SYSTEM AND METHODS FOR DETERMINING THE EFFECT OF FRACTURE INTERFERENCE ON SHALE WELL PERFORMANCE

A system for hydraulic fracturing in a shale layer of a geological formation is described. The system includes a borehole which extends between surface of geological formation and shale layer, and a horizontal fracturing pipe which extends perpendicularly from borehole into the shale layer. The horizontal fracturing pipe includes a number of periodic perforations. The system includes a pump and a fracturing fluid to be injected by the pump into borehole and horizontal fracturing pipe. The fracturing fluid is injected through periodic perforations and stimulates fractures in shale layer. The system includes a pressure sensor and a fluid meter. The pressure sensor measures pressure of fracturing fluid in horizontal fracturing pipe. A computing device determines the spacing distance of the perforations based on a percentage of interference between the perforation and a net present value of production.

BACKGROUND

Technical Field

The present disclosure is directed to system and methods for determining the effect of fracture interference on shale well performance.

Description of Related Art

Horizontal drilling and multistage hydraulic fracturing processes are employed in shale formations over the past few years for extraction of fuel and minerals. Various hydraulic fracturing fluid systems that can be used in the fracturing process include cross-linked high viscosity systems, foam-based fluids, and slickwater systems. Cluster spacing (also referred to as fracture spacing) is a crucial factor in shale gas hydraulic fracturing design. A cluster is a group of fractures at a fracturing zone. In the situation of cluster spacings which are too close together, a stimulated reservoir volume may be affected by major fracture interference where the fractures may overlap each other and decrease the hydraulic fracturing treatment efficiency. However, overly large cluster spacing may lead to a large unstimulated reservoir volume in the middle of hydraulic fractures, which may result in poor recovery. In either situation, hydraulic fracturing would be inefficient. Consequently, a well-defined design for cluster spacing is essential to improve the stimulated reservoir volume and increase the fracturing efficiency. For example, a well-defined cluster spacing is essential to create more fractures in a large volume and improve well productivity. Horizontal drilling now allows operators to drill and set pipe for a mile or more horizontally through the same rock formation. Directional drilling contractors use sensors to detect particularly promising rock intervals within the formation and are able to move the drill string up or down, left or right as they drill the horizontal section to target intervals. However, due to high completion costs and production interference, there is a limitation to cluster spacing.

US2020/0291774 A1 describes determination of effective fracture surface-area per cluster of hydraulic fractures of the hydraulically-fractured well by estimating total effective fracture-area associated with a wellbore and estimating the relative distribution of effective fracture surface-area along the wellbore. However, the estimated effective fracture surface-area is the relative distribution of cracking and is not assocated with fracture interference.

US20070272407 A1 describes a fracture model (which is a numerical model) generated from fracture treatment of a well having a naturally fractured formation. A fracture simulator is used to determine efficacy of the well. However, the efficiency may not be reliable due lack of knowledge of the natural fracture. Therefore, none of the prior art references discloses an efficient technique of calculating a percentage of interference and determining the effect of fracture interference as a function of cluster spacing.

Accordingly, there is a need for systems and methods that determine the number of periodic perforations in a horizontal fracturing pipe which maximize a net present value of production which minimizing the percentage of interference between the cluster spacings.

SUMMARY

In an exemplary embodiment, a horizontal fracture field system for hydraulic fracturing in a shale layer of a geological formation is disclosed. The horizontal fracture field system includes a borehole which extends between a surface of the geological formation and the shale layer, a tubing which extends into the borehole between a surface of the geological formation and the shale layer; and a horizontal fracturing pipe connected to the tubing which extends perpendicularly from the borehole into the shale layer, wherein the horizontal fracturing pipe has a number of stages, each stage having at least one perforation, wherein the at least one perforation of a first stage is separated by a spacing distance from at least one perforation of a neighboring stage, wherein each spacing distance corresponds with a fracture zone in the shale layer. The horizontal fracture field system further includes a pump located at the surface of the geological formation, and a fracturing fluid configured to be injected under pressure by the pump into the borehole and into the horizontal fracturing pipe, wherein the pump is configured to inject the fracturing fluid under pressure through the perforations of the stages to fracture a fracture zone in the shale layer. The horizontal fracture field system further includes a pressure sensor configured to measure the pressure of the fracturing fluid in the horizontal fracturing pipe. The horizontal fracture field system includes a fluid meter configured to measure a volume of a material forced out of the fractures by the fracturing fluid. The horizontal fracture field system includes a computing device connected to the pump, the pressure sensor, and the fluid meter. The computing device includes electrical circuitry, a memory storing program instructions and at least one processor configured to execute program instructions to estimate a percentage of interference PI between fracture zones of neighboring stages, according to the formula:

where ACerepresents an estimated fracture surface area of the horizontal fracture field and ACarepresents an actual fracture surface area of the horizontal fracture field; determine a net present value NPV for each spacing distance; and determine the spacing distance which minimizes the percentage of interference PI while maximizing the net present value NPV.

In another exemplary embodiment, a method for building a horizontal fracture field having low cluster interference is disclosed. The method includes determining reservoir properties of a shale layer of a geological formation of interest, and calculating, by a computing device including electrical circuitry, a memory storing program instructions and at least one processor configured to execute the program instructions, an actual fracture surface area (ACa) of the horizontal fracture field, exporting, by the computing device, production data from a predetermined stimulated fracture surface area, conducting, by the computing device, a rate transient analysis (RTA) of the production data to estimate an effective stimulated fracture surface area (ACe) for a given number of periodic perforations in a horizontal fracturing pipe, calculating, by the computing device, a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa), storing, in the memory of the computing device, the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations, and iterating, by the computing device, the calculation of the ratio for a second number of periodic perforations, where the second number is greater than the first number by a step amount. The method also includes continuing, by the computing device, to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount, building, by the computing device, a proxy model to estimate a percentage of interference between the fractures as a function of spacing distance between the number of perforations and the formation properties, determining, by the computing device, a net present value (NPV) from the proxy model, estimating, by the computing device, the number of perforations which maximizes the NPV from the proxy model while minimizing the percentage of interference PI from the RTA; installing perforated sections and unperforated sections of the horizontal fracturing pipe in the horizontal fracture field based on the estimated number of perforations; and stimulating the horizontal fracture field by injecting a fracturing fluid under pressure into the horizontal fracturing pipe through the number of perforations.

In yet another exemplary embodiment, a method for hydraulic fracturing in a shale layer of a geological formation is disclosed. The method includes installing a tubing in a borehole which extends between a surface of the geological formation and the shale layer and installing a horizontal fracturing pipe which extends perpendicularly from the borehole into the shale layer, wherein the horizontal fracturing pipe has a number of stages, each stage having at least one perforation, wherein the at least one perforation of a first stage is separated by a spacing distance from at least one perforation of a neighboring stage, wherein each spacing distance corresponds with a fracture zone in the shale layer. The method further includes installing the tubing in the horizontal fracturing pipe and installing a pump at the surface of the geological formation, wherein the pump is configured to inject a fracturing fluid under pressure into the tubing, wherein the pressure of the fracturing fluid is configured to inject the fracturing fluid through the perforations and stimulate fractures in the shale layer. The method includes installing a pressure sensor at the surface of the geological formation, where the pressure sensor is configured to measure the pressure of the fracturing fluid. The method also includes installing a fluid meter at the surface of the geological formation, wherein the fluid meter is configured to measure a volume of the fracturing fluid injected into the horizontal fracturing pipe or a volume of a material forced out of the borehole by the fracturing fluid, wherein the material is one or more of oil and natural gas. The method includes connecting a computing device to the pump, the pressure sensor and the water meter, wherein the computing device includes electrical circuitry, a memory storing program instructions and at least one processor configured to execute the program instructions to estimate a percentage of interference PI between fracture zones of neighboring stages, according to the formula:

where ACerepresents an estimated fracture surface area of the horizontal fracture field and ACarepresents an actual fracture surface area of the horizontal fracture field; determining a net present value NPV for each spacing distance; and determining the spacing distance which minimizes the percentage of interference PI while maximizing the net present value NPV.

DETAILED DESCRIPTION

Aspects of the present disclosure are directed to system and methods for determining the effect of fracture interference on shale well performance so as to improve oil and gas recovery from a geological formation. Frocking fluid is composed of water, chemicals and sand, and is forcefully injected into the hydrocarbon-containing shale layer. The force of the injections props the shale open, creating cracks and fissures that allow large volumes of hydrocarbons to be extracted.

The borehole of a shale well may have horizontal shaft in which multistage hydraulic fracturing processes are employed through drilling or production tubing to extract hydrocarbons and minerals. Some of the hydraulic fracturing fluids used in the fracturing process include cross-linked high viscosity systems, foam-based fluids, and slickwater systems. Each perforation in a horizontal shaft generates a cluster of fractures at a fracturing zone. When the spacing distance of the clusters are too close together, fracture interference may occur during stimulation of the well. The fractures may overlap each other and decrease the hydraulic fracturing treatment efficiency. However, overly large fracture spacing may lead to a large unstimulated reservoir volume in the middle of hydraulic fractures, which may result in poor recovery. Aspects of the present disclosure provide a method and system for determining cluster spacing which functions to improve the stimulated reservoir volume and increase the fracturing efficiency.

Aspects of the present disclosure include determining the spacing distance between the perforations which yields the highest volume of oil/gas production and determining a number of perforations which are designed to create fractures at the fracture spacings when the well is stimulated by the forceful injection of fracturing fluid through a horizontal fracturing pipe.

A horizontal fracturing pipe may include many components, including valves, packers, liners and pressure sensors as well as pipe regions which are thin and capable of perforation by the fracturing fluid. These thin pipe regions are referred to as perforations in the present disclosure. Each section of fracturing pipe is referred to as a stage. In the present disclosure, the term “horizontal fracturing pipe” is defined as the continuous pipe formed by installing stages of sections of fracturing pipe. The pipe need not be precisely horizontally disposed in a geological formation.

FIG.1Adepicts a horizontal fracture field system100for hydraulic fracturing in a shale layer120of a geological formation132. In an example, the geological formation132may include a well.

The horizontal fracture field system100includes tubing disposed in a borehole102. The borehole102extends between a surface of the geological formation132and the shale layer120. The horizontal fracture field system100also includes a horizontal fracturing pipe104. The horizontal fracturing pipe104extends perpendicularly from the borehole102into the shale layer120. The horizontal fracturing pipe104is configured to have a number of periodic perforations. In an example, the number of perforations may be denoted by “Nf”. The horizontal fracturing pipe104includes pipe sections which connect together, where each pipe section is configured as one of a pipe section with at least one perforation and an unperforated pipe section. In an example, the type of the horizontal fracturing pipe104may be chosen or selected based on the spacing of the perforations.

The horizontal fracture field system100further includes a pump106. The pump106is located at the surface of the geological formation132. The horizontal fracture field system100also includes a fracturing fluid134. The fracturing fluid134is injected under pressure by the pump106into the borehole102through the tubing and into the horizontal fracturing pipe104.20The pump ejects the fracturing fluid134at high pressure through the periodic perforations and stimulates fractures in the shale layer120.

The horizontal fracture field system100includes at least one pressure sensor108. At least one pressure sensor108may be located at the surface of the geological formation132. There may be multiple pressure sensors located at a plurality of locations in the borehole or the horizontal fracturing pipe. The pressure sensor108is configured to measure the pressure of the fracturing fluid134in the horizontal fracturing pipe104. The horizontal fracture field system100further includes a fluid meter110. The fluid meter110may also be referred to as a flowmeter. The fluid meter110is located at the surface of the geological formation132. The fluid meter110is configured to measure the amount of fracturing fluid injected into the tubing and/or a volume of a material forced out of the fractures by the fracturing fluid134. The volume of material the fractures may include hydrocarbons, such as oil and gas, as well as drilling rock, water and small particulate matter. The fluid meter110may measure the volume of material which flows from the borehole per unit time. The fluid meter110may include a hollow cylinder through which a portion of material flows. The fluid meter110may measure the velocity of the material (or flow rate) exiting the borehole per unit time and calculate the volume of material recovered per unit time from this measurement. There may be multiple fluid meters, pressure sensors and pumps in a borehole and/or the fracturing pipe as is known in the art. For the sake of simplicity, the fluid meter110, pressure sensor108and pump106are interpreted as representing these multiple fluid meters, pressure sensors and pumps. In a non-limiting example, the fluid meter may be an E-M Flowmeter, manufactured by Century Wireline Services, Tulsa, Oklahoma, United States of America.

The horizontal fracture field system100also includes a computing device112. The computing device112is connected to the pump106, the pressure sensor108, and the fluid meter110. As shown inFIG.1A, the computing device112is wirelessly connected to the pump106, the pressure sensor108, and the fluid meter110. The computing device112includes a memory114storing program instructions and at least one processor116configured to execute program instructions and an electrical circuitry118to determine the number of the periodic perforations in the horizontal fracturing pipe104which produce a maximum volume of material forced out of the fractures without interference from breakdowns in the shale layer120between the fractures. In an example, the material forced out of the fractures includes at least one of oil and natural gas. The at least one processor is configured to the execute program instructions to estimate a percentage of interference PI between fracture zones of neighboring stages, according to the formula:

where ACerepresents an estimated fracture surface area of the horizontal fracture field and ACarepresents an actual fracture surface area of the horizontal fracture field, determine a net present value NPV for each spacing distance, and determine the spacing distance which minimizes the percentage of interference PI while maximizing the net present value NPV.

FIG.1Bdepicts an expanded view of the horizontal fracturing pipe104having perforations and located in a shale layer120.fInFIG.1B, five perforations (i.e., Nf=5) are shown. The five perforations are represented by reference numerals “124-1”, “124-2”, “124-3”, “124-4”, and “124-5”, respectively. As shown inFIG.1B, each perforation generates a cluster of fractures. In the example shown inFIG.1B, the fracture half-length (denoted by “Xf”) is represented by reference numeral “126”. In an example, the fracture half-length is 250 feet (76 meters). The cluster spacing (also referred to as fracture spacing) is represented by reference numeral “130” inFIG.1B. In an example, the cluster spacing distance is 80 feet (about 24 meters). A length of assembled horizontal fracturing pipe may extend up to a mile (1.6 km) within the shale layer120.

FIG.2depicts a flow chart200for investigating fracture interference as a function of formation properties and cluster facing.

At step202of the flow chart200, a simulated reservoir is built using data input by a user or accessed from reservoir statistics. In an implementation, the computing device112is configured to build the simulated reservoir based on a horizontal fracture field for a first number of periodic perforations. In an example, the computing device112is configured to build the simulated reservoir by calculating a function which includes a length of the reservoir, a thickness of the reservoir, an initial reservoir pressure, a reservoir bottom-hole pressure, a reservoir temperature, a reservoir formation porosity, and a reservoir permeability. The length of the reservoir, the thickness of the reservoir, the initial reservoir pressure, the reservoir bottom-hole pressure, the reservoir temperature, the reservoir formation porosity, and the reservoir permeability are known parameters which are characteristic of the borehole and reservoir, and which have been previously measured.

At step204of the flow chart200, an actual fracture surface area (ACa) of the horizontal fracture field is calculated. In an implementation, the computing device112is configured to calculate the actual fracture surface area (ACa) of the horizontal fracture field. In an example, the computing device112is configured to calculate the actual fracture surface area (ACa) based on Equation (1) provided below.

where, Hfrepresents a fracture height, Xfrepresents a fracture half-length, and Nfrepresents the number of perforations.

At step206of the flow chart200, production data and reservoir properties of a predetermined simulated fracture surface area of the horizontal fracture field are determined. In an implementation, the computing device112is configured to determine the production data and reservoir properties of the predetermined stimulated fracture surface area of the horizontal fracture field from the pump pressure, the measurements of pressure sensor108, and the fluid meter110.

At step208of the flow chart200, the production data and the reservoir properties are exported from the simulated reservoir. In an implementation, the computing device112is configured to export the production data and the reservoir properties from the simulated reservoir at the predetermined stimulated fracture surface area.

At step210of the flow chart200, a rate transient analysis (RTA) of the production data is conducted to estimate an effective fracture surface area (ACe). The computing device112is configured to conduct the rate transient analysis (RTA) of the production data to estimate the effective fracture surface area (ACe) for the given number of periodic perforations. The computing device112is configured to conduct the RTA based on a fracture half-length which ranges from 200 feet to 400 feet.

In a rate transient analysis (RTA) for a gas well, a bottom-hole pressure (denoted by “pwf”) is converted into a pseudo bottom-hole pressure (denoted by “m(pwf)”), where m is the slope. The pseudo-pressure difference between the pseudo bottom-hole pressure and the bottom-hole pressure is then normalized using the gas production rate of the gas well. The normalized pseudo-pressure difference and linear superposition time (super-t) is used to plot the RTA for Accharacterization. Normalized pseudo-pressure and linear superposition time may be calculated using Equations (2), (3), and (4), provided below.

where pirepresents the initial reservoir pressure, pwfrepresents the bottom-hole pressure, p represents the gas viscosity, z represents the compressibility factor, n represents the time step at which super-t is calculated, j represents the time step from 0 to n, and qgrepresents the gas production rate.

At step212of the flow chart200, a ratio of the ACeto the ACais calculated. In an implementation, the computing device112is configured to calculate the ratio of the ACeto ACa. The computing device112is configured to store the ratio of the ACeto the ACafor the first number of periodic perforations in the memory114.

At step214of the flow chart200, the calculation of the ratio of the ACeto the ACais iterated with different numbers of periodic perforations. The computing device112is configured to iterate the calculation of the ratio for a second number of periodic perforations. In an example, the second number is greater than the first number by a step amount. The computing device112is configured to continue to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount. In an example, the computing device112is configured to iterate the calculation of the ratio for the number of periodic perforations ranging from 2 perforations to 20 perforations with a cluster spacing ranging from 20 feet to 200 feet. In a non-limiting example, the threshold amount is 50%. In another non-limiting example, the threshold amount is 80%. The threshold amount may be selected from the range of 20% to 99% and may change as the production increases or decreases.

At step216of the flow chart200, a proxy model is built to estimate a percentage of interference (interchangeably referred to as a degree of interference) between the fractures as a function of spacing between the number of perforations and the formation properties. The computing device112is configured to build the proxy model to estimate the percentage of interference between the fractures as the function of spacing distance between the number of perforations and the formation properties.

At step218of the flow chart200, a net present value (NPV) is determined from the proxy model. The computing device112is configured to determine the net present value (NPV) from the proxy model. The proxy model is a random forest (RF) model, where the RF model is configured to estimate the percentage of interference based on the simulated reservoir and the RTA. The RF model is trained on production data from the RTA which is randomly split into a training data set and a testing data set, where a ratio of the training data set to the testing data set is selected from a range of 60:40 to 80:20. In an example, the ratio of the training data set to the testing data set is 70:30.

At step220of the flow chart200, a number of perforations are calculated as a function of the net present value (NPV) from the proxy model and a degree of interference from the rate transient analysis (RTA). The computing device112may be configured to calculate the number of perforations needed in the horizontal fracturing pipe104as the function of the net present value (NPV) from the proxy model and the degree of interference from the rate transient analysis (RTA).

In an implementation, the ratio of the ACeto the ACarepresents the degree of interference between the fractures. The computing device112is configured to calculate the percentage of interference (PI) based on Equation (5) provided below.

In some examples, the simulated reservoir may be built to simulate gas recovery from the simulated reservoirs for different numbers of periodic perforations and/or cluster spacings.

FIG.3depicts a schematic representation300of a simulated reservoir for a hydraulically fractured horizontal well. In an example, the simulated reservoir was simulated as a unit for the hydraulically fractured horizontal well shown inFIG.3. The length of the simulated reservoir was kept constant to be 250 feet in the different cases. The thickness of the simulated reservoir was selected to be 120 feet. The initial reservoir pressure was set at 5000 pound per square inch (psi), while the gas production was constrained to a bottom-hole pressure of 1000 psi. The gas gravity and the simulated reservoir temperature were set to be 0.65 and 200° F., respectively. A base case was conducted with a formation porosity of 0.065 and permeability of 100 nanoDarcies (nD).

FIG.4AandFIG.4Bdepict an RTA analysis for gas shale well. In particular,FIG.4Adepicts a diagnostic plot400of a pseudopressure difference between the pseudo bottom-hole pressure and the bottom-hole pressure divided by the gas production rate versus time. The diagnostic plot400depicts a linear flow with a slope of one half. InFIG.4A, arrow402represents an end of the linear flow.

FIG.4Bdepicts a specialized plot404for linear flow regime. A straight line (represented by reference numeral “406”) was found in the plot404with a slope (m). In an implementation, √{square root over (k)}Acmay be calculated from the slope (m) using Equation (6) provided below.

where Acrepresents the total fracture surface area which reflects the effective area for the fluid production, ∅ represents formation porosity, μ represents gas viscosity, ctrepresents total compressibility, T represents the temperature, and k represents the formation permeability.

EXAMPLES AND EXPERIMENTS

The following examples are provided to illustrate further and to facilitate the understanding of the present disclosure.

Experimental Data and Analysis

In order to examine the percentage of fracture interference, the ratio between the effective fracture surface area (ACe) to the actual fracture surface area (ACa) was calculated. In an example, a numerical simulator was run using five fractures, where the cluster spacing was 80 feet. The single fracture half-length of 250 feet was used. Hence, the actual fracture surface area was calculated from Equation (1) to be ACa=6E5 ft2(ACa=4×120×5×250).

The numerical simulator was run to predict the production rate at constant bottom-hole pressure of 1000 psi, a formation porosity of 0.06, and a permeability of 0.0005 mD. The production and pressure data were analyzed using RTA to estimate the effective fracture surface area. The RTA analysis was conducted as shown inFIG.3,FIG.4AandFIG.4B. The slope of the linear flow regime was found to be m=153 (psi2/cp/(Mscf/d)/Day0.5). This slope was used to calculate the effective surface area. In an example, the calculated effective surface area (ACe) is 4.5E5 ft2. Hence, the ratio was found to be 0.75.

A similar analysis was conducted by changing the number of fractures from 2 fractures to fractures and the cluster spacing distance from 200 feet to 20 feet.FIG.5depicts an RTA diagnostic plot500for different numbers of perforations (or fractures).FIG.5shows the RTA diagnostic plot500of a pseudopressure difference between the pseudo bottom-hole pressure and the bottom-hole pressure divided by the gas production rate [m(pi)−m(pwf)]/qgversus time. In particular,FIG.5depicts different cases for different number of perforations (or fractures), denoted by “Nf”. Plot line502depicts a case for Nf=2, plot line504depicts a case for Nf=3, plot line506depicts a case for Nf=4, plot line508depicts a case for Nf=7, plot line510depicts a case for Nf=10, and plot line512depicts a case for Nf=20. In the example shown inFIG.5, all cases showed a linear flow regime first with a ½ slope. The data then deviated from the straight line which shows the end of the linear flow regime and the beginning of fracture interference. Once the linear flow reached the end, depletion started and the production rate started to decline rapidly. In an example, the gas viscosity and the stimulated area permeability were set to be constant for the different cases. Hence, the change in the linear flow is a function of the fracture spacing distance. At a small number of fractures and long spacing, the linear fracture region was dominant, and the fracture did not interfere, or the interference occurred at a later time. With decreased fracture spacing, the linear flow regime ended earlier.

FIG.6Aillustrates the ratio of effective fracture surface area (ACe) to actual fracture surface area (ACa) as a function of the number of fractures andFIG.6Billustrates the ratio of effective fracture surface area (ACe) to actual fracture surface area (ACa) as a function of fracture spacing.

In particular,FIG.6Ashows the ratio between the ACeto the ACaas the function of the number of fractures andFIG.6Bshows the ratio between the ACeto the ACaas the function of the fracture spacing. InFIG.6A, a plot line602depicts the ratio between the ACeto the ACaas the function of number of fractures. InFIG.6B, a plot line604depicts the ratio between the ACeto the ACaas the function of the fracture spacing. In the example shown inFIG.6AandFIG.6B, as the fracture spacing decreased, the interference increased. In an example, at fracture spacing of 20 feet, the interference was about 50%. In addition, decreasing the cluster spacing to increase the total number of fractures significantly reduced gas recovery, where the width growth of fractures is strongly inhibited because of the mechanical interaction and stress shadow effects.

To examine the effect of the formation properties on the degree of interference between the fractures, different cases were conducted by changing the formation permeability from 0.00005 mD to 0.005 mD, setting the formation porosity as 0.065, and varying the number of fractures from 1 fracture to 20 fractures per stage.

FIG.7illustrates a graphical representation700of the ratio of the effective fracture surface area to the actual fracture surface area (ACe/ACa) as a function of the reciprocal of cluster spacing that represents the number of fractures per unit length at different permeability values. In the example shown inFIG.7, plot line702depicts permeability equal to 0.00005 mD, plot line704depicts permeability equal to 0.0001 mD, plot line706depicts permeability equal to 0.0005 10 mD, plot line708depicts permeability equal to 0.001 mD, plot line710depicts permeability equal to 0.003 mD, and plot line712depicts permeability equal to 0.005 mD. At a low permeability of 0.00005 mD, the fracture interference was very small and became more effective at short spacing with 15% interference at a spacing of 20 feet. At high permeability (for example, 0.005 mD), the fracture interference was significant even at fracture spacing of 100 feet and the fracture interference was 35%.

To examine the effect of formation porosity in the interference profile, the analysis was conducted at different porosities from 2% to 10% with formation permeability of 0.0001 mD.

FIG.8illustrates a graphical representation800of the ratio of the effective fracture surface area to the actual fracture surface area (ACe/ACa) as a function of reciprocal cluster spacing at different formation porosities.

InFIG.8, plot line802depicts formation porosity of 0.02, plot line804depicts formation porosity of 0.04, plot line806depicts formation porosity of 0.06, plot line808depicts formation porosity of 0.08, and plot line810depicts formation porosity of 0.1. As shown inFIG.8, the effect of the formation porosity on the interference profile was much less than the permeability effect. As can be seen, with changing the formation porosity from 2% to 10%, the interference increased from 15% to 25%.

As described earlier, the proxy model is a RF model used to determine interference ratio as a function of formation properties and cluster spacing. The input features for the RF model were the formation properties and the cluster spacing, while the target was the interference ratio.

FIG.9displays a cross plot900between the actual and the predicted interference ratio using the RF model. In the example shown inFIG.9, most of the data is aligned to the 45 degree line with an R2of 0.996, which confirms the high accuracy of the RF model and its capability to predict the interference ratio.

The RF model was then used to run a Monte Carlo sensitivity analysis on the effect of formation properties and the fracture spacing on the interference between the fractures. Table 1 provided below shows the ranges for the input parameters for the sensitivity analysis. The porosity ranged from 2% to 10% with the fracture spacing distance varying from 20 feet to 200 15 feet and permeability ranging from 50 nD to 5000 nD.

FIG.10depicts a graphical representation1000showing the degree of importance of the different parameters on the interference ratio.FIG.10shows that the formation permeability k is the most effective parameter in the interference performance followed by the cluster spacing. Also, the porosity has the lowest correlation coefficient (R) of 0.23 with the ACe/ACaratio. The sign of the correlation coefficient reflects a direct or reverse relationship. For example, correlation coefficient (R) between cluster spacing and ACe/ACaratio has a positive sign. Therefore, as the cluster spacing distance increases, the ACe/ACaratio increases and the interference between the fracture decreases. While the correlation coefficient (R) for the permeability and the porosity have a negative sign. Therefore, as the porosity and the permeability increase, the ACe/ACaratio decreases and the interference between the fracture increases.

A Monte Carlo sensitivity analysis was used to investigate the effect of uncertainty of the reservoir parameters on the interference performance at different fracture spacing values.FIG.11depicts a graphical representation1100of the Monte Carlo sensitivity of frequency versus ACe/ACafor uncertainty in the input parameters. InFIG.11, plot line1102shows a fracture spacing of 20 feet, plot line1104shows a fracture spacing of 60 feet, plot line1106shows a fracture spacing of 100 feet, plot line1108shows a fracture spacing of 140 feet, and plot line1110shows fracture spacing of 200 feet. With decreasing fracture spacing, the whole curve shifted to the left and the ACe/ACaratio decreased. As a result, interference increased. At a fracture spacing of 200 feet, 90% of the wells have ACe/ACaratio higher than 0.97, indicating that the interference is less than 3%. With decreased fracture spacing, the ACe/ACaratio decreased. At a fracture spacing of 100 feet, 50% of the wells had an ACe/ACaratio higher than 0.8, indicating that the interference was less than 20%. At a tight spacing of 20 feet, 50% of the wells have ACe/ACaratio higher than 0.53, indicating that the interference was less than 47%.

P10, P50, and P90 refer to percentiles of the distribution. P50 (and P90, Mean, Expected and P10) is the methodology based on simulating potential scenarios with Monte Carlo simulations, where the P stands for percentile. In the oil and gas industry, P90 should be at least a 90% probability that the quantities actually recovered will equal or exceed the low estimate; P50 should be at least a 50% probability that the quantities actually recovered will equal or exceed the best estimate; P10 should be at least a 10% probability that the quantities actually recovered will equal or exceed the high estimate. P50 is a good middle estimate, mean and expected. (See “P50 (and P90, Mean, Expected and P10)”, Posted on 13 Dec. 2015 by ThePD (The Project Definition)).

Table 2 provided below summarizes P10, P50, and P90 for the different fracture spacing cases.

There are numerous economic analysis approaches in the oil and gas industry including discounted cash flow analysis, cost-benefit incremental method, cost component method, etc. In the present disclosure, discounted cash flow analysis was applied. The analysis is based on calculating the net present value (NPV) from the gas production as a function of capital cost (CAPEX), gas price, and interest rate (IRR). A base case was conducted as the numerical simulator was run to predict the production rate at constant bottom-hole pressure of 1000 psi, a formation porosity of 0.06, and a permeability of 0.0005 mD. The capital cost was assumed to be $40,000 per stage, gas price of $3/Mscf, and an interest rate of 20%.

FIG.12shows a graphical representation1200of NPV as a function of fracture spacing distances. In particular,FIG.12shows NPV as a function of fracture spacing distance for k=0.0005 mD, Pwf=1000 psi, and ∅=0.06. InFIG.12, plot line1202represents the NPV. As can be seen inFIG.12, at a wider spacing distance of 400 feet, NPV was estimated to be 0.3 MM$. As the number of fractures increased, which decreased the spacing distance, the value of NPV increased until it reached its defined value at a spacing distance of 60 feet. As the fracture spacing distance increased, the NPV sharply declined.

To examine the effect of permeability on the defined cluster spacing, the previous analysis was conducted at different formation permeabilities from 0.00005 mD to 0.005 mD.FIG.13shows a graphical representation1300of the NPV as a function of fracture spacing for different formation permeabilities. InFIG.13, plot line1302represents permeability of 0.005 mD, plot line1304represents permeability of 0.00005 mD, plot line 1306 represents permeability of 0.0001 mD, and plot line1308represents permeability of 0.0001 mD. As shown inFIG.13, as the permeability increased, the entire set of curves shifted up and the NPV increased. As shown inFIG.7, as the formation permeability increases, the fracture interference also increases. Hence, as the permeability increases, the defined cluster spacing increases. For example, the cluster spacing increased from 50 feet to 120 feet when the permeability increased from 0.00005 mD to 0.005 mD. Similarly, the effect of interest rate, gas price, and capital completion cost were investigated.

FIG.14shows a graphical representation1400of NPV as function of a fracture spacing for different interest rates.

InFIG.14, plot line1402represents an interest rate of 0.01, plot line1404represents an interest rate of 0.1, plot line1406represents an interest rate of 0.2, plot line1408represents an interest rate of 0.4, and plot line1410represents an interest rate of 0.55. The interest rate showed a slight effect on the defined spacing. As the interest rate increased from 0.05 to 0.55, the entire set of NPV curves shifted down, and defined spacing became tighter from 70 feet to 40 feet in order to accelerate the hydrocarbon recovery.

FIG.15shows a graphical representation1500of NPV as function of a fracture spacing for different gas prices. Mscf is a production testing abbreviation for a thousand standard cubic feet per day, a common measure for volume of gas. Standard conditions are normally set at 60 degF and 14.7 psia. Psia is defined as pounds per square inch absolute.

InFIG.15, plot line1502represents gas price equal to 3.5 $/Mscf, plot line1504represents gas price equal to 3 $/Mscf, plot line1506represents gas price equal to 2.5 $/Mscf, plot line1508represents gas price equal to 3 $/Mscf, and plot line1510represents gas price equal to 1.5 $/Mscf. As shown inFIG.15, as the gas prices increased from 1.5 to 3.5 $/Mscf, the NPV increased, and the set of curves shifted upwards. The defined spacing decreased from 100 feet to 40 feet in order to accelerate the gas production and increase the profit.

FIG.16shows a graphical representation1600of NPV as a function of a fracture spacing for different capital completion costs in U. S. dollars, simply referred to below as the symbol $. MM$ refers to millions of dollars.

InFIG.16, plot line1602represents cost equal to 20000 $, plot line1604represents cost equal to 40000 $, plot line1606represents cost equal to 60000 $, and plot line1608represents cost equal to 80000 $. As shown inFIG.16, as the cluster spacing decreases, the hydrocarbon production increases. However, the capital cost is increased with tight spacing. Hence, as the completion cost becomes cheaper and changes from 0.8 MM$ to 0.2 MM$, a tighter spacing is recommended (for example, from 90 feet to 40 feet) to accelerate the production and improve profitability.

A case study was conducted for the production data for two gas wells (well-1 and well-2) in the Barnett shale formation. The two wells were completed with an almost similar design as shown in Table 3 provided below.

TABLE 3Completion design for the two wells in the Barnett formationWell-1Well-2Difference %Water: gal/ft1715189210%Sand: lb/ft150315302%Cluster3117.4−44%Spacing, ftAVG BPM6763−6%Cost, $X1.3X30%

AVG BPM refers to average barrels per million.

As shown in Table 3, the cluster spacing in well-1 (also referred to as first well) was almost double the cluster spacing in well-2 (also referred to as second well). For the same lateral length, the completion cost for well-2 was 30% higher than the completion cost for well-1.

FIG.17shows gas production for well-1 and well-2 versus time in days. InFIG.17, production data for well-1 and well-2 are represented by reference numeral “1702” and “1704”, respectively.

FIG.18shows the production data for well-1 and well-2 versus time in days for production per stage, i.e., time from 0 days to 100 days and time from 100 days to 200 days. In

FIG.18, the production data for well-1 and well-2 are represented by reference numerals “1802” and “1804”, respectively. Well-2 with tight fracture spacing showed higher gas production data compared to well-1. However, production rate declined faster. By comparing the production per stage for each well, well-1 showed a higher production rate per stage compared to well-2. Moreover, RTA and PTA analyses were conducted in both wells to estimate the fracture surface area. Even with a lower number of clusters and wider cluster spacing, well-1 has an almost similar surface area as the one estimated from well-2. That proves that a higher number of fractures with tighter cluster spacing does not always give a higher performance. However, an economic study should be conducted to examine the effect of production acceleration by increasing the number of fractures versus increasing the capital cost of well completion. Bbl/psi is defined as barrel per (pound per square inch).

The higher stage number and tighter cluster spacing will have high cluster interference with low effective to actual fracture surface area ratio. The formation permeability is the dominant parameter in fracture interference behavior. The porosity correlated with effective to actual fracture surface area ratio by an R-value of −0.23 compared to −0.56 in case of formation permeability. The R-value is a correlation coefficient. The sample correlation coefficient (r) is a measure of the closeness of the association of the points in a scatter plot to a linear regression line based on those points. The R-squared value, denoted by R2, is the square of the correlation coefficient. It measures the proportion of variation in the dependent variable that can be attributed to the independent variable. The R-squared value R2 is always between 0 and 1 inclusive. A proxy model was built to predict the degree of fracture interference as a function of formation properties and the cluster spacing with R2 of 0.96 between the actual and the predicted values. Based on the uncertainty analysis, regardless of the formation properties, at a spacing of 100 ft, 50% of the wells have means interference higher than 20%. At a tight spacing of 20 ft, 90% of the wells have interference higher than 20%. From the economic study, spacing of 60 ft was found to be the optimum spacing based on the formation properties, capital cost, and gas price. As the interest rate gas prices increased, or a low capital costs, the optimum completion tends to be with tighter spacing to accelerate the production. Based on the Barnett wells case study, regardless of the number of fracturing stages, for the same lateral length and the same injected frac proppant, the cumulative gas production will be the same. A well with a higher stage number and tighter cluster spacing will drain the production area faster with a high initial production rate. A well with low number of stages will drain the same area but for a longer time and at a lower initial production rate.

FIG.19illustrates a flowchart1900for building a horizontal fracture field having low cluster interference.

At step1902of the flowchart1900, reservoir properties of a shale layer120of a geological formation132of interest are determined. The computing device112may be configured to determine the reservoir properties of the shale layer120of the geological formation132of interest.

At step1904of the flowchart1900, a simulation reservoir of the shale layer120of the geological formation132is built based on the reservoir properties. The computing device112may be configured to build the simulation reservoir of the shale layer120of the geological formation132based on the reservoir properties.

At step1906of the flowchart1900, an actual fracture surface area (ACa) of the horizontal fracture field is calculated. The computing device112is configured to calculate the actual fracture surface area (ACa) using Equation (1).

At step1908of the flowchart1900, production data from a predetermined stimulated area of the simulation reservoir is exported. The computing device112is configured to export the production data from the predetermined stimulated area of the simulation reservoir.

At step1910of the flowchart1900, a rate transient analysis (RTA) of the production data is conducted to estimate an effective stimulated fracture surface area (ACe) for a given number of periodic perforations in a horizontal fracturing pipe104. The computing device112is configured to conduct the rate transient analysis (RTA) of the production data to estimate the effective stimulated fracture surface area (ACe) for the given number of periodic perforations (for example, first number of periodic perforations) in the horizontal fracturing pipe104.

At step1912of the flowchart1900, a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa) is calculated. The computing device112is configured to calculate the ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa).

At step1914of the flowchart1900, the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations is stored. The computing device112is configured to store the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations in the memory114.

At step1916of the flowchart1900, the calculation of the ratio for a second number of periodic perforations is iterated, where the second number is greater than the first number by a step amount. The computing device112is configured to iterate the calculation of the ratio for the second number of periodic perforations.

At step1918of the flowchart1900, iteration to calculate the ratio is continued by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount. The computing device112is configured to continue the iteration to calculate the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to the threshold amount.

At step1920of the flowchart1900, a proxy model is built to estimate a percentage of interference between the fractures as a function of spacing between the number of perforations and the formation properties. In an implementation, the computing device112is configured to calculate the percentage of interference (PI) using Equation (5). In an example, the proxy model is a random forest (RF) model. In an example, the RF model is trained on production data from the RTA which is randomly split into a training data set and a testing data set, where a ratio of the training data set to the testing data set is selected from a range of 60:40 to 80:20. Also, the percentage of interference is estimated based on the simulated reservoir and the RTA. In an implementation, the RF model may run a Monte Carlo sensitivity analysis on an effect of formation properties and a fracture spacing on an interference between the fractures. In an example, the porosity is ranged from 2% and 10%, the fracture spacing is varied from 20 to 200 ft, and the permeability is varied from 50 to 5000 nanoDarcies (nD). In an implementation, the computing device112may be configured to conduct the RTA by converting a bottom-hole pressure to a pseudo bottom-hole pressure and normalizing a pseudo-pressure difference between the pseudo bottom-hole pressure and the bottom-hole pressure via a gas production rate of the well.

At step1922of the flowchart1900, a net present value (NPV) from the proxy model is determined. In an implementation, the computing device112may be configured to determine the net present value (NPV) from the proxy model.

At step1924of the flowchart1900, the number of perforations needed in the horizontal fracturing pipe104is estimated as a function of the NPV from the proxy model and the degree of interference from the RTA. In an implementation, the computing device112is configured to estimate the number of perforations needed in the horizontal fracturing pipe104as a function of maximizing the NPV from the proxy model and minimizing the degree of interference from the RTA.

At step1926of the flowchart1900, perforated sections and unperforated sections of the horizontal fracturing pipe are installed in the horizontal fracture field based on the estimated number of perforations needed to create clusters of fractures in the fracture field. In an implementation, the perforated sections and unperforated sections of the horizontal fracturing pipe104are installed in the horizontal fracture field based on the estimated number of perforations needed to create clusters fractures in the fracture field.

At step1928of the flowchart1900, the horizontal fracture field is stimulated by injecting a fracturing fluid134under pressure into the horizontal fracturing pipe.

At step1930of the flowchart1900, material forced out of the fractures is recovered over a given time period. In an example, the material forced out of the fractures includes at least one of oil and natural gas.

FIG.20illustrates a flowchart2000for hydraulic fracturing in a shale layer120of a geological formation132.

At step2002of the flowchart2000, a borehole102is drilled and cased which extends between a surface of the geological formation132and the shale layer120.

At step2004of the flowchart2000, sections of horizontal fracturing pipe104are installed which extend perpendicularly from the borehole102into the shale layer120, where each section of the horizontal fracturing pipe104is configured as one of a perforated pipe section and an unperforated pipe section. The number of perforations in each pipe section and the length of each pipe section are selected such that a fully installed length of horizontal fracturing pipe has the number of periodic perforations determined by the model.

At step2006of the flowchart2000, a pump106is installed at the surface of the geological formation132, where the pump106is configured to inject a fracturing fluid13420under pressure into the borehole102and into the horizontal fracturing pipe104, and where the pressure of the fracturing fluid134is configured to inject the fracturing fluid134through the perforations and stimulate fractures in the shale layer120.

At step2008of the flowchart2000, a pressure sensor108is installed at the surface of the geological formation132, wherein the pressure sensor108is configured to measure the pressure of the fracturing fluid134.

At step2010of the flowchart2000, a water meter (also referred to as fluid meter110) is installed at the surface of the geological formation132, where the water meter is configured to measure a volume of a material forced out of the fractures by the fracturing fluid134, and where the material is one or more of oil and natural gas.

At step2012of the flowchart2000, a computing device112is connected to the pump106, the pressure sensor108and the water meter, where the computing device112includes electrical circuitry118, a memory114storing program instructions and at least one processor116configured to execute the program instructions to determine the number of the periodic perforations in the horizontal fracturing pipe104which produces a maximum volume of material forced out of the fractures without interference from breakdown in the shale layer120between the fractures.

The computing device112is configured to build a simulation reservoir of the shale layer120of the geological formation132based on the reservoir properties. The computing device112is configured to calculate an actual fracture surface area (ACa) of the horizontal fracture field. The computing device112is configured to export production data from a predetermined stimulated area of the simulation reservoir and conduct a rate transient analysis (RTA) of the production data to estimate an effective stimulated fracture surface area (ACe) for a given number of periodic perforations in a horizontal fracturing pipe104.

The computing device112is further configured to calculate a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa) and store the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations in a memory114. The computing device112is configured to iterate the calculation of the ratio for a second number of periodic perforations, where the second number is greater than the first number by a step amount. The computing device112is configured to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount. The computing device112is configured to build a proxy model to estimate a percentage of interference between the fractures as a function of spacing between the number of perforations and the formation properties and determine a net present value (NPV) from the proxy model. The computing device112is configured to estimate the number of the perforated pipe sections needed in the horizontal fracturing pipe104as a function of the NPV from the proxy model and the degree of interference from the RTA. The installation of the perforated sections and unperforated sections of the horizontal fracturing pipe104in the horizontal fracture field based on the estimated number of perforations needed to create clusters fractures in the fracture field is based on the number of perforations determined in the proxy model. Once the horizontal fracturing pipe sections are installed, the computing device112is configured to stimulate the horizontal fracture field by injecting a fracturing fluid134under pressure into the horizontal fracturing pipe104and recover material forced out of the fractures over the given time period.

The first embodiment is illustrated with respect toFIGS.1-20. The first embodiment describes a horizontal fracture field system100for hydraulic fracturing in a shale layer120of a geological formation132. The horizontal fracture field system100includes a borehole102which extends between a surface of the geological formation132and the shale layer120, a tubing which extends into the borehole between a surface of the geological formation and the shale layer; a horizontal fracturing pipe104which extends perpendicularly from the borehole102into the shale layer120, wherein the horizontal fracturing pipe has a number of stages, each stage having at least one perforation, wherein the at least one perforation of a first stage is separated by a spacing distance from at least one perforation of a neighboring stage, wherein each spacing distance corresponds with a fracture zone in the shale layer. The horizontal fracture field system100further includes a pump106located at the surface of the geological formation132, and a fracturing fluid134configured to be injected under pressure by the pump106into the borehole102and into the horizontal fracturing pipe104, wherein the pump is configured to inject the fracturing fluid134under pressure through the perforations of the stages to fracture a fracture zone in the shale layer120. The horizontal fracture field system100includes a pressure sensor108configured to measure the pressure of the fracturing fluid134in the horizontal fracturing pipe104. The horizontal fracture field system100also includes a fluid meter110located at the surface of the geological formation132, where the fluid meter110is configured to measure a volume of a material forced out of the fractures by the fracturing fluid134. The horizontal fracture field system100includes a computing device112connected to the pump106, the pressure sensor108, and the fluid meter110, where the computing device112includes an electrical circuitry118, a memory114storing program instructions and at least one processor116configured to execute program instructions to to estimate a percentage of interference PI between fracture zones of neighboring stages, according to the formula:

where ACerepresents an estimated fracture surface area of the horizontal fracture field and ACarepresents an actual fracture surface area of the horizontal fracture field; determine a net present value NPV for each spacing distance; and determine the spacing distance which minimizes the percentage of interference PI while maximizing the net present value NPV.

The material forced out of the fractures includes at least one of oil and natural gas.

The computing device112is configured to calculate an actual fracture surface area (ACa) of the horizontal fracture field, determine production data and reservoir properties of a predetermined stimulated fracture surface area of the horizontal fracture field from a pump pressure, the measurements of pressure sensor108, and the fluid meter, export the production data and reservoir properties from the simulated reservoir at the predetermined stimulated fracture surface area, conduct a rate transient analysis (RTA) of the production data to estimate an effective fracture surface area (ACe) for the given number of periodic perforations, calculate a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa), store the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations in the memory114, iterate the calculation of the ratio for a second number of periodic perforations, where the second number is greater than the first number by a step amount, continue to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount, build a proxy model to estimate a percentage of interference between the fractures as a function of spacing distance between the number of perforations and the formation properties, determine a net present value (NPV) from the proxy model, and calculate the number of perforations needed in the horizontal fracturing pipe104as a function of the NPV from the proxy model and the degree of interference from the RTA, and actuate the pump to inject fracturing fluid through the number of perforations.

The computing device100is configured to calculate the NPV based on the production data, a capital cost of the fracturing, a current price of gas, and a current interest rate.

The computing device112is configured to build the simulated reservoir by calculating a function which includes a length of the reservoir, a thickness of the reservoir, an initial reservoir pressure, a reservoir bottom-hole pressure, a reservoir temperature, a reservoir formation porosity, and a reservoir permeability.

The computing device112is configured to iterate the calculation of the ratio for the number of periodic perforations ranging from 2 perforations to 20 perforations with a spacing distance ranging from 20 feet to 200 feet.

The computing device100is configured to conduct the RTA based on a fracture half-length which ranges from 200 feet to 400 feet.

The computing device100is configured to calculate the actual fracture surface area, ACA, based on ACa=4HfNfXf, wherein Hfis a fracture height, Xfis a fracture half-length, and Nfis the number of perforations.

The proxy model is a random forest (RF) model, where the RF model is configured to estimate the percentage of interference based on the simulated reservoir and the RTA. The RF model is trained on production data from the RTA which is randomly split into a training data set and a testing data set, where a ratio of the training data set to the testing data set is selected from a range of 60:40 to 80:20.

The horizontal fracturing pipe104includes pipe sections which connect together, where each pipe section is configured as one of a pipe section with a perforation and an unperforated pipe section.

The second embodiment is illustrated with respect toFIGS.1-20. The second embodiment describes a method for building a horizontal fracture field having low cluster interference. The method includes determining reservoir properties of a shale layer120of a geological formation132of interest, calculating, by a computing device112including an electrical circuitry118, a memory114storing program instructions and at least one processor116configured to execute the program instructions, an actual fracture surface area (ACa) of the horizontal fracture field, exporting, by the computing device112, production data from a predetermined stimulated area of the simulation reservoir, conducting, by the computing device112, a rate transient analysis (RTA) of the production data to estimate an effective stimulated fracture surface area (ACe) for a given number of periodic perforations in a horizontal fracturing pipe104, calculating, by the computing device112, a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa), storing, in the memory114of the computing device112, the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations, iterating, by the computing device112, the calculation of the ratio for a second number of periodic perforations, where the second number is greater than the first number by a step amount, continuing, by the computing device112, to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount, building, by the computing device112, a proxy model to estimate a percentage of interference between the fractures as a function of spacing distance between the number of perforations and the formation properties, determining, by the computing device112, a net present value (NPV) from the proxy model, estimating, by the computing device112, the number of perforations which maximizes the NPV from the proxy model while minimizing the percentage of interference PI from the RTA; installing perforated sections and unperforated sections of the horizontal fracturing pipe in the horizontal fracture field based on the estimated number of perforations; and stimulating the horizontal fracture field by injecting a fracturing fluid under pressure into the horizontal fracturing pipe through the number of perforations. The material forced out of the fractures comprises at least one of oil and natural gas.

The computing device112is configured to calculate the percentage of interference (PI) based on Equation (5).

The computing device112is configured to calculate the actual fracture surface area, ACA, based on Equation (1).

The proxy model is a random forest (RF) model, and the method comprises training the RF model on production data from the RTA which is randomly split into a training data set and a testing data set, where a ratio of the training data set to the testing data set is selected from a range of 60:40 to 80:20 and estimating the percentage of interference based on the simulated reservoir and the RTA.

The method includes running, by the RF model, a Monte Carlo sensitivity analysis on an effect of formation properties and fracture spacing distance on an interference between the fractures, where the porosity is ranged from 2% and 10%, the fracture spacing is varied from 20 to 200 ft, and the permeability is varied from 50 to 5000 nanoDarcies (nD).

Conducting, by the computing device112, the RTA further includes converting a bottom-hole pressure to a pseudo bottom-hole pressure and normalizing a pseudo-pressure difference between the pseudo bottom-hole pressure and the bottom-hole pressure via a gas production rate of the well.

The third embodiment is illustrated with respect toFIGS.1-20. The third embodiment describes a method for hydraulic fracturing in a shale layer120of a geological formation132. The method includes installing a tubing in a borehole102which extends between a surface of the geological formation132and the shale layer120, installing sections of horizontal fracturing pipe104which extend perpendicularly from the borehole102into the shale layer120, wherein the horizontal fracturing pipe has a number of stages, each stage having at least one perforation, wherein the at least one perforation of a first stage is separated by a spacing distance from at least one perforation of a neighboring stage, wherein each spacing distance corresponds with a fracture zone in the shale layer, installing the tubing in the horizontal fracturing pipe, installing a pump106at the surface of the geological formation132, where the pump106is configured to inject a fracturing fluid134under pressure into the borehole102and into the horizontal fracturing pipe104, where the pressure of the fracturing fluid134is configured to inject the fracturing fluid134through the perforations and stimulate fractures in the shale layer120, installing a pressure sensor108configured to measure the pressure of the fracturing fluid134,15installing a fluid meter at the surface of the geological formation132, where the fluid meter is configured to measure a volume of a material forced out of the fractures by the fracturing fluid134, where the material is one or more of oil and natural gas, connecting a computing device112to the pump106, the pressure sensor108, and the fluid meter, where the computing device112includes an electrical circuitry118, a memory114storing program instructions and at least one processor116configured to execute the program instructions to estimate a percentage of interference PI between fracture zones of neighboring stages, according to the formula:

where ACerepresents an estimated fracture surface area of the horizontal fracture field and ACarepresents an actual fracture surface area of the horizontal fracture field; determining a net present value NPV for each spacing distance; and determining the spacing distance which minimizes the percentage of interference PI while maximizing the net present value NPV. The method further comprises calculating, by the computing device112, an actual fracture surface area (ACa) of the horizontal fracture field, exporting, by the computing device112, production data from a predetermined stimulated area of the simulation reservoir, conducting, by the computing device112, a rate transient analysis (RTA) of the production data to estimate an effective stimulated fracture surface area (ACe) for a first number of periodic perforations in a horizontal fracturing pipe104, calculating, by the computing device112, a ratio of the effective fracture surface area (ACe) to the actual fracture surface area (ACa), storing, in the memory114of the computing device112, the ratio of the effective fracture surface area to the actual fracture surface area for the first number of periodic perforations, iterating, by the computing device112, the calculation of the ratio for a second number of periodic perforations, where the second number is greater than the first number by a step amount, continuing, by the computing device112, to iterate the calculation of the ratio by adding the step amount to each previous number of periodic perforations until the production is less than or equal to a threshold amount, building, by the computing device112, a proxy model to estimate a percentage of interference between the fractures as a function of spacing between the number of perforations and the formation properties, determining, by the computing device112, a net present value (NPV) from the proxy model, and estimating, by the computing device112, the number of the perforated pipe sections needed in the horizontal fracturing pipe104as a function of the NPV from the proxy model and the degree of interference from the RTA, installing the perforated sections and unperforated sections of the horizontal fracturing pipe104in the horizontal fracture field based on the estimated number of perforations needed to create clusters fractures in the fracture field, stimulating the horizontal fracture field by injecting a fracturing fluid134under pressure into the horizontal fracturing pipe104.

FIG.21is an illustration of a non-limiting example of details of computing hardware used in the computing device, according to exemplary aspects of the present disclosure. InFIG.21, a controller2100is described which is a computing device (for example, the computing device112) and includes a CPU2100which performs the processes described above/below. The process data and instructions may be stored in memory2102. These processes and instructions may also be stored on a storage medium disk2104such as a hard drive (HDD) or portable storage medium or may be stored remotely.

The hardware elements in order to achieve the computing device may be realized by various circuitry elements, known to those skilled in the art. For example, CPU2101or CPU2103may be a Xenon or Core processor from Intel of America or an Opteron processor from AMD of America or may be other processor types that would be recognized by one of ordinary skill in the art. Alternatively, the CPU2101,2103may be implemented on an FPGA, ASIC, PLD or using discrete logic circuits, as one of ordinary skill in the art would recognize. Further, CPU2101,2103may be implemented as multiple processors cooperatively working in parallel to perform the instructions of the inventive processes described above.

The computing device inFIG.21also includes a network controller2106, such as an Intel Ethernet PRO network interface card from Intel Corporation of America, for interfacing with network2160. As can be appreciated, the network2160can be a public network, such as the Internet, or a private network such as an LAN or WAN network, or any combination thereof and can also include PSTN or ISDN sub-networks. The network2160can also be wired, such as an Ethernet network, or can be wireless such as a cellular network including EDGE, 3G, 4G and 5G wireless cellular systems. The wireless network can also be WiFi, Bluetooth, or any other wireless form of communication that is known.

The computing device further includes a display controller2108, such as a NVIDIA GeForce GTX or Quadro graphics adaptor from NVIDIA Corporation of America for interfacing with display2110, such as a Hewlett Packard HPL2445w LCD monitor. A general purpose I/O interface2112interfaces with a keyboard and/or mouse2114as well as a touch screen panel2116on or separate from display2110. General purpose I/O interface also connects to a variety of peripherals2118including printers and scanners, such as an OfficeJet or DeskJet from Hewlett Packard.

A sound controller2120is also provided in the computing device such as Sound Blaster X-Fi Titanium from Creative, to interface with speakers/microphone2122thereby providing sounds and/or music. The general purpose storage controller2124connects the storage medium disk2104with communication bus2126, which may be an ISA, EISA, VESA, PCI, or similar, for interconnecting all of the components of the computing device. A description of the general features and functionality of the display2110, keyboard and/or mouse2114, as well as the display controller2108, storage controller2124, network controller2106, sound controller2120, and general purpose I/O interface2112is omitted herein for brevity as these features are known.

FIG.22shows a schematic diagram of a data processing system2200for performing the functions of the exemplary embodiments. The data processing system2200is an example of a computer in which code or instructions implementing the processes of the illustrative embodiments may be located.

InFIG.22, data processing system2200employs a hub architecture including a north bridge and memory controller hub (NB/MCH)2225and a south bridge and input/output (I/O) controller hub (SB/ICH)2220. The central processing unit (CPU)2230is connected to NB/MCH2225. The NB/MCH2225also connects to the memory2245via a memory bus, and connects to the graphics processor2250via an accelerated graphics port (AGP). The NB/MCH2225also connects to the SB/ICH2220via an internal bus (e.g., a unified media interface or a direct media interface). The CPU Processing unit2230may contain one or more processors and even may be implemented using one or more heterogeneous processor systems.

For example,FIG.23shows one implementation of CPU2230. In one implementation, the instruction register2338retrieves instructions from the fast memory2340. At least part of these instructions are fetched from the instruction register2338by the control logic2336and interpreted according to the instruction set architecture of the CPU2230. Part of the instructions can also be directed to the register2332. In one implementation, the instructions are decoded according to a hardwired method, and in another implementation, the instructions are decoded according to a microprogram that translates instructions into sets of CPU configuration signals that are applied sequentially over multiple clock pulses. After fetching and decoding the instructions, the instructions are executed using the arithmetic logic unit (ALU)2334that loads values from the register2332and performs logical and mathematical operations on the loaded values according to the instructions. The results from these operations can be feedback into the register and/or stored in the fast memory2340. The instruction set architecture of the CPU2230can use a reduced instruction set architecture, a complex instruction set architecture, a vector processor architecture, a very large instruction word architecture. Furthermore, the CPU2230can be based on the Von Neuman model or the Harvard model. The CPU2230can be a digital signal processor, an FPGA, an ASIC, a PLA, a PLD, or a CPLD. Further, the CPU2230can be an x86 processor by Intel or by AMD; an ARM processor, a Power architecture processor by, e.g., IBM; a SPARC architecture processor by Sun Microsystems or by Oracle; or other known CPU architecture.

Referring again toFIG.23, the data processing system2200can include that the SB/ICH2220is coupled through a system bus to an I/O Bus, a read only memory (ROM)2256, universal serial bus (USB) port2264, a flash binary input/output system (BIOS)2268, and a graphics controller2258. PCI/PCIe devices can also be coupled to SB/ICH2220through a PCI bus2262.

The PCI devices may include, for example, Ethernet adapters, add-in cards, and PC cards for notebook computers. The Hard disk drive2260and CD-ROM2256can use, for example, an integrated drive electronics (IDE) or serial advanced technology attachment (SATA) interface. In one implementation, the I/O bus can include a super I/O (SIO) device.

Further, the hard disk drive (HDD)2260and optical drive2266can also be coupled to the SB/ICH2220through a system bus. In one implementation, a keyboard2270, a mouse2272, a parallel port2278, and a serial port2276can be connected to the system bus through the I/O bus. Other peripherals and devices that can be connected to the SB/ICH2220using a mass storage controller such as SATA or PATA, an Ethernet port, an ISA bus, a LPC bridge, SMBus, a DMA controller, and an Audio Codec.

The functions and features described herein may also be executed by various distributed components of a system. For example, one or more processors may execute these system functions, wherein the processors are distributed across multiple components communicating in a network. The distributed components may include one or more client and server machines, which may share processing, as shown byFIG.24, in addition to various human interface and communication devices (e.g., display monitors, smart phones, tablets, personal digital assistants (PDAs)).

More specifically,FIG.24illustrates client devices including a smart phone2411, a tablet2412, a mobile device terminal2414and fixed terminals2416. These client devices may be commutatively coupled with a mobile network service2420via base station2456, access point2454, satellite2452or via an internet connection. Mobile network service2420may comprise central processors2422, a server2424and a database2426. Fixed terminals2416and mobile network service2420may be commutatively coupled via an internet connection to functions in cloud2430that may comprise security gateway2432, data center2434, cloud controller2436, data storage2438and provisioning tool2440. The network may be a private network, such as a LAN or WAN, or may be a public network, such as the Internet. Input to the system may be received via direct user input and received remotely either in real-time or as a batch process. Additionally, some implementations may be performed on modules or hardware not identical to those described. Accordingly, other implementations are within the scope that may be claimed.