Induced Fractures Modelling in Reservoir Dynamic Simulators Khaldoon AlObaidi Institute of Petroleum Engineering MSc Petroleum Engineering Project Report 2013/2014 Supervisor – Heriot Watt University
This study was completed as part of the Masters of Science in Petroleum Engineering at the Heriot Watt University.
P a g e ii
Declaration I, Khaldoon AlObaidi, confirm that this work submitted for assessment is my own and is expressed in my own words. Any uses made within it of the works of other authors in any form (e.g. ideas, equations, figures, text, tables, programs) are properly acknowledged at the point of their use. A list of the references employed is included.
Signed…………K.A.………………..
Date 27 August 2014
P a g e iii
Dedication
To my family for their support. To my uncle for his continuous encouragement.
P a g e iv
Acknowledgments Thanks also go to NSI Technologies Inc. for providing me with StimPlan software and licenses which helped me establishing the basis of this work.
Pa ge v
Abstract Since the middle of the twentieth century, hydraulic fractures and fractures created due to injection under fracturing conditions have been proven to be effective in increasing the productivity and injectivity factors of wells considerably. In this work, an algorithms for determining the optimum hydraulic fracture dimensions, the growth of induced fractures created due to injection under fracturing conditions and modelling fractures in dynamic reservoir simulators are introduced. Additionally, the optimum dimensionless conductivity is derived to be 1.6363 and is used in addition to practical limitations and econo mic considerations to determine the optimum hydraulic fracture dimensions result in maximum folds of increase in production. Also in this work, an algorithm adopting Perkins-Kern-Nordgren -α (PKN-α) and Ahmed and Economides notation after Simonson analysis is adopted to determine the dimensions of the induced fractures created due to injection under fracturing conditions. The induced fractures are implemented in reservoir dynamic simulators using gridblocks refinement and properties multiplications to increase net to gross, porosity and permeability to mimic the fracture properties. For two simple box models, only approximately 42% increase in run time due to implementing this algorithm in reservoir dynamic simulator is resulted. Therefore, the algorithm presented provides a good approximation for modelling induced fractures growth with reduced simulation run time and storage capacity compared to three-dimensional fracture models. Also, it provides more accurate results compared to the simple two-dimensional models that assumes fixed fracture height. The advantage of the algorithms presented is they combine the fracturing physics with the reservoir dynamic simulator constraints. Therefore, implementing this work provides robust reserves estimation and forecasts for wells with induced fractures warning of fractures propagation into unintended with relatively fast running simulation models.
P a g e vi
Table of Contents Declaration ............................................. ................................................................... ............................................ ............................................ ....................................... .................ii Dedication........................................... ................................................................. ............................................ ............................................ ..........................................iii ....................iii Acknowledgments Acknowledgments ............................................. ................................................................... ............................................ ............................................. ........................... .... iv Abstract .......................................... ................................................................ ............................................ ............................................. .............................................. ......................... v Table of Contents .......................... ................................................. .............................................. ............................................. ............................................. ....................... vi vi List of Figures ........................................... .................................................................. ............................................. ............................................ ................................viii ..........viii List of Tables .......................................... ................................................................ ............................................ ............................................ ...................................... ................ ix Nomenclature Nomenclature ............................................ ................................................................... ............................................. ............................................ ................................... ............. x 1
Project Scope and Objectives ....................................................... ............................................................................. ................................... ............. 1
1.1
Induced Fractures .......................................... ................................................................ ............................................ ....................................... ................. 1
1.1.1
Fracture Orientation ......................................................... ............................................................................... ....................................... ................. 3
1.1.2
Leak-off Test ......................................... ............................................................... ............................................ ........................................... ..................... 4
1.1.3
Hydraulic Fracturing Procedure .......................................... ................................................................. ................................... ............ 6
1.1.4
Analytical and Numerical Models for Estimating Fracture Dimensions,
Propagation and Recession ................................................... ......................................................................... ............................................ ........................ .. 7
2
1.1.4.1
PKN-α Model ........................................... ................................................................. ............................................ ................................ .......... 8
1.1.4.2
Fracture Height Growth ................................ ...................................................... ............................................. ............................ ..... 9
1.2
Dynamic Simulation of Hydraulic Fractures ......................................... ............................................................ ................... 10
1.3
Objectives ........................................... ................................................................. ............................................ ............................................. .......................... ... 11
Methodology Methodology .......................................... ................................................................ ............................................ ............................................. .............................. ....... 12
2.1
Determining the Optimum Hydraulic Fracture Dimensions Dimensio ns for a Well ................... ................... 12
2.1.1
Cases Input for Testing the Procedure Used to Determine the Optimum Hydraulic
Fracture Dimensions for a Well................................................... Well......................................................................... ..................................... ............... 19
P a g e vii
2.1.1.1
Low Permeability Reservoir Case .......................................... ................................................................ ...................... 20
2.1.1.2
High Permeability Perm eability Reservoir Case ............................................................... ............................................................... 20
2.2
Incorporating Hydraulic Fractures Fractur es in Reservoir Dynamic Simulators ..................... ..................... 21
2.3
An Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Reservo ir Dynamic Simulators .................................................... .................................................... 24
3
2.3.1
Fracture Height Growth .................................... .......................................................... ............................................ .............................. ........ 24
2.3.2
Fracture Width and Half-Length ............................................................... .......................................................................... ........... 27
Results and Discussion ........................................... .................................................................. ............................................. ................................. ........... 33
3.1
Determining the Optimum Hydraulic Fracture Dimensions Dimensio ns for a Well ................... ................... 33
3.1.1
Low Permeability Permeabilit y and High Permeability Case Results R esults ....................................... ....................................... 33
3.1.1.1
Low Permeability Reservoir Case .......................................... ................................................................ ...................... 34
3.1.1.2
High Permeability Perm eability Reservoir Case ............................................................... ............................................................... 36
3.2
Incorporating Hydraulic Fractures Fractur es in Reservoir Dynamic Simulators ..................... ..................... 38
3.3
Algorithm for Modelling Induced Fractures Created During Injection under
Fracturing Conditions in Reservoir Reservo ir Dynamic Simulators .................................................... .................................................... 40 4
Conclusions and Recommendations............... Recommendations..................................... ............................................ ......................................... ................... 42
References References........................................... ................................................................. ............................................ ............................................ ......................................... ................... 43 Appendices ............................................. ................................................................... ............................................ ............................................ ....................................... ................. I
A.1
Fracture Height Equations ................................................... ......................................................................... ........................................I ..................I
P a g e viii
List of Figures Figure 1. Principal stresses (Anon. g 2014)...................... 2014)............................................. .............................................. ................................... ............ 3 Figure 2. 2 . Extended Exte nded leak-off results (Crain 2013) 2 013) ........................ ............................................... .............................................. ......................... 5 Figure 3. Fracture geometry (a) PKN type (b) KGD type (c) Pseudo 3D cell approach (d) Glo bal 3D, parameterised (e) Full 3D, meshed (Yang 2011)...................... 2011)............................................ ........................................... ..................... 8 Figure 4. Warpinski and Smith analysis and notation (Valko and Economides 1995) ............ 10 Figure 5. Cinco-Ley and Samaniego graph for Hydraulic Fracture Performance with f = sf + ln (xf/rw) (Valko 2005) ............................................. .................................................................... ............................................. ............................................ ...................... 13 Figure 6. Prat’s dimensionless effective wellbore radius (Valko 2005) . .................................. .................................. 17 Figure 7. Low permeability p ermeability case model ......................................................... ................................................................................ .......................... ... 22 Figure 8. 8 . Hydraulic Hydr aulic fracture f racture for low lo w permeability perme ability case ......................................... ............................................................ ................... 22 Figure 9. High permeability case model .......................................... ................................................................. ......................................... .................. 23 Figure 10. Hydraulic fracture f racture for high permeability pe rmeability case ......................................... ........................................................ ............... 23 Figure 11. Ahmed and Economides notation for fracture height (Valko and Economides 1995) .......................................... ................................................................. ............................................. ............................................ ............................................. ..................................... .............. 24 Figure 12. Algorithm for estimating fracture dimensions created due to injection under fracturing conditions ........................................... ................................................................. ............................................ ............................................. .......................... ... 32 Figure 13. Folds of increase and fracture fractur e volume vs. folds of increase for low permeability permeabil ity case .......................................... ................................................................. ............................................. ............................................ ............................................. ..................................... .............. 35 Figure 14. Folds of increase and fracture volume vs. folds of increase for high permeabilit y case .......................................... ................................................................. ............................................. ............................................ ............................................. ..................................... .............. 37 Figure 15. Increase in cumulative oil production for low permeability permeabilit y case ........................... ........................... 38 Figure 16. Increase in cumulative c umulative oil production for high permeabilit y case .......................... .......................... 38
P a g e ix
List of Tables Table 1: Low permeability permeab ility case input .......................................... ................................................................ ............................................ ...................... 20 Table 2: High permeability case input .......................................... ................................................................ ............................................ ...................... 20 Table 3: Model dimensions summary .......................................... ................................................................ ............................................ ...................... 21 Table 4: Low permeability permeab ility case results ............................................... ...................................................................... ..................................... .............. 34 Table 5: High permeability case results .......................................... ................................................................. ......................................... .................. 36 Table 6: Run time and storage capacity requirement for base cases and cases with induced fracture modelling...................................................... ............................................................................ ............................................ ......................................... ...................40
Pa ge x
Nomenclatu Nomen clature re A = the fracture surface area at any instant during injection, ft2 Ae = the fracture surface area at the end of pumping, ft2 Bo= the oil formation volume factor, rb/STB CL = leak-off coefficient ft/s0.5 E’ = strain modulus, psi
Fcd = the fracture dimensionless conductivity, dimensionless FOI = folds of increase, dimensionless h = the flow unit height, ft hd = the lower height growth, ft hds = the dimensionless thickness, dimensionless hf = = fracture height, ft h p = the perforation interval length, ft hs = the thickness of a symmetry element, ft hu = the upper height growth, ft i = half injection rate, ft3/s k = permeability, mD k 00 00 = the pressure at the middle of the crack, psi k 1 = the slope of net pressure, psi 0.5 K (C,2) (C,2) = fracture toughness in the upper layer, psi.ft 0.5 K (C,3) (C,3) = fracture toughness in the lower layer, psi.ft
k f f = = the fracture permeability, mD k h = the horizontal permeability, mD k v = the vertical permeability, mD
P a g e xi
N prop = the dimensionless proppant number, dimensionless p bhpf = = the bottom-hole flowing pressure, psi pcp = the pressure at mid perforation, psi pn,w = the net wellbore pressure, psi r e = the drainage radius, ft r w = the wellbore radius, ft r w’ is the effective wellbore radius, ft Sf = = the skin factor due to fracture, dimensionless S p = spurt loss coefficient, ft t = time, second vf = the total fracture volume of both wings, ft3 vL = leak-off velocity, ft/s w = average fracture width, ft wf = fracture width, ft ww,0 = the maximum fracture width at the wellbore, ft xf = fracture half-length, ft α = the exponent of fracture length growth (constant), dimensionless
µ = the viscosity, cP ρ = density, lb/ft3 σ1 = the minimum horizontal stress in the targeted layer, psi σ2 = the minimum horizontal stress in the upper layer, psi σ3 = the minimum horizontal stress in the lower layer, psi σmin = the minimum horizontal stress, psi
Pa ge 1
1
Project Scope and Objectives
1.1 I nduce nduced d F ractur es
Induced fracturing is a stimulation method used to accelerate the production and increase the ultimate recovery of hydrocarbon reservoirs by fracturing the reservoir rock (Anon. a 2013). Fracturing the rocks creates high conductivity channels growing into the reservoir away from the wellbore, providing communication between the two (Anon. b 2013). These fractures are called induced fractures since they are introduced to the reservoir and are not formed due to natural causes (e.g. tectonic activities). Since the 1940s, induced fracturing has proven to be an effective method for developing low permeability reservoirs and increasing the commercial viability of the development of conventional reservoirs (Taleghani et al. 2013). Also, induced fractures have made it possible to produce hydrocarbon from shale formations (tight reservoirs) where conventional technologies are ineffective (Anon. c 2014). Progress in hydraulic fracturing technologies has resulted in a huge increase in the oil and gas reserves worldwide by making the development of unconventional reservoirs feasible (Anon. d 2014). 2014). There are three types of induced fractures: hydraulic fractures; fractures created by fluid (usually water and/or polymer) injection under fracturing conditions; and thermal fracturing (Taleghani et al. 2013). Hydraulic fractures are created by injecting specially engineered fluid under high pressure for a short period of time to break the rocks. The created fractures are kept open after treatment using proppant (a material materi al similar to sand grains) of a particular size, which is mixed with the treatment fluid (Anon. e 2014). Another type of induced fracture is created by the continuous injection of fluid under high pressure into the reservoir (greater than the fracture initiation pressure to create the fracture, greater than the closure pressure to keep the fracture open and greater than the fracture
Pa ge 2
propagation pressure to extend ex tend the fracture). These fractures are closed once on ce the fluid injection stops or the injection pressure becomes less than the fracture closure pressure (Moreno et al. 2005). The final type of induced fracture is thermal fracturing. Thermal fractures are created due to the difference between the temperature of the reservoir rock and that of the inj ected fluid, with the latter being colder (Anon. f 2013). 2013). Only the first two types of induced fractures will be considered in this work. Fracture dimensions are considered the most important factor in induced fracturing for three main reasons: the incremental increase of production/injection rates is directly dependent on the fracture dimensions; the cost of creating the fracture is directly proportional to the fracture volume; and there is the possibility of induced fractures growing into unintended zones like fresh water zones. The environmental impacts associated with hydraulic fracturing fracturi ng are the main reason for it being a controversial topic among the public (Shukman 2013). Therefore, it is necessary to simulate the induced fracture propagation, dimensions and recession before the actual operations take place (Xiang 2011). Extensive work has been done to simulate the fracture propagation and dimensions. There are multiple analytical and numerical models available in the literature for estimating fracture dimensions, propagation and recession with different geometries. They include two-dimensional, three-dimensional and pseudo three-dimensional models (Yang 2011). The advantage of simulating fracture dimensions and propagation using the algorithms and methods introduced in this work is that they incorporate the actual reservoir dynamic simulator constraints and pressure data for the whole life of the field. Also, they take into account the practical limitations to estimate the optimum fracture dimensions, resulting in the maximum possible increase in production or injection rates for the wells. Therefore, Theref ore, this results in robust production and injection forecasts for reservoirs with induced fractured wells, and thus more
Pa ge 3
representative economics for field development. Estimating the optimum hydraulic fracture dimensions, modelling hydraulic fracture dimensions, induced fracture prop agation in reservoir dynamic simulators, and estimating the height growth of induced fractures are all covered in this work. Over the past 70 years, extensive work has been done on induced fracturing. This work is documented and can be found in the literature. The following sections discuss topics related to induced fracturing available in the literature. 1.1.1 F racture Orientation Orientation
Based on rock mechanics, there are three principal stresses acting on underground formations. These are the overburden stress, the maximum horizontal stress, and the minimum horizontal stress, as shown in Figure in Figure 1.
Figure 1. Principal stresses (Anon. g 2014) 2014)
These stresses are usually anisotropic in that they differ in magnitude based on direction (Anon. stres s (i.e. opening a 2013). Fractures propagate in a direction which is perpendicular to the least stress in the direction of the least resistance) (Anon. h 2010). The overburden stress acting on a
Pa ge 4
formation is due to the weight of the rocks above that formation, which depends on the formation depth (Golf-Racht 1980). Based on practical experience, for formations deeper than 2000 ft, the overburden stress is the largest principal stress, followed by the maximum horizontal stress; minimum horizontal stress is the smallest principal stress and the fractures are more likely to be vertical (Anon. h 2010). For formations shallower than 2000 ft, the maximum horizontal stress is the largest stress, followed by the minimum horizontal stress, and the overburden stress is the smallest principal stress (Anon. h 2010). Therefore, for such formations, the fractures will be horizontal, opening in the vertical direction with an environmental risk, since it may propagate to the surface. It can be concluded that the magnitude and direction of the principal stresses play a major role in determining the required pressure for fracture creation and propagation (Hudson 2005). The interaction between the fluid pressure in the fracture and the principa l stresses defines the shape, the vertical extent and the propagation direction of the fracture (Dubey et al. 2012). 1.1.2 L eak-off Tes Testt
This is a test performed to measure the formation fracturing pressure usually carried immediately after drilling below a new casing shoe. The test is performed by shutting-in the well and pumping fluid, usually mud, into the wellbore to gradually increase the pressure experienced by the formation. At some pressure, the fluid enters the formation (or leaks-off) by leaks-off) by fracturing the rock (Anon. e 2014). If the test is stopped just after the leak-off happens then it is called a leak-off test (LOT). If the test is extended longer until several iterations of pumping and discontinuing pumping have been performed then it is called an extended leak-off leak-o ff test (XLOT). From the XLOT, XLOT, more important parameters can be estimated and used in the propagation and recession models. Figure Figure 2 depicts XLOT results.
Pa ge 5
2 Bottomhole Pressure
3
3 ΔP
friction
4 6 5 Injection Rate 1
Time 1. 2. 3. 4. 5. 6.
Hydrostatic pressure Breakdown pressure Fracture extension pressure Initial shut-in pressure (fracture gradient) Fracture closure pressure (closure stress gradient) Fracture reopening Pressure
Figure 2. Extended leak-off results (Crain 2013)
From XLOT results, vital parameters for simulating the fracture propagation, opening and closure are estimated. These include the fracture initiation pressure, fracture propagation pressure, fracture reopening reop ening pressure and fracture fractur e closure pressure (which is synonymous s ynonymous with minimum in-situ stress and minimum horizontal stress) (Anon. (Ano n. a 2013). These data will be used as an input to modelling induced fractures created due to injection under fracturing conditions using the PKN-α method.
Pa ge 6 1.1.3 H yd ydrauli rauli c F racturin g Proce Procedure
The process of hydraulic fracturing consists of injecting specially engineered fluid at high pressure to break the formations and create high permeability channels extending away from the wellbore into the formation and establishing communication between the two. To keep the fracture open, proppant with specific grain diameter is used. The stages of hydraulic fracturing, as covered in the literature (Anon. h 2010), include: i.
Spearhead stage or acid stage which consists of water mixed with acid. The purpose
of this stage is to remove the debris and clean the wellbore. This will provide a clean wellbore and an open path for the fluid to be injected in subsequent stages. ii.
Pad stage which consists of slick water that is used to initiate the hydraulic fracture
in the formation. If the pressure stopped during this stage, the fractures would close since no proppant material has yet been used. iii.
Proppant stage which consists of injecting water and proppant material into the
fractured formation to keep the fractures open. Proppant is a non-compressible material, like sand grains, that is carried into the fractured formation to be left there after the job has been completed. Once the pressure drops, the proppant will prevent the fractures from closing, thus maintaining the enhanced permeability channels, created in the pad stage, throughout the well’s life.
iv.
Flush stage which consists of fresh water being pumped into the wellbore to flush out
and remove the excess proppant from the wellbore.
Pa ge 7 1.1.4 An alytical and Numeri ca call M ode odels ls for E stimati ng F ractur e Di me mens nsions, ions, Propaga Propagation tion and Recession
There are multiple analytical and numerical models in the literature for estimating fracture dimensions, propagation and recession. These include two-dimensional, three-dimensional and pseudo three-dimensional models (Yang 2011). Geometries of these models are shown in Figure 3. 3. The fracture geometry in reality is more complicated than the simple geometries described in these models and is governed by many parameters related to rock mechanics, insitu stresses and the fluids used (Warpinski 1989). However, these models are commonly used in industry and are widely accepted as providing an acceptable approximation for the estimation of fracture dimensions. The two famous 2D analytical models - PKN, developed by Perkins, Kern and Nordgren in 1961, and KGD, developed by Khristianovitch, Zheltov, Geertsma and de Klerk in 1955 - are widely used and often referred to in the oil and gas industry (Yang 2011). The PKN model assumes an elliptical cross-section fracture shape; fracture height is constant and fracture length is significantly greater than fracture height. The KGD model assumes a rectangular crosssection fracture shape, constant fracture height and fracture height significantly greater than fracture length (Valko and Economides 1995). The plane strain direction assumption differs between the two; a vertical direction for PKN and a horizontal direction for KGD (Xiang (Xiang 2011). Based on these assumptions, assumption s, the KGD model could be used to estimate fracture dimensions dimensio ns and shape for small fracture treatments and/or when fracture height is uncontrolled and significan tly greater than fracture length. PKN-type fractures are more interesting from a production point of view since reservoir layers are usually contained by shale layers. Therefore, it represents a case of an elongated fracture whose length is significantly greater than its height (Valko and Economides 1995).
Pa ge 8
Figure 3. Fracture geometry (a) PKN type (b) KGD type (c) Pseudo 3D cell approach (d) Global 3D, parameterised (e) Full 3D, meshed (Yang 2011)
1.1.4.1 PKN PKN-α α Model
As mentioned in Section 1.1.4, Section 1.1.4, the the PKN model assumes the fracture has constant height and that fracture length is significantly greater than fracture height. The PKN geometry depicted in Figure 3(a), 3(a), which shows an approximately elliptical shape in the vertical and the horizontal directions, is more interesting from the production point of view. The PKN-α model assumes the power law surface growth and Carter I leak-off to perform the material balance at any time during injection.
Pa ge 9
The power law surface growth assumes that the fracture surface grows according to a power law relating the area of the fracture at any time during injection to the area of the fracture at the end of the injection with an exponent, α, that is constant during the period of injection (No lte
1986). Carter introduced the leak-off velocity by relating a leak-off coefficient to the elapsed time since the start of the leak-off process and spurt loss based on the concept of Howard and Fast (Howard 1957). Equations related to both assumptions are discussed in detail s in chapter 2. 1.1.4.2 Fracture Height Growth
The two-dimensional models suggested in the previous sections are simplified approximation of the fracture dimensions and geometry. These models assume constant fracture height and leave the half-length and fracture width to be estimated from injected fluid volume. However, practical experience showed that fractures in some cases grow into unintended zones up and down the targeted interval (Valko and Economides 1995). This observation triggered the attempts to develop models able to simulate the fracture height. Since there are many variables in the system of equations, simplifying the approach is essential to result in an acceptable approximation used the simplest case by neglecting hydrostatic pressure inside the fracture and using similar properties for the upper and lower layers for approximating fracture height growth (Simonson et al. 1978). Another analysis that is widely acceptable in oil and gas industry is Warpinski and Smith analysis with a more complex case (Warpinski and Smith 1989). The notation used by them is shown in in Figure 4. 4. Alternative notation is used by Ahmed and Economides which is discussed in chapter 2.
P a g e 10
Figure 4. Warpinski and Smith analysis and notation (Valko and Economides Economides 1995)
The assumptions of Warpinski and Smith analysis (Valko and Economides 1995) are: i.
The minimum horizontal stress of the upper and lower layers can be different, but higher than minimum horizontal stress of the targeted layer.
ii.
The critical stress intensity factor (stress intensity near the tip) can be different for the upper and lower layers.
iii.
The density of the fluid is considered in the analysis
The notation will be used in this work is Ahmed and Economides notation and the set of the equations used to determine the fracture height growth is presented in the methodology chapter. 1.2 Dynamic Simul Simul at ation ion of H yd ydraul raul ic F ract ractur ur es
As for modelling the effects of induced fractures in the reservoir dynamic simulators, there are multiple approaches, which include: using a negative skin factor, creating channels of enhanced permeability gridblocks in the direction of fracture orientation, using non-neighbourhood non-neighb ourhood connections and/or a local increase of absolute permeability near the wellbore (Carlson 2006; Owen1983).
P a g e 11
These approaches are helpful to a certain extent for increasing productivity, but they do not incorporate the physics behind fracture propagation and recession (Carlson 2006; Owen1983). Also, some of the routines used for 3D pseudo models result in long run times, making them impractical for large reservoir models (Economides 2000). 1.3 Objectives
The objectives of this work are: i.
To develop an algorithm for determining the optimum hydraulic fracture dimensions of a well and incorporating hydraulic fractures in reservoir dynamic simulators.
ii.
To model induced fractures in fluid (usually water and/or polymer) injectors created during injection under fracturing conditions using reservoir dynamic simulators.
iii.
To develop an algorithm for modelling the height growth of induced fractures during injection under fracturing conditions using reservoir dynamic simulators.
These algorithms and methods are simple and easy to incorporate in the reservoir dynamic simulators to provide robust production and injection forecasts. This work is of great economic and environmental benefit because the fracture dimensions are the single most important factor which determines the increase of production/injection rates, the volume and cost of used fracturing material, and the zones into which fractures propagate.
P a g e 12
2
Methodology
This chapter represents the methodology followed to achieve the stated objectives. Derivation, calculations and Eclipse modelling are shown in this chapter for each objective. 2.1 Dete Determ rm in in g the Optimum H yd ydraul raul ic F r ac actur tur e Di me mens nsions ions for a Well Well
For the first objective of determining the optimum hydraulic fracture dimensions, the optimum fracture conductivity for pseudo-steady state and steady state flow conditions is calculated. For conventional reservoirs, reservoirs , since most wells spend the majority of their lifetime in a pseudo-steady state flow regime, the solution reached should represent the optimum hydraulic fracture dimensions of a well (Richardson 2000). The analysis starts with the use of Darcy law for pseudo-steady state flow conditions, as shown in Eq.1:
2ℎ/ 34 ………………………………………………1
where: k is permeability, h is the flow unit height, µ is the viscosity, Bo is the oil formation volume factor, r e is the drainage radius, r w is the wellbore radius and Sf is is the skin factor due to fracture. It needs to be noted that the assumption here is that the skin due to damage is not a part of the optimum fracture dimension calculations since it happens due to drilling, production and/or completions. However, skin will be used later as a check that the wellbore radius, due to damage (r s), is less than half the length of the fracture (xf ), ), to confirm that the hydraulic fracture bypasses the damage zone.
| Chapter 2 Methodology
P a g e 13
In order to maximise the production rate, the denominator of Eq. 1 has to be minimised. Defining function G as the denominator of Eq.1, as shown in Eq.2, which has to be minimised to increase rate.
34 → ………………………….…2 ………………………………………. . … ………3
Now, defining function A, as shown in Eq.3. Eq.3 .
Based on Figure 5, 5, A is the y-axis of the Cinco-Ley and Samaniego graph (Valko and Economides 1995).
Figure 5. Cinco-Ley and Samaniego graph for Hydraulic Fracture Performance Performance with f = sf + + ln (xf /r /rw) (Valko 2005)
| Chapter 2 Methodology
P a g e 14
As shown in Eq. 4, function G becomes:
34 →……………..4 34 …………. … . 5 34 ……………………………. … . 6 34 ………. … ……………. . … …………. . 7
Simplifying function G, as shown in Eqs. 5 through 7.
Two functions should be introduced here: the fracture dimensionless conductivity and the fracture volume as shown in Eqs. 8 and 9.
…………………………………………………8
where Fcd is the fracture dimensionless conductivity, k f f is is the fracture permeability, wf is is the fracture width, k is the matrix permeability and xf is is the fracture half-length. The fracture dimensions are related to each other by the fracture volume, as shown in Eq. 9.
2ℎ ……………………………………………. . 9
where vf is the total fracture volume of both wings and hf is is the fracture height.
By combining Eqs. 8 and 9, the fracture half-length can be estimated using Eq. 10.
2ℎ ……………………………………………. 10 By substituting Eq.10 in Eq. 6, as shown in Eq. 11, the G function becomes:
2ℎ 34 …………………………………………….…... 11 | Chapter 2 Methodology
P a g e 15
where A is defined in Eq. 12, as shown in Figure in Figure 5 as:
1. 65 6 5 0. 328 3 2 8 0. 1 16 1 0.18 0.064 0.005 ………………….…………… ………………….…………… 1212
To determine the Fcd value that will result in the minimum function G, the function is derived
with respect to Fcd. Substitution of function A in function G and the derivation is shown in Eqs. 13 and 14.
1. 65 6 5 0. 328 3 2 8 0. 1 16 16 l n 2ℎ 1 0.18 0.06464ln 0.00505ln 34 …………………………………………………………………………….…13 21 23. 2 5. 6 552 29. 5 21 35. 8 62 1077. 5 9 ….14 12.8 36 200
By setting the derivative equal to zero and solving for the fracture dimensionless conductivity, Fcd that results in minimum value of the G function can be found; Fcd = 1.6363. Thus, the optimum fracture dimensionless conductivity value for a fracture in a well flowing under pseudo-steady state flow conditions is 1.6363. The partial penetration skin is the function of two parameters; the penetration ratio and dimensionless thickness (b and hds) (Brons et al. 1961). The penetration ratio (b) is assumed to be set dependent upon given facts of a specific reservoir to ensure reduction in water and/or gas production and that the best part of the reservoir is targeted. Thus, the only variable to be considered for the calculation of the optimum hydraulic fracture dimensions is the
| Chapter 2 Methodology
P a g e 16
dimensionless thickness (hds). Brons and Marting defined the hds of a fractured well as shown in Eq. 15.
ℎ ℎ′ ……… ……………… ……………… ……………… ……… ……… ……………. …….…… ……115 where hds is the dimensionless thickness, hs is the thickness of a symmetry element, r w’ is the effective wellbore radius, k h is the horizontal permeability and k v is the vertical permeability (Brons et al. 1961). By analysing Eq. 15, the goal of minimising hd can be achieved by increasing r w’ is w’. Since Sf is inversely proportional to rw’, determining the minimum F cd using Sf , as above, results in the
maximum r w’ w’. The method described in this work includes starting from the minimum additional economic value gain required from a hydraulic fracturing project. Let us assume that the screening criterion of a small project for a company is a net present value of x $. Based on the oil price, the production forecast without hydraulic fracturing and hydraulic fracturing job cost, the additional increase in oil production rate results in a net present value of x$ due to accelerated production can be estimated. esti mated. Thus, the minimum required folds of increase (FOI) for the project to pass the screening criterion are calculated. To estimate the optimum fracture dimensions, relating FOI to the fracture half-length would provide a tool to directly determine the optimum fracture dimensions from a known or targeted FOI value. This is shown by relating the effective wellbore radius to FOI and using Prat’s dimensionless effective wellbore radius, as explained below. FOI and skin due to fracture are related, as shown in Eq. 16.
………………………………. … . … ………16 | Chapter 2 Methodology
P a g e 17
where the skin due to fracture is related to the effective wellbore radius, as shown in Eq. 17.
′ ……………………………………………………17 ′ …………………………18 ′ ……………………………………………………19
Thus, FOI can be related to the effective wellbore radius, as shown in Eqs. 18 and 19.
Using Eq. 19, a table of rw’ vs. FOI can be developed with the FOI value of the minimum
estimated from economics or greater. Using Prat’s dimensionless effective wellbore radius and knowing the optimum Fc d is 1.6363, rw’/xf can be found, as shown in Figure 6.
Figure 6. Prat’s dimensionless effective wellbore radius (Valko 2005)
results Thus, the optimum rw’/xf value is 0.2534, which can be used for finding the optimum x f results in the maximum FOI value. It is important to note that there is a maximum theoretical value of | Chapter 2 Methodology
P a g e 18
xf that that is equal to the drainage radius (r e), which is used as a maximum constraint for the fracture half-length calculation. It is also important to mention that the work thus far only assumes the theoretical value and does not include the practical aspect of hydraulic fracturing. For example, is it possible to achieve a fracture half-length equal to the drainage drain age radius of the reservoir? Is it possible to have all of the injected fluid contained in the pay zone, or intended zone? Valko introduced a parameter called the dimensionless dimen sionless proppant number nu mber (N prop) as shown in Eq. 20 (Valko 2001).
4 …………………………………………. . … 20
According to Valko, since the proppant cannot be contained in the pay zone and within the drainage area and for large treatments there is a great uncertainty as to where the proppant goes in both horizontal and vertical directions, direct ions, there is a practical limit to the dimensionless proppant number (Valko 2001). The practical N number is less than or equal to 0.1 for medium and high permeability formations (50 mD and above), while for low permeability reservoirs a dimensionless proppant number more than 0.5 is rarely realised. Therefore, another condition is applied in this work to the calculation performed, which is the use of N of 0.1 or less for formations with a permeability of 50mD and above, and 0.5 or less for the formations with a permeability of less than 50mD (Valko 2001). Also, it is preferable to have the fracture half-length longer than the damage radius to eliminate the impact of damage on production. If the fracture half-length is increased, the width also has to be increased to maintain the optimum Fcd value. Thus, the proppant volume required is increased so that the economic value resulted from increasing production by increasing the volume of the fracture versus the economic saving made on the proppant cost by keeping the fracture half-length less than the damaged radius has to be evaluated. Finally, Eq. 8 is used to calculate the fracture width, since everything else is known. | Chapter 2 Methodology
P a g e 19
In the case of low permeability reservoirs, the fracture width calculated by the method above can be small. Practically, the fracture width has to be large enough for the proppant pro ppant to be placed in the fracture to keep it open. Therefore, another condition to be applied is that the fracture width has to be at least two to three (2-3) times the mesh proppant grain diameter. In such a case, starting with a fracture width of 2-3 times the proppant grain diameter, the length can be calculated using N value of 0.5 or lower (applying the condition that the calculated half-length fracture is equal to or less than drainage radius). By analysing Eq.8, for low permeability reservoirs, it can be inferred that a long fracture is required for a certain minimum width determined to result in optimum Fcd value. Thus, in cases of low permeability low drainage radius reservoirs, the theoretical limitation on the maximum possible fracture half-length in addition to the practical limitations previously mentioned may result in Fcd values more than 1.6363. An excel workbook is developed to perform all the calculations mentioned in this section. Further work can be performed by linking this workbook to Eclipse Dynamic Simulator so that refinements and calculations are performed automatically.
2.1.1 Cas Case es In put f or Tes Testin tin g the Procedure Procedure Used Used to Determi Determi ne the Optimu Optimu m H yd ydrr auli c F r ac actur tur e Di me mens nsions ions for a Well
For the first objective, two cases from literature (Valko and Economides 1995) are used to test the analysis of this work, perform the calculations for the optimum fracture dimensions and perform the Eclipse Dynamic Simulation. The results r esults match very ver y well, as shown s hown in the results r esults and discussion chapter. The two cases are for a low permeability reservoir and a high permeability reservoir. Each reservoir has six water injectors and one oil producer. The oil producer is to be hydraulically
| Chapter 2 Methodology
P a g e 20
fractured to increase the reservoir’s production rate. It is necessary to determine the optimum hydraulic fracture dimensions, estimate the increase in production rate and develop the new production forecast. forecast . 2.1.1.1 Low Permeability Reservoir Case
Input data for the low permeability reservoir case are shown in Table in Table 1. Table 1: Low permeability case input
Horizontal Permeability
0.5 mD
Formation Height
105 ft
Fracture Height
35 ft
Fracture Permeability Proppant Mesh Diameter
60000 mD 70 mesh (420 µm)
Drainage radius
2100 ft
Wellbore radius
0.328 ft
Damage skin
0
2.1.1.2 High Permeability Reservoir Case
Input data for the high permeability reservoir case is shown in Table in Table 2. Table 2: High permeability case input Horizontal Permeability 500 mD
Formation Height
150 ft
Fracture Height
30 ft
Fracture Permeability Proppant Mesh Diameter
100000 mD 40 mesh (840 µm)
Drainage radius
1000 ft
Wellbore radius
0.328 ft
Damage skin
0
| Chapter 2 Methodology
P a g e 21
2.2 I ncorporatin g Hydraul ic F ractur es in Re Res servoir Dynamic Simu Simu lators
To estimate the impact of hydraulic fracturing on reservoir production and/or injection rates, a high permeability channel in a refined box model is simulated using Eclipse Reservoir Simulator. The results of the optimum dimensions for hydraulic fracture (Section 2.1) (Section 2.1) are are used to create a high permeability channel near the wellbore, extending away from it by fracture half-length in each direction. In the two cases of this work, the model is refined to have the width of the gridblocks equal to the hydraulic fracture width, as shown in Figure in Figure 8 and Figure and Figure 10. In both cases, the models have six water injectors and one hydraulically fractured oil producer, as shown in Figure 7 and and Figure 9. 9. A permeability multiplier, NTG multiplier and porosity multiplier are used for the gridblocks representing the fracture to mimic the hydraulic fracture permeability, increase the porosity of the gridblocks to 100% and increase NTG to 100%. Table Table 3 summarises the Eclipse dimensions used for the two cases.
Item
Table 3: Model dimensions summary Low permeability case High permeability case
Number of gridblocks
11 x 1000 x 3
11 x 10000 x 5
Model dimensions (ft)
410.8 x 0.014 x 35
87.2 x 1.783 x 30
| Chapter 2 Methodology
P a g e 22
Figure 7. Low permeability case model
Figure 8. Hydraulic fracture for low permeability case
| Chapter 2 Methodology
P a g e 23
Figure 9. High permeability case model
Figure 10. Hydraulic fracture for high permeability case
In other cases, models can be refined so that the gridblock width is less than the fracture width (i.e. the fracture channel includes more than one gridblock in the width direction). In the case of large models, local gridblock refinement can be performed instead to mimic the same | Chapter 2 Methodology
P a g e 24
procedure followed f ollowed in this work. Also, fracture half-length should be taken into in to consideration consider ation of refinement in case fracture half-length estimated is less than gridblock length. 2.3 An Algorithm for M od ode ell ing I nduc nduce ed F racture ractures s Cre Create ated d Dur ing I njec njection tion un de derr F r ac actur tur in g Conditi Conditi ons in Re Res ser vo voir ir Dynamic Simulators
The following sections introduce the methodology used in this work to develop an algorithm to be used to simulate the propagation, recession and dimensions dimen sions induced fractures created due to injection under fracturing conditions. 2.3.1 F racture Height Growth Growth
As mentioned in the Section 1.1.4.2, Section 1.1.4.2, Ahmed Ahmed and Economides notation (Economides 1992) is used in this work. The variables to be estimated as shown in the notation (Figure 11) are 11) are the upper (∆hu) and lower (∆h d) height growth.
Figure 11. Ahmed and Economides notation for fracture height (Valko and Economides 1995)
The solution can be achieved by solving for two unknowns in two equations (Eqs. 21 and 22).
| Chapter 2 Methodology
P a g e 25
, ℎ . { , , 1,1, , , , , , 1, , , , } , , 22 ℎ ℎ ℎ … … … … … … … … … … … … . … 21 21 , ℎ . { , , 1,1, , , , , , 1, , , , } , ,33 ℎ ℎ ℎ … … … … … … … … … … … … . . … 22 22 1 ℎ ∆ℎ2∆ℎ ∆ℎ …………………………………………………………. . … …23 1 ℎ ∆ℎ2∆ℎ ∆ℎ ………………………………………………………. . … …24 ∆ℎ 2 ∆ℎ …………………………………………………………. … …25 2ℎ ……………………………………………………………………. … …26 1 2 . 1 . 2 2 ⁄ 11 22 .tan− 11 1 …………………………. . … 27 where:
| Chapter 2 Methodology
P a g e 26
1 2 . 1 . 2 2 ⁄1 …………………………. . 28 22 .tan− 1 1 It should be noted that the following limits (Eqs. 29 through 32) are required to perform the calculation:
1,1,, 4 2 ……………………………………………………………. … 29 1,1,, 4 2 …………………………………………………………. … 30 1,1,, 4 2 ……………………………………………………………. … 31 1,1,, 2 ………………………………………………………. . … …32 where: h p is the perforation interval length, hu is the upper height growth, hd is the lower height growth, ρ is the density, σ 1 is the minimum horizontal stress in the targeted layer, σ2 is the minimum horizontal stress in the upper layer, σ3 is the minimum horizontal stress in the lower
layer, K(C,2) is fracture toughness in the upper layer, k0 is a constant, k1 is the slope of net pressure, k00 is the pressure at the middle of the crack, K(C,3) is fracture toughness in the lower layer and pcp is the pressure at mid perforation. All of the parameters in these two equations are inputs except hd and hu are the variables to be solved for. These two variables are calculated at each time step and the fracture height results is used in PKN-α calculation for determining the fracture half -length -length and width. In this work, these two equations were combined and simplified. The final complete version of these two equations with two unknowns are shown in appendix A.1. appendix A.1.
| Chapter 2 Methodology
P a g e 27 2.3.2 F racture Width and H alf-L ength
As mentioned in Chapter 1, the 1, the PKN geometry assumes an elliptical shape in the vertical and the horizontal directions for the hydraulic hydrauli c fracture. It assumes that the height, hf , is constant and that the half-length, xf , is considerably greater than the th e width, wf . The method used in this work to simulate induced fractures developed develo ped due to injection under fracturing conditions condit ions is the PKNα method, which assumes:
i.
The power law surface growth, which is represented in Eq. 33.
…………………………………………. … ………. 33
where A is the fracture surface area at time t, Ae is the fracture surface area at the end of pumping, t is time, te is the time at the end of pumping, and α is the exponent of fracture length growth and is constant during the injection period.
ii.
Carter equation I for leak-off, which is shown by Eqs. 34 and 35.
√ ……………………………………. … …………. … . . 34 2√ ……………. … ……………………. . … . 35
which has an integrated form of:
where
is leak-off velocity,
is the leak-off coefficient and t is the time elapsed since the
start of leak-off.
iii.
α is the exponent and is assumed to be known. It is equal to 4/5 fo r the case with no
leak-off and it is reasonable to assume that the exponent remains the same in the presence of leak-off. leak-of f.
| Chapter 2 Methodology
P a g e 28
With the above assumptions, the material balance at any time during injection can be written as Eq. 36.
┌ _ 23√ ┌ 2 2 …………………………. 36 √ ┌( ) 2
where A is the fracture surface area at time t, which equals xf .h .hf ; i is half of the injection rate or the injection rate for one wing of the fracture, hf is is fracture height,
_
is the average width of
the fracture, S p is the spurt-loss coefficient, CL is the leak-off coefficient, t is time, α is the
┌
exponent of fracture length growth and is the Euler Gamma Function, which can be calculated calcul ated using Eq. 37.
∞ − − ┌t ∫ …………………………………………37 Substituting for the fracture surface area to incorporate fracture half-length and fracture height, the material balance can be written as shown in Eq. 38.
_ ℎ 23√ ┌┌ √ 2 2 ………………………38 ┌( ) 2
To solve for fracture half-length, Eq. 35 can be re-arranged as shown in Eq. 39.
ℎ _ 2 2 √ √ ┌┌ ………………. … . 39 ┌(3) 2
The procedure to be followed for the calculations consists of using the input data in simple calculations and testing conditions at each time step. In the beginning, at each time step a comparison of bottom-hole flowing pressure to the fracture initiation pressure is performed and fracture is only initiated if the former is greater than or equal to the latter. Once the fracture is initiated, it either closes, remains open, closes then reopens, or propagates. At each time step following the fracture initiation, condition testing is performed and a decision is made on the | Chapter 2 Methodology
P a g e 29
fracture simulation for the next time step. In case the bottom-hole pressure is greater than or equal to the fracture propagation pressure, the PKN-α calculation method is performed and the half-length and width of the fracture are estimated. For the PKN-α model, the fracture’s dimensions can be estimated as shown in Eqs. 40 through 43.
, =− ……………………………………………. 40
where pn,w is the net wellbore pressure, p bhpf is is the bottom-hole flowing pressure and σmin is the minimum horizontal stress. Once the net wellbore pressure is calculated, the maximum fracture width at the wellbore can be found thus:
, = , ……………………………………………. . … 41
where E’ is the plane strain modulus (which can be calculated from Young’s modulus and Poisson’s ratio) and w w,0 is the maximum fracture width at the wellbore.
To solve the maximum fracture width at the wellbore, Eq. 41 can be re-arranged as shown in Eq. 42.
, 2ℎ (′ ) …………………. … …………42
The average fracture width is related to the maximum fracture width at the wellbore, as shown in Eq. 43.
where
_
283199 , ……………. … ………………………. 43 _ 0.62831
is the average fracture width and 0.628319 is the shape factor (π/5). The shape factor
contains π/4 because the vertical shape is an ellipse. Also, it contains another factor (4/5) which
accounts for the lateral variation of the width for the PKN model (Yang 2011). Once the average fracture width has been estimated, the fracture half-length is related to it as shown in Eq. 39.
| Chapter 2 Methodology
P a g e 30
To determine the fracture half-length and width, fracture height is required as an input. From fracture height calculation Section 2.3.2, Section 2.3.2, the the result is used as an input to the PKN-α calculation to estimate the maximum fracture width near the wellbore wellb ore which is then used to carry the of the t he calculations to estimate the fracture average width and half-length. To incorporate the fracture in the dynamic model, local grid refinement is performed based on the new fracture height, width and half-length calculated after each time step. Also, permeability, NTG and porosity multipliers should be applied to the gridblocks representing the fracture. The logic behind that should be performing performin g NTG and porosity multiplying to result in gridblocks NTG of 1 and porosity of 100%. As for the permeability multipliers, analogues can be used to relate the fracture width to certain fracture permeability value. Then, permeability multiplier should be used to increase the gridblocks permeability to the fracture permeability. The algorithm algorith m for the procedure described descr ibed is shown in Figure in Figure 12.
| Chapter 2 Methodology
P a g e 31
| Chapter 2 Methodology
P a g e 32
Figure 12. Algorithm for estimating fracture dimensions created due to injection under fracturing conditions
| Chapter 2 Methodology
P a g e 33
3
Results and Discussion
This chapter introduces the results of the investigation to determine the optimum hydraulic fracture dimensions for low and high permeability reservoir cases. Furthermore, it discusses the results of modelling hydraulic fractures and induced fractures created due to injection under fracturing conditions in reservoir dynamic simulators. For each of these topics, the results are discussed and further improvements are suggested.
3.1 Dete Determ rm in in g the Optimum H yd ydrr auli c F r ac actur tur e Di me mens nsions ions for a Well Well
The optimum hydraulic fracture width and half-length are estimated using the Excel workbook developed, based on the derived optimum dimensionless fracture conductivity, the practical dimensionless proppant number constraint and the minimum possible hydraulic fracture width related to proppant grain diameter.
3.1.1 L ow Per Per meab meabilil it y and and H igh Perm eabil i ty Case Case Re Res sul ts
The results of the low permeability case and the high permeability case are tabulated and discussed below. The same procedure can be followed to determine the optimum hydraulic fracture dimensions for other cases, to which the issues discussed also apply.
| Chapter 3 Results and Discussion
P a g e 34
3.1.1.1 Low Permeability Reservoir Case
The optimum hydraulic fracture dimensions estimated for the low permeability case are shown in Table in Table 4.
Half-length (xf)
Table 4: Low permeability case results 1027 (ft)
Fracture width (wf)
0.014 (ft)
Fracture volume (vf)
1010 (ft3)
FOI Skin due to fracture (sf) N Fcd
4.2 -6.676 0.5 1.643
Although the results shown in Table 4 represent the optimum fracture dimensions for the maximum folds of increase, it can be inferred from Figure from Figure 13 and Figure and Figure 14 that reducing the fracture volume to half will result in a reduction of only 0.5 in FOI. For a fracture volume of about 1000 ft3, FOI of about 4.2 is calculated, while FOI of 3.7 is calculated for a fracture volume of 570 ft3. Therefore, the cost of fracturing material and the expected increase in production due d ue to the larger FOI value should be taken in consideration co nsideration when determining the optimum hydraulic fracture dimensions for a well.
| Chapter 3 Results and Discussion
P a g e 35
Figure 13. Net present bbls increase in production and fracture volume vs. folds of increase for low permeability case
For economics to be calculated there are multiple factors that need to be taken into consideration. These include: i.
Capacity of the production system and facilities. If additional equipment and/or larger equipment sizes are required, there is an additional cost encountered for each barrel of oil produced and the additional folds of increase also incur more cost. Thus, the comparison should include this factor when estimating the saving versus the cost.
ii.
Other small projects that require investment (e.g. artificial lift, increasing the injection rate and/or deploying EOR methods). Ranking of the additional fracturing volume cost and gain versus the cost and gain of other methods should be performed to facilitate the selection of the best project for investment (the one with the highest net present value index, the highest net present value and/or the highest internal rate of return).
iii.
Additional investment in production facilities due to earlier water and/or gas breakthrough. Since created hydraulic fractures are high permeability channels, they can result in faster breakthrough of water and/or gas from aquifers, injectors and/or gas cap | Chapter 3 Results and Discussion
P a g e 36
to producers. The dimensions of the hydraulic fracture should be selected carefully to delay breakthrough since this requires larger equipment sizes and/or additional equipment for separation and treatment. iv.
Depth of damage due to drilling and/or completion phases. The depth of the damaged zone near the wellbore might be longer than the optimum fracture half-length in a few special cases. In such a case, the optimum fracture half-length can be increased (while also increasing the width to result in the same optimum fracture conductivity) to bypass formation damage.
All of these factors should be taken into account when selecting sele cting the optimum dimensions of the hydraulic fracture. 3.1.1.2 High Permeability Reservoir Case
The optimum hydraulic fracture dimensions estimated esti mated for the high permeability case are shown in Table in Table 5 and Figure and Figure 14.
Half-length (xf)
Table 5: High permeability case results 218 (ft)
Fracture width (wf)
1.783 (ft)
Fracture volume (vf)
23322 (ft3)
FOI
2.77
Skin due to fracture (sf)
-5.13
N Fcd
0.1 1.6363
| Chapter 3 Results and Discussion
P a g e 37
Figure 14. Net present bbls increase in production and fracture volume vs. folds of increase for high permeability case
Similar to the low permeability case, it can be observed that for FOI of 2.5, a fracture volume of 12500 ft3 is required. Increasing the fracture volume to 23300 ft3 (approximately double), will result in only approximately 0.25 increase increas e in FOI value. Therefore, the cost of the fracturing material and the additional gain in oil production should be taken into consideration before deciding the optimum fracture dimensions for a well, as has been shown in the two cases tested above.
| Chapter 3 Results and Discussion
P a g e 38
3.2 I ncorporatin g Hydraul ic F ractur es in Re Res servoir Dynamic Simu Simu lators
The increases in production due to hydraulic fracture fractu re for the low permeability case and the high permeability case are shown sho wn in Figure in Figure 15 and Figure and Figure 16.
Figure 15. Increase in cumulative oil production for low permeability case
Figure 16. Increase in cumulative oil production for high permeability case
| Chapter 3 Results and Discussion
P a g e 39
It can be observed that the production increase for the low permeability case is higher than the increase for the high permeability case. Creating a 600,000 mD channel inside a 0.5 mD reservoir provides a high permeability pathway for the fluid to flow through, which significantly impacts the production. On the other hand, for the high permeability case, the reservoir is able to produce at a good rate and thus the impact of the high permeability channel is not as great as for the low permeability case. Also, it can be observed that the average FOI is different from the estimated FOI from the optimum hydraulic fracture calculations. The first reason for this is that the calculations were based on the assumption of pseudo-steady state flow conditions, while in a dynamic simulation the well flows under transient flow conditions followed by pseudosteady state conditions. The second reason is that water breakthrough can be expected to occur earlier for the hydraulic fracture case, impacting the well-lifting ability and thus the oil production rate. Once the water has created a path to the well, water production will increase incre ase rapidly, since the fracture will act as a short circuit for water conducting. Therefore, it is expected that for wells with hydraulic fractures, there is faster water and/or gas breakthrough and a subsequent reduction in oil production.
| Chapter 3 Results and Discussion
P a g e 40
3.3 Al go gori ri thm f or M od ode ell ing I nduce nduced d F ract ractur ur es Crea Create ted d Dur ing I njec njection tion u nde nderr F r ac actur tur in g Conditi Conditi ons in Re Res servoir Dynamic Simulators
The impact of implementing the algorithm shown in Figure 12 in the reservoir simulator is examined using the injectors of the two cases from Section 3.1. 3.1. The procedure followed involved manually stopping the simulator after each time step to check the pressure and then manually performing the calculations, refinement and properties multiplying. This resulted in an average increase of 42% in run time for a simulation period of 200 days with an average time step length of 10 days as shown in Table in Table 6.
Table 6: Run time and storage capacity requirement requirement for base cases and cases with induced fracture modelling
Run Time for Case with No Fracture (Minutes) Run Time for Case with Induced Fracture (Minutes) Storage Required for Case with No Fracture (Megabytes) Storage Required for Case with Induced Fracture (Megabytes)
Low Permeability Case
High Permeability Case
3.3
3.1
4.9
4.1
359
342
573
512
It can be inferred that the run time and storage capacity for the low permeability case are more than those for the high permeability case. The reason is the fracture dimensions of the low permeability case is smaller than the fracture dimensions of the high permeability case and therefore more gridblocks are required due to more refinement. Additionally, the algorithm is not fully automated in the Eclipse Dynamic Simulator, but it can be easily observed that such an increase in run time is not very signific ant. Still, there are other | Chapter 3 Results and Discussion
P a g e 41
factors that can increase the expected run time, such as performing the calculations within the dynamic simulator and having a case of smaller fracture dimensions which results in increasing the number of gridblocks due to more refinement. The numerical three-dimensional fracture models are based on moving coordinate system governed by partial by partial differential differenti al equations with five unknowns that t hat need to be b e solved for either explicitly or implicitly (Xiang 2011). Such calculations are time consuming since for each time step five unknowns are required to be solved for in addition mass and pressure. In contrast to the numerical three-dimensional fracture models, the proposed algorithm has only two sets of equations to be solved for the fracture three dimensions. dimensi ons. Therefore, a reduction in both run time and storage capacity is achieved by implementing the proposed algorithm compared to using three-dimensional models. Still, due to the assumptions and simplifications in both PKN-α model and Ahmed and Economides notation after Simonson analysis mentioned in Section 1.1.4, Section 1.1.4, the the accuracy of the results of using this algorithm is expected to be lower than those of the numerical three-dimensional fracture models. Therefore, the algorithm presented provides a good approximation for modelling induced fractures growth with reduced simulation run time and storage capacity compared to three dimensional fracture models. Also, it provides more accurate results compared to the simple two-dimensional models that assumes fixed fracture height.
| Chapter 3 Results and Discussion
P a g e 42
4
Conclusions and Recommenda Recommendations tions
The work presented is of significant economic and environmental importance for oil and gas companies. In this work, optimum dimensionless hydraulic fracture conductivity is mathematically determined for pseudo-steady state and steady state flow conditions. The optimum Fcd is found to be 1.6363 and this value, in addition additio n to the practical limitations, limitations , is then used in an algorithm to determine and simulate the optimum hydraulic fracture dimensions. Refinement and gridblock properties multiplying are then performed to incorporate the effect of hydraulic fractures on production and injection forecasts from reservoir dynamic models. Additionally, in this work an algorithm to simulate induced fractures created due to injection under fracturing conditions is developed. The advantage of the algorithm is that it incorporates the pressure data and field constraints from the dynamic simulator to simulate the fracture progression, recession and dimensions dimens ions for the full life of the field. field . Also, the algorithm algori thm acts as an alerting tool for fracture growth into unintended zones. All in all, the results of this work represent a thorough tool for determining the optimum hydraulic fracture dimensions and simulating the impact of induced fractures on the field’s production and injection forecasts
using reservoir dynamic simulators. Future work can include incorporating the algorithms in reservoir dynamic simulators so that the calculations and induced fracture modelling can be performed automatically in the background.
| Chapter 4 Conclusions and Recommendations
P a g e 43
References Anon.
a 2013. Fracture mechanics. PetroWiki (16 September http://petrowiki.org/Fracture_mechanics (accessed 3 August 2014).
2013
revision),
Anon.
b 2013. Fracture. Schlumberger Oilfield Glossary, 14 November 2013, http://www.glossary.oilfield.slb.com/en/Terms/f/fracture.aspx (accessed 20 July 2014).
Anon.
c 2014. What is Fracking?. Energy From Shale, 27 June 2014, http://www.energyfromshale.org/hydraulic-fracturing/what-is-fracking (accessed 14 July 2014).
Anon. d 2014. Natural Gas Extraction - Hydraulic Fracturing. EPA, 16 July 2014, http://www2.epa.gov/hydraulicfracturing (accessed 4 August 2014). Anon. e 2014. Hydraulic fracturing. Schlumberger Oilfield Glossary, 11 January 2014, http://www.glossary.oilfield.slb.com/en/Terms/h/hydraulic_fracturing.aspx (accessed 21 July 2014). Anon.
f 2013. Thermal and Hydraulic Fracturing. PETEX , http://www.petex.com/products/?id=53 (accessed 5 August 2014).
9
July
2013,
Anon. g 2014. 2014. Mini-Frac (or DFIT) & Caprock Integrity. Big Guns Energy Services, 18 July 2014, http://www.bges.ca/cat/engineering/mini_frac.php (accessed 13 August 2014). Anon. h 2010. Hydraulic Fracturing: The Process. Fracfocus Chemical Disclosure Registry, 20 July 2010, http://fracfocus.ca/hydraulic-fracturing-how-it-works/hydraulic-fracturing process (accessed 19 July 2014). Brons, F., Marting, V. 1961. The Effect of Restricted Fluid Entry on Well Productivity. Journal of Petroleum Technology, 13 (2): 172-173. Carlson, M.R. 2006. Practical Reservoir Simulation - Using, Assessing, and Developing Results. Oklahoma, USA: PennWell Corporation. Crain, E. 2013. Fracture Pressure Basics. Crain’s Petrophysical Handbook , 21 December 2013, http://www.spec2000.net/10-closurestress.htm (accessed 8 August 2014).
| References
P a g e 44
Dubey, Dubey, S., Gudmund Gudmundsso sson, n, A. 2012. 2012. Field Field Study and Numeri Numerical cal Modeli Modeling ng of Fract Fracture ure Netwo Net work rks: s: Appl Ap plic icat atio ion n to Petroleum Reservoirs. M&S: Schlumberger J. of Modeling, Design, and Simulation 3 (1): 5-9. Economides, M.J. 1992. A Practical Companion to Reservoir Stimulation. Amsterdam: Elsevier. Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, third edition. New York: John Wiley and Sons. Golf-Racht, T. 1982. Fundamentals of fractured reservoir engineering , First edition. Amsterdam: Elsevier. Howard G.C. and Fast, c.R.: Optimum Fluid Characteristics for Fracture Extension, Drilling and Production Prac., API, 261-270, 1957 (Appendix by E.D. Carter). Hudson, J., and Harrison, J. 2005. Engineering rock mechanics, First edition. Tarrytown, NY: Pergamon. Moreno, J., Ligero, E., and Schiozer, D. 2005. Effects of Water Injection under Fracturing Conditions on the Development of Petroleum Reservoirs. International Congress of Mechanical Engineering, Ouro Preto, MG, November 6-11. Nolte, K.G.: Determination of Proppant and Fluid Schedules from Fracturing Pressure Decline, SPEPE, (July), 225-265, 1986 (originally paper SPE 8341, 1979). Owen, D. R. J. and Fawkes, A. J. 1983. Engineering Fracture Mechanics: Numerical Methods and Applications. Swansea: Pineridge Press Ltd. Richardson, M. 2000. A new and practical p ractical method for fracture design and optimisation. SPE 59736, SPE/CERI Gas Technology Symposium, Calgary, Alberta, Canada, April 3 – 5. 5. Simonson, E., Abou-Sayed, AS., and Clifton, RJ. 1978. Containment of Massive Hydraulic Fractures, SPEJ, (Feb.), 27-32, 1978. Shukman, D. 2013. What is fracking and why is it controversial?. BBC BBC NEWS, 27 June 2013, http://www.bbc.com/news/uk-14432401 (accessed 2 August 2014).
| References
P a g e 45
Taleghani, A., Ahmadi, M., and Olson, J. 2013. Secondary Fractures and Their Potential Impacts on Hydraulic Fractures Efficiency. In Effective and Sustainable Hydraulic Fracturing , first edition, Andrew P. Bunger, John McLennan and Rob Jeffrey, Chap. 38, 785-789. Brisbane: INTECH. Valko, P. (2001). HF2D Frac Design Spreadsheet. Lecture conducted from Texas A&M University, Houston, TX. Valko, P. (2005). Hydraulic Fracturing Short Course. Lecture conducted from Texas A&M University, Houston, TX. Valko, P., and Economides, M. J. 1995. Hydraulic Fracture Mechanics Mecha nics, first edition. Chichester, England: John Wiley & Sons. Warpinski, N. R., and Smith, M. B. 1989. Rock mechanics and fracture geometry. In: Recent Advances in Hydraulic Fracturing, Monograph Vol. 12, Gidley, J. L. et al. (Eds.). Richardson, TX: SPE. Xiang, J. 2011. A PKN Hydraulic Fracture Model Study and Formation Permeability Determination. MS thesis, Texas A&M University, Houston, Texas (December 2011). Yang, M. 2011. Hydraulic Fracture Optimization with a Pseudo-3d Model in Multi-Layered Lithology. MS thesis, Texas A&M University, Houston, Texas (August 2011).
| References
I
Appendices A .1 F racture Height Equations
Using Texas Instrument (TI-89) calculator, the two equations with the two unknowns to be solved for are shown below:
( ).). √ {.(++). .() −. −(−(++)} [ ( ] (++) ( ).). −(++)} √ {.(++). .() +(+(+) −( [ .(( + +] ) (−+). .
,
0.399. (ℎ(ℎ ℎ ℎ ) . [ ] ( ) + − . 0.399. (ℎ(ℎ ℎ ℎ) . .(+)
.(+). − . +.((++)..+(+(.−.) …………. . 1 1 (++) =
,2
| Appendices – Fracture Fracture Height Equations
II
().). −(++)} √ {.(++). . +(+(+) −( [ ( ] (++) ( ).). −(++)} √ {.(++). .() − −( [ ( ] (++) ( +−). . ( ) − + . .(+)
,
0.399. (ℎ(ℎ ℎ ℎ ) . 0.399. (ℎ(ℎ ℎ ℎ ) .
.(+). − . −.((++)..+(+(.−.) …………. . 1 2 (++)
,,33
=
| Appendices – Fracture Fracture Height Equations
