fluid flow in hydraulically fractured wells

Fluid flow in hydraulically fractured wells

Many wells, particularly gas wells in lowpermeability formations require hydraulic fracturing (/Hydraulic_fracturing) to be commercially viable. Interpretation of pressuretransientdata (/Pressure_transient_testing) in hydraulically fractured wells is important for evaluating the success of fracture treatments and predicting the future performance of fracturedwells (/Postfracture_well_behavior). This page includes graphical techniques for analyzing postfracture pressure transient tests (/Pressure_transient_testing) after identifying severalflow patterns that are characteristic of hydraulically fractured wells. Often, identification of specific flow patterns can aid in well test analysis.

Contents

1 Flow patterns in hydraulically fractured wells1.1 Example 1: Estimating duration of flow periods in a hydraulically fractured well

2 Flow geometry and depth of investigation of a vertically fractured well3 Fracture damage4 Specialized methods for postfracture welltest analysis

4.1 Bilinear flow method4.2 Linear flow method4.3 Pseudoradial flow method

5 Using type curves for hydraulically fractured wells5.1 Procedures for analyzing fractured wells with type curves5.2 Type curves used for analysis in fractured wells

5.2.1 Chokedfracture type curve5.2.2 Wellborestorage type curve

6 Limitations of typecurve analysis7 Nomenclature8 References9 Noteworthy papers in OnePetro10 External links11 See also

Flow patterns in hydraulically fractured wells

Five distinct flow patterns (Fig. 1) occur in the fracture and formation around a hydraulically fractured well.[1] Successive flow patterns, which often are separated by transitionperiods, include fracture linear, bilinear, formation linear, elliptical, and pseudoradial flow. Fracture linear flow (Fig. 1a) is very shortlived and may be masked by wellborestorageeffects. During this flow period, most of the fluid entering the wellbore comes from fluid expansion in the fracture, and the flow pattern is essentially linear.

(/File%3AVol5_Page_0786_Image_0001.png)

Fig. 1 Flow periods in a vertically fracturedwell.[1]

Because of its extremely short duration, the fracture linear flow period often is of no practical use in well test analysis. The duration of the fracture linear flow period is estimatedby[1]

(/File%3AVol5_page_0785_eq_001.png)....................(1)

where tLfD is dimensionless time in terms of fracture halflength,


The dimensionless fracture conductivity, Cr, is


and ηfD is dimensionless hydraulic diffusivity defined by

http://petrowiki.org/Hydraulic_fracturing

http://petrowiki.org/Pressure_transient_testing

http://petrowiki.org/Post-fracture_well_behavior

http://petrowiki.org/Pressure_transient_testing

http://petrowiki.org/File%3AVol5_Page_0786_Image_0001.png

http://petrowiki.org/File%3AVol5_page_0785_eq_001.png




Bilinear flow (Fig. 1b) evolves only in finiteconductivity fractures as fluid in the surrounding formation flows linearly into the fracture and before fracture tip effects begin toinfluence well behavior. Fractures are considered to be finite conductivity when Cr < 100. Most of the fluid entering the wellbore during this flow period comes from the formation.

During the bilinear flow period, BHP, pwf, is a linear function of t1/4 on Cartesian coordinates.

A loglog plot of (pi – pwf) as a function of time exhibits a slope of 1/4 unless the fracture is damaged. The pressure derivative also has a slope of 1/4 during this same time period.

The duration of bilinear flow depends on dimensionless fracture conductivity and is given by Eqs. 5a through 5c[1] for a range of dimensionless times and fracture conductivities:

(/File%3AVol5_page_0786_eq_001.png)....................(5a)

(/File%3AVol5_page_0786_eq_002.png)....................(5b)

and (/File%3AVol5_page_0786_eq_003.png)....................(5c)

Formation linear flow (Fig. 1c) occurs only in highconductivity (Cr ≥ 100) fractures. This period continues to a dimensionless time of tLfD ≅ 0.016. The transition from fracture

linear flow to formation linear flow is complete by a time of tLfD = 10–4 . On Cartesian coordinates, p wf is a linear function of t 1/2 , and a loglog plot of (pi – pwf) has a slope of 1/2unless the fracture is damaged. The pressure derivative plot exhibits a slope of 1/2. Elliptical flow (Fig. 1d) is a transitional flow period that occurs between a linear or nearlinearflow pattern at early times and a radial or near—radial flow pattern at late times.

Pseudoradial flow (Fig. 1e) occurs with fractures of all conductivities. After a sufficiently long flow period, the fracture appears to the reservoir as an expanded wellbore (consistentwith the effective wellbore radius concept suggested by Prats et al.[2]). At this time, the drainage pattern can be considered as a circle for practical purposes. (The larger the fractureconductivity, the later the development of an essentially radial drainage pattern.) If the fracture length is large relative to the drainage area, then boundary effects distort or entirelymask the pseudoradial flow regime. Pseudoradial flow begins at tLfD ≅ 3 for highconductivity fractures (Cr ≥ 100) and at slightly smaller values of tLfD for lower values of Cr.

These flow patterns also appear in pressurebuildup tests and occur at approximately the same dimensionless times as in flow tests. The physical interpretation is that the pressure hasbuilt up to an essentially uniform value throughout a particular region at a given time during a buildup test. For example, at a given time during bilinear or formation linear flow,pressure has built up to a uniform level throughout an approximately rectangular region around the fracture. At a later time during elliptical flow, pressure has built up to a uniformlevel throughout an approximately elliptical region centered at the wellbore. At a given time during pseudoradial flow, pressure has built up to a uniform level throughout anapproximately circular region centered at the wellbore. The area of the region and the pressure level within that area increase with increasing shutin time. Example 1 illustrates howto estimate the duration of flow periods for hydraulically fractured wells.

Example 1: Estimating duration of flow periods in a hydraulically fractured well

For each case, estimate the end of the linear flow period and the time at which pseudoradial flow period begins. Assume that pseudoradial flow begins when tLfD = 3. Table 1 givesthe data for each case.


Table 1

Solution. The end of the linear flow regime occurs at a dimensionless time of tLfD ≅ 0.016 or, using Eq. 2,

(/File%3AVol5_page_0787_eq_001.png)

Similarly, the time to reach pseudoradial flow is tLfD ≅ 3, or

(/File%3AVol5_page_0787_eq_002.png)

Table 1 summarizes the results.








Flow geometry and depth of investigation of a vertically fractured well

Fluid flow in a vertically fractured well has been described using elliptical geometry. [3] The equation for an ellipse with its major axis along the xaxis and minor axis along the yaxis is


where the endpoints of the major and minor axes are (±af, 0) and (0, ±bf), respectively. The foci of the ellipse are ±cf where cf2 = af2 – bf2. In terms of a well with a single vertical

fracture with two wings of equal length, Lf, the relation becomes Lf2 = af2 – bf2, where Lf is the focal length of the ellipse. Fig. 8.76 shows the elliptical geometry of a verticallyfractured well.


Fig. 2 – Elliptical flow pattern around a verticallyfractured well.

Hale and Evers[3] defined a depth of investigation for a vertically fractured well. Their definition is based on a definition of dimensionless time at a distance bf, the length of theminor axis:


Solving for the length of the minor axis,


Assuming that pseudosteadystate flow exists out to distance, bf, at dimensionless time tbD = 1/π as in linear systems, Eq. 8 becomes


which represents the depth of investigation in a direction perpendicular to the fracture at time, t, for a vertically fractured well. In gas wells, the terms μ and ct should be (/File%3AVol5_page_0789_inline_001.png) and (/File%3AVol5_page_0789_inline_002.png), evaluated at average drainagearea pressure, (/File%3AVol5_page_0781_inline_001.png).

The elliptical pattern of the propagating pressure transient can be fully described in terms of the lengths of the major axis, af, the minor axis, bf, and the focus, Lf. Using the estimateof bf from Eq. 9 and an estimate of Lf obtained by one of the methods described in sections that follow, the length of the major axis can be estimated from


Given values of af and bf, the depth of investigation at a particular time, t, in any direction from the fracture can be calculated using Eq. 6. Furthermore, the area, A, enclosed by theellipse at time, t (the area of the reservoir sampled by the pressure transient), is given by


The coefficient 0.0002878 in Eq. 9 is strictly correct only for highly conductive fractures (Cr ≥ 100). As Cr becomes smaller, the ratio af/bf also becomes smaller. The lower bound ofaf/bf is 1 (a circle) as Cr approaches 0.

Fracture damage

Two major types of fracture damage are frequent: choked fracture damage and fractureface damage. The chokedfracture damage means that the fracture has a reduced permeabilityin the immediate vicinity of the wellbore (Fig. 3). In this case, kf is used for the permeability in the propped portion of the fracture farther along the wellbore, and kfs for reducedpermeability near the wellbore, out to a length, Ls, in the fracture.






http://petrowiki.org/File%3AVol5_page_0789_inline_001.png






Fig. 3 – Permeability differs between propped andnearwellbore portions of fracture.

The chokedfracture skin factor, sf, is[4]


Fracture face damage in a hydraulically fractured well (Fig. 4) is a permeability reduction around the edges of the fracture, usually caused by invasion of the fracture fluid into theformation or an adverse reaction with the fracturing fluid. The equation for fracture face skin is[4]



Fig. 4 – Permeability reduction around edges offracture represents fracture face damage.

Specialized methods for postfracture welltest analysis

Generally, the objectives of postfracture pressuretransient test analysis are to assess the success of the fracture treatment and to estimate:

The fracture halflengthFracture conductivityFormation permeability

Three specialized methods of analyzing these postfracture transient tests are included here:

Pseudoradial flowBilinear flowLinear flow

Bilinear flow method

The bilinear flow method[5] applies to test data obtained during the bilinear flow regime in wells with finiteconductivity vertical fractures. Bilinear flow is indicated by a quarterslope line on a loglog graph of pressure derivative vs. t or Δte.

During bilinear flow,


and (/File%3AVol5_page_0790_eq_002.png)....................(15)







The following procedure is recommended for analyzing test data obtained in the bilinear flow regime (that is, data in the time range with quarter slope on the diagnostic plot). In Step1, note the use of "bilinear equivalent time," ΔtBe. Radial equivalent time is rigorously correct as a plotting function only for infiniteacting radial flow.

1. For a constantrate flow test, plot pwf vs. t1/4 on Cartesian coordinates. For a buildup test, plot pws vs. ΔtBe1/4, where


2. Determine the slope, mB, of the straight line region of the plot.3. Determine the pressure extrapolated to time zero, po, and the fracture skin, sf, from


for drawdown and buildup tests, respectively.

4. From independent knowledge of k (for example, from a prefracture well test), estimate the fracture conductivity, wfkf, using mB and the relationship


where (/File%3AVol5_page_0789_inline_001.png) and (/File%3AVol5_page_0789_inline_002.png), evaluated at (/File%3AVol5_page_0781_inline_001.png),are used for a gas well test.

Fig. 5 is an example of bilinear flow analysis. The bilinear flow analysis method has the following important limitations.

No estimate of fracture halflength, Lf.In wells with lowconductivity fractures, wellbore storage frequently distorts early test data for a sufficient length of time so that the quarterslope line characteristic of bilinearflow may not appear on a loglog plot of test data.An independent estimate of k is required. This suggests that prefracture well tests should be conducted before fracturing the well, thus obtaining independent estimates offormation properties.


Fig. 5 – Bilinear flow analysis.

Linear flow method

The linear flow method[5] applies to test data obtained during formation linear flow in wells with highconductivity fractures (Cr ≥ 100). After wellbore storage effects have ended,formation linear flow occurs up to a dimensionless time of tLfD = 0.016, which means that a loglog plot of pressure derivative against time will have a slope of onehalf. The plot ofpressure change vs. time, however, will have a halfslope only if the fracture skin is zero. The pressure and pressure derivative are


and (/File%3AVol5_page_0791_eq_002.png)....................(20)

so that


which indicates that a loglog plot of the derivative against time will have a slope of onehalf. Radial equivalent time applies rigorously only for radial flow in an infiniteactingreservoir. When linear flow is the flow pattern occurring at both times (tp + Δt) and Δt, a more useful equivalent time function is the linear equivalent time, ΔteL.


Test conditions in which linear flow occurs at both (tp + Δt) and Δt are rare, and, consequently, Eq. 22 is not necessarily rigorously correct for welltest analysis. Fortunately, when tp>> Δtmax, ΔteL ≈ Δt. Fig. 6 is an example of a plot used in linear flow analysis.












The linear flow analysis method also has limitations.

The method applies only for fractures with high conductivities. Strictly speaking, linear flow occurs for the condition of uniform flux into a fracture (same flow rate from theformation per unit crosssectional area of the fracture at all points along the fracture) rather than for infinite fracture conductivity. Therefore, only very early test data (tLf D ≤0.016) exhibit linear flow in a highconductivity fracture.Some or all of these early data may be distorted by wellbore storage, further limiting the amount of linearflow data available for analysis.Estimating fracture halflength requires an independent estimate of permeability, k, which suggests the need for a prefracture well test.


Fig. 6 – Plot used in linear flow analysis.

Pseudoradial flow method

The pseudoradial flow method applies when a short, highly conductive fracture is created in a highpermeability formation, so that pseudoradial flow develops in a short time. Thetime required to achieve pseudoradial flow for an infinitely conductive fracture (Cr ≥ 100) in either a flow test or a pressure buildup test is estimated by


The beginning of pseudoradial flow is characterized by the flattening of the pressure derivative on a loglog plot and by the start of a straight line on a semilog plot. Hence, when thepseudoradial flow regime is reached, conventional semilog analysis can be used to calculate permeability and skin factor. For a highly conductive fracture, skin factor is related tofracture halflength by[2]


Fig. 7 shows an example.


Fig. 7 – Pseudoradial flow analysis.

A recommended procedure for analyzing test data from the pseudoradial flow regime is as follows.

For a drawdown test, plot pwf vs. log t. For a buildup test, plot pws vs. the Horner time ratio (HTR).Determine the position and slope, m, of the semilog straight line and the intercept, p1hr on the line.Using m, calculate values of k and s (or s′ for a gas well).Calculate the fracture halflength, Lf, using Eq. 24.

The pseudoradial flow method has the following limitations that seldom make it applicable in practice. [5]

The conditions that are most favorable for the occurrence of pseudoradial flow are short, highly conductive fractures in highpermeability formations. These formations,however, are rarely fractured. The most common application of hydraulic fractures—wells with long fractures in lowpermeability formations—require impractically long testtimes to reach pseudoradial flow.For gas wells, the apparent skin factor, s′, calculated from test data is often affected by nonDarcy flow.The pseudoradial method applies only to highly conductive (Cr ≥ 100) fractures. For lower conductivity fractures, fracture lengths calculated using the skin factor (Eq. 24) willbe too low.

Using type curves for hydraulically fractured wells





Type curves (/Type_curves) are the most common method of analyzing hydraulically fractured wells. The independent variable for most type curves for analyzing hydraulicallyfractured wells is the dimensionless time based on hydraulic fracture halflength, tLf D. The dependent variable is usually the dimensionless pressure, pD.

For type curves used for manual typecurve matching, most vary only one parameter. The Cinco type curve[1] is obtained for zero CLf D and sf ; the only parameter is dimensionlessfracture conductivity, Cr or FcD (where FcD = πcr). The chokedfracture skin is analyzed by assuming CLf D and infinite Cr with single parameter sf. The wellborestorage type

curve[6] sets sf to 0 and Cr (FcD) to infinity and varies the coefficient CLf D.

When using type curves in commercial software, the computer can set any two of the three parameters to fixed values (other than their limiting values) and vary the third parameter toobtain the matching stems.

Procedures for analyzing fractured wells with type curves

The following steps outline the procedure for analyzing fractured wells with type curves.

Graph field data pressure change and pressure derivatives.Match field data to the appropriate type curve.Find the match point and matching stem.Calculate the formation permeability from the pressure match point.Calculate Lf from the time match point.Interpret the matching stem value appropriate for a given type curve. For one type curve, this can be wfkf, which will provide an estimate of fracture conductivity. For another,it can be sf, the chokedfracture skin, or, for a third, it can be C, the wellborestorage coefficient.

To interpret the match points for a test with unknown permeability, use Eqs. 25 and 26. The formation permeability, k, is determined from the pressure match point; that is, therelationship between the pressure derivative and pressure change found at a match point given by


From the time match point, calculate the fracture halflength:


Matching can be ambiguous for hydraulically fractured wells; the data can appear to match equally well in several different positions. The ambiguity can be reduced or eliminated if aprefracture permeability is determined, and the postfracture test data forced to match the permeability.

Type curves used for analysis in fractured wells

The Cinco type curve (Fig. 8), [1] assumes that CLf D = 0 and sf = 0. The typecurve stems on this curve are obtained by varying values of Cr or FcD. With the Cinco type curve, thefracture conductivity, wfkf, can be determined from the matching parameter:


Chokedfracture type curve

Fig. 9 shows the chokedfracture type curve. [4] The chokedfracture type curve is generated with wellborestorage coefficient, CLf D, of zero and infinite fracture conductivity, Cr.On this type curve, the stems represent different values of the fracture skin, sf. The fracture skin, sf, can be used to find the additional pressure drop from


Wellborestorage type curve

The wellborestorage type curve (Fig. 10) takes into account the possibility of wellbore storage. The wellborestorage type assumes sf = 0 and Cr = ∞. To interpret a bestfitting stemfor this type curve, use the following:


http://petrowiki.org/Type_curves







Fig. 8 – Cinco type curve.


Fig. 9 – Chokedfracture type curve.


Fig. 10 – Wellborestorage type curve.

Limitations of typecurve analysis

Although it is the most common methodology for analyzing hydraulically fractured well, typecurve analysis still has some limitations.

First, typecurves for analysis of hydraulically fractured wells are usually based on solutions for constantrate drawdown tests. For buildup tests, shutin time itself may possibly beused as a plotting function in those cases in which producing time is much greater than the shutin time. Equivalent time can be used in some cases, but equivalent time has differentdefinitions depending on the flow regime: radial, linear, and bilinear flow. Another possibility is to use a "superposition" type curve, which depends on the specific durations of flowand buildup periods. Superposition type curves can be readily generated with computer software.

Another problem with type curves is that they may ignore important behavior. The type curve that takes into account wellbore storage does not consider a variable wellbore storagecoefficient. This can be caused by phase redistribution in the wellbore, for example. The widely available type curves that have been discussed do not include boundary effects. Withgas wells, the probability of nonDarcy flow is high, but available type curves don’t take this into account.

An independent estimate of permeability may also be needed. A number of different type curves or a variety of stems on a given type curve may seem to match test data equally well.To remove this ambiguity, the best solution is to have an independent estimate of permeability.

Nomenclature

a = (/File%3AVol5_page_0879_inline_001.png), stabilized deliverability coefficient, psia2

cp/MMscfDa = total length of reservoir perpendicular to wellbore, ftah = length of reservoir perpendicular to horizontal well, ft

af = (/File%3AVol5_page_0879_inline_002.png), depth of investigation along major axis in fractured well, ft

at = (/File%3AVol5_page_0879_inline_002.png), transient deliverability coefficient, psia2cp/MMscfD

A = drainage area, sq ftA = πafbf , area of investigation in fractured well, ft2

Af = crosssectional area perpendicular to flow, sq ftAwb = wellbore area, sq ft

b = (/File%3AVol5_page_0880_inline_001.png) (gas flow equation)

bf = (/File%3AVol5_page_0880_inline_002.png), depth of investigation of along minor axis in fractured well, ft

B = formation volume factor, res vol/surface volcf = formation compressibility, psi–1

ct = Soco + Swcw + Sgcg + cf = total compressibility, psi–1

CLfD = 0.8936 (/File%3AVol5_page_0880_inline_004.png), dimensionless wellbore storage coefficient in fractured wellCr = wfkf/πkLf, fracture conductivity, dimensionlessD = nonDarcy flow constant, D/MscfEf = flow efficiency, dimensionlesshD = (h/rw)(kh/kv)1/2, dimensionlesshf = fracture height, fthp = perforated interval thickness, fthpD = hp/htht = total formation thickness, ftk = matrix permeability, md

(/File%3AVol5_page_0800_inline_001.png) = average permeability, md

kf = permeability of the proppant in the fracture, mdL = distance from well to noflow boundary, ftLf = fracture half length, ft











Ls = length of damaged zone in fracture, ftpf = formation pressure, psipi = original reservoir pressure, psips = stabilized shutin BHP measured just before start of a deliverability test, psiapt = surface pressure in tubing, psipwf = flowing BHP, psipws = shutin BHP, psipD = 0.00708 kh(pi – p)/qBμ, dimensionless pressure as defined for constantrate productionq = flow rate at surface, STB/Dqw = water flow rate, STB/Dr = distance from the center of wellbore, ftrp = radius of perforation tunnel, ftrs = outer radius of the altered zone, ftrsp = radius of source or inner boundary of spherical flow pattern, ftrw = wellbore radius, ftrD = r/rw, dimensionless radiussf = skin of hydraulically fractured well, dimensionlesstbD = dimensionless time in linear flow, hourstLfD = 0.0002637 kt/ϕμetLf2, dimensionless time for fractured wellstp = constantrate production period, t, hoursT = reservoir temperature, °Ru = dummy variableV = volume, bblVf = fraction of bulk volume occupied by fractureswf = fracture width, ftwkf = fracture conductivity, mdftws = width of damaged zone around fracture face, ftΔp = pressure change since start of transient test, psiΔt = time elapsed since start of test, hoursΔta = (/File%3AVol5_page_0884_inline_001.png), normalized or adjusted pseudotime, hours

Δtap = (/File%3AVol5_page_0884_inline_002.png), pseudotime, hrpsia/cp

ΔtBe = bilinear equivalent time, hoursΔte = radial equivalent time, hoursΔtLe = linear equivalent time, hours

η = 0.0002637 k/ϕμct, hydraulic diffusivity, ft2/hrηfD = hydraulic diffusivity, dimensionlessλ = interporosity flow coefficient

λt = (/File%3AVol5_page_0885_inline_001.png), total mobility, md/cp

α = exponent in deliverability equationα = parameter characteristic of system geometry in dualporosity systemμ = viscosity, cpμw = water viscosity, cp

(/File%3AVol5_page_0844_inline_002.png)= gas viscosity evaluated at average pressure, cp

ϕf = fraction of fracture volume occupied by pore space, ≅ 1ϕ = porosity, dimensionless

References

1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 CincoLey, H. and SamaniegoV., F. 1981. Transient Pressure Analysis for Fractured Wells. J Pet Technol 33 (9): 17491766. SPE7490PA.http://dx.doi.org/10.2118/7490PA (http://dx.doi.org/10.2118/7490PA)

2. ↑ 2.0 2.1 Prats, M., Hazebroek, P., and Strickler, W.R. 1962. Effect of Vertical Fractures on Reservoir BehaviorCompressibleFluid Case. SPE J. 2 (2): 8794.http://dx.doi.org/10.2118/98PA (http://dx.doi.org/10.2118/98PA)

3. ↑ 3.0 3.1 Hale, B.W. and Evers, J.F. 1981. Elliptical Flow Equations for Vertically Fractured Gas Wells. J Pet Technol 33 (12): 2489–2497. SPE8943PA.http://dx.doi.org/10.2118/8943PA (http://dx.doi.org/10.2118/8943PA)

4. ↑ 4.0 4.1 4.2 CincoLey, H. and SamaniegoV., F. 1981. Transient Pressure Analysis: Finite Conductivity Fracture Versus Damaged Fracture Case. Presented at the SPE AnnualTechnical Conference and Exhibition, San Antonio, Texas, 4–7 October. SPE10179MS. http://dx.doi.org/10.2118/10179MS (http://dx.doi.org/10.2118/10179MS)

5. ↑ 5.0 5.1 5.2 Lee, W.J. 1989. Postfracture Formation Evaluation. In Recent Advances in Hydraulic Fracturing, J.L. Gidley, S.A. Holditch, D.E. Nierode, and R.W. Veatch Jr.eds., Vol. 12. Richardson, Texas: Monograph Series, SPE.

6. ↑ Ramey, H.J. Jr. and Gringarten, A.C. 1975. Effect of High Volume Vertical Fractures on Geothermal Steam Well Behavior. Proc., Second United Nations Symposium on theUse and Development of Geothermal Energy, San Francisco.





http://dx.doi.org/10.2118/7490-PA



http://dx.doi.org/10.2118/10179-MS

Noteworthy papers in OnePetro

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See also

Fluid flow through permeable media (/Fluid_flow_through_permeable_media)

Type curves (/Type_curves)

Hydraulic fracturing (/Hydraulic_fracturing)

Hydraulic fracturing in tight gas reservoirs (/Hydraulic_fracturing_in_tight_gas_reservoirs)

PEH:Fluid_Flow_Through_Permeable_Media (/PEH%3AFluid_Flow_Through_Permeable_Media)

Category (/Special%3ACategories): 5.3 Reservoir fluid dynamics (/Category%3A5.3_Reservoir_fluid_dynamics)

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