*A Data-Driven Workflow Approach to Optimization of Fracture Spacing in Multi-Fractured Shale Oil Wells*

## Abstract:

A data-driven workflow approach is presented in this study for optimizing fracture spacing of multifractured horizontal wells (MFHW) in shale oil reservoirs. The workflow employs a simple well productivity model for the initial design of hydraulic fracturing well completions. This provides a transparent approach to the identification of key fracturing parameters affecting well productivity. The workflow uses transient pressure or production data to identify fracture interference.

#### Authors

#### Xu Yang^{1} and Boyun Guo^{2}

^{1}School of Oil & Gas Engineering, Southwest Petroleum University, Chengdu 610500, China. ^{2}Department of Petroleum Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA

Received: 2 April 2019 / Accepted: 21 May 2019 / Published: 23 May 2019

This offers a reliable and cost-effective means for assessment of well production potential in terms of optimization of fracture spacing in the MFHW. Result of a field case study indicated that three wells were drilled in an area with dense natural fractures, and the fracture spacing of MFHW in this area was short enough to effectively drain the stimulated reservoir volume (SRV), while the other three wells were drilled in an area with less natural fractures, and the fracture spacing of MFHW in this area could be shortened to double well productivity.

## Introduction

Thanks to multifractured horizontal well (MFHW) technology, development of shale oil fields in the past five years has made United States energy self-sufficient. However, the results of the technology in other regions of the world are mixed. This is partially attributed to inadequate effort in optimizing a completed design of MHFW.

Modern MFHW techniques include simul frac, zipper frac, and modified zipper frac. Simul frac creates simultaneous hydraulic fractures in symmetric stages in two wells. Zipper frac creates alternate hydraulic fractures in symmetric stages in two wells. Modified zipper frac creates hydraulic fractures in nonsymmetric stages in two alternate wells [1]. These fracturing techniques create symmetric, transverse fractures of ideally the same length and spacing. This common structure of multifractured horizontal wells allows for using general mathematical models to predict well productivity in the stage of well completion design.

The available methods for predicting shale well productivity include analytical transient flow models [2,3,4,5,6] and numerical computer models [7,8,9,10,11]. Analytical transient flow models are mostly used in pressure transient test analyses rather than in optimizing well completion design. Numerical computer models are flexible in handling systems with nonsymmetrical fractures and multiphase flows [12].

In addition to model complicity, the uncertainty in locations of natural fractures is a concern regarding the accuracy of computer simulation results. Based on the work of Guo et al. [13], Zhang et al. [14] presented an analytical solution for estimating long-term productivity of multifractured shale gas wells by coupling the linear flow in the reservoir and the linear flow in hydraulic fractures. Li et al. [15] extended the analytical solution to shale oil wells and validated the solutions with field data from an oil well and a gas well.

The results of MFHW technology in different regions of the world are inconsistent. This is believed partially because of the lack of optimization of MHFW parameters, especially fracture spacing. Optimization of such spacing is considered as one of the most critical steps in enabling economic of horizontal wells and requires a lot of attention [7]. A data-driven workflow procedure, combined with simple well productivity models, is presented in this paper for fracture spacing optimization. This workflow procedure has the advantage of using a simple analytical well productivity model driven by real production data, making it a practical approach to optimize multistage fracturing of horizontal wells in shale oil reservoirs.

## Concept of Fracture Spacing

Modern shale oil and gas horizontal wells are mostly fractured in multiple stages utilizing plug and perf methodology, where the stages are separated by frac plugs set inside the casing. Perforation clusters are created for each stage. The explosive energy during perforating should induce microcracks from the perforations [16]. When fracturing fluid is forced to go through the perforations, multiple fractures may be initiated from these microcracks or other heterogeneities such as natural fractures, drilling-induced fractures, rock texture, orientation and magnitude of formation stresses, etc. The orientations of fractures near the wellbore area are complicated because the wellbore and perforations alter the state of stress in this area [16].

A number of fracture propagation mechanisms may exist. Fractures may re-orientate from the perforations towards preferred fracture planes, owing to stress anisotropy. Fractures may also interact with and merge to natural fractures if the latter exists. As a result, multiple and tortuous fractures are anticipated near the wellbore area. When these initial fractures propagate away from the wellbore area, they may converge or diverge depending on stress field and natural fractures.

Branching due to shale heterogeneities may develop from a single fracture. All fractures initiated from a perforation cluster should form a hydraulic fracture in the plane normal to the minimum principal stress to achieve the minimum strain energy in the shale. Twelve hydraulic fractures created from 12 perforation clusters are depicted in Figure 1. The fracture spacing is defined in this study as the distance between the centerlines of two adjoined hydraulic fractures, which are expected to be equal to the distance between the two adjoined perforation clusters.

**Figure 1.** Twelve hydraulic fractures developed from 12 perforation clusters in three stages of fracturing.

Although well productivity models, such as those presented by Zhang et al. [14] and Li et al. [15], suggest reducing fracture spacing for maximizing well productivity, short spacing may cause early interferences between fractures as a result of fracture branching. Whether early interference exists or not depends on local geological conditions, especially natural fractures and local rock stress fields. Fracture interference can be identified by pressure transient data analyses and/or production rate transient data analyses.

## Workflow for Optimization

The proposed workflow to optimize fracture spacing is based on industry practice [16], with the addition of data analysis, to identify fracture interference. It is summarized in the following steps:

- Design a fracturing job for the first well in the area for a desirable production rate using a well productivity model. Fracture spacing is selected based on horizontal wellbore length, volumes of fracturing fluid and proppant, and completion tools.
- Execute the fracturing job using the designed fracture spacing and other parameters.
- Run a pressure transient test on the well if possible, and put the well into production.
- Perform transient pressure or transient production rate data analyses to identify fracture interference.
- If well completion permits, refracture the well based on the identified fracture interference.
- Modify the well completion design including the fracturing treatment design and/or the spacing between perforation clusters for the next well on the basis of fracture interference in the previous well.

Some of these workflow steps are further outlined in the subsections that follow.

### Fracturing Design

The physics of fluid flow in shale oil reservoirs is adequately described in the literature. The assumptions employed in this study were oversimplified, as the desorption of hydrocarbon from rock matrix and non-Darcy flow were not considered. However, it is a fact that pressure transient and production data support the mathematical models derived from Darcy’s law. This implies that fluid flow in shale oil reservoirs is dominated by Darcy’s law.

Fracturing design can be guided by mathematical models derived from Darcy’s law for shale gas and oil well production under pseudosteady flow conditions. For multifractured horizontal oil wells, Li et al.’s model for oil production rate is expressed as [15]:

where c is expressed as:

where q_{o} is the well production rate in stb/d, n_{f} is the number of perforation clusters (hydraulic fractures), km is the matrix permeability in m_{d}, h_{f} is the fracture height in ft, **p** is the average formation pressure in psia, p_{w} is the wellbore pressure in psia, μ_{o} is the oil viscosity in c_{p}, B_{o} is the oil formation factor in rb/stb, Sf is the fracture spacing in ft, e is an exponential function, x_{f} is the hydraulic fracture half-length in ft, k_{f} is the fracture permeability in md, and w is the average fracture width in inches.

Substituting Equation (2) into Equation (1) yields:

Although Equation (3) shows that maximum well productivity can be obtained by optimizing the effects of the number of hydraulic fractures, hydraulic fracture spacing, and hydraulic fracture width, this is not true in reality as fracture complexity and additional factors such as frac hits also exist. As pointed out by Potapenko et al. [17], in most of the unconventional reservoirs where the majority of multistage wells are drilled, the fracture geometry is quite complex and interaction between fractures starts very early. In this case, spacing between perforation clusters should not have much impact on well productivity.

However, in situations where a significant portion of hydraulic fractures is damaged during well startup, resulting in disconnections of such fractures from the wellbore, having small spacing between perforation clusters still appears to be beneficial because disconnected fractures still may contribute to production through other nondamaged perforation clusters [17]. The issues of fracture complexity, interaction, and disconnection are quite difficult to consider in mathematical modeling because there is a lack of data to explicitly describe their configurations and dynamics [18]. These complication issues are assumed to be negligible in the analysis that follows.

For a given horizontal wellbore length L, well operators tend to increase the number of perforation clusters during the well completion optimization process. It brings some additional considerations about fracture length, the number of frac stages, and the volume of frac treatment. The number of clusters is expressed as:

For a given total volume of fracture proppant V_{f} in ft^{3}, the following material balance holds:

It should be mentioned that w in Equation (4) is in inches, and V_{f} is the bulk volume (not the physical volume) of proppant.

Substituting Equation (4) into Equation (5) and rearranging the latter gives:

Substituting Equations (4) and (6) into Equation (3) results in:

The average reservoir pressure is [15]:

where p_{e} is the reservoir pressure in psia.

It can be shown that in the practical ranges of parameters the sum of the two terms in the bracket in the denominator is very close to unity. Therefore, if fracture spacing is reduced, both the number of clusters and the total fracture surface will increase. Under the assumption of reservoir linear flow (RLF) with infinite fracture conductivity, the well production rate is proportional to the total fracture surface area. This supports the concept of massive volume fracturing where many clusters with the shortest possible spacings are used for pumping massive proppant into the created hydraulic fractures.

Although cluster spacing should be theoretically as low as possible for maximizing well productivity, a minimum required cluster spacing (MRCS) has to be considered in practice if temporal change and well lifetime are not considered. MRCS is controlled by (1) well completion design and equipment limitations and (2) hydraulic fracture interference. In well completion design, frac plugs and perforation clusters themselves are spaced apart, and casing couplings have to be avoided in perforation clusters.

Perf gun can carry a limited number of charges, which are used for the creation of perf clusters. Adding a higher number of perf clusters may require a higher number of perf trips, which impacts overall cost and the operational efficiency. For the concern of hydraulic fracture interferences, sever connections of hydraulic fractures from different perforation clusters are usually not desirable, although overlapping of the frac networks from different perforation clusters may be quite beneficial to well productivity. This interference can be assessed using transient pressure or transient production data analysis.

### Transient Pressure Analysis for Fracture Interference Identification

The theoretical basis of pressure transient data analysis can be found in numerous references [19,20,21]. Modern computer software packages available for pressure transient and production data analyses include F.A.S.T. WellTest [22] and PanSystem [23]. Applications of the pressure transient data analysis theory to shale gas and oil wells are shown by a number of investigators such as Shan et al. [24], Pang et al. [25], and He et al. [26]. Figure 2 presents a diagnostic plot of pressure transient data for flow regime identification where the vertical axis is the pressure derivative defined by:

where Δp is the pressure change, defined as reservoir pressure minus flowing bottom hole pressure for drawdown tests and shut-in bottom pressure minus the last flowing bottom hole pressure before shutting-in for pressure buildup tests. t is the test time defined as the flow time for drawdown tests and shut-in time for pressure buildup tests.

**Figure 2.** Diagnostic plot of pressure transient data for flow regime identification.

Mathematical models describing reservoir transient linear flow to fractures are found in the literature [27,28]. For a well with infinite conductivity fractures, reservoir linear flow (RLF) can be identified by the half-slope of the pressure derivative data versus time data plotted on a log–log scale. For a well with finite conductivity fractures, a bilinear flow may occur in the fracture and in the formation matrix during the initial stages.

Pressure derivative data versus time data plotted on a log–log scale should show a straight line with a slope of 0.25 [29]. After the pressure change propagates to the midline between fractures, pressure derivative data versus time data plotted on a log–log scale should show a straight line with the unit slope for boundary dominated flow (BDF) during the “depletion” in the fractured volume. If a slope value greater than 0.5 is observed soon after wellbore storage, interference between fractures is indicated.

### Transient Rate Analysis for Fracture Interference Identification

Applications of the transient production data analysis theory to shale oil wells are also demonstrated by previous investigators [30,31,32]. Figure 3 shows a diagnostic plot of rate transient data for flow regime identification. For a well with infinite conductivity fractures, the production rate data versus time data plotted on a log–log scale should show a straight line with a slope of −0.5 during the RLF.

For a well with finite conductivity fractures, a bilinear flow may occur in the fracture and in the formation matrix during the initial stages. Rate data versus time data plotted on a log–log scale should show a straight line with a slope of −0.25. After the depth of investigation propagates to the midline between fractures, rate data versus time data plotted on a log–log scale should show a straight line with a slope of −1 for BDF. If a slope value between −0.5 and −1 is observed early on, interference between fractures is indicated.

**Figure 3.** Diagnostic plot of rate transient data for flow regime identification.

## Field Case Studies

The Tuscaloosa Marine Shale (TMS) formation, deposited during the Upper Cretaceous, extends from Louisiana to the southern portion of the Mississippi. Little Creek Field is located in Lincoln and Pike Counties, southwestern Mississippi, on the south rim of the Mississippi Salt Basin. It is within the Upper Cretaceous Mid-Dip Tuscaloosa trend, which occurs updip of the Lower Cretaceous shelf margin. In the Mississippi, production from the Mid-Dip trend extends 150 mi (240 km) to the east-southeast from the Mississippi River in a belt 30 to 60 mi (50–100 km) wide.