reservoir base fracture optimization approach

Copyright 2004, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting held in Bakersfield, California, U.S.A., 16–18 March 2004. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract A new methodology to obtain the optimum fracture treatment design for a wide range of reservoir conditions has been developed and successfully implemented. The approach discussed here significantly reduces the time required to evaluate an optimum design and limits the materials considered to only those that are appropriate for the reservoir conditions. These improvements make it an ideal methodology for real- time re-design of fracture treatments after feedback from minifrac data has been implemented. This innovative fracture design methodology has capability to determine appropriate fracture conductivity and an economic optimum fracture length while reconciling these with actual fracture growth behavior in the reservoir. The technique incorporates the following simple, automated steps: 1. Selects the most cost-effective fluid that will meet a minimum apparent viscosity requirement at a specified shear rate and temperature condition from a large industry fluid library to ensure that the proppant will be placed within the pay zone. 2. Selects a proppant that will provide the required fracture conductivity at the cheapest cost from a large industry library. 3. Determines the proppant concentration that is required at the wellbore to achieve a user-specified dimensionless conductivity criterion for a range of fracture lengths. 4. Evaluates economic criteria such as net present value (NPV) and return on investment (ROI) for different fracture lengths by comparing fracture treatment cost and revenues from production response. 5. Determines the optimum fracture conductivity profile that will have a uniform pressure drop down the fracture. The conductivity is adjusted for potential losses from non-Darcy and multi-phase flow, gel damage, embedment, and other proppant damage effects. 6. Iterates a fracture treatment schedule that will result in the best fit of the optimum conductivity profile. The methodology can help optimize fracture treatments in any type of environment. The technique is simple and can be run quickly in a real-time environment after a minifrac is conducted to make changes to the propped fracture treatment. The procedure has been implemented in a commercially available fracture design program. Introduction/Background During the last two decades, the oil and gas industry has actively been seeking methods to optimize its various processes. In the most recent activity, the drive for optimization has focused on operator cost reduction to improve project NPV. In the completion of a well, the fracturing process has the potential to add the most value because of the enormous effect it can have on overall reservoir performance, and consequently, on the economic outlook of a project. Since production pays for the entire cost of the well construction and completion, fracturing efficiency is a key factor in enabling production to meet economic needs. Another need has also been evidenced in the industry; i.e., transferring the knowledge of the aging workforce in our industry to the younger generation in order to prepare for the needs of the next two decades. By developing a computer model that captures the optimization processes that an experienced fracture designer would follow when designing a fracturing treatment, a vast store of knowledge can be transferred to the new workforce to provide the tools needed to design an optimized fracturing treatment. The optimization approach to fracture design given in this paper is new to our industry in that it approaches the problem from the opposite direction than other methods; i.e., it uses the conventional design method in most cases. What this approach accomplishes is that it reduces the time to develop an optimized solution and constantly considers economic drivers in order to find the treatment that will provide the greatest value for the given reservoir parameters. Since fracture optimization has been considered critical to economic success for quite some time, several approaches have been devised. The oldest attempt at fracture optimization was described by Prats. 1 The approach that Prats took was to optimize fracture dimensions based on a pre-determined proppant volume. Prats discovered that for a certain fracture volume, the fracture that gives the optimum performance should have a dimensionless conductivity of 1.6. Since then, several other authors have re-confirmed Prats’ findings. SPE 86991 Reservoir-Based Fracture Optimization Approach M. Y. Soliman, SPE, Audis Byrd, SPE, Harold Walters, SPE, Halliburton Energy Services, Inc., and Leen Weijers, SPE, Pinnacle Technologies, Inc. 2 SPE 86991 Theoretically speaking, this approach is probably the most effective, but unfortunately, several factors can compromise its general application. First, the fracture volume is not usually the controlling parameter unless the reservoir is highly permeable. Thus, high fracture conductivity is required to achieve a dimensionless fracture conductivity of 1.6. If the formation permeability is low, then it would be advantageous to design the fracture with significantly higher dimensionless conductivity than 1.6. Second, fracture conductivity always changes with time; proppant failure, and embedment would cause conductivity to decline with stress and time. 2 It is easy to see that loss of conductivity when starting with relatively low conductivity could seriously compromise the fracture performance. Third, it has been found that the clean up of fracturing fluid and the associated multi-phase flow in the fracture would require higher conductivity to be effective. 3 This is especially true for tighter gas-bearing formations. Fourth, the presence of several fluids inside the fracture, as could be expected in all but dry gas reservoirs, would require higher fracture conductivity than 1.6 to efficiently produce the reservoir. The potential presence of turbulence would also dictate the creation of highly conductive fractures. As an example, if the formation permeability is 0.1 md, and we design a 500-ft fracture with a dimensionless conductivity of 1.6, the required fracture conductivity is only 80 md-ft. This low conductivity would impair the cleanup of the fracture, and consequently, would negatively affect the productivity of the well. On the other hand, increasing the conductivity to the level advocated in reference 3 would be fairly inexpensive. Another optimization technique was presented by Poulsen and Soliman. 4 In their approach, Poulsen and Soliman optimized the proppant distribution inside a fracture in order to achieve an equivalent fracture with uniform conductivity. 5 Although the approach did consider some of the reservoir properties, it did not optimize the total process. In other words, the designed fracture was not necessarily the optimum fracture that had the best economical return. In addition, the process used a two-dimensional reservoir simulator approach. The technique considered state-of-the-art in today’s oilfield is to run a simulator and develop a matrix of possible solutions for the design parameters. Then, the NPV is evaluated for each design. This process is very tedious because of the many variables that come into play. There are different fluids, fluid concentrations, chemical additives, proppants, proppant concentrations, and pump rates that can make this a tedious task. The most significant problem with this approach is that the designer has to select the materials for the design matrix, and because of the numerous possibilities available, the designer may not select the best combination of fluids, fluid concentrations, proppant type, proppant size, etc. to produce the optimum solution for reservoir. This approach only picks the best option in the matrix and is not a true optimization process. For this reason, many people give up on the optimization process. This process may be also considered a simulation process, and therefore, needs to be differentiated from the design process. A design process consists of assembling the building blocks  one after another  to eventually build the best fracture design. After the optimization has been done, it is common to perform a pump-in shut-in test to verify the reservoir inputs prior to the treatment on the day of the treatment. At this point, there is not enough time on location to re-do the design matrix for the optimization process prior to pumping the treatment. It is for this reason that most of the changes on the day of the treatment are limited to adjusting the PAD volume only and not the proppant pumping schedule. Some of the new 3-D geometry models have a design tool to speed the process. The software integrates the desired proppant concentration into a pumping schedule to provide the desired proppant concentration in the fracture from the tip to the wellbore. This approach provides the speed to do the computation on location but only provides a change in the PAD volume and the pumping schedule. A true design model would use the rock mechanics and stress layers to evaluate the fracture-growth profile predicted by the model, and then, would create an optimized conductivity profile for the permeability of the reservoir. It would also create the needed geometry to develop a treatment that may deliver the selected conductivity profile using the best combinations of all the design-material options based on a cost- versus-results basis. In this way, the design model can iterate all the variables available to the fracture designer. This process can be accomplished successfully if the material criteria limits are defined in a database that the design program can use. In cases where no real data base exists, a rule-based system is developed by experts and used to fill in the gaps. The criteria can be established by testing, or in other cases, by expert opinion on the appropriate application ranges. This allows the developed technique to iterate or make selections on the rule- based system during the process to prioritize the materials appropriate for the design criteria. These criteria would include temperature, closure stress, conductivity, two-phase flow, and any other parameters that an expert would deem appropriate. By developing a design process as described above, a consistent design philosophy can be deployed to transfer best practices and enable the novice to design fracture treatments based on the latest technology. Using a consistent approach will help prove new technology and any new design philosophies developed as result of applying the new concept. This approach will ensure that the new philosophies will be transferred to everyone using this optimization approach, and thus, reduce the learning curve and training requirements. In this paper, the authors will present a methodology for designing a fracture that results in optimum return from the reservoir. This approach relies not only on theoretical considerations, but also on practical experience and considerations. Field examples illustrating the application of this methodology will be presented and discussed later in this paper. Fractured Well Productivity Ratio Fractured-well productivity has been extensively studied, and several production-increase curves have been developed and presented in literature. 6-8 These production-increase curves varied in complexity, but all predicted increase in well productivity as a result of fracturing treatments. The curves presented by Tinsley, et al 6 and Soliman 7 are probably the most comprehensive. They consider not only the effect of fracture SPE 86991 3 conductivity and length relative to the reservoir radius, they consider the effect of fracture height to the total formation height. However, most of the production increase curves and ratios are given in terms of dimensionless parameters. Using this type of presentation, it is often difficult to translate to practical values. This is the motivation for determining a new dimensional approach to presenting production increase concepts to average users. A transient pressure analysis of a vertical fractured well in pseudo-radial flow, as described by Cinco-Ley and Samaniego- V. 9 , forms the basis for the new technique. Pseudo-radial flow is appropriate for evaluating long-term production trends, which is our area of interest. The basic idea was to present the production increase contours as a function of fracture half length and fracture conductivity, both of which are widely understood variables. The process is as follows: For a given reservoir, wellbore conditions and production increase ratio contours are used to calculate the infinitely conductive fracture half length. () () ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= PI rr rL wd df /ln 2lnexp (1) Then, for the finite conductivity fracture half lengths, calculate () () ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= PI rr rr wd dw /ln lnexp ' (2) Using the dimensionless curves in Cinco-Ley and Samaniego-V, 9 calculate the dimensionless fracture conductivity, and finally, the fracture conductivity. ffDf kLCwk = (3) An example of this new type of production increase ratio curve presentation is given in Figure 1. The figure is for a well spacing of 320 acres and a wellbore diameter of 7.875 in. Reproducing the figure with a formation permeability of 0.1 md yields Figure 2. Assuming that for an efficient fracture cleanup a fD C of approximately 30 is required, if a production increase ratio of 4 is desired, then a fracture conductivity of about 1300 md-ft would be required. The relationship between the parameters that can be changed by fracture design, which include fracture half length and conductivity, are now easily related in a dimensional fashion to production increase ratios and dimensionless fracture conductivity. The average user is now able to easily examine the tradeoffs between these variables and make informed decisionsconcerning their use. Other production increase curves could be plotted easily in the fashion that would make them more valuable to the practicing engineer. Outline of the Optimization Process The integrated computer-aided design and completion approach presented in this paper includes at least three steps, and possibly, a fourth step as well. The goal of the first step is to calculate the parameters of an approximately optimized fracture using a simple graphical approach. This step includes selecting initial fracture parameters. This step also provides an initial completion design to be further optimized in the next steps. The second step involves a comprehensive approach to optimizing fracture design based on economics. The initial design of step one is the starting point of the optimization process of step two. Step three includes adjusting the model parameters on location using real data from the subject well to create an optimized treatment schedule for the fluid and proppant available on location at the time of treatment. The fourth step is the inclusion of risk analysis in this optimization process. The fourth step is optional, but it will provide another quantitative measure to the optimized design, and while not required for generating the optimum fracture design, does add an important analysis to the process. The four steps may be based on computational algorithms or may be based on neural network algorithms. The neural network algorithm accurately mimics the behavior of various computational algorithms such as fracture geometry calculation. Each of these steps will be described in more detail in the following sections. Initial Design 1. Run logs to determine physical and mechanical properties of the formation. The physical properties may include, for example, permeability, porosity, type of the fluid and fluid saturation. The physical properties are usually obtained from a combination of logs such as gamma ray, density, sonic, electric, and pulse neutron logs. The mechanical properties include Young’s Modulus and Poisson’s Ratio. The stress field, including in-situ stresses at different height locations, can also be determined. Logs such as long-spaced sonic and dipole sonic may be used for this task. If a magnetic resonance imaging (MRI) tool is used, the list of parameters may also include irreducible fluid saturation, hydrocarbon, and water permeability. The MRI log gives a strong indication of the grain size and distribution, and in some cases, clay content. Whatever parameters are selected should be digitally encoded. 2. Divide the measured and calculated formation parameters into zones from a fracturing point of view. Usually, this is done based on the calculated or measured in-situ stress. 3. Develop a limit on fracture-design parameters using the physical properties of the formation and a production increase curve such as the one discussed in the previous section. It is possible to use other production increase curves described in literature. 6-8 Unsteady-state production increase calculations may be also used. For illustration of this concept using steady-state conditions, the production increase curves discussed in the previous section and Figure 1 are used. The production- increase curves are dependent on formation permeability, fracture length, fracture conductivity, drainage area, and wellbore diameter. For example, if one is to stimulate a formation with a permeability of only 0.1 millidarcy (md), the graph of Figure 2 reveals that a fairly long fracture with conductivity in excess of 1,000 md-ft would be beneficial. This is shown more clearly in the expanded section shown in Figure 3. The graph of Figure 3 indicates that a production increase (PI) ratio of 7.5 is attainable with a fracture 4 SPE 86991 conductivity of 2,000 md-ft and a fracture length of 667 feet shown as intersection point A. To allow for an efficient fracture clean up in a fairly tight formation, a dimensionless fracture conductivity approaching 30 is usually recommended. 3 The line for a dimensionless fracture conductivity of 30 is shown in Figure 3. If the formation permeability is 100 md and the curve for dimensionless conductivity of 30 is again considered, creating a fracture length of 33 feet requires a fracture conductivity of 100,000 md-ft as shown in Figure 4 at point A. Such conductivity would be difficult to attain if not impossible. In addition, this high dimensionless conductivity is no longer required for clean up. Thus, the design should be only considering the well productivity. In this case, the program then may opt to use a dimensionless conductivity of 3, yielding a required fracture conductivity of 10,000 md-ft (see point B in Figure 4). Such fracture conductivity may be attainable using special fracture design procedures (tip screen out). In a high- conductivity fracture such as this, the use of an optimum dimensionless conductivity of 1.6 (discussed earlier in the paper) may be acceptable provided degradation of conductivity is taken into consideration. If turbulent flow is expected to take place inside the fracture (from calculated flow rate), adjustment of designed conductivity should be considered as the effective fracture conductivity is lower than the actual fracture conductivity. First, the potential for turbulence using established techniques should be calculated. A factor based on degree of turbulence and the effective fracture conductivity should be determined. The actual flow rate is then calculated. In case of steady state, the calculation can be done once; however, in the case of unsteady state, the calculation of the turbulent factor is done in steps at different times. 4. Calculate an approximate fracture width using the mechanical properties of rock (Young’s Modulus and Poisson’s Ratio). For example, a two-dimensional model equation such as those developed by Perkins and Kern can be used. 5. Calculate the required proppant deposition (such as in pounds per square feet) given the conductivity that has been determined using published tables or equations. Such determination should account for stress carried by the proppant type(s) and size of the proppant(s). Allow for possible proppant embedment, especially in soft formations, and any effect of proppant embedment in filtercake. Referring to Figure 5, the graphs show that different proppants have different disposition requirements at a conductivity of 10,000 md-ft, for example. The one requiring the least amount per square foot for this condition is a resin- coated proppant indicated at point A of Figure 5 (slightly less than four lbm per square foot). This material is suitable for a stress characteristic of approximately 3,000 psi at a conductivity of 10,000 md-ft shown as point A in Figure 6. Thus, given a calculated desired conductivity, a desired concentration, and a stress parameter, the list of available proppants may be quickly narrowed. 6. Calculate the required sand concentration in pounds per gallon (lbm/gal or ppg) for a given width and desired conductivity using digitally encoded published equations or graphs such as those illustrated in Figure 7. For the above example of a proppant deposition of about four pounds per square foot and a calculated width of 0.875 inch. Figure 7 shows that the proppant concentration in the fracturing fluid should be 10 lbm/gal; point A. 7. Calculate downhole temperature at each fluid stage using a temperature calculation model/correlation. 8. Define the best fluid to carry the proppant and keep the majority of the proppants in suspension (70%) using the calculated temperature. Factors that may be considered include leak-off coefficient, closure time, and degradation of fluid viscosity with time. 9. If it is found that the designed proppant concentration is higher than could be normally achieved, a tip-screen-out (TSO) design should be considered. In tip screen out, the fracture is designed so that the proppant reaches the tip of the fracture at the time the fracture reaches the desired length. When the proppant reaches the tip of the fracture, the fracture will stop growing in length. Then, by continuing to inject sand-laden fluid, the fracture will grow in width (balloon). After the fracture is allowed to close, the sand concentration will be significantly higher than would otherwise be achieved. Steps 6 through 9 may be reiterated to conclude the best proppant, average proppant concentration, and fluid system for the treatment. Preferably, the foregoing will be performed using a suitable software that includes digital implementations or representations of computational and materials information (for example, suitable programming to permit use of the information and relationships as represented in Figures 5-10). Refined Design The above is done more for materials selection, whereas the following fine tunes the design using the lowest cost materials. The initial run uses more generic information to limit the materials list, and in this stage of selection, the various chosen materials are run in one or more models provided in commercially available simulators. One may have noted from the above discussion that a specialized approach is needed to obtain the desired conductivity and that this phase is where that process will be optimized. The following steps should be followed: 1. Generate a desired fracture conductivity using the initial design given above and the determined desired fracture conductivity. This fracture conductivity is the fracture conductivity at the wellbore; therefore, a conductivity profile that creates a fracture with constant pressure drop down the fracture is generated. 10 2. Run a fracture simulation using the mechanical properties of rock (Young’s Modulus and Poisson’s Ratio), physical properties, zoning of the formation, and calculated in-situ stresses The simulator uses the fluid and proppant type or types that were determined in the initial design. 3. Calculate downhole temperature using a temperature calculation model/correlation. This temperature profile is used to determine the fluid degradation, and thus, proppant transport and settling to develop the in-situ proppant conductivity. 4. Define the best fluid needed to carry the proppant and keep the majority (for example, 70%) of the proppants in suspension using the calculated temperature. Factors that should be considered include leak-off coefficient, closure time, and degradation of fluid viscosity with time and temperature. If the original fluid mixture is insufficient, then more polymer or less SPE 86991 5 breaker will be adjusted to achieve the desired proppant suspension. Determine the feasibility of propped fracture length and width by running a fracturing model using selected fluid/fluids to determine the effect on the fracture geometry. This process examines whether the fracture geometry (length, height, and width profile) would significantly change from the original design. 6. Calculate the proppant profile inside the fracture, both settled or in suspension. These calculations take into consideration fluid rheology, proppant size, density and concentration. This is needed in the event that all the proppant is not perfectly transported to the designed location within the fracture (which it will not be but it should be close if the fluids are adjusted correctly), the ideal conductivity will be affected. 7. Determine proppant concentration needed at each location to produce the non-uniform fracture conductivity. This could be based on the theoretical curve developed by Soliman, 5 who developed a set of curves describing the change in conductivity with distance inside the fracture. As described by Soliman, if the conductivity inside the fracture changes, then the fracture will behave as if it has a uniform conductivity. 8. Determine initial proppant in slurry and fluid for each location. This is done by dividing the fracture into segments and adding the fluid that was lost during its transport down the fracture to give the needed concentration at the surface. This calculation considers the physical properties of the rock, the rheological properties of the fluid, and the concentration of the proppant in the fluid. 9. Adjust for settled proppant and determine proppant schedule. The fluid degradation may cause some settling, and this is where the final fluid mixture is adjusted to achieve the proppant transport needed for the conductivity profile. Steps 4 through 9 may be reiterated to conclude the best proppant, average proppant concentration, and fluid system for the treatment. 10. Run a reservoir simulation to predict well performance using the optimum fracture designs with and without fracturing and for the different designs that will result from the material selections. The reservoir simulator produces a profile of well productivity for each local optimum fracture design. Based on the chosen economic drivers (see next item) a global optimum is determined. 11. Run an economics model and plot a selected economic parameter such as NPV, Benefit/Cost Ratio, ROI, etc., versus fracture length. If working with a 3-D design, only concentration against the pay zone is considered. The above design was essentially for a two-dimensional model. It may be expanded to a three- dimensional situation by considering that the formation consists of a contributing formation and non contributing formation. The proppant concentration against the contributing formation is the critical factor. Real Time Modification to Design After the desired fluid and proppant have been determined using the above steps, those materials in suitable quantities are delivered to the actual well site (if they are not already there). Before the fracturing job is performed, however, a pumping or treatment schedule must be determined. This is accomplished by conducting the following steps: 1. Pump mini-frac job with step-down test to perform a fluid efficiency test. 2. Determine if and how much near-wellbore friction exists. 3. Determine closure, net pressure, and fluid efficiency for formation. 4. Adjust fracture-design program-model parameters to match net-pressure and leak-off rate from mini-frac. 5. Use fracture-design program model design mode to optimize fluid and proppant on location for new model parameters matched in step 4 of this section. 6. Pump treatments as per new optimized design in step 5 of this section. 7. Monitor treatment with fracture-design program in real time model to predict fracture growth during treatment. 8. Make adjustments to treatment based on model prediction as required. Real-Time Application Implementation of this design methodology in a commercial simulator allows the design strategy to be revisited many different times as the amount of knowledge about a reservoir increases during the development cycle of a well or a field. An initial design based on log-based reservoir information can be created using this methodology and can be redone in real time once additional data from breakdown injections and/or minifracs (fluid efficiency test) becomes available. These injection tests provide necessary information about fracture-closure stress, level of net pressure, and fracture-fluid efficiency (or leakoff behavior). These simple and direct measurements can have a big impact on fracture designs and should be incorporated in the final treatment design. For example, leakoff behavior observed during a minifrac has a big impact on sizing the pad to obtain a TSO in a high-permeability reservoir. In a field development situation, once a single fracture treatment is conducted, fracture design work is not finished. Instead, fracture design is a continuous task that slowly evolves as more data become available, for example, from net pressure matching of the propped fracture treatment data, from direct measurements of fracture growth using direct fracture diagnostics (such as tiltmeter or microseismic fracture mapping), or from longer-term production data. Implementation into Fracturing Simulator This methodology was recently implemented into a commercial hydraulic-fracture-growth system to 1) make the methodology widely available, and 2), to come to a more uniform design approach throughout the company. This method is illustrated in the chart in Figure 8. Once the most applicable and cheapest proppant and fluids are selected, the simulator will approximate how much proppant and fluid will be required to obtain a certain fracture length, given a user-defined dimensionless conductivity criterion. As shown in Figure 9, the simulator will determine the fracture height, conductivity, net pressure, etc. for every length the user wants, Figure 10 shows a fracture profile as a function of all the fracture lengths for which the model has been run. Once the fracture dimensions are known as well as how the actual reservoir impacts fracture growth, it also becomes 6 SPE 86991 possible to estimate a theoretical production response using the PI-conductivity plot in Figure 11. The black dots in this figure provide the solution from the simulator that is closest to a desired dimensionless conductivity criterion that is specified by the user. If the required fracture width at closure time is smaller than the width during the fracture opening in the baseline design, we do not have to go into a TSO. The required width at the wellbore at closure on proppant is a function of the width at the end of pumping and the actual proppant concentration in the fracture (close to the wellbore) at that time: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − = max max 1 )1/( CX CX ww propvol proppropvol pumpingendproppantonclosed φ (4) where Cmax is the maximum proppant concentration, φprop is the proppant porosity and Xpropvol is the proppant volume factor in gal/lbs (which equals 1/ (SG*8.345404)) with SG being the proppant’s Specific Gravity in kg/l. The desired width to obtain a certain fD C goal is calculated by embedment f ffD goalC Md k kLC w fD 2+= (5) where k is the average height-weighted permeability for all pay zones combined, L f is the fracture half-length, and k f is the permeability (after damage) of the proppant pack. M is the number of conductive multiples and d embedment is the embedment thickness of one fracture wall. Now, we can determine the maximum proppant concentration that needs to be pumped to obtain the required propped width by setting proppantonclosedgoalC ww fD = (6) If proppantonclosedgoalC ww fD > with 15 ppg is being set at the default proppant concentration, then the simulator will automatically consider a TSO design. To do this, we will keep the maximum proppant concentration at 15 ppg (or anything else the user has defined in the screen above) and keep the tip screen-out net pressure increase within user-defined limits. The net pressure increase to reach the fD C goal can be estimated as follows: () max ,, Cw w pp proppantonclosure goalC pumpingofendnetgoalCnet fD fD = (7) The net pressure at the end of pumping would be the net pressure taken at the required fracture half-length in the baseline calculation. When conducting a design, it could very well be possible (as shown in Figure 11) that the fD C goal cannot be achieved, in which case the only other available alternative is to pump better proppant or a higher proppant concentration. Economic Analysis The simulator contains a large library with fluid and proppant properties as well as pricing. Up to date pricing information is obtained from the service company’s price book. The simulator has calculated how much fluid and proppant is required for every fracture half-length, how long it will take to pump the job, and what the required horsepower will be. With this information, it is possible to calculate the approximate cost of each job as a function of the obtained propped fracture half- length as shown in Figure 12. Figure 13 shows results when a single-layer single-phase finite difference simulator is used to forecast production response of the stimulated fracture. To do a proper economic analysis, both treatment cost and expected revenues from production should be evaluated. The simulator can then be used to select the treatment with the best NPV or ROI for a user-specified time period as shown in Figure 14. Determine Treatment Schedule The proppant distribution is provided by the following equations 4 : 8 8 2 210 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ++ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ += ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ffff fD L x a L x a L x aa L x C (8) with () () () 2 2,1, 0, 0 0 fD j fD j jj C A C A Aa ++= , f L x being the distance in the fracture away from the wellbore divided by the fracture half-length, and fD C (0) is the fD C goal at the wellbore. The simulator will iterate on the proppant profile within the fracture and minimize a weighted, least-squares error of the difference between the ideal proppant profile and the actual proppant profile. The error is weighted by distance away from the wellbore to allow the profile at the wellbore to be more important than if matching it far away into the fracture. The following error is minimized while using a constant of approximately 1: )9( ))/1(( ))/1(()( 2 constantfraclengthdistanceideal constantfraclengthdistanceidealmodel error ii +− +−− = ∑ SPE 86991 7 Example Application 1 - Moderate permeability oil well in Venezuela Figures 9-14 show fracture design and optimization results for an oil reservoir at a depth of 6100 ft in the Lagunillas field in Venezuela. The horizontal section has moderate permeability of about 60 md and requires a TSO design strategy in order to obtain fD C ’s within a reasonable range. Fracture growth is believed to be somewhat confined based on anecdotal evidence that certain fracture treatment sizes do not penetrate specific layers. The stress profile is not well known – the stress in the producing sand comes from pressure- decline analysis of breakdown injections, while the sand-shale stress contrast is “guesstimated,” based on pore-pressure differences. To mimic the slight fracture confinement, a composite layering effect was used. The permeability, the driving parameter for the type of design, was determined from pressure buildup tests in nearby wells, and therefore, is relatively well known. Two selection criteria dominated the analysis: 1. What treatment can maximize economic benefits? The economic analysis resulted in a maximum NPV for a fracture half-length of about 240 ft. 2. What treatment can avoid growth in a water-bearing zone approximately 100 ft above the top perforation? Since the fracture profile for a fracture with a 240-ft half length is clearly penetrating the water-bearing zone above, a smaller half length of 150 ft was selected to avoid growth into this unfavorable zone. Example Application 2 - Low permeability Gas well in the Rockies This application is in a sandstone reservoir bounded by shale layers, all with moderate to high Young's modulus of about 3,500,000 psi which is typical for the US Rockies. The closure stress gradients are modest at about 0.55 - 0.60 psi/ft, and reservoir permeability is of order 0.1 md. A Borate Guar fluid with relative low gel loading was used to stimulate these wells. Many times, when people design a fracture, they usually do not incorporate any feedback from real data. Engineers could use what they have learned from indirect measurements such as net-pressure history matching and production data analysis to estimate what they are achieving with their propped fracture treatments. Although this type of analysis can be very beneficial to obtain a basic understanding of what is achieved, a problem with these types of analyses is that solutions can be non-unique. As a result, economic optimization may not provide a true design optimum. To address this shortcoming, the capability to calibrate fracture models with directly measured fracture dimensions, for example, using tiltmeter fracture mapping or microseismic fracture mapping is now possible. Figure 15 shows the net pressure history match. The uncalibrated net pressure inferred geometry in Figure 16 (top) shows significant out-of-zone growth. This match was conducted using the “classical” assumption that confinement was only caused by fracture closure stress contrast. However, microseismic mapping showed an actual fracture height of only 130 ft and a fracture half-length of 700 ft – very different from the uncalibrated pressure-matching result. Net pressure history matching was redone to match the actual geometry. First, we determined that a closure stress gradient in excess of 1 psi/ft was required in the shale to obtain the observed confinement, and this was considered unrealistic. Therefore, a composite layering effect was introduced. Most fracture-growth models in the industry assume that there is perfect coupling of the fracture walls along its height. As a fracture tip grows through layer interfaces, some of these interfaces may become partially de-bonded, and the fracture may start growing again at a local weakness offset from the original path, slowing vertical fracture growth. Figure 16 (bottom) shows the final fracture geometry from the calibrated model. Now that a calibrated model has been obtained by matching net pressure response AND directly measured fracture dimensions, the fracture model can be run in predictive mode to evaluate alternative designs. In this particular example, production data showed that effective propped half-length was far shorter than the 700-ft hydraulic fracture half-length, most likely due to insufficient cleanup farther away in the fracture. Significant cost savings have been achieved by pumping smaller treatments on subsequent jobs, reducing hydraulic fracture half-length while maintaining effective propped fracture half-length and production response. Figure 17 shows the fracture treatment cost for typical fracture treatments in this area. These treatment costs incorporate variable costs dictated by horsepower, level of surface pressure and rate, job duration, quantity of fluid and proppant used, and fixed costs such as mobilization. The dashed curve shows the dramatic increase in costs for the near- radial fracture growth anticipated in the initial design, which was not calibrated using direct fracture growth measurements. The solid curve shows the modest increase in costs for the confined fracture growth that was measured using direct fracture growth measurements. Figure 18 shows the differences in NPV for a 1-year period following the propped fracture treatments, assuming the following facts: 1) monthly production maintenance cost of about $500 2) average cost for fracture job with 500,000 lbs Ottawa and about 5000 bbl fluid of approximately $100,000 3) expected IP at 500 to 700 Mscfd, 35 ft pay, 0.1 mD permeability and 200 ft half-length 4) approximately 75% decline. Due to the differences in height/length growth, NPV estimates for both designs are very different. Due to dramatically increasing cost when assuming near-radial fracture growth, the NPV maximizes for a much shorter propped half-length of about 280 ft. This requires a treatment volume of about 800 bbl. The calibrated design, which incorporates the measurement of significant fracture confinement, provides a maximum NPV at a fracture half- length of more than 600 ft, and will require a fracture treatment volume of about 1500 bbl. This calibrated design and larger optimum length also requires the use of a larger amount of proppant. 8 SPE 86991 Conclusions A comprehensive methodology that equally considers both theoretical and practical aspects has been developed to optimize fracture design. 1. The procedure can help to effectively optimize fracture treatments in any type of environment and can be done quickly in real-time after a minifrac is conducted to make changes to the propped fracture treatment. 2. The methodology has been successfully implemented in fracture design software. 3. The presented field examples illustrate the validity of the presented methodology. Acknowledgments The authors of this paper would like to express their thanks to Halliburton Energy Services, Inc. and Pinnacle Technology for allowing this work to be published. They would also like to thank Nancy Woods, Carolyn Williams, and Sam Moore for their efforts in preparing the manuscript. Nomenclature , 0 a = constants , , ji A = constants fD C = dimensionless fracture conductivity max C = the maximum proppant concentration embedment d = the embedment thickness of fracture wall wk f = fracture conductivity, md-ft k = reservoir permeability, md f k = fracture permeability, md f L = fracture half length, ft M = the number of conductive multiples p = pressure net p = pressure above closure pressure (net pressure) P I = production increase ratio d r = drainage radius, ft w r = wellbore radius, ft ' w r = effective wellbore radius, ft w = fracture width proppvol X = the proppant volume factor, gal/lbs propp φ = the proppant porosity References 1. Prats, M.: “Effect of Vertical Fracture on Reservoir Behavior – Incompressible Fluid Case,” JPT (June, 1961) 105-118. 2. McDaniel, B. W.: “Conductivity Testing of Proppants at High Temperature and Stress,” SPE 15067 presented at the 56th California Regional Meeting, held in Oakland, California, April 2-4, 1986. 3. Soliman, M.Y. and Hunt, J.: “Effect of Fracturing Fluid and Its Clean-up on Well Performance,” SPE 14514, presented at the Eastern Regional Meeting held in Morgantown, West Virginia, Nov. 6-8, 1985. 4. Poulsen, D., and Soliman, M. Y.: "A Procedure for Optimal Fracturing Treatment Design," SPE 15940, presented at the Eastern Regional Meeting held in Columbus, Ohio, November 12-14, 1986. 5. Soliman, M. Y.: "Fracture Conductivity Distribution Studied,” Oil & Gas Journal, February 10, 1986. 6. Tinsley, J. M., Tiner, R., Williams, J. and Malone, W. T.: “Vertical Fracture Height — Its effect on Steady State Production Increase,” JPT, May 1969, 633-638. 7. Soliman,M.Y.:“Modifications to Production Increase Calculations for a Hydraulically Fractured Well,” JPT, Jan. 1983. 8. McGuire, W.J, and Sikora, V. J.: “The Effect of Vertical Fracture on Well Productivity,” Trans. AIME, (1960) 219, 401-405. 9. Cinco-Ley, H. and Samaniego-V., F.:“Transient Pressure Analysis for Fractured Wells,” JPT, Sept. 1981, 1749-1758. 10. Perkins, T. K. and Kern, L. R.: “Width of Hydraulic Fractures,” JPT (Sept. 1961) 937-49. SI Metric Conversion Factors bbl x 1.589 873 E - 01 = m 3 gal x 3.785 412 E - 0 3 = m3 bbl/min x 2.649 788 E - 02 = m 3 /h ft x 2.831 685 E - 02 = m 3 in x 2.54* E + 01 = mm md x 9.869 233 E - 04 = m 3 psi x 6.894 757 E + 00 = kPa *Conversion factor is exact SPE 86991 9 Figure 1 - Fractured Well Production Increase Curves 1E3 1E4 1E5 1E6 1E7 0 200 400 600 800 1000 Fracture Cunductivity (md-ft) Fracture Half Length Well Diameter 7.875 (in) Spacing 80 (acre) 8765432 1 10 100 1E3 1E4 0.1 1 10 100 1E3 10 100 1E3 1E4 1E5 100 1E3 1E4 1E5 1E6 Permeability 0.1 Production Increase 0.01 1 10 100 10 SPE 86991 Figure 2  Fractured Well Production Increase Example Figure 3 - Expanded view o f Production Increase Curve Figure 4  Production Increase curves. 1 Permeability 0.1 md Well Spacing 320 acre Hole Diameter 7.875 in 0 100 200 300 400 500 600 700 800 900 1000 Fracture Half Length (ft) 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8 9 10 100 1000 10000 Fracture Conductivity (md-ft) 3 2 C fD 10 30 5 4 PI 6 Fracture Conductivity (md-ft) Fracture Half Length (ft) 2000 1000 600 610 620 630 640 650 660 670 680 690 700 30 A B PI C fd 7 7.5 [...]... half-lengths 1.0 6250 14 SPE 86991 107 Fracture Conductivity md-ft Permability; 60 0md Well spacing; 320.0 acres CfD goal; 1.6 4 PI 3 106 2 105 104 1 103 102 0 100 200 300 400 500 600 700 800 900 1000 Fracture Half Length Figure 11 - Estimated PI ratio as a function of fracture half-length, together with dimensionless fracture conductivity for various different fracture half-lengths Note that in the... 0 0 0.0 150.0 300.0 450.0 600.0 0.00e+00 750.0 0.00e+00 Final Prop Len (ft) Figure 17 - Estimated fracture treatment cost as a function of propped fracture length for uncalibrated design (green) and calibrated design (black) For radial fracture growth, fracture costs increase dramatically to obtain a fracture half-length beyond 300 ft The uncalibrated design calls for a treatment volume of about 800... -100 0.0 150.0 300.0 450.0 600.0 750.0 Final Prop Len (ft) Figure 18 - NPV as a function of propped fracture length for uncalibrated design (green) and calibrated design (black) For radial fracture growth, NPV maximizes around a fracture half-length of 280 ft, whereas the Optimum fracture half-length based on a calibrated model analysis is larger than 600 ft ... 5000 0 0.0 180.0 360.0 540.0 720.0 Final Fracture Half Length (ft) Figure 12 Fracture treatment cost as a function of fracture half-length 900.0 SPE 86991 15 Lifetime PI Ratio Cum HC Prod (Mbbls) 2.5 2.0 1.5 1.0 0.5 0.0 0.0 160.0 320.0 480.0 640.0 800.0 Final Fracture Length (ft) Figure 13 Production response as a function of fracture half-length Incr’l NPV (M$) Incr’l ROI (%) Final NPV (M$) Return On... 720.0 Fracture Half Length (ft) Figure 9 - Figure Design Criteria vs Length Concentration of Proppant in Fracture (lb/ft2) Width Profile (in) 0.25 0 0.25 250 500 750 FracproPT Layer Properties Rocktype 1000 Shale 5750 Stress (p 5750 Shale 6000 6000 Shale Shale 6250 Proppant Concentration (lb/ft2) 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Shale 0.80 0.90 Figure 10 - Fracture Profile for various different fracture. .. approximate proppant and fluid required as a function of fracture half-length • All for a user-defined CfD NPV analysis Price book information • Forecast production response for all fracture lengths • Obtain cost for approximate fracture treatment requirements (fluid, proppant mobilization and horsepower) Select optimum economic treatment • Cross check with reservoir limitations (e.g Avoiding growth in water-bearing... pressure history match using initial physical assumptions Figure 16 - Estimated fracture for net pressure history match using initial physical assumptions (top) and utilizing matching of both net pressure history and directly observed fracture geometry (bottom) The dots represent the microseismic events that were measured during the fracture treatment SPE 86991 17 Total Inj Vol (A) (bbls) Total Inj Vol (bbls)... C of 1.6 for fD fracture half-lengths beyond 140 ft as it is impossible for the given reservoir conditions to obtain more conductivity 2000 2.50e+06 25000 TSO Pressure Increase (psi) treatment Cost ($) Total Inj Vol (bbls) Max Surface Pressure (psi) Max Proppant conc (ppg) 1600 2.00e+06 20000 1200 1.50e+06 15000 800 1.00e+06 10000 400 5.00e+05 5000 0 0.0 180.0 360.0 540.0 720.0 Final Fracture Half Length... (e.g Avoiding growth in water-bearing zones) Determine accurate treatment schedule • Match actual conductivity vs Length to ideal conductivity vs Length profile Figure 8 - Fracture design and optimization process using a commercial fracture growth system SPE 86991 13 Payzone Height Coverage Ra Slurry total (bbls) Average width (in) Total Frac Ht (ft) Slurry Efficiency Surf Pressure (psi) Net Pressure... Figure 7 - Proppant Width as a Function of Concentration 20 12 SPE 86991 Import log/layer properties Insert design input parameters • Wellbore diagram • Reservoir properties • Proppant and fluid library Select optimum fluid • Select suitable fluid type for reservoir conditions • Select lowest gel loading that provides minimum apparent viscosity • Select cheapest fluid per volume Select optimum proppant . of Proppant Type 0 0 S ACFRAC Black S ACFRAC SB Ultra S ACFRAC SB Ultra-6000 S ACFRAC PR-4000 S ACFRAC PR-4000W S ACFRAC PR-6000 S ACFRAC CR S ACFRAC CR-4000 S ACFRAC CR-5000 S TEMPERED DC S. (psi) Fracture Conductivity (md-ft) 3000 6000 9000 12000 15000 10000 20000 Figure 5 - Effect of Proppant Type 0 0 S ACFRAC Black S ACFRAC SB Ultra S ACFRAC SB Ultra-6000 S ACFRAC PR-4000 S ACFRAC. optimized. The following steps should be followed: 1. Generate a desired fracture conductivity using the initial design given above and the determined desired fracture conductivity. This fracture