft.The reservoir lithology is clayey silt with three intervals.In interval“a,”the mean effective porosity is 35%,the mean hydrate saturation is about 34%,and the mean permeability is 2.9 md.In interval“b,”the mean effective porosity is 33%,the mean hydratesaturation is 31%,and the mean permeability is 1.5 md.While in interval“c,”the mean effective porosity is 32%,the mean gas saturation is 7.8%,and the mean permeability is 7.4 md[33].The gas compressibility factor z is 0.815,and it is estimated using Brill and Beggs correlation[73].The gas viscosity μgis 0.014cp,and it is estimated using Carr-Kobayashi-Burrow Correlation[73].Table 1 summarizes the NGH parameters from the site SH7 of GMGS-1 and GMGS-3 in the Shenhu area[72].

Table 1 NGH reservoir Parameters used for the study[72].

4.1.Proppant sizing and permeability estimation

Table 2 shows an estimated particle size distribution of the NGH sediments located in the Shenhu field[33].The maximum formation particle size from all three intervals is 29 μm,which is characterized as formation fines(＜44 μm).Estimation of the following:(a)minimum allowable proppant size,Dminp(μm),(b)maximum allowable proppant size,Dmaxp(μm),(c)average median diameter of proppant,D50(μm),(d)the sorting term P,and(e)the proppant or fracture permeability are based on the formation particle size distribution of the hydrate-bearing layer in the interval“a.”Based on the steps outlined in Equation(37)to Equation(43),the average median diameter of proppant(D50)is estimated as 54.38 μm(0.00214 inch),the maximum allowable proppant size,Dmaxpis 91 μm(～0.004 inch),the minimum proppant size is 32.5 μm(～0.0013 inch),and the proppant or fracture permeability estimation is 1187.The estimated variables from this study are shown in Table 3.

4.2.Productivity of frac-pack well with a vertical fracture

Table 4 shows a complete summary of the parameters used in estimating the productivity of a Frac-pack NGH well with a vertical fracture in the Shenhu area.An assumed 50,000 Ibm of proppant mass pumped during the fracture treatment resulted in a proppedvolume of 504 ft3.Based on the Unified Fracture design methodology[41,46],the optimum fracture propped width is estimated as 1.361 inch,the optimum fracture length(Xf)is estimated as 32 ft,and lastly,a gas production rate of 14.9 MMScf/d is obtained using Equation(8),under pseudo steady-state flow condition.

Table 2 Reservoir properties of three intervals in the Shenhu field[33].

4.3.Productivity of frac-pack well with a horizontal fracture

Table 5 shows a summary of the parameters used in estimating the productivity of a Frac-pack NGH well with a horizontal fracture in the Shenhu area.An assumption is made with the fracture-tip pressure equivalent to the minimum formation stress(in the vertical direction).Estimating the vertical stress(= fracture tip pressure)yields 2345 psi at the mid-zone depth of 4,415 ft.The vertical stress or fracture tip pressure is calculated based on a pressure gradient of 0.456 psi/ft above the mud line and an overburden stress gradient of 1.0 psi/ft below the mud line.The same propped volume of 504 ft3(used for the Frac-Pack NGH well with a vertical fracture)is used during the treatment operation,which gives a resultant fracture radius of 111 ft.The estimated gas production rate using Equation(17)yields 5.621 MMscf/d.

4.4.The productivity of cased-hole gravel-packed well

The optimal perforation parameters in Table 6,are assumed to minimize gravel pack skin factor.The estimated gas productionrate,Qg,using the conventional gas productivity model shown in Equation(36),under pseudo steady flow condition gave a value of 11.47 MMscf/d.Table 7 shows a summary of the parameters used in estimating the productivity of a cased hole gravel pack well in the Shenhu NGH reservoir.

Table 3 Estimated proppant size and permeability from study.

Table 4 Summary parameters for well productivity estimation.

Table 5 Summary parameters for estimation of well Productivity.

5.Sensitivity analysis

A sensitivity analysis was conducted to determine influencing parameters affecting the productivity of Frac-pack NGH well based on the parameters shown in Tables 4 and 5

Table 6 Summary of parameters used for well productivity estimation.

Table 7 Summary of perforation parameters used for study.

5.1.Effect of proppant mass on frac-pack well productivity

The influence of proppant mass(Ibm)and proppant volume on a Frac pack NGH well(Both Frac-pack well with horizontal and vertical fracture)is determined by varying the proppant mass.Fig.2 and Fig.3 show the effect of proppant mass(Ibm)on well productivity.Both figures show that well productivity is improved slightly with the increase in proppant mass(Ibm)for the Frac-pack NGH well with a vertical fracture and horizontal fracture,respectively.However,for a frac-pack well with a horizontal fracture,an increase in proppant mass(Ibm)above 100,000 Ibm creates a lesser improvement in productivity.

5.2.Effect of fracture permeability on frac-pack well productivity

The sensitivity analysis on fracture permeability's impact on well productivity for the Frac-Pack NGH well with a vertical fractureand a horizontal fracture are displayed in Fig.4 and Fig.5,respectively.The frac-pack NGH well with a vertical fracture case shows that the well productivity increases linearly with an increase in fracture permeability.However,it is essential to note that the fracture permeability is a function of the proppant size distribution,which is sized based on the formation particle size distribution.The Frac-pack NGH well horizontal fracture case indicates that the well productivity increases nonlinearly with fracture permeability,but at larger values of fracture permeability,Kf,the well productivity plateaus.That means when the fracture permeability exceeds a threshold value of 50,000 md,the well productivity tends to flatten out.

6.Discussion

An assessment study was conducted on the productivity of a frac-packed natural gas hydrate well with a vertical hydraulic fracture,a frac-pack NGH well with a horizontal fracture,and a cased hole gravel pack well in a class 1G NGH reservoir located in the Shenhu area,South China Sea,China,under pseudo-steady state flow condition.The productivity ratio between the fracpacked well and cased-hole gravel pack well might be used as a reference to select well completion types in a marine class 1G gas hydrate reservoir with clayey silt lithology.The productivity ratio benchmark for well completion selection types will help minimize the uncertainties associated with the well productivity models’assumptions.

The assumption of a single-phase of gas flow during the gas recovery process from the Class 1 G hydrate reservoir is based on the free gas present in the hydrate-bearing zone(i.e.,the hydratebearing layer contains free gas plus hydrate)and the underlying free gas layer beneath the hydrate-bearing area.

The frac-pack NGH well(vertical hydraulic fracture)productivity was estimated using the Unified Fracture Design method developed by Economides et al.[41,46].The estimated productivity for this case was 14.89 MMscf/d.Whereas,For the frac-packed NGH well with a horizontal fracture,the modified Shan et al.’s[40]model was used,which gave an estimated production rate of 5.62 MMscf/d.Also,using conventional gas well productivity models found in most standard petroleum engineering textbooks for the case of a cased-hole gravel pack well in the Shenhu NGH reservoir,a gas production rate of 11.35 MMscf/d was obtained.It is crucial to note that the lower productivity obtained from the frac-packed well with a horizontal fracture compared to the cased hole gravel pack well is due to a converging horizontal flow,which creates a choking effect wellbore flow area.That is,the wellbore flow area is the limiting factor.Therefore,the decision to carry out a fracpacking or conventional gravel packing depends on the fracpacked wells' productivity ratio to the case-hole gravel pack well,and this is also further dependent on the orientation of the minimum formation stress.From the study,we anticipate that designing for frac-packing might be the preferred choice for a case where the vertical stress is the maximum(i.e.,minimum formation stress is in the horizontal direction).In contrast,for a case where the vertical stress is the least(i.e.,minimum formation stress is in the vertical direction),designing for a cased-hole gravel pack well system should be considered since preparing for frac-packing(fracture orientation is horizontal)for this case might give lower well productivity compared to a cased-hole gravel pack well.

Overall,the well productivity models'applicability for this study is limited to only Class 1G marine gas hydrate reservoir where the gas hydrate has dissociated into gas and water.

7.Conclusions

In this study,the productivity of frac-packed wells(with vertical hydraulic fracture and horizontal hydraulic fracture)and casedhole gravel-packed wells in a Class 1G NGH reservoir are assessed using the data from the NGH accumulations in the Shenhu area of the Northern South China Sea.The gas hydrate resource in this location is Class 1G because a free gas bearing section underlies it,and owing to this,the free gas will be produced before the dissociated gas in the hydrate-bearing area via depressurization.The Unified Fracture Design methodology proposed by Economides et al.[41]was used to estimate fracture geometry for the fracpacked well with a vertical hydraulic fracture.An existing fracpack well productivity model was modified to account for flow across all reservoir sections(fractured and un-frac areas).The size distribution of formation particles was used to design proppant size requirements and as well as to estimate fracture permeability.Sensitivity analysis was conducted to investigate parameters affecting well productivity.The following conclusions are drawn:

(1)The productivity of a frac-packed well with a horizontal fracture increases nonlinearly with fracture permeability;however,the increasing trend levels off above a value of 50,000md.Thus,further increasing fracture permeability will not significantly improve well productivity.This is explained as the result of the choking effect near the wellbore.

(2)The well productivity of a frac-packed well with vertical hydraulic fracture increases nonlinearly with fracture permeability.The increasing trend does not level off,indicating a preferable behavior of the well type.

(3)Productivity of both types of frac-packed wells(horizontal and vertical fracture)increases with proppant mass;however,proppant mass has a more significant effect on the fracpacked well with vertical fracture than the frac-packed well with a horizontal fracture.

(4)Case studies show that,with a proppant mass of 50,000 lbm and a corresponding proppant volume of 504 ft3,gas production rates of 14.89 MMscf/d,5.621 MMscf/d,and 11.35 MMscf/d can be achieved using frac-packed well with vertical fracture,frac-packed well with horizontal fracture,and gravel-packed well,respectively.These numbers are not considered accurate due to the assumption of single-phase gas flow.Their ratios(14.89/11.35 = 1.3,5.621/11.35 = 0.5)can be used as references for well-type selection for marine Class 1G NGH reservoirs with clayey silt lithology,especially for those in the Shenhu Area of South China Sea,China.

Declaration of competing interest

The authors(Ellis Ekhator and Boyun Guo)declare no conflict of interest.

Abbreviations

[56]S.Locke,An advanced method for predicting the productivity ratio of a perforated well,J.Petrol.Technol.33(1981)2481-2488,https://doi.org/10.2118/8804-PA.

[57]J.Bellarby,Well Completion Design,Elsevier,2009.

[58]M.Golan,C.H.Whitson,Well Performance,second ed.,Prentice Hall Inc.,Englewood Cliffs:New Jersey,U.S.A,1991,p.315.

[59]P.Li,J.G.Deng,W.L.Zhao,J.Y.Zhao,The optimization of sand control completion in bohai bay,Petrol.Sci.Technol.30(2012)1704-1714,https://doi.org/10.1080/10916466.2010.535084.

[60]C.J.Coberly,E.M.Wagner,Some considerations in the selection and installation of gravel pack for oil wells,Petrol.Tech.1(1938)1-20,https://doi.org/10.2118/938080-G.

[61]Hill,K.E.Factors Affecting the Use of Gravel in Oil Wells 1941.

[62]L.E.Buzarde Jr.,R.L.Karl,B.W.T.,Lecture Notes for:Production Operations Course 1:Well Completions,SPE of AIME,Dallas.,1982.

[63]G.P.Maly,R.F.Krueger,Improper formation sampling leads to improper selection of gravel size,J.Petrol.Technol.23(1971)1403-1408,https://doi.org/10.2118/3041-PA.

[64]D.H.Schwartz,Successful sand control design for high rate oil and water wells,J.Petrol.Technol.21(1969)1193-1198,https://doi.org/10.2118/2330-PA.

[65]R.J.Saucier,Considerations in gravel pack design,J.Petrol.Technol.26(1974)205-212,https://doi.org/10.2118/4030-PA.

[66]Jennings Jr.,A.R.Laboratory,Studies of fines movement in gravel packs,SPE Drill.Complet.12(1997)275-281,https://doi.org/10.2118/36420-PA.

[67]W.C.Krumbein,G.D.Monk,Permeability as a function of the size parameters of unconsolidated sand,Trans.AIME 151(1943)153-163,https://doi.org/10.2118/943153-G.

[68]D.C.Beard,P.K.Weyl,Influence of texture on porosity and permeability of unconsolidated Sand1,Am.Assoc.Petrol.Geol.Bull.57(1973)349-369,https://doi.org/10.1306/819A4272-16C5-11D7-8645000102C1865D.

[69]J.P.Van Baaren,Quick-look permeability estimates using sidewall samples and porosity logs,in:Proceedings of the 6th Annual European Logging Symposium Transactions,Society of Professional Well Log Analysts.,1979.

[70]P.H.Nelson,Permeability-porosity relationships in sedimentary rocks,Log.Anal.35(1994)38-62.

[71]N.R.Morrow,J.D.Huppler,A.B.Simmons,Porosity and permeability of unconsolidated,upper miocene sands from grain-size analysis,J.Sediment.Petrol.39(1969)312-321,https://doi.org/10.1306/74D71C3F-2B21-11D7-8648000102C1865D.

[72]M.Su,R.Yang,N.Y.Wu,Structural characteristics in the Shenhu Area,northern continental slope of South China Sea,and their influence on gas hydrate,Acta Geol.Sin.88(2014)318-326.

[73]B.Guo,X.Liu,X.Tan,Petroleum Production Engineering,2017.