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Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests

Cong  Wang, Yushu Wu

 

Colorado School of Mines, United States

Abstract

 

 

Hydraulic fracturing combined with horizontal drilling has been the technology that  makes it possible to economically produce natural gas  from unconventional shale gas  or tight gas  reservoirs. Hydraulic fracturing operations, in  particular, multistage fracturing treatments  along with horizontal wells in unconventional formations create complex fracture geometries or  networks, which are difficult to characterize. The  traditional analysis using a  single vertical or  horizontal fracture concept may be  no  longer applicable. Knowledge of these created fracture properties, such as their spatial distribution, extension and fracture areas, is essential information to evaluate stimulation results. However, there are currently few  effective approaches available for  quantifying hydraulic fractures in  unconventional reservoirs.

 

This  work presents an  unconventional gas  reservoir simulator and its  application to quantify hydraulic fractures in  shale gas  reservoirs using transient pressure data. The  numerical model in- corporates most known physical processes for  gas   production from unconventional reservoirs, including two-phase  flow of  liquid and gas,  Klinkenberg effect, non-Darcy  flow, and nonlinear adsorption. In  addition, the model is  able to handle various types and scales of  fractures or  heterogeneity using continuum, discrete or  hybrid modeling approaches under different well production  conditions of  varying rate  or   pressure. Our   modeling studies indicate that  the  most sensitive parameter  of  hydraulic fractures to early transient  gas   flow through  extremely  low permeability rock is  actually the fracture-matrix contacting area, generated by  fracturing stimulation. Based on  this observation, it is possible to use transient pressure testing data to estimate the area of fractures generated from fracturing operations. We  will  conduct a series of modeling studies and present a methodology using typical transient pressure responses, simulated by the numerical model, to estimate fracture areas created or to quantity hydraulic fractures with traditional well testing technology. The  type curves of pressure transients from this study can be  used to quantify hydraulic fractures in  field application.

1.Introduction

For  the unconventional gas  reservoirs,  hydraulic fractures characterization is  important in  assuring the maximum stimulation efficiency [1-3].  A lot of researches have been carried out on  the flow behavior analysis of vertical wells with finite-conductivity or infinite-conductivity hydraulic fractures. Cinco-Ley  and  Samaniego  summarized  fluids  flow  in   a  hydraulic fractured  well   could  be   divided  into  four periods:  fracture linear flow, bilinear flow, formation linear flow and pseudo-radial  flow [4].

Nobakht and  Clarkson  pointed out that  the dominant flow regime observed in  most fractured tight/shale gas  wells is  the third one,  formation linear flow, which may continue  for several years [5].

Transient  pressure  analysis of this linear flow behavior is  able   to  provide plenty of  useful information,  especially,  the  total  contact area  between  hydraulic fractures and tight matrix. Pseudo-pressure,  a   mathematical  pressure  function  that accounts for the variable compressibility and viscosity of  gas with  respect  to   pressure,  is  widely  used  for  the  transient pressure analysis in conventional gas  reservoirs [6].

 

Compared with  conventional reservoirs,  gas   flow  in   ultra-low  permeability unconventional reservoirs is subject to  more nonlinear, coupled processes,  including nonlinear adsorption/desorption, non-Darcy  flow  (at  both  high  flow  rate  and  low  flow  rate), strong  rockefluid   interaction,   and  rock   deformation within nanopores or  micro-fractures,  coexisting with complex flow geometry and  multi-scaled heterogeneity.  Therefore,  quantifying  flow in  unconventional gas  reservoirs has  been a significant  challenge  and  traditional  REV-based   Darcy    law,    for example, may not be generally applicable. For gas flow in these unconventional  reservoirs,  our  previous work indicates that gas-slippage effect and adsorption/desorption  play  an  important role  to describe the subsurface flow mechanisms, which cannot be  neglected [7]. To the authors' knowledge, these two factors were not considered in  the previous pseudo-pressure derivation.  In this paper,  a new derivation of pseudo-pressure is provided.

 

This  paper presents our  continual efforts in  developing numerical models and  tools for  quantitative  studies of  unconventional  gas   reservoirs  [8,9].   Specifically,  we   explore the possibility of performing well testing analysis using the developed simulator.  The  numerical model is able  to  simulate realistic     processes   of    single-phase   or    two   phase   flow   in unconventional  reservoirs, which  considers  the  Klinkenberg effects and gas  adsorption/desorption. We  use   the numerical model to verify our  new derived pseudo-pressure formulation. We  also  apply it to generate type-curves of transient gas flow in unconventional reservoirs with horizontal well and multistage hydraulic fractures. The  type curves of pressure transients from this study can  be utilized to quantify hydraulic fractures in field application.

2.Derivation of  new pseudo pressure

 

 

In 1965, Al-Hussainy and Ramer derived the pseudo pressure which has  been successfully used to analyze the flow of real gas in the gas  reservoirs.

where P0 is the reference pressure; P is gas pressure; µ is the gas viscosity and Z is gas  pressure Z factor.

 

The  concept of  the  real gas   pseudo-pressure  promises a considerable simplification.  It  brings improvement in  all  phases  of gas  well  aWnalysis and gas  reservoir calculations. These analysis and  calculations in  terms of  pseudo-pressure  work very  well  for  the  conventional  reservoirs  but  meet  some problems when  it is  directly applied  in  the unconventional reservoirs analysis.  This  is  mainly because gas  flow in  ultralow   permeability  unconventional  reservoirs,  different  from the gas   flow  in  conventional reservoirs,  is  subject to more nonlinear, coupled processes, including nonlinear adsorption/desorption, non-Darcy flow, and strong rockefluid interaction, and  rock deformation within  nanopores  or  micro-fractures, coexisting with complex flow geometry and multi-scaled heterogeneity.

Considering the Klinkenberg effects and gas  adsorption, the principle of conversation of mass for isothermal gas flow through a porous media is expressed by the expression:

The pressure-dependent permeability for gas is expressed by Klinkenberg as:

where k is constant, absolute gas-phase permeability in  high pressure (where the Klinkenberg effect is minimized); and b is the Klinkenberg b-factor, accounting for gas-slippage effect.

The mass of adsorbed gas in formation volume, V, is described by Refs. [10,11,7]:

where mg(V) is absorbed gas mass in a volume V, ρK  is rock  bulk density; ρg is  gas   density at   standard  condition; f(P)  is  the adsorption isotherm function. If the adsorbed gas  terms can  be

represented by  the  Langmuir isotherm (Langmuir,  1916), the dependency of  adsorbed gas  volume on  pressure at constant temperature is given below,

where VL  is the gas  content or Langmuir's volume in scf/ton (or standard volume adsorbed per  unit rock  mass); P is reservoir gas pressure; and PL  is Langmuir's pressure, the pressure at which 50% of the gas  is desorbed.

For real  gas,

Substitute Equations (3)-(6) into Equation (2),

From  the definition of the isothermal compressibility of gas:

We  also  define the “compressibility” from the adsorption:

Let the total compressibility:

Equation (7) will be:

Assume the viscosity and gas law deviation factors change slowly with pressure changes; the second part of Equation (11) becomes negligible. Equation (11) becomes:

We define the new pseudo-pressure m(P) as follows:

Equation (2) can be rewritten in terms of variable m(P) using the definition of Ct(P) given by Equations (8)e(10) as

Based  on  Equation (14),  we  could apply this form of  the flow equation, quasi-linear flow equation, to  the analysis of real  gas flow behavior in unconventional reservoirs.

 

 

3.Linear gas  flow

 

 

The  early flow regime observed in  fractured tight/shale gas wells is  linear flow from formation, which may continue  for several years. Sometimes decline curve may indicate outer boundary effects, but no pseudo-radial flow. Wattenbarger et al. gave  the “short-term” approximations for  this linear flow with constant rate production conditions [12];

In  Equation (15),  mD  is  the pseudo pressure; q is  the gas  production rate; B is the gas FVF; ϕ is the formation porosity; ct is the total compressibility, k is  the formation permeability; A is  the hydraulic fracture area; t is the time; and subscript i refers to initial  condition  and  subscript  wf   refers  to  the  wellbore condition.

Equation (15)   indicates that  for  the constant-flowing-rate production condition, linear flow appears as  a straight line  on the plot of normalized pressure vs. the square root of time. The slope of this square-root-of-time plot can be used to estimate the total contact area between hydraulic fracture and the tight matrix.  The  estimation accuracy is  influenced by  initial pressure, formation average permeability and total compressibility [5].

This model is limited by the assumptions of only  one infinite-conductivity hydraulic fracture and the neglect of  gas  adsorption/desorption effect. For the  gas  flow analysis in  unconventional reservoirs, these assumptions are  generally unacceptable. Multi-stage hydraulic fracturing is the key  technology in developing the unconventional shale gas  or  tight gas  reservoirs.  In addition, our  previous work indicates that adsorbed gas  could contribute more than 30% to  the total production in  some unconventional shale gas  reservoirs [7].  For  the above situations, estimations considering the effects of gas adsorption/desorption will be more accurate and it will avoid the overestimation of total

hydraulic fracture area.

One efficient approach to include the adsorption is by adding an “adsorption compressibility” term into the total compressibility. Based on the derived “adsorption compressibility” formulation in Equation (9), the value of adsorption compressibility is calculated below. Table 1 lists the data used in this

calculation and Fig. 1 shows the gas corresponding Z factor value with pressure.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

Fig. 2 is the calculated adsorption compressibility value and this value is in the same magnitude with the rock and fluids total compressibility. These calculation results indicate that when the pressure increases from 2000 psi to 5000 psi, this compressibility drops significantly from 2.7x10-4/psi to 4.29x10-5/psi.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

4.Numerical model

 

 

The   unconventional  oil/gas reservoir  simulator  developed coupled multiphase fluid flow with the effects of  rock  deformation, gas  slippage, non-Darcy flow and chemical reaction of adsorption and desorption processes in  unconventional reservoirs. In  numerical formulation, the  integral finite difference method [13] is used for space discretization of multidimensional fluid and heat flow in porous and fractured reservoirs using an unstructured/structured grid.  Time  is discretized fully  implicitly as  a first-order backward finite difference. Time  and space discretization of mass balance equations results in a set  of coupled non-linear equations, solved fully  implicitly using Newton iteration [7].

 

In our  model, a hybrid-fracture modeling approach, defined as  a combination of explicit-fracture (discrete fracture model), MINC (Multiple Interacting Continua) approach [13]  on  the stimulated zones, and single-porosity modeling approaches on unstimulated areas (Figs. 3 and 4), is used for  modeling a shale gas reservoir with both hydraulic fractures and natural fractures [14-16]. This  is  because hydraulic fractures, which have to  be dealt with for  shale gas  production, are  better handled by  the explicit fracture method. On  the other hand, natural fractured reservoirs are  better modeled by  a  dual-continuum approach, such as MINC for extremely low-permeability matrix in shale gas formations, which cannot be  modeled by  an  explicit fracture model.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

Fig. 4 illustrates the conceptual model including a horizontal well,   multistage  hydraulic fractures and  their  corresponding stimulated reservoir volume (SRV). The stimulated reservoir volume (SRV) is defined as the 3D volume of microseismic-event cloud nearby  the  hydraulic fractures, inside which  complex natural fracture networks are  stimulated. We  apply the method of  MINC  to model this the porous and fractured medium. A single-porosity model is applied in the region outside the SRV. In this  method,  hydraulic  fractures  are    represented  by   grids matching the real  fracture geometric data. Then the properties of the  fractures,  such  as   permeability  and  permeability,   are assigned to the corresponding fracture grids.

 

 

5.  Model applications

 

 

In  this section, we   apply the numerical model to  analyze transient pressure behaviors vs. fracture areas. Here we present a set  of simulation cases to  study the gas  flow characteristics in fractured wells.

In  the first simulation case,  the formation is  homogeneous with no  natural fractures. A refining grid  system is built for  the simulation. The simulation input parameters are summarized in Table  2. The fluids include gas and water, but water is at residual or   immobile,  so  it  is  a  single-phase gas   flow  problem.  The hydraulic fractures are  represented by  a discrete fracture with infinite conductivity. With the input parameters as  shown in Table  2, the dimensionless fracture conductivity is calculated by its  definition, Cfd =kf wf =km wm . Its  value is large enough thus the hydraulic fracture could be treated as infinite conductivity.

Three different fracture models with the same total fracture matrix contact area are built, as demonstrated in Figs. 5-7. Fig. 8 illustrates the simulated wellbore bore pseudo-pressure vs. time for these three cases. Their pressure change with time are almost same, which indicates that fracture number and fracture geometry, as long as the total fracture area keep the same, have little influence on the wellbore pressure change for gas production from extremely low permeability rock.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

Next  we compare the transient pressure behavior in  early time with different fracture-matrix total contact area. Two cases with different area are  run and Fig. 9 is the simulation result. A larger surface area will  lead to a slower increase of the dimensionless pseudo-pressure. Slope  of this line  is inversely proportional to the fracture area.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

Gas  adsorption influence is  also  analyzed. Two  cases with different initial pressures are run, one is 2350 psi and the other is 3800 psi,  respectively. The  results are  illustrated in Figs. 10  and 11.   Two conclusions  could  be   drawn  from these  simulation works:

 

1.  Gas  flow with adsorption will  also  behave straightly in  the normalized pressure vs. the square root of time plot for  the linear flow period. This is identical with our  previous analysis that adsorption could be treated by a compressibility factor if the pressure changes a little.

 

2.  Adsorption will  have different influences on  the linear flow behavior at  different initial pressure, as shown in Fig. 2 that “adsorption compressibility” drops with pressure increases.

Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

6.Conclusions

 

 

In  this paper, we  derive a  new formulation of  gas  pseudo- pressure for  the transient pressure analysis in  unconventional gas reservoirs. We prove its efficiency and accuracy by running a set  of relevant simulation examples. We  use  the developed numerical model to  simulate shale gas  production with a continuum,  discrete  or  hybrid  modeling  approach.  Our   modeling studies indicate that the most sensitive parameter of hydraulic fractures to early transient gas flow responses through extremely low  permeability rock  is actually the fracture-matrix contacting area, generated by fracturing stimulation. We  observed that gas flow with adsorption will  also  behave straightly in the normalized  pressure vs. the square root of time plot for the linear flow period,  if  an   adsorption  term  is   included  in   the  total  gas compressibility. Based  on this observation, we  demonstrate that it is possible to use transient pressure testing data to estimate the area of fractures generated from fracturing operations. A methodology using typical transient pressure responses, simulated by the numerical model, to  estimate fracture areas created or  to quantity hydraulic fractures with traditional well testing technology is presented. The methodology as well as type curves of pressure transients  from this study can   be  used for  quantify hydraulic fractures in field application.

Acknowledgments

 

 

This work was supported in part by EMG Research Center and UNGI of Petroleum Engineering Department at Colorado School of Mines, and by Foundation CMG.

 

 

Authors: Cong  Wang*, Yushu Wu

 

Colorado School of Mines, United States

 

*  Corresponding author. E-mail addresses: cowang@mines.edu, congwang268@gmail.com (C. Wang), ywu@mines.edu (Y. Wu).

 

Peer review under responsibility of  Southwest Petroleum University.

 

http://dx.doi.org/10.1016/j.petlm.2015.05.002

 

2405-6561/Copyright © 2015,  Southwest Petroleum University.  Production and hosting by Elsevier B.V. on behalf of  KeAi  Communications Co., Ltd.  This is  an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 

Article history:

 

Received 21 April 2015

Accepted 29 May 2015

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Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper
Characterizing hydraulic fractures in shale gas  reservoirs using transient pressure tests. Cong  Wang, Yushu Wu, Allaboutshale.com, Shale Paper

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