Estimated Ultimate Recovery (EUR) as a Function of Production ...
SPE 147623 Estimated Ultimate Recovery (EUR) as a Function of Production Practices in the Haynesville Shale V. Okouma, F. Guillot, M. Sarfare, Shell Canada Energy, V. Sen, Taurus Reservoir Solutions Ltd., D. Ilk, DeGolyer and MacNaughton, T.A. Blasingame, Texas A&M University
Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 30 October–2 November 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract Recent developments in well completion technologies have transformed the unconventional reservoir systems into economically feasible reservoirs. However, the uncertainty associated with production forecasts and non-uniqueness related with well/reservoir parameter estimation, are the main issues in future development of these reservoirs. In addition, recent operational methods such as restricting rates by decreasing the choke size add up to the uncertainty in production forecasts. This work attempts to investigate the effect of production practices on ultimate recovery. It is observed that wells producing in the Haynesville shale gas play exhibit severe productivity loss throughout their producing life. Production practices such as controlling the drawdown or restricting rates by decreasing the choke size are employed by several operators to deal with the severe productivity loss. In this work our main objective is to investigate the issues (such as stress dependent permeability, proppant embedment, operational problems, etc.) contributing to decreasing well productivity over time. In particular, from modeling standpoint, we focus on stress-dependent permeability as a mechanism, which affects well performance over time. Using a horizontal well with multiple fractures numerical simulation model coupled with geomechanics, we generate synthetic simulation cases including several drawdown scenarios. It is shown that high drawdown cases result in higher effective stress fields around the well and fracture system. We therefore infer that higher effective stress fields result in lower well productivity over time. Based on this hypothesis and diagnostics of field data, we model two different scenarios (i.e., high drawdown and low drawdown cases) for a horizontal well with multiple fractures using two different permeability decay functions and same well/formation model parameters. Our modelling results indicate that low drawdown case yields higher recovery suggesting that rate restriction could be a mitigating factor in decreasing well productivity over time. Introduction Hydrocarbon production from unconventional reservoir systems (e.g., tight gas sands, shale gas, tight/shale oil, etc.) has become significant in recent years due to recent advances in the technology allowing to drill and complete wells in these complex reservoir systems at lower costs. The developments in the technology to develop and produce complex unconventional reservoir systems such as shale gas reservoirs bring the difficulties and uncertainty associated with well performance. The uncertainty is mainly due to the lack of our complete understanding of the production mechanisms and behavior of these reservoir systems. And the difficulty is therefore associated with establishing the long term production decline in these reservoirs. In simple terms this study focuses on the factors affecting well performance and productivity in the Haynesville shale. Significant amount of natural gas has been produced from the Haynesville shale since 2008 and the Haynesville shale is considered as one of the largest natural gas fields in the United States. The Haynesville shale is a black, organic rich shale of Upper Jurassic age located in east Texas and northwest Louisiana, which is deposited with mainly heavier clay minerals, silica, and calcite. The depth of the Haynesville shale ranges from approximately 10,000 ft in the northwest part to 14,000 ft in the southeast (Buller et al. 2010). It is overpressured with pressure gradients higher than 0.9 psi/ft. Due to high reservoir pressure of the Haynesville shale, production practices has been shifted to control drawdown or to restrict the rates by the operators to avoid any damage occuring in the well/reservoir during production.
2
SPE 147623
Currently a discussion exists in the industry on whether restricting the rates could yield higher estimated ultimate recovery (EUR) values than for the case of producing the wells without restricting the production. Generally, a steep decline trend is observed for the unrestricted wells producing in the Haynesville shale. Diagnostic methods, which involve the interpretation of time-pressure-rate data (Ilk et al. 2011) from these wells, suggest that productivity of these wells decrease significantly over time — this signature can be observed by the depletion like behavior of pressure drop normalized rate data and its' auxiliary functions with respect to time on log-log scale or quick deviation of the rate normalized pressure drop data from straight line behavior on square root time plot. On the other hand, from a diagnostic point of view restricted rate wells do not exhibit the behavior of unrestricted wells with the current amount of production data. We have to recognize the fact that production data of the restricted rate wells is relatively shorter, thus preventing a strong conclusion of how to establish their production behavior. Also, their rate decline is almost flat and flowing pressures are declining smoothly which makes it almost impossible to apply decline curve analysis methods (Arps 1945, Ilk et al. 2008, Valko 2009) to estimate ultimate recovery using only rate-time data. For the reasons above a thorough understanding of the severe productivity loss has to be incorporated into analysis/modeling efforts. If it is believed that the unrestricted rate wells exhibit significant productivity loss over time due to damage and/or other issues, these issues have to be accounted for in the analysis/modeling. Once these issues are identified, then it could be tested that if the restricted rate wells would exhibit the same performance or not. We believe that production data diagnostics would be a very efficient way to identify production performance of such wells. Below we list several mechanisms that could be specaluted as the primary cause in the severe productivity loss in the producing life of the Haynesville shale wells. ● Fracture closure: Near wellbore hydraulic fracture closure (might be due to high effective stress) ● Matrix permeability reduction: Stress dependent permeability (might be due to high effective stress) ● Relative permeability, back pressure: Water/condensate loading ● Permeability plugging: Fines migration, proppant embedment/crushing, scaling and clay swelling ● Thermal expansion: Joule-Thompson effect, temperature fluctuation during shut-in/re-open All of the issues above or several of them may mainly contribute to productivity loss of the unrestricted rate wells. At this point we emphasize that fracture closure and/or matrix permeability reduction are not the only causes of the productivity loss, but we can state that these issues have main impact on the long-term productivity of these wells. Therefore, we can incorporate the stress dependent permeability as a means of modeling the productivity loss in the unrestricted rate wells and investigate the effect of controlling drawdown or restricting rates on estimated ultimate recovery via numerical simulation coupled with geomechanics. Description of the Generic Models for Geomechanics Study A generic simulation model is created with the Haynesville shale properties. This model is built as a coupled geomechanical flow simulation using a numerical simulator to track stress changes as opposed to reservoir simulators which only track pressure changes. For the purpose of the geomechanics study, 4 models are run using different drawdown scenarios (i.e., different constant bottomhole pressures (pwf)). The reservoir is characterized by a gridded network and hydraulic fractures are modeled using local grid refinement with an enhanced permeability localized in the hydraulic fracture plane. The model includes one geological unit of 150 ft at a depth of 12,000 ft. The corresponding model parameters are given in Table 1 below as: Table 1 — Well/Reservoir input parameters for the generic model.
Effective permeability, k Fracture half-length, xf Fracture conductivity, FcD Number of fractures, nf Horizontal well length, Lw Initial reservoir pressure, pi Specific gas gravity, γ Reservoir temperature, TR Drainage area, A Drawdown values, pwf/pi
= = = = = = = = = =
0.0015 md 200 ft 30 (dimensionless) 12 4,786 ft 10,500 psia 0.60 360 oF 160 acres (5,280 ft x 1,320 ft) 0.14 (pwf =1,450 psia), 0.40 ((pwf =4,350 psia), 0.69 (pwf =7,250 psia), 0.86 ((pwf =9,000 psia)
Having defined the base reservoir model above, this model was then re-gridded for a coupled geomechanical and flow simulation study. The local grid refinement around fracture planes and fracture tips was implemented using a geometirc progression based algorithm. The model was also gridded into 19 layers in depth where the finest gridding was around the horizontal well at 12,075 ft and progressively coarsened away from the well. A geomechanical model comprising 680 ft overburden and 150 ft underburden in addition to the 19 layer reservoir model was also built.
SPE 147623
3
Areal grids were coincident for the reservoir and geomechanical models. Simulations were run with constant bottomhole pressure constraints (given in Table 1 above) and the mean effective stress field resulting from the drawdown was computed for each case (under an assumption of linear elasticity) for 1,080 days which approximately represent a 3 year period. The change in mean effective stress is most drastic for the highest drawdown which might be representative of an unrestricted rate well. Figs. 1-4 present the changes in mean effective stress maps for the four (4) different drawdown scenarios at the end of 75 days of simulation on constant bottomhole pressure driven production. The early time stress fields can be compared under a common color map whereas the differences between the four cases are too large at later times to be demonstrated in detail with a single color scheme. However, the trends and differences shown in Figs. 1-4 continue to grow and are even more pronounced at later times. We note that numerical simulation runs for only about three years with a 9,000 psia constant bottomhole pressure constraint — this is due to the fact that the pressure values at the gridblocks around the wellbore and fractures tend to approach constant bottomhole pressure constraint and much tighter numerical controls are needed to continue the runs at the cost of computation time. The runs with 1,450 psia, 4,350 psia, and 7,250 psia constant bottomhole pressure constraints go further in time, but are being considered up to 1,080 days to bring the four runs to a common reference. We suggest that geomechanically induced permeability decay in the reservoir will be proportional to the mean effective stress at any time in the producing life of the well. The higher the effective stress, the greater the extents of permeability decay that can be expected. We also note that the effective stress maps are presented as half elements of symmetry in plan view at the wall level where the horizontal well is assumed to extend along the top margin of the box and only one wing of each of 12 fractures is shown. Symmetry implies that the other half of the map would be a mirror image of the plan view shown here. Fig. 5 shows the stress history at a specific point within the reservoir. The different stress paths results resulting from the four different drawdown scenarios can be clearly distinguished. The Effects of Geomechanics on Drawdown One of the objectives of this study is to evaluate the first order impact of in-situ stress variation on productivity decline and hence the estimated ultimate recovery (EUR). As in conventional reservoirs, changes in reservoir temperature and pressure of unconventional reservoirs result in changes in the in-situ stress magnitudes (Settari et al. 2005, Chin et al. 2000). Pressure or temperature induced stress change in the subsurface cause deformation of the system (both rock matrix and induced/natural fractures) that alters reservoir properties impacting flow and production behavior. Coupled flow and deformation analyses model porosity and permeability as a function of effective in-situ stress ( σ ). For the case of isothermal reservoir production, depletion results in increasing the effective stresses in the formation. Based on poroelastic theory this condition can be stated as follows:
σ = σ − α p p ..................................................................................................................................................................... (1) Depletion results in reducing average reservoir pressure, which in turn impacts the in-situ stresses. However, the change in in-situ stress is typically about 0.4-0.7 times the change in formation pore pressure (Addis 1997) with the assumption uniaxial strain theory. For the high drawdown and low drawdown cases considered in this study, the change in reservoir pressure would be expected to result in higher and lower effective stresses in the system, respectively (see Figs. 1-4). Our hypothesis is that the varying in-situ stress conditions result in changing permeability decay functions for the cases, which would be described in detail in later sections. In other words we suggest that different permeability decay functions should be used for the analysis and modeling of different drawdown cases in the same reservoir. In the following sections we will use production data diagnostics to support our hypothesis. At this point we would describe the function to model permeability decay as a function of reservoir pressure. In this work we use the Yilmaz and Nur correlation (Yilmaz et al. 1991), which should be suitable for modeling permeability decay as a function of pressure — in fact we believe that this correlation should be useful in the high pressure and temperature Haynesville shale where excessive drawdowns are observed. The correlation introduces a "permeability modulus" which has a form identical to compressibility term.
γ =
1 dk ............................................................................................................................................................................ (2) k dp
Solving Eq. 2 for permeability term yields: k = k i e −γ Δp ....................................................................................................................................................................... (3) Eq. 3 suggests that permeability of the system changes exponentially with respect to reservoir pressure drop. Also, Eq. 1 and Eq. 2 imply that for a given permeability modulus, the higher the mean effective stress, permeability decay would be higher and Eq. 3 shows that the lower the depletion is, permeability decay would be lower.
4
SPE 147623
For the Haynesville shale, we note that the effective stress at discovery is very low — in fact at discovery the effective stress in the Haynesville shale is typically of order 1000-2000 psia due to high initial pore pressure. The overburden gradient could be observed as slightly above 1.0 psi/ft and pore pressure gradient could be found up to 0.95 psi/ft in some places. We expect that with drawdown the pore pressure around the well/fracture system drops and the effective stress increases leading to compaction and therefore loss of permeability (Miller et al. 2011). Recent work carried out on carefully handled core by the Stim-Lab consortium, suggests that the loss of permeability becomes severe at net stress above 3000 psi. We therefore imply that there might be a long term benefit in maintaining this maximum drawdown as long as possible. Production Data Diagnostics for Modeling the Effect of Permeability Decay Function
So far we have shown via numerical simulation coupled with geomechanics that high drawdown cases yield higher net effective stress values around the well/fracture system whereas low drawdown cases result in lower effective stress values. Therefore it is our belief that different drawdown cases should be modeled using different permeability decay functions. In this section we attempt to verify our hypothesis by presenting field examples of unrestricted and restricted wells producing in the same field in the Haynesville shale. For our purposes we use the plots below: Plot 1:
Δp q versus qi q
Plot 2:
Δp versus q
Plot 3: t
t
d ⎡ Δp ⎤ ⎢ ⎥ versus t mb dt ⎣ q ⎦
We note that these plots are only used for diagnostic purposes — i.e., these plots should guide us in distinguishing the performance of unresticted and restricted rate wells, and could lead us to the conclusion on the behavior of permeability decay function for unrestricted and restricted rate cases. Fig. 6 presents the change in rates with respect to initial rate as a function of rate normalized pressure. We note that there may not be a theoretical basis for this plot, and we intuitively develop this plot to relate the changes in rates with the changes in permeability (analogous to Darcy's law). Also we use the rate normalized pressure drop instead of pressure drop to account for variable rate/pressure production data. Fig. 6 clearly suggests that the decrease in the rate change much more significant for the unrestricted rate well case as a function of rate normalized pressure drop. This indicates that permeability decay for the unrestricted rate case might be higher than the restricted rate case. Fig. 7 presents the rate normalized pressure drop data and square root of time. The underlying basis of this plot is the linear flow theory which indicates that lower slope of rate normalized pressure drop data would exhibit higher productivity. In Fig. 7 it can be observed that restricted rate case exhibit higher productivity than the unrestricted rate case. Fig. 8 can be considered as a well-test analog plot where logarithmic derivative of rate normalized pressure drop data is plotted against material balance time. Derivative for the restricted rate case lies below the unrestricted rate case, which might indicate that productivity is higher for the restricted rate case.
Based on our diagnostic efforts, we can conclude that restricted rate well has higher productivity than the unrestricted rate well and if these wells are modeled then different permeability decay functions should be used. Since these two wells are producing in the same field, we attribute this difference to higher productivity loss caused by excessive drawdown for the unrestricted rate well. In the next section, we attempt to quantify the difference in the EUR based on our observation. Modeling the Effect of Permeability Decay Function on EUR
The generic model attempts to evaluate the impact of using different permeability decay functions on EUR when the same well is flowed with lower drawdown (restricted) and higher drawdown (unrestricted). We use the same model parameters as given before in Table 1 for our purposes. We incorporate the effect of pressure-dependent permeability in the two cases. However, for modeling the unrestricted rate case we use a higher value for the permeability modulus (4.3x10-4 psi-1) and correspondingly we use a lower permeability modulus value (2.0x10-4 psi-1) for the restricted rate case. The rationale for the selection of different permeability modulus coefficient values is based on our diagnostic efforts as described earlier. The common values for permeability modulus coefficients for unrestricted and restricted rate wells are obtained using production data analysis (history matching) of these wells. These values of permeability moduli are in line with what has been measured in Haynesville (and other shales gas plays) cores by various operators. We run two models based on generic trends from the current Haynesville shale wells. We attempt to mimic the production of restricted and unrestricted rate wells by imposing synthetic bottomhole pressure profiles for the unrestricted and restricted rate cases. For reference, Fig. 9 presents the synthetic bottomhole pressures for the unrestricted and restricted rate cases. These bottomhole pressure profiles are essentially used to create the rate responses for the two cases. The two models exhibit
SPE 147623
5
decreasing rates and bottomhole pressures throughout time. For forecasting the production to the EUR, we use a constant bottomhole pressure constraint of 1,450 psia and let the bottomhole pressure profiles reach to the bottomhole pressure constraint then keep the bottomhole pressure constant. Our results indicate that a difference of 28 % in EUR is observed for the two cases over a period of 30 years of production. Fig. 10 presents the production forecast for the two cases, as mentioned earlier higher EUR is observed for the restricted rate well case. Fig. 11 demonstrates the bottomhole pressure with respect to cumulative gas production. In closure, we state that the difference in the EUR is attributed to the use of different permeability decay functions for simulating the same well to represent restricted and unrestricted producing conditions. It is worth noting that if permeability is not a strong function of reservoir pressure, then the EUR should not change whatever the production mode is. Summary and Conclusions
Summary: In this work we attempt to demonstrate that severe productivity loss exhibited by the unrestricted rate Haynesville shale wells could be attributed to excessive drawdown. We use a numerical horizontal well with multiple fractures model coupled with geomechanics to show that effective stress fields are different for various drawdown scenarios. It is stated that higher effective stress results in lower productivity around well/fracture system. Therefore, lower drawdowns are recommended for production in the Haynesville shale. For modeling the difference in the EUR of unrestricted and restricted rate wells, we incorporate the use of a permeability decay function. It is expected that permeability decay function would behave differently for a certain field for various production modes (e.g., restricted or unrestricted) due to altered effective stress fields. Diagnostics of production data of unrestricted and restricted wells support this hypothesis. When production is modeled for two different scenarios for a single well, 28 % difference in the EUR is observed at 30 years of production. Conclusions: We state the following conclusions based on this work: 1. For reservoirs which are significantly overpressured as in the case of the Haynesville shale, it should be kept in mind that permeability would likely decrease as a function of reservoir pressure. Higher drawdown would cause higher effective stress fields, which would decrease productivity. Under these circumstances, controlling or better managing drawdown could be a solution to prevent severe productivity loss. 2. There are several factors, which contribute to the severe productivity loss of the Haynesville shale wells. Stress dependent permeability can be considered as one of the major factors affecting productivity. Therefore, it is recommended that permeability change as a function of pressure should be included in modeling efforts. However, it should not be concluded from this work that stress dependent permeability is the only reason for severe productivity loss of the Haynesville shale wells. 3. Production data diagnostics is crucial in understanding the behavior/characteristics of the permeability decay during production. We believe that the behavior of the permeability decay function would be different for the same field (considering unique rock type) for various drawdown scenarios. Diagnostic plots could be utilized to support this hypothesis. In this work we have shown that from a diagnostic point of view, a restricted rate well has higher productivity than an unrestricted rate well producing in the same field. For the purpose of analysis and modeling this difference can be quantified by the behavior of the permeability decay function. 4. We believe that as far as the Haynesville shale is concerned, controlling drawdown or restricting the rates prevents the damage when the wells are produced with excessive/uncontrolled drawdown, and thus preventing the loss of productivity and EUR throughout time. We also believe that geology/location is an important factor, and this statement may not hold for all the fields in the Haynesville shale. Therefore, we recommend that more work needs to be performed for the investigation of this issue.
6
SPE 147623
Nomenclature
Variables: A EUR FcD Gp k ki Lw nf pi pp pwf q qi xf t tmb TR
= = = = = = = = = = = = = = = = =
Drainage area, acres Estimate of ultimate recovery, BSCF Fracture conductivity, dimensionless Cumulative gas production, MSCF or BSCF Formation permeability, md Initial formation permeability, md Horizontal well length, ft Number of fractures, dimensionless Initial reservoir pressure, psia Pore pressure, psia Flowing bottomhole pressure, psia Production rate, MSCF/D or STB/D Initial production rate, MSCF/D Fracture half-length, ft Production time, days Material balance time (Gp/q), days Reservoir temperature, oF
Greek Symbols: α φ γ
γ
σ σ
= = = = = =
Biot coefficient, dimensionless Porosity, fraction Specific gas gravity, dimensionless Permeability modulus, psi-1 Effective in-situ stress, psia In-situ stress, psia
References
Addis, M.A. 1997. Stress Depletion Response of Reservoirs. Paper SPE 38720 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, 05-08 October. Arps, J.J. 1945. Analysis of Decline Curves. Trans. AIME 160: 228-247. Buller, D., Hughes, S., Market, J., Petre, E., Spain, D., and Odumosu, T. 2010. Petrophysical Evaluation for Enhancing Hydraulic Stimulation in Horizontal Shale Gas Wells. Paper SPE 132990 presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September. Chin, L., Raghavan, R., and Thomas, L.K. 2000. Fully-coupled Geomechanics and Fluid Flow Analysis of Wells with Stressdependent Permeability. SPEJ 3 (5): 435-443. Ilk, D., Perego, A.D., Rushing, J.A., and Blasingame, T.A. 2008. Exponential vs. Hyperbolic Decline in Tight Gas Sands — Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves. Paper SPE 116731 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 21-24 September. Ilk, D., Jenkins, C.D., and Blasingame, T.A. 2011. Production Analysis in Unconventional Reservoirs — Diagnostics, Challenges, and Methodologies. Paper SPE 144376 presented at the SPE North American Unconventional Gas Conference and Exhibition, The Woodlands, TX, 14-16 June. Miller, R.S., Conway, M., Salter, G. 2011. Pressure-Depenedent Permeability in Shale Reservoirs, Implication for Estimated Ultimate Recovery (EUR). AAPG Article # 90122. AAPG Hedberg Conference, December 5-10, 2010, Austin, TX. Settari, A.T., Bachman, R.C., and Walters, D.A. 2005. How to Approximate Effects of Geomechanics in Conventional Reservoir Simulation. Paper SPE 97155 presented at the SPE Annual Technical Conference and Exhibition, Dallas, TX, 0912 October. Valkó, P.P. 2009. Assigning Value to Stimulation in the Barnett Shale: A Simultaneous Analysis of 7000 Plus Production Histories and Well Completion Records. Paper SPE 119369 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, TX, 19-21 January. Yilmaz, O., Nur, A., and Nolen-Hoeksema, R. 1991. Pore Pressure Profiles in Fractured and Compliant Rocks. Paper SPE 22232 unsolicited.
SPE 147623
7
Appendix
In this Appendix we attempt to derive that the effective stress for a restricted rate scenario would be lower than an uncontrolled drawdown case. We start with the description for the effective stresses. Effective stress at initial conditions (i.e., state 1) can be given as:
σ 1 = σ 1 − α p p1 ............................................................................................................................................................... (A.1) Effective stress after depletion (state 2) can be expressed as:
σ 2 = σ 2 − α p p 2 ............................................................................................................................................................ (A.2) In terms of initial conditions and stress change due to depletion, Eq. A.2 can be written as:
σ 2 = (σ 1 − Δσ 1 ) − (α p p1 − Δp p ) ................................................................................................................................... (A.3) Change in stress due to depletion is usually a fraction of change in pore pressure such that Δσ 1 = δ Δp p ................................................................................................................................................................... (A.4)
where, δ is less than 1 and typically between 0.4 and 0.7. Eq. A.3 then can be written as:
σ 2 = (σ 1 − δ Δp p ) − (α p p1 − Δp p ) ................................................................................................................................ (A.5) rearranging the terms in Eq. A.5 above we have:
σ 2 = (σ 1 − α p p1 ) + (1 − δ ) Δp p ...................................................................................................................................... (A.6) inserting Eq. A.1:
σ 2 = σ 1 + (1 − δ ) Δp p ...................................................................................................................................................... (A.7) Eq. A.7 indicates that effective stress at state 2 increases with depletion such that
σ 2 ≥ σ 1 ........................................................................................................................................................................... (A.8) In order to evaluate the effect of constant bottomhole pressure production on effective stress, let's consider the following cases: Case 1: Restricted Rate Well (Higher pwf)
σ 2, c = σ 1 + (1 − δ ) Δp p ................................................................................................................................................... (A.9) The restricted rate scenario would result in higher average reservoir pressure due to lower drawdown yielding
σ 2, c = σ 1 + (1 − δ ) ( p p1 − p p1, c ) ................................................................................................................................... (A.10) where pp1,c is the average reservoir pressure of post rate restricted depletion Case 2: Unrestricted Rate Well (Lower pwf)
σ 2, c = σ 1 + (1 − δ ) Δp p ................................................................................................................................................... (A.9) The restricted rate scenario would result in higher average reservoir pressure due to lower drawdown yielding
σ 2, c = σ 1 + (1 − δ ) ( p p1 − p p1, c ) ................................................................................................................................... (A.10) If pp2,u represents the average reservoir pressure after high drawdown, then Eq. A.7 can be given as:
σ 2, f = σ 1 + (1 − δ ) ( p p1 − p p 2, u ) ................................................................................................................................. (A.11) For a given reservoir, the unrestricted drawdown (lower pwf) will result in lower average reservoir pressure as compared to the average reservoir pressure under restricted rate condition. Thus, the pressure change term in Eq. A.11 is always greater than in Eq. A.10. Therefore we can deduct that (Δp p ) unrestricted > (Δp p ) restricted ................................................................................................................................. (A.12)
Hence, effective stress in the system for choked scenario is lower, this suggests that permeability decay is slower in the rate restricted well case.
8
SPE 147623
Fig. 1
— Change in mean effective stress for the highest drawdown constant bottomhole pressure production (pwf=1,450 psia).
Fig. 2
— Change in mean effective stress for constant bottomhole pressure production numerical simulation (pwf=4,350 psia).
SPE 147623
9
Fig. 3
— Change in mean effective stress for constant bottomhole pressure production numerical simulation (pwf=7,250 psia).
Fig. 4
— Change in mean effective stress for the lowest drawdown constant bottomhole pressure production (pwf=9,000 psia).
10
SPE 147623
Fig. 5
— Mean effective stress at a reference point location between two fracture planes within the reservoir for all simulation cases.
Fig. 6
— Data diagnostic plot: Change in rate versus rate normalized pressure drop.
SPE 147623
11
Fig. 7
— Data diagnostic plot: Rate normalized pressure drop versus square root of production time.
Fig. 8
— Data diagnostic plot: Rate normalized pressure drop derivative versus material balance time.
12
SPE 147623
Fig. 9
— Synthetic pressure profiles for unrestricted and restricted well cases.
Fig. 10 — Production forecast for unrestricted and restricted well cases using numerical simulation.
SPE 147623
13
Fig. 11 — Bottomhole pressure versus cumulative gas production trends for unrestricted and restricted well cases using numerical simulation.
Copyright 2011, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Denver, Colorado, USA, 30 October–2 November 2011. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract Recent developments in well completion technologies have transformed the unconventional reservoir systems into economically feasible reservoirs. However, the uncertainty associated with production forecasts and non-uniqueness related with well/reservoir parameter estimation, are the main issues in future development of these reservoirs. In addition, recent operational methods such as restricting rates by decreasing the choke size add up to the uncertainty in production forecasts. This work attempts to investigate the effect of production practices on ultimate recovery. It is observed that wells producing in the Haynesville shale gas play exhibit severe productivity loss throughout their producing life. Production practices such as controlling the drawdown or restricting rates by decreasing the choke size are employed by several operators to deal with the severe productivity loss. In this work our main objective is to investigate the issues (such as stress dependent permeability, proppant embedment, operational problems, etc.) contributing to decreasing well productivity over time. In particular, from modeling standpoint, we focus on stress-dependent permeability as a mechanism, which affects well performance over time. Using a horizontal well with multiple fractures numerical simulation model coupled with geomechanics, we generate synthetic simulation cases including several drawdown scenarios. It is shown that high drawdown cases result in higher effective stress fields around the well and fracture system. We therefore infer that higher effective stress fields result in lower well productivity over time. Based on this hypothesis and diagnostics of field data, we model two different scenarios (i.e., high drawdown and low drawdown cases) for a horizontal well with multiple fractures using two different permeability decay functions and same well/formation model parameters. Our modelling results indicate that low drawdown case yields higher recovery suggesting that rate restriction could be a mitigating factor in decreasing well productivity over time. Introduction Hydrocarbon production from unconventional reservoir systems (e.g., tight gas sands, shale gas, tight/shale oil, etc.) has become significant in recent years due to recent advances in the technology allowing to drill and complete wells in these complex reservoir systems at lower costs. The developments in the technology to develop and produce complex unconventional reservoir systems such as shale gas reservoirs bring the difficulties and uncertainty associated with well performance. The uncertainty is mainly due to the lack of our complete understanding of the production mechanisms and behavior of these reservoir systems. And the difficulty is therefore associated with establishing the long term production decline in these reservoirs. In simple terms this study focuses on the factors affecting well performance and productivity in the Haynesville shale. Significant amount of natural gas has been produced from the Haynesville shale since 2008 and the Haynesville shale is considered as one of the largest natural gas fields in the United States. The Haynesville shale is a black, organic rich shale of Upper Jurassic age located in east Texas and northwest Louisiana, which is deposited with mainly heavier clay minerals, silica, and calcite. The depth of the Haynesville shale ranges from approximately 10,000 ft in the northwest part to 14,000 ft in the southeast (Buller et al. 2010). It is overpressured with pressure gradients higher than 0.9 psi/ft. Due to high reservoir pressure of the Haynesville shale, production practices has been shifted to control drawdown or to restrict the rates by the operators to avoid any damage occuring in the well/reservoir during production.
2
SPE 147623
Currently a discussion exists in the industry on whether restricting the rates could yield higher estimated ultimate recovery (EUR) values than for the case of producing the wells without restricting the production. Generally, a steep decline trend is observed for the unrestricted wells producing in the Haynesville shale. Diagnostic methods, which involve the interpretation of time-pressure-rate data (Ilk et al. 2011) from these wells, suggest that productivity of these wells decrease significantly over time — this signature can be observed by the depletion like behavior of pressure drop normalized rate data and its' auxiliary functions with respect to time on log-log scale or quick deviation of the rate normalized pressure drop data from straight line behavior on square root time plot. On the other hand, from a diagnostic point of view restricted rate wells do not exhibit the behavior of unrestricted wells with the current amount of production data. We have to recognize the fact that production data of the restricted rate wells is relatively shorter, thus preventing a strong conclusion of how to establish their production behavior. Also, their rate decline is almost flat and flowing pressures are declining smoothly which makes it almost impossible to apply decline curve analysis methods (Arps 1945, Ilk et al. 2008, Valko 2009) to estimate ultimate recovery using only rate-time data. For the reasons above a thorough understanding of the severe productivity loss has to be incorporated into analysis/modeling efforts. If it is believed that the unrestricted rate wells exhibit significant productivity loss over time due to damage and/or other issues, these issues have to be accounted for in the analysis/modeling. Once these issues are identified, then it could be tested that if the restricted rate wells would exhibit the same performance or not. We believe that production data diagnostics would be a very efficient way to identify production performance of such wells. Below we list several mechanisms that could be specaluted as the primary cause in the severe productivity loss in the producing life of the Haynesville shale wells. ● Fracture closure: Near wellbore hydraulic fracture closure (might be due to high effective stress) ● Matrix permeability reduction: Stress dependent permeability (might be due to high effective stress) ● Relative permeability, back pressure: Water/condensate loading ● Permeability plugging: Fines migration, proppant embedment/crushing, scaling and clay swelling ● Thermal expansion: Joule-Thompson effect, temperature fluctuation during shut-in/re-open All of the issues above or several of them may mainly contribute to productivity loss of the unrestricted rate wells. At this point we emphasize that fracture closure and/or matrix permeability reduction are not the only causes of the productivity loss, but we can state that these issues have main impact on the long-term productivity of these wells. Therefore, we can incorporate the stress dependent permeability as a means of modeling the productivity loss in the unrestricted rate wells and investigate the effect of controlling drawdown or restricting rates on estimated ultimate recovery via numerical simulation coupled with geomechanics. Description of the Generic Models for Geomechanics Study A generic simulation model is created with the Haynesville shale properties. This model is built as a coupled geomechanical flow simulation using a numerical simulator to track stress changes as opposed to reservoir simulators which only track pressure changes. For the purpose of the geomechanics study, 4 models are run using different drawdown scenarios (i.e., different constant bottomhole pressures (pwf)). The reservoir is characterized by a gridded network and hydraulic fractures are modeled using local grid refinement with an enhanced permeability localized in the hydraulic fracture plane. The model includes one geological unit of 150 ft at a depth of 12,000 ft. The corresponding model parameters are given in Table 1 below as: Table 1 — Well/Reservoir input parameters for the generic model.
Effective permeability, k Fracture half-length, xf Fracture conductivity, FcD Number of fractures, nf Horizontal well length, Lw Initial reservoir pressure, pi Specific gas gravity, γ Reservoir temperature, TR Drainage area, A Drawdown values, pwf/pi
= = = = = = = = = =
0.0015 md 200 ft 30 (dimensionless) 12 4,786 ft 10,500 psia 0.60 360 oF 160 acres (5,280 ft x 1,320 ft) 0.14 (pwf =1,450 psia), 0.40 ((pwf =4,350 psia), 0.69 (pwf =7,250 psia), 0.86 ((pwf =9,000 psia)
Having defined the base reservoir model above, this model was then re-gridded for a coupled geomechanical and flow simulation study. The local grid refinement around fracture planes and fracture tips was implemented using a geometirc progression based algorithm. The model was also gridded into 19 layers in depth where the finest gridding was around the horizontal well at 12,075 ft and progressively coarsened away from the well. A geomechanical model comprising 680 ft overburden and 150 ft underburden in addition to the 19 layer reservoir model was also built.
SPE 147623
3
Areal grids were coincident for the reservoir and geomechanical models. Simulations were run with constant bottomhole pressure constraints (given in Table 1 above) and the mean effective stress field resulting from the drawdown was computed for each case (under an assumption of linear elasticity) for 1,080 days which approximately represent a 3 year period. The change in mean effective stress is most drastic for the highest drawdown which might be representative of an unrestricted rate well. Figs. 1-4 present the changes in mean effective stress maps for the four (4) different drawdown scenarios at the end of 75 days of simulation on constant bottomhole pressure driven production. The early time stress fields can be compared under a common color map whereas the differences between the four cases are too large at later times to be demonstrated in detail with a single color scheme. However, the trends and differences shown in Figs. 1-4 continue to grow and are even more pronounced at later times. We note that numerical simulation runs for only about three years with a 9,000 psia constant bottomhole pressure constraint — this is due to the fact that the pressure values at the gridblocks around the wellbore and fractures tend to approach constant bottomhole pressure constraint and much tighter numerical controls are needed to continue the runs at the cost of computation time. The runs with 1,450 psia, 4,350 psia, and 7,250 psia constant bottomhole pressure constraints go further in time, but are being considered up to 1,080 days to bring the four runs to a common reference. We suggest that geomechanically induced permeability decay in the reservoir will be proportional to the mean effective stress at any time in the producing life of the well. The higher the effective stress, the greater the extents of permeability decay that can be expected. We also note that the effective stress maps are presented as half elements of symmetry in plan view at the wall level where the horizontal well is assumed to extend along the top margin of the box and only one wing of each of 12 fractures is shown. Symmetry implies that the other half of the map would be a mirror image of the plan view shown here. Fig. 5 shows the stress history at a specific point within the reservoir. The different stress paths results resulting from the four different drawdown scenarios can be clearly distinguished. The Effects of Geomechanics on Drawdown One of the objectives of this study is to evaluate the first order impact of in-situ stress variation on productivity decline and hence the estimated ultimate recovery (EUR). As in conventional reservoirs, changes in reservoir temperature and pressure of unconventional reservoirs result in changes in the in-situ stress magnitudes (Settari et al. 2005, Chin et al. 2000). Pressure or temperature induced stress change in the subsurface cause deformation of the system (both rock matrix and induced/natural fractures) that alters reservoir properties impacting flow and production behavior. Coupled flow and deformation analyses model porosity and permeability as a function of effective in-situ stress ( σ ). For the case of isothermal reservoir production, depletion results in increasing the effective stresses in the formation. Based on poroelastic theory this condition can be stated as follows:
σ = σ − α p p ..................................................................................................................................................................... (1) Depletion results in reducing average reservoir pressure, which in turn impacts the in-situ stresses. However, the change in in-situ stress is typically about 0.4-0.7 times the change in formation pore pressure (Addis 1997) with the assumption uniaxial strain theory. For the high drawdown and low drawdown cases considered in this study, the change in reservoir pressure would be expected to result in higher and lower effective stresses in the system, respectively (see Figs. 1-4). Our hypothesis is that the varying in-situ stress conditions result in changing permeability decay functions for the cases, which would be described in detail in later sections. In other words we suggest that different permeability decay functions should be used for the analysis and modeling of different drawdown cases in the same reservoir. In the following sections we will use production data diagnostics to support our hypothesis. At this point we would describe the function to model permeability decay as a function of reservoir pressure. In this work we use the Yilmaz and Nur correlation (Yilmaz et al. 1991), which should be suitable for modeling permeability decay as a function of pressure — in fact we believe that this correlation should be useful in the high pressure and temperature Haynesville shale where excessive drawdowns are observed. The correlation introduces a "permeability modulus" which has a form identical to compressibility term.
γ =
1 dk ............................................................................................................................................................................ (2) k dp
Solving Eq. 2 for permeability term yields: k = k i e −γ Δp ....................................................................................................................................................................... (3) Eq. 3 suggests that permeability of the system changes exponentially with respect to reservoir pressure drop. Also, Eq. 1 and Eq. 2 imply that for a given permeability modulus, the higher the mean effective stress, permeability decay would be higher and Eq. 3 shows that the lower the depletion is, permeability decay would be lower.
4
SPE 147623
For the Haynesville shale, we note that the effective stress at discovery is very low — in fact at discovery the effective stress in the Haynesville shale is typically of order 1000-2000 psia due to high initial pore pressure. The overburden gradient could be observed as slightly above 1.0 psi/ft and pore pressure gradient could be found up to 0.95 psi/ft in some places. We expect that with drawdown the pore pressure around the well/fracture system drops and the effective stress increases leading to compaction and therefore loss of permeability (Miller et al. 2011). Recent work carried out on carefully handled core by the Stim-Lab consortium, suggests that the loss of permeability becomes severe at net stress above 3000 psi. We therefore imply that there might be a long term benefit in maintaining this maximum drawdown as long as possible. Production Data Diagnostics for Modeling the Effect of Permeability Decay Function
So far we have shown via numerical simulation coupled with geomechanics that high drawdown cases yield higher net effective stress values around the well/fracture system whereas low drawdown cases result in lower effective stress values. Therefore it is our belief that different drawdown cases should be modeled using different permeability decay functions. In this section we attempt to verify our hypothesis by presenting field examples of unrestricted and restricted wells producing in the same field in the Haynesville shale. For our purposes we use the plots below: Plot 1:
Δp q versus qi q
Plot 2:
Δp versus q
Plot 3: t
t
d ⎡ Δp ⎤ ⎢ ⎥ versus t mb dt ⎣ q ⎦
We note that these plots are only used for diagnostic purposes — i.e., these plots should guide us in distinguishing the performance of unresticted and restricted rate wells, and could lead us to the conclusion on the behavior of permeability decay function for unrestricted and restricted rate cases. Fig. 6 presents the change in rates with respect to initial rate as a function of rate normalized pressure. We note that there may not be a theoretical basis for this plot, and we intuitively develop this plot to relate the changes in rates with the changes in permeability (analogous to Darcy's law). Also we use the rate normalized pressure drop instead of pressure drop to account for variable rate/pressure production data. Fig. 6 clearly suggests that the decrease in the rate change much more significant for the unrestricted rate well case as a function of rate normalized pressure drop. This indicates that permeability decay for the unrestricted rate case might be higher than the restricted rate case. Fig. 7 presents the rate normalized pressure drop data and square root of time. The underlying basis of this plot is the linear flow theory which indicates that lower slope of rate normalized pressure drop data would exhibit higher productivity. In Fig. 7 it can be observed that restricted rate case exhibit higher productivity than the unrestricted rate case. Fig. 8 can be considered as a well-test analog plot where logarithmic derivative of rate normalized pressure drop data is plotted against material balance time. Derivative for the restricted rate case lies below the unrestricted rate case, which might indicate that productivity is higher for the restricted rate case.
Based on our diagnostic efforts, we can conclude that restricted rate well has higher productivity than the unrestricted rate well and if these wells are modeled then different permeability decay functions should be used. Since these two wells are producing in the same field, we attribute this difference to higher productivity loss caused by excessive drawdown for the unrestricted rate well. In the next section, we attempt to quantify the difference in the EUR based on our observation. Modeling the Effect of Permeability Decay Function on EUR
The generic model attempts to evaluate the impact of using different permeability decay functions on EUR when the same well is flowed with lower drawdown (restricted) and higher drawdown (unrestricted). We use the same model parameters as given before in Table 1 for our purposes. We incorporate the effect of pressure-dependent permeability in the two cases. However, for modeling the unrestricted rate case we use a higher value for the permeability modulus (4.3x10-4 psi-1) and correspondingly we use a lower permeability modulus value (2.0x10-4 psi-1) for the restricted rate case. The rationale for the selection of different permeability modulus coefficient values is based on our diagnostic efforts as described earlier. The common values for permeability modulus coefficients for unrestricted and restricted rate wells are obtained using production data analysis (history matching) of these wells. These values of permeability moduli are in line with what has been measured in Haynesville (and other shales gas plays) cores by various operators. We run two models based on generic trends from the current Haynesville shale wells. We attempt to mimic the production of restricted and unrestricted rate wells by imposing synthetic bottomhole pressure profiles for the unrestricted and restricted rate cases. For reference, Fig. 9 presents the synthetic bottomhole pressures for the unrestricted and restricted rate cases. These bottomhole pressure profiles are essentially used to create the rate responses for the two cases. The two models exhibit
SPE 147623
5
decreasing rates and bottomhole pressures throughout time. For forecasting the production to the EUR, we use a constant bottomhole pressure constraint of 1,450 psia and let the bottomhole pressure profiles reach to the bottomhole pressure constraint then keep the bottomhole pressure constant. Our results indicate that a difference of 28 % in EUR is observed for the two cases over a period of 30 years of production. Fig. 10 presents the production forecast for the two cases, as mentioned earlier higher EUR is observed for the restricted rate well case. Fig. 11 demonstrates the bottomhole pressure with respect to cumulative gas production. In closure, we state that the difference in the EUR is attributed to the use of different permeability decay functions for simulating the same well to represent restricted and unrestricted producing conditions. It is worth noting that if permeability is not a strong function of reservoir pressure, then the EUR should not change whatever the production mode is. Summary and Conclusions
Summary: In this work we attempt to demonstrate that severe productivity loss exhibited by the unrestricted rate Haynesville shale wells could be attributed to excessive drawdown. We use a numerical horizontal well with multiple fractures model coupled with geomechanics to show that effective stress fields are different for various drawdown scenarios. It is stated that higher effective stress results in lower productivity around well/fracture system. Therefore, lower drawdowns are recommended for production in the Haynesville shale. For modeling the difference in the EUR of unrestricted and restricted rate wells, we incorporate the use of a permeability decay function. It is expected that permeability decay function would behave differently for a certain field for various production modes (e.g., restricted or unrestricted) due to altered effective stress fields. Diagnostics of production data of unrestricted and restricted wells support this hypothesis. When production is modeled for two different scenarios for a single well, 28 % difference in the EUR is observed at 30 years of production. Conclusions: We state the following conclusions based on this work: 1. For reservoirs which are significantly overpressured as in the case of the Haynesville shale, it should be kept in mind that permeability would likely decrease as a function of reservoir pressure. Higher drawdown would cause higher effective stress fields, which would decrease productivity. Under these circumstances, controlling or better managing drawdown could be a solution to prevent severe productivity loss. 2. There are several factors, which contribute to the severe productivity loss of the Haynesville shale wells. Stress dependent permeability can be considered as one of the major factors affecting productivity. Therefore, it is recommended that permeability change as a function of pressure should be included in modeling efforts. However, it should not be concluded from this work that stress dependent permeability is the only reason for severe productivity loss of the Haynesville shale wells. 3. Production data diagnostics is crucial in understanding the behavior/characteristics of the permeability decay during production. We believe that the behavior of the permeability decay function would be different for the same field (considering unique rock type) for various drawdown scenarios. Diagnostic plots could be utilized to support this hypothesis. In this work we have shown that from a diagnostic point of view, a restricted rate well has higher productivity than an unrestricted rate well producing in the same field. For the purpose of analysis and modeling this difference can be quantified by the behavior of the permeability decay function. 4. We believe that as far as the Haynesville shale is concerned, controlling drawdown or restricting the rates prevents the damage when the wells are produced with excessive/uncontrolled drawdown, and thus preventing the loss of productivity and EUR throughout time. We also believe that geology/location is an important factor, and this statement may not hold for all the fields in the Haynesville shale. Therefore, we recommend that more work needs to be performed for the investigation of this issue.
6
SPE 147623
Nomenclature
Variables: A EUR FcD Gp k ki Lw nf pi pp pwf q qi xf t tmb TR
= = = = = = = = = = = = = = = = =
Drainage area, acres Estimate of ultimate recovery, BSCF Fracture conductivity, dimensionless Cumulative gas production, MSCF or BSCF Formation permeability, md Initial formation permeability, md Horizontal well length, ft Number of fractures, dimensionless Initial reservoir pressure, psia Pore pressure, psia Flowing bottomhole pressure, psia Production rate, MSCF/D or STB/D Initial production rate, MSCF/D Fracture half-length, ft Production time, days Material balance time (Gp/q), days Reservoir temperature, oF
Greek Symbols: α φ γ
γ
σ σ
= = = = = =
Biot coefficient, dimensionless Porosity, fraction Specific gas gravity, dimensionless Permeability modulus, psi-1 Effective in-situ stress, psia In-situ stress, psia
References
Addis, M.A. 1997. Stress Depletion Response of Reservoirs. Paper SPE 38720 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, 05-08 October. Arps, J.J. 1945. Analysis of Decline Curves. Trans. AIME 160: 228-247. Buller, D., Hughes, S., Market, J., Petre, E., Spain, D., and Odumosu, T. 2010. Petrophysical Evaluation for Enhancing Hydraulic Stimulation in Horizontal Shale Gas Wells. Paper SPE 132990 presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September. Chin, L., Raghavan, R., and Thomas, L.K. 2000. Fully-coupled Geomechanics and Fluid Flow Analysis of Wells with Stressdependent Permeability. SPEJ 3 (5): 435-443. Ilk, D., Perego, A.D., Rushing, J.A., and Blasingame, T.A. 2008. Exponential vs. Hyperbolic Decline in Tight Gas Sands — Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves. Paper SPE 116731 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, 21-24 September. Ilk, D., Jenkins, C.D., and Blasingame, T.A. 2011. Production Analysis in Unconventional Reservoirs — Diagnostics, Challenges, and Methodologies. Paper SPE 144376 presented at the SPE North American Unconventional Gas Conference and Exhibition, The Woodlands, TX, 14-16 June. Miller, R.S., Conway, M., Salter, G. 2011. Pressure-Depenedent Permeability in Shale Reservoirs, Implication for Estimated Ultimate Recovery (EUR). AAPG Article # 90122. AAPG Hedberg Conference, December 5-10, 2010, Austin, TX. Settari, A.T., Bachman, R.C., and Walters, D.A. 2005. How to Approximate Effects of Geomechanics in Conventional Reservoir Simulation. Paper SPE 97155 presented at the SPE Annual Technical Conference and Exhibition, Dallas, TX, 0912 October. Valkó, P.P. 2009. Assigning Value to Stimulation in the Barnett Shale: A Simultaneous Analysis of 7000 Plus Production Histories and Well Completion Records. Paper SPE 119369 presented at the SPE Hydraulic Fracturing Technology Conference, College Station, TX, 19-21 January. Yilmaz, O., Nur, A., and Nolen-Hoeksema, R. 1991. Pore Pressure Profiles in Fractured and Compliant Rocks. Paper SPE 22232 unsolicited.
SPE 147623
7
Appendix
In this Appendix we attempt to derive that the effective stress for a restricted rate scenario would be lower than an uncontrolled drawdown case. We start with the description for the effective stresses. Effective stress at initial conditions (i.e., state 1) can be given as:
σ 1 = σ 1 − α p p1 ............................................................................................................................................................... (A.1) Effective stress after depletion (state 2) can be expressed as:
σ 2 = σ 2 − α p p 2 ............................................................................................................................................................ (A.2) In terms of initial conditions and stress change due to depletion, Eq. A.2 can be written as:
σ 2 = (σ 1 − Δσ 1 ) − (α p p1 − Δp p ) ................................................................................................................................... (A.3) Change in stress due to depletion is usually a fraction of change in pore pressure such that Δσ 1 = δ Δp p ................................................................................................................................................................... (A.4)
where, δ is less than 1 and typically between 0.4 and 0.7. Eq. A.3 then can be written as:
σ 2 = (σ 1 − δ Δp p ) − (α p p1 − Δp p ) ................................................................................................................................ (A.5) rearranging the terms in Eq. A.5 above we have:
σ 2 = (σ 1 − α p p1 ) + (1 − δ ) Δp p ...................................................................................................................................... (A.6) inserting Eq. A.1:
σ 2 = σ 1 + (1 − δ ) Δp p ...................................................................................................................................................... (A.7) Eq. A.7 indicates that effective stress at state 2 increases with depletion such that
σ 2 ≥ σ 1 ........................................................................................................................................................................... (A.8) In order to evaluate the effect of constant bottomhole pressure production on effective stress, let's consider the following cases: Case 1: Restricted Rate Well (Higher pwf)
σ 2, c = σ 1 + (1 − δ ) Δp p ................................................................................................................................................... (A.9) The restricted rate scenario would result in higher average reservoir pressure due to lower drawdown yielding
σ 2, c = σ 1 + (1 − δ ) ( p p1 − p p1, c ) ................................................................................................................................... (A.10) where pp1,c is the average reservoir pressure of post rate restricted depletion Case 2: Unrestricted Rate Well (Lower pwf)
σ 2, c = σ 1 + (1 − δ ) Δp p ................................................................................................................................................... (A.9) The restricted rate scenario would result in higher average reservoir pressure due to lower drawdown yielding
σ 2, c = σ 1 + (1 − δ ) ( p p1 − p p1, c ) ................................................................................................................................... (A.10) If pp2,u represents the average reservoir pressure after high drawdown, then Eq. A.7 can be given as:
σ 2, f = σ 1 + (1 − δ ) ( p p1 − p p 2, u ) ................................................................................................................................. (A.11) For a given reservoir, the unrestricted drawdown (lower pwf) will result in lower average reservoir pressure as compared to the average reservoir pressure under restricted rate condition. Thus, the pressure change term in Eq. A.11 is always greater than in Eq. A.10. Therefore we can deduct that (Δp p ) unrestricted > (Δp p ) restricted ................................................................................................................................. (A.12)
Hence, effective stress in the system for choked scenario is lower, this suggests that permeability decay is slower in the rate restricted well case.
8
SPE 147623
Fig. 1
— Change in mean effective stress for the highest drawdown constant bottomhole pressure production (pwf=1,450 psia).
Fig. 2
— Change in mean effective stress for constant bottomhole pressure production numerical simulation (pwf=4,350 psia).
SPE 147623
9
Fig. 3
— Change in mean effective stress for constant bottomhole pressure production numerical simulation (pwf=7,250 psia).
Fig. 4
— Change in mean effective stress for the lowest drawdown constant bottomhole pressure production (pwf=9,000 psia).
10
SPE 147623
Fig. 5
— Mean effective stress at a reference point location between two fracture planes within the reservoir for all simulation cases.
Fig. 6
— Data diagnostic plot: Change in rate versus rate normalized pressure drop.
SPE 147623
11
Fig. 7
— Data diagnostic plot: Rate normalized pressure drop versus square root of production time.
Fig. 8
— Data diagnostic plot: Rate normalized pressure drop derivative versus material balance time.
12
SPE 147623
Fig. 9
— Synthetic pressure profiles for unrestricted and restricted well cases.
Fig. 10 — Production forecast for unrestricted and restricted well cases using numerical simulation.
SPE 147623
13
Fig. 11 — Bottomhole pressure versus cumulative gas production trends for unrestricted and restricted well cases using numerical simulation.
