WO2023149814A1

WO2023149814A1 - Method for measuring proppant bridging

Info

Publication number: WO2023149814A1
Application number: PCT/RU2022/000031
Authority: WO
Inventors: Vladimir Alexandrovich PLYASHKEVICH; Dmitry Viktorovich Badazhkov; Ilya Andreevich STARKOV; Dmitry Sergeevich Kuznetsov
Original assignee: Schlumberger Canada Limited; Services Petroliers Schlumberger; Schlumberger Technology Corporation; Schlumberger Technology B.V.
Priority date: 2022-02-04
Filing date: 2022-02-04
Publication date: 2023-08-10
Also published as: AR128442A1

Abstract

A candidate hydraulic fracturing fluid composition containing proppant is selected for stimulating a subterranean formation. A bridging criterion is calculated based on the candidate fracturing fluid composition and the fracture geometry. A mathematical model and a hydraulic fracturing design are developed that consider the bridging criterion. The hydraulic fracturing design is further simulated using a computer-based fracturing simulator. Adjustments are made to the hydraulic fracturing design based on the simulation results such that bridging is minimized or avoided. A hydraulic fracturing treatment according to the final design is then performed.

Description

METHOD FOR MEASURING PROPPANT BRIDGING

Background

[0001] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0002] For decades, the oil and gas industry has performed hydraulic fracturing to enhance or prolong well productivity. Without fracturing, producing from most hydrocarbon reservoirs being developed today would not be technically or economically feasible.

[0003] During a fracturing treatment, specialized equipment pumps fluid into a well faster than can be absorbed by the formation. This causes pressure on the formation to rise until the rock fractures, or breaks down. Continued pumping causes the fracture to propagate away from the wellbore, increasing the formation surface area from which hydrocarbons can flow into the wellbore. This helps the well achieve a higher production rate than would otherwise be possible. As a result, the volume of produced hydrocarbons increases dramatically, and operators recover their development investments more quickly.

[0004] Fracturing operations employ two principal substances — proppants and fracturing fluid. Proppants are particles that hold the fractures open, preserving the newly formed pathways. Fracturing fluids may be aqueous or nonaqueous and must be sufficiently viscous to create and propagate a fracture and also transport the proppant down the wellbore and into the fracture. Once the treatment ends, the fracturing fluid viscosity must decrease enough to promote its rapid and efficient evacuation from the well.

[0005] Traditional fracturing treatments consist of two fluids. The first fluid, or pad, does not contain proppant and is pumped through casing perforations at a rate and pressure sufficient to break down the formation and create a fracture. The second fluid, or proppant slurry, transports proppant through the perforations into the open fracture. When pumping ceases, the fractures close, holding the proppant pack in place, and the fracturing fluid flows back into the wellbore to make way for hydrocarbon production.

[0006] Fracturing fluids may also contain functional additives such as fibers, fluid-loss additives, buffers, crosslinkers and the like.

[0007] To achieve adequate fracture conductivity and well production, effective proppant transport into the fracture is desirable. It is particularly desirable for the proppant to penetrate as deeply into the fracture and away from the wellbore as possible. Failure to do so may lead to proppant “bridging,” leaving a portion of the fracture unsupported.

[0008] A detailed discussion concerning proppant transport and proppant admittance into a fracture may be found in the following publication. Smith MB and Shlyapobersky JW: “Basics of Hydraulic Fracturing,” in Economides MJ and Nolte KG (eds.): Reservoir Stimulation - 3^rd Edition, John Wiley & Sons, New York (2000) 5-23-5-25.

[0009] The ability of a fracturing fluid system to adequately transport proppant may be studied in the laboratory, thereby allowing engineers to design and formulate effective fracturing fluids for a particular treatment. US Patent Application No. 2016/0320528 describes details of a laboratory apparatus and methodology for studying complex fracture networks. The technique utilizes a slot manifold having a system of branched thin channels that are joined at intersections. Fluids a pumped through the channels and intersections, enabling an evaluation of fluid flow.

Summary

[0010] The present disclosure proposes improved methods for studying proppant transport and proppant admittance into a fracture, designing hydraulic fracturing treatments based on improved mathematical models describing proppant bridging in a fracture, and performing hydraulic fracturing treatments such that proppant bridging is minimized or avoided.

[0011] In an aspect, embodiments relate to methods of formation fracturing. A candidate hydraulic fracturing fluid composition comprising proppant is selected. A bridging criterion is calculated based on the candidate fracturing fluid composition and the fracture geometry. A mathematical model of bridging is developed using the bridging criterion. A hydraulic fracturing design is then selected that takes the mathematical model into account. The hydraulic fracturing treatment is simulated based on the selected hydraulic fracturing design. Then, the hydraulic fracturing design is adjusted based on results of the simulation, such that bridging is minimized. The hydraulic fracturing treatment is performed with the adjusted hydraulic fracturing design.

[0012] In an aspect, embodiments relate to methods for identifying and evaluating proppant distribution in fractures during a hydraulic fracturing treatment. A candidate hydraulic fracturing fluid composition comprising proppant is selected. A bridging criterion is calculated based on the candidate fracturing fluid composition and the fracture geometry. A mathematical model of bridging is developed using the bridging criterion. A hydraulic fracturing design is then selected that takes the mathematical model into account. The hydraulic fracturing treatment is simulated based on the selected hydraulic fracturing design. Then, the hydraulic fracturing design is adjusted based on results of the simulation, such that bridging is minimized. A decision is made to stop or continue the hydraulic fracturing operation.

Brief Description of the Drawings

[0013] Figure 1 is a plot showing how proppant bridging in a fracture is influenced by proppant size, fracture width and proppant concentration.

[0014] Figure 2 is a schematic diagram of a laboratory apparatus for observing bridging behavior of fiber-laden proppant slurries flowing through a slot that represents a hydraulic fracture.

[0015] Figures 3a and 3b present velocity fields detected in the slot by analyzing images of an experiment using fluorescent proppant. No bridging events registered.

[0016] Figures 4a and 4b present velocity fields detected in the slot by analyzing images of an experiment using fluorescent proppant. Bridging event registered.

[0017] Figure 5 is a plot showing bridging and non-bridging zones for a series of experiments using test fluids without fibers present.

[0018] Figure 6 is an analogous plot to Fig. 7, showing bridging and non-bridging zones for a series of experiments using test fluids without fibers present.

[0019] Figure 7 is a plot showing bridging and non-bridging zones for a series of experiments using test fluids with fibers present.

[0020] Figure 8 is an alternate plot that is analogous to Fig. 9.

[0021] Figure 9 is a plot that shows the effect of fiber type on bridging behavior in the slot.

[0022] Figure 10 is a plot that shows the effect of temperature on bridging behavior in the slot.

[0023] Figure 11 shows the initial time step of a hydraulic fracturing simulation, with no bridging in the slot.

[0024] Figure 12 shows an intermediate time step of a hydraulic fracturing simulation, with some cell blockage taking place as predicted by the bridging criterion.

[0025] Figure 13 shows the final time step of a hydraulic fracturing simulation, with cell blockage taking place as predicted by the bridging criterion and the critical proppant concentration.

[0026] Figure 14 is a representation of an experiment duplicating the hydraulic fracturing simulation, showing the partial blockage at the intermediate time step.

[0027] Figure 15 is a representation of an experiment duplicating the hydraulic fracturing simulation, showing the final time step with both the blockage criterion and the critical proppant concentration are satisfied.

[0028] Figure 16 is a plot showing agreement between the simulated and actual experimental results.

Detailed Description

[0029] In the following description, numerous details are set forth to provide an understanding of the present disclosure. However, it may be understood by those skilled in the art that the methods of the present disclosure may be practiced without these details and that numerous variations or modifications from the described embodiments may be possible.

[0030] At the outset, it should be noted that in the development of any such actual embodiment, numerous implementation — specific decisions are made to achieve the developer's specific goals, such as compliance with system related and business related constraints, which will vary from one implementation to another. Moreover, it will be appreciated that such a development effort might be complex and time consuming but would nevertheless be a routine undertaking for those of ordinary skill in the art having the benefit of this disclosure. In addition, the composition used/disclosed herein can also comprise some components other than those cited. In the summary of the disclosure and this detailed description, each numerical value should be read once as modified by the term "about" (unless already expressly so modified), and then read again as not so modified unless otherwise indicated in context. The term about should be understood as any amount or range within 10% of the recited amount or range (for example, a range from about 1 to about 10 encompasses a range from 0.9 to 11). Also, in the summary and this detailed description, it should be understood that a concentration range listed or described as being useful, suitable, or the like, is intended that any concentration within the range, including the end points, is to be considered as having been stated. For example, “a range of from 1 to 10” is to be read as indicating each possible number along the continuum between about 1 and about 10. Furthermore, one or more of the data points in the present examples may be combined together, or may be combined with one of the data points in the specification to create a range, and thus include each possible value or number within this range. Thus, even if specific data points within the range, or even no data points within the range, are explicitly identified or refer to a few specific, it is to be understood that inventors appreciate and understand that any data points within the range are to be considered to have been specified, and that inventors possessed knowledge of the entire range and the points within the range.

[0031] As used herein, “embodiments” refers to non-limiting examples disclosed herein, whether claimed or not, which may be employed or present alone or in any combination or permutation with one or more other embodiments. Each embodiment disclosed herein should be regarded both as an added feature to be used with one or more other embodiments, as well as an alternative to be used separately or in lieu of one or more other embodiments. It should be understood that no limitation of the scope of the claimed subject matter is thereby intended, any alterations and further modifications in the illustrated embodiments, and any further applications of the principles of the application as illustrated therein as would normally occur to one skilled in the art to which the disclosure relates are contemplated herein.

[0032] Moreover, the schematic illustrations and descriptions provided herein are understood to be examples only, and components and operations may be combined or divided, and added or removed, as well as re-ordered in whole or part, unless stated explicitly to the contrary herein. Certain operations illustrated may be implemented by a computer executing a computer program product on a computer readable medium, where the computer program comprises instructions causing the computer to execute one or more of the operations, or to issue commands to other devices to execute one or more of the operations.

[0033] In an aspect, embodiments relate to methods of formation fracturing. A candidate hydraulic fracturing fluid composition comprising proppant is selected. A bridging criterion is calculated based on the candidate fracturing fluid composition and the fracture geometry. A mathematical model of bridging is developed using the bridging criterion. A hydraulic fracturing design is then selected that takes the mathematical model into account. The hydraulic fracturing treatment is simulated based on the selected hydraulic fracturing design. Then, the hydraulic fracturing design is adjusted based on results of the simulation, such that bridging is minimized. The hydraulic fracturing treatment is performed with the adjusted hydraulic fracturing design. [0034] In an aspect, embodiments relate to methods for identifying and evaluating proppant distribution in fractures during a hydraulic fracturing treatment. A candidate hydraulic fracturing fluid composition comprising proppant is selected. A bridging criterion is calculated based on the candidate fracturing fluid composition and the fracture geometry. A mathematical model of bridging is developed using the bridging criterion. A hydraulic fracturing design is then selected that takes the mathematical model into account. The hydraulic fracturing treatment is simulated based on the selected hydraulic fracturing design. Then, the hydraulic fracturing design is adjusted based on results of the simulation, such that bridging is minimized. A decision is made to stop or continue the hydraulic fracturing operation.

[0035] Applicant has performed experimental laboratory work to investigate dynamic bridging of proppants and fibers in fracturing fluids during placement in a fracture. As is known in the art, proppants support a fracture and preserve conductivity and well productivity after pumping has ceased and the overburden closes upon the fracture. Fibers may be present in the fracturing fluid to increase the effective viscosity, assist in proppant transport and reduce the proppant settling velocity. The positive effects of fibers may be accompanied by a negative phenomenon. Fiber-laden fluids may have a tendency to bridge across fracture openings at the wellbore, or as the fracture narrows away from the wellbore. This may result in what is known in the art as a “screenout,” meaning that the designed amount of proppant and fibers fails to enter and fill the fracture. Such operational failures may result in lower than desired well productivity.

[0036] Bridging may be classified as arising from one or more of the following phenomena.

1. Blockage owing to channel narrowness. This phenomenon is related to the proppant particle size relative to the fracture width. The larger the particle size, the greater the chance of bridging.

2. Concentration. High concentrations of particles and fibers in the fracturing fluid increase the probability of bridging.

3. Energy partitioning. Available flow energy, including shear work and kinetic energy, is considered. The greater the energy lost from inter-particle collisions, the greater the chance of bridging.

[0037] More detailed information may be found in the following publications. Vasudevan S et al.: “Field Test of a Novel Low Viscosity Fracturing Fluid in the Lost Hills Field, California,” paper SPE-68854-MS (2001).

Vasudevan S et al.: “Development of a New Bridging Criterion for Hydraulic Fracturing,” Proc. 6^th World Congress of Chemical Engineering, 23-27 September 2001, pp. 1-11.

[0038] The present study focused mainly on the blockage and concentration criteria. The bridging criterion presented by Vasudevan et al. is represented by the following equation.

where = 2.5, Cp is the volume concentration of proppant, w_cr is the critical fracture width, d is the mean proppant diameter. When the actual fracture width w exceeds w_cr, bridging may occur. An example is shown in Fig. 1, with Cp at approximately 0.175. A non-bridging zone 101 and a bridging zone 102 are indicated. Eq. 1 considers proppant only, not mixtures of proppant and fibers. The present experimental study endeavored to determine bridging criteria for such mixtures.

[0039] Dynamic bridging tests were performed in a laboratory apparatus illustrated by the schematic diagram in Fig. 2. A blender 201 for preparing test fluid mixtures is connected to a pump 202. The blender may be thermostatically controlled. Valve 203 may be opened to allow circulation of the test fluid and ensure homogeneity. Closure of valve 203 and opening of valve 204 diverts the test fluid into a transparent slot 206 that lies in a horizontal plane. The behavior of the test fluid is monitored by a pressure sensor 207, a flow meter 205 and a camera 209. Data are recorded by a computer 208. An ultraviolet light source 210 illuminates the slot for imaging studies. Waste test fluid flows into a tank 211. The channel width in slot 206 may be adjusted. Slot widths of 1, 2 or 5 mm are available.

[0040] Bridging events in the slot may be manifested in several ways: pressure increases, reduced flow rate and reduced proppant particle velocities in the slot. Observation of proppant particle velocities may be facilitated by including colored proppant which also may be fluorescent when exposed to ultraviolet light. This is particularly useful for detecting local flow discontinuities in the slot. Video recording of fluid progression through the slot is useful for observing and quantifying the fluid behavior. [0041] Therefore, the laboratory apparatus allows one to vary the following experimental parameters.

1. Component concentrations: fiber, proppant and other functional additives.

2. Flow channel width.

3. Proppant type and size.

4. Temperature. For the experiments described herein, the fluid temperature was 65°C (150°F).

5. Pumping rate. A peristaltic pump was used, and the flow rate through the slot varied between 0.5 and 1.8 L/min. Fluid velocity is calculated by factoring in the dimensions of the slot channel.

[0042] The general experimental workflow is given below. Normally, initial conditions should not cause an immediate bridging event, in order to establish the boundary of the region of proven bridging. There are two ways to conduct the experiment: (1) fix the proppant concentration and add fiber to the mixture gradually until a bridging event occurs; or (2) fix the fiber concentration and add proppant gradually.

[0043] Prepare a base fracturing fluid (e.g., a water soluble polymer gel or a viscoelastic surfactant gel). The gel may be mixed in mixing tank 201 as shown in Fig. 2. Having a uniform distribution of gelling agent in the fluid is important to avoid formation of non-dispersed aggregates (so-called “fish-eyes”) that may plug the slot, resulting in erroneous results. This may be accomplished by closing valve 204 and opening valve 203, allowing the fluid to circulate and homogenize. Temperature control is also important for experimental consistency. Therefore, using a thermostat in the test fluid reservoir is recommended, even at room temperature.

[0044] Close valve 203, open valve 204, and ensure the fluid is pumped into the slot 206 at a fixed rate. The same rate should be used during a series of experiments. Adjustment of the pump speed (RPM) is also recommended for measuring and calibrating pump performance as the fluid viscosity or channel geometry is changed.

[0045] Gradually add fiber or proppant to the mixing tank 201. The blender speed should be adjusted to maintain effective mixing. Circulation pumping as described above is recommended to ensure homogeneity of the fiber-laden proppant slurry. [0046] Observe bridge formation in the slot 206 and/or pressure increases. These are signs of a bridging event.

[0047] Video recording is useful source of supportive information for the experiments. This may be enhanced by coating up to about 5% of the proppant with a UV fluorescent material (e.g., an acrylic-base spray or other non-water-base material). During the experiment the slot is continuously exposed to UV light 210 (preferably at a frequency between 365 and 385 nm) and images are recorded by a digital camera 209.

[0048] After the experiment, each video frame is processed using a particle image velocimetry (PIV) method at each time step. A velocity profile is calculated in the chosen region of interest (ROI) of the video frames. A velocity decrease detected in the ROI indicates a bridging event. Bridging criteria are then calculated based on the experimental data for a given set of conditions, ft is possible to identify the velocities when bridging begins to occur in local areas of the slot as well as when total bridging takes place.

[0049] Examples of video frames are given in Figs. 3 and 4. The velocity field at the frames was calculated by the PIV method. A rectangular field is the ROI for analysis of bridging events. No bridging events are registered in Fig. 3a. A bridging event is registered in the circle within the ROI in Fig. 4a, denoting a zero-velocity region. The velocity distributions in the ROIs of Figures 3a and 4a are presented in Figs. 3b and 4b, respectively. Based on the velocity distribution, the velocity at which local bridging begins may be observed as a mean velocity distribution in the ROI for given conditions.

EXAMPLES

[0050] Using the aforementioned experimental apparatus and technique, a series of experiments were performed with a linear guar solution as the base gel, fibers at concentrations between 0 and 20 g/L and proppant at concentrations between 0 and 0.9 kg/L. The guar concentration varied from 0.4 to 10 g/L. The fiber and proppant descriptions are presented in Tables 1 and 2.

Table 1. List of polymer fibers.

Table 2. List of proppants.

Example 1 — No Fibers

[0051] The first set of experiments was performed without fibers in the test fluid. The fluid composition and test conditions are presented in Table 3.

Table 3. Fluid compositions and test conditions for experiments with no fibers.

[0052] The results are presented in Fig. 5. The bridging zone may be approximated as

where the actual values for dependent variables have the following values: £ = 0.065, ft = 1.75, a = 0.67. When w < w_cr , bridging occurs. The parameters

and a are the dependent characteristics related to the hydrodynamic model of fluid flow. Exact values are generated at the step of fluid-flow characterization prior to applying the bridging criterion in the calculation.

[0053] If one compares Eq. 2 with Eq. 1, it is evident that the bridging zone of Eq. 1 has a higher w/d bridging level. It should be mentioned that the experimental results that generated Eq. 2 did not depend on fluid viscosities because the guar loading was constant throughout the series of experiments.

[0054] The experimental data can be further summarized by Eq. 3, depicted graphically in Fig. 6:

Example 2 — Fluids Containing Fibers

[0055] A series of experiments was performed with fluids containing a linear guar gel, proppant and Fiber 1, as described in Table 4.

Table 4. Experimental conditions for experiments with fiber-laden fluids. * pounds of proppant added to one gallon of base fluid; ** pounds per thousand gallons of base fluid. These abbreviations are common oilfield units. [0056] The zones of bridging as a function of fiber concentration may be approximated as:

where £ = 0.065, = 1.75, a=0.67, d = —1.37, d₂ = 0.979, d is proppant mean diameter, Pf is fibers density, C* is volume proppant concentration, Cf is volume concentration of fibers in clean fluid, and d_r and d₂ are fitting coefficients. When w < w_cr , bridging occurs.

[0057] In Figs. 7 and 8, a summary of the experimental data with bridging and non-bridging areas is presented. This may also be expressed in Eq. 5:

vs w/D.

[0058] The blockage criterion from Eq. 4 has the same form as the original blockage criterion (Eq. 1), with additional fiber concentration dependence. For all proppant concentrations, the presence of fibers additively increased the area of the bridging zone, and it was seen that size of the zone increases nonlinearly as function of fiber concentration. This result may have arisen from the compressibility of the fiber pack. Each successive linear increase of w/d required significantly more fibers to cause bridging than at the previous step.

[0059] Additional experiments were performed with Fibers 1—4 in a linear gel fluid. Figure 9 shows that, while maintaining a constant w /d, C_p and Cf, each fiber had a different bridging concentration. Analysis of the experimental data suggests using Cf from Eq. 4 for Fl as Cf = Cf_X,

are actual volume concentrations of corresponding fibers. L is a fitting function:

a = 2.15, b = 9.33, c = 0.15, d = 1.14 for f2.

The terms a, b, c and d are coefficients that are directly related to the elasticity and stiffness of the fiber polymer, which are a function of temperature. The values of the coefficients apply to a temperature of 20°C. Further correction of these values for an actual treatment is explained in the next paragraph. This means that F3 has nearly the same similar bridging ability as F 1 ; F4 has bridging ability approximately 1.5 time lower than Fl; and F2 has a bridging ability 2 times lower than Fl. These correlations are applicable for cases when Cp < 0.15. For higher proppant concentrations, the difference between different fiber types becomes negligible. The absence of differences between fibers at high concentration of proppant may also be explained by strong compressibility of fiber pack. High proppant concentrations squeeze the fiber pack and dominate the fiber properties.

[0060] Experiments were performed to characterize the role of temperature on bridging of fiberladen slurries. A 12-g/L linear guar gel (Gel 2) was used to minimize the fluid viscosity impact at elevated temperatures. Gel 2 had the same rheological properties at 65 °C (149°F) as the previous 4- g/L linear gel (Gel 1) at room temperature — 24.4°C (76°F). The experimental results are presented in Fig. 10. The behavior of the temperature impact is very remarkable. At proppant concentration higher than 0.08, fewer fibers are necessary for bridging at 65°C than at 25°F. At proppant concentrations lower than 0.08, more fibers are required to achieve bridging at the higher temperature. This effect may be explained by a sufficient change of fiber flexibility at elevated temperature, and resultant ability to be compressed at higher concentrations before bridging. The experimental data may be approximated by Eq. 6 with the following coefficients: a = 0.2, b = 12.15, c =0.075, d = 1.45. For temperatures higher than 60°C (140°F), C from Eq. 4 may be replaced by Cf /L, where L is calculated from Eq. 6.

[0061] The bridging criterion proposed here may be integrated into a hydraulic fracturing simulator. It was implemented as a prototype in a hydraulic fracturing simulator comprising a fine- scale fracture hydrodynamics and in situ kinetics model (Kinetix stimulation software suite, available from Schlumberger). This simulator accounts for the influence of the distribution of mixtures of multiple fracturing materials (fluids, proppants, fibers, etc.) on fracture propagation, and calculates fracture conductivity distribution. The geomechanics model was deactivated in the simulator and it is used as simulation of 2D flow complex slurry behavior in a Hele-Shaw cell. [0062] Hele-Shaw flow is defined as Stokes flow between two parallel flat plates separated by an infinitesimally small gap, named after Henry Selby Hele-Shaw, who studied the problem. Various problems in fluid mechanics may be approximated to Hele-Shaw flows.

[0063] An example of a bridging event in the simulation is given below. For simplicity, slurry flow was modeled in a flow channel the same size as that of the bridging apparatus. The zone is a matrix of 9 x 9 cells. Each cell has a bridging flag with values of 0, 1 and 2. 0 means no bridging in a cell. 1 means bridging occurred in a cell as predicted by the blockage criterion. 2 means bridging occurred as predicted by the critical proppant concentration in a cell.

[0064] A slurry with the composition described in Table 4 was pumped in the simulated flow channel in the direction shown in Fig. 11. Figure 11 shows the Initial time step of the simulation. During pumping, bridging occurred where the slot width was minimal (Fig. 12). Bridging occurred here due to fulfillment of the blockage criterion in some of the cells (i.e., 1). Finally, bridging occurred due to fulfillment of the blockage criterion and the critical proppant concentration in other cells (i.e., 1 and 2) (Fig. 13). The simulation presented in Figs. 12 and 13 also correspond to an actual experiment. Representations are shown in Figs. 14 and 15. Bridging begins in Fig. 14 1401 and, eventually a complete proppant bridge is seen in Fig. 15 1501. The presence of bridging was further confirmed by a pressure increase in the slot.

[0065] Numerous runs with different conditions (e.g., fiber type, fiber concentration, proppant concentration and slot width) were performed in the simulator. The results are presented in Fig. 16, are based on Eq. 6., and show that the bridging criterion presented here may simulate bridging events that agree with the experimental data. Within the Kinetix simulator, bridging may also be addressed by the calculating the Bagnold criterion, which is based on the partitioning of energy in the fracture. Additional information concerning the Bagnold criterion may be found in the following publication. Garcia MH: “Sediment Transport and Morphodynamics,” Chapter 2 in Sedimentation Engineering: Processes, Measurements, Modeling and Practice, ASCE (2008).

[0066] The Bagnold criterion is given in the following equation.

Ba

fcy where Ba is the Bagnold number, Cp is the volume concentration of proppant, p is the proppant density, C _norm, is the volume concentration of fibers in fluid with proppant,

is the fiber length, k is the fluid consistency index, n is the fluid behavior index, and y is the shear rate. Eq. 7 assumes the fluid conforms to the Power Law rheological model. The simulator predicts bridging when Ba exceeds 500. In addition to the bridging criterion and the critical proppant concentration, the Bagnold criterion may be considered in the performance of the disclosed methods.

[0067] Although the preceding discussion has concentrated on the behavior of continuous proppant slurries, the present disclosure is equally valid for techniques whereby proppant is introduced to the fracture in pulses, thereby forming proppant pillars in the fracture for enhanced fracture conductivity and well productivity. An example of this technique is the HiWAY® flowchannel fracturing technique, available from Schlumberger.

[0068] For both aspects of the disclosure, the hydraulic fracturing design comprises a flow rate of the hydraulic fracturing fluid, a duration of the hydraulic fracturing stages, the total duration of the hydraulic fracturing treatment, the pressure of the hydraulic fracturing fluid and proppant mass.

[0069] For both aspects of the disclosure, the mathematical model further comprises proppant concentration, proppant average size, fiber type, fiber concentration, functional additive concentrations, temperature and fluid velocity.

[0070] The preceding description has been presented with reference to present embodiments. Persons skilled in the art and technology to which this disclosure pertains will appreciate that alterations and changes in the described structures and methods of operation can be practiced without meaningfully departing from the principle, and scope of this present disclosure. Accordingly, the foregoing description should not be read as pertaining only to the precise structures described and shown in the accompanying drawings, but rather should be read as consistent with and as support for the following claims, which are to have their fullest and fairest scope.

Claims

1. A method of formation fracturing, comprising: a. selecting a candidate hydraulic fracturing fluid composition comprising the proppant; b. calculating a bridging criterion based on the candidate fracturing fluid composition and a fracture geometry; c. developing a mathematical model of bridging using the bridging criterion calculated at step (b); d. selecting a hydraulic fracturing design that takes into account the mathematical model of step (c); e. simulating the hydraulic fracturing treatment based on the selected hydraulic fracturing design; f. adjusting the hydraulic fracturing design based on results of the simulation such that bridging is minimized; and. g. performing the hydraulic fracturing treatment with the adjusted hydraulic fracturing design. . The method of claim 1 , wherein bridging is evaluated in a laboratory slot-flow apparatus that uses optical methods for monitoring particle flow, the methods comprising Particle Image Velocimetry (PIV), Particle Tracing Velocimetry (PTV) and visual analysis.

3. The method of claim 2, wherein the optical methods comprise algorithms of connected domains identification and analysis, a local maximum identification algorithm, and a gradient analysis algorithm that is calculated at every time stage. . The method of claim 2, wherein a portion of proppant is colored with a fluorescent compound, and the slot-flow apparatus is illuminated by ultraviolet light. . The method of claim 1, wherein the mathematical model further comprises proppant concentration, proppant average size, fiber type, fiber concentration, functional additive concentrations, temperature and fluid velocity. . The method of claim 1 , wherein the mathematical model is further corrected using the Bagnold criterion. The method of claim 1, wherein the mathematical model of bridging is coupled with a mathematical model of formation fracturing according to the design of step (d). The method of claim 1, wherein the hydraulic fracturing design comprises a flow rate of the hydraulic fracturing fluid, a duration of hydraulic fracturing stages, total duration of the hydraulic fracturing treatment, a pressure of the hydraulic fracturing fluid and proppant mass. The method of claim 1, wherein the hydraulic fracturing design comprises placing the proppant in pulses. The method of claim 1, wherein the hydraulic fracturing fluid composition further comprises fibers and functional additives. A method for identifying and evaluating proppant distribution in fractures during a hydraulic fracturing treatment, comprising: a. selecting a candidate hydraulic fracturing fluid composition comprising the proppant; b. calculating a bridging criterion based on the candidate fracturing fluid composition and a fracture geometry; c. developing a mathematical model of bridging using the bridging criterion calculated at step (b); d. selecting a hydraulic fracturing design that takes into account the mathematical model of step (c); e. simulating the hydraulic fracturing treatment based on the selected hydraulic fracturing design; f. adjusting the hydraulic fracturing design based on results of the simulation such that bridging is minimized; and g. deciding whether to stop or continue the hydraulic fracturing treatment. The method of claim 11, wherein bridging is evaluated in a laboratory slot-flow apparatus that uses optical methods for monitoring particle flow, the methods comprising Particle Image Velocimetry (PIV), Particle Tracing Velocimetry (PTV) and visual analysis. The method of claim 12, wherein the optical methods comprise algorithms of connected domains identification and analysis, a local maximum identification algorithm, and a gradient analysis algorithm that is calculated at every time stage. The method of claim 12, wherein a portion of proppant is colored with a fluorescent compound, and the slot-flow apparatus is illuminated by ultraviolet light. The method of claim 11, wherein the mathematical model further comprises proppant concentration, proppant average size, fiber type, fiber concentration, functional additive concentrations, temperature and fluid velocity. The method of claim 11, wherein the mathematical model is further corrected using the Bagnold criterion. The method of claim 11, wherein the mathematical model of bridging is coupled with a mathematical model of formation fracturing according to the design of step (d). The method of claim 11, wherein the hydraulic fracturing design comprises a flow rate of the hydraulic fracturing fluid, a duration of hydraulic fracturing stages, total duration of the hydraulic fracturing treatment, a pressure of the hydraulic fracturing fluid and proppant mass. The method of claim 11, wherein the hydraulic fracturing design comprises placing the proppant in pulses. The method of claim 11, wherein the hydraulic fracturing fluid composition further comprises fibers and functional additives.