## Abstract

Accurate placement of multiple horizontal wells drilled from the same well pad plays a critical role in the successful economical production from unconventional gas reservoirs. However, there are high cost and uncertainty due to many inestimable and uncertain parameters such as reservoir permeability, porosity, fracture spacing, fracture half-length, fracture conductivity, gas desorption, and well spacing. In this paper, we employ response surface methodology to optimize multiple horizontal well placement to maximize Net Present Value (NPV) with numerically modeling multistage hydraulic fractures in combination with economic analysis.

#### Author

Wei Yu and Kamy Sepehrnoori

Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA

Received 27 May 2013; Accepted 2 August 2013

Academic Editor: Alireza Bahadori

This paper demonstrates the accuracy of numerical modeling of multistage hydraulic fractures for actual Barnett Shale production data by considering the gas desorption effect. Six uncertain parameters, such as permeability, porosity, fracture spacing, fracture half-length, fracture conductivity, and distance between two neighboring wells with a reasonable range based on Barnett Shale information, are used to fit a response surface of NPV as the objective function and to finally identify the optimum design under conditions of different gas prices based on NPV maximization. This integrated approach can contribute to obtaining the optimal drainage area around the wells by optimizing well placement and hydraulic fracturing treatment design and provide insight into hydraulic fracture interference between single well and neighboring wells.

## 1. Introduction

The combination of horizontal drilling and multistage hydraulic fracturing technology has made possible the current flourishing gas production from shale gas reservoirs in the United States, as well as the global fast growing investment in shale gas exploration and development. Multiple transverse hydraulic fractures are generated when all wellbores are drilled in the direction of the minimum horizontal stress. Maximizing the total stimulated reservoir volume (SRV) plays a major role in successful economic gas production.

The unprecedented growth of shale reservoirs has brought a new perspective and focus to the optimization of multiwell placement in the same pad. Drilling multiple horizontal wells from a single pad has increasingly become a common approach for developing shale reservoirs due to significant cost, time, and environmental savings. The surface footprint is reduced greatly by drilling multi-well from the same pad due to minimizing the number of surface locations required while increasing the bottom hole contact of the shale resource [1].

Zipper fracturing (zipper-frac) and simultaneous fracturing (simul-frac) [2], where two adjacent horizontal wells are hydraulically fractured alternatingly and simultaneously, respectively, are two commonly used hydraulic fracturing techniques to stimulate multi-well from the same pad. Although hydraulic fractures improve gas production from shale gas wells, the cost of operation is expensive. Long laterals require greater volume of liquids and proppants which contribute to greater cost [3].

The well economics is also sensitive to well performance and natural gas price due to higher drilling and completion costs. Therefore, optimizing well parameters such as well number and well distance in conjunction with hydraulic fracture parameters, such as fracture spacing and fracture half-length based on economic analysis, are very important, especially in the current environment of low natural gas prices.

Optimization of multi-well placement is primarily valuable for overall project economic viability and minimizing the risks of well collision in shale gas reservoirs. Closer well placement will result in stimulated reservoir volume intersects, leading to well competition and penalizing overall production [5]. However, only recently there have been limited studies of optimizing fracturing design together with multi-well placement simultaneously.

Esmaili et al. [6] defined three types of horizontal well based on the number of neighboring wells for sharing drainage area when drilling multiple wells from a pad. Rafiee et al. [7] proposed a new design for two horizontal wells by the modification of the traditional zipper-frac and demonstrated this new design maximized reservoir contact and improved well performance when compared to the original zipper-frac design from both rock mechanics and fluid production aspects. However, such a design assumed a larger fracture spacing of 500 ft and did not optimize well placement and fracture spacing simultaneously to obtain the optimal design for economic gas production.

Díaz de Souza et al. [8] did sensitivity studies of three different wells placement with 2, 3, and 4 horizontal wells within the same stimulation volume in the Haynesville Shale to obtain the optimal well spacing. They stated that four horizontal wells with a well distance of 660 ft was a near-optimal solution for this reservoir. However, critical parameters for developing a play economically, such as fracture spacing and fracture half-length, have not been considered for optimization based on optimal well spacing. Harpel et al. [9] reported that well spacing becomes tighter in parts of the Fayetteville Shale from 600 ft to 400 ft or 300 ft, leading to fluid and proppant volume reductions, while further optimization of stimulation design, especially fracture half-length, is very much required for future development.

Ramakrishnan et al. [10] suggested that it is particularly challenging to optimize the stimulation treatment in a multi-well design drilled with few hundreds feet of spacing between one another to maximize coverage around each horizontal well, because the optimization process involves perforation and stage placements, sequential stimulation of these wells, fluid and proppant schedules, treatment rates, and application of diversion technology in an effort to achieve effective stimulation along these wells and between the wells. Hence, a detailed study and a comprehensive approach for optimization of fracturing design and multi-well placement are still significantly necessary.

In this paper, we employed response surface methodology to build the response surface in terms of NPV with six parameters such as reservoir porosity, permeability, fracture half-length, fracture conductivity, fracture spacing, and well distance from Barnett Shale, to obtain the best economic scenario for a given range of these influential parameters. The effect of gas desorption is integrated in the numerical modeling of multistage hydraulic fractures. The impact of different gas prices is also taken into account for the optimization process. The goal of this work is to provide insights into the effective exploitation of shale gas reservoirs via optimization of the fracturing design and multiple wells placement simultaneously.

## 2. Shale Gas Reservoir Modeling

Given the complex nature of hydraulic fracture growth and the very low permeability of the matrix rock in shale gas reservoirs, coupled with the predominance of horizontal completions, reservoir simulation is the preferred method to predict and evaluate well performance [11–13]. Local grid refinement with logarithmic cell spacing is used in the simulation to accurately model flow from the shale to the fracture, that is, properly incorporate the transient flow behavior from the matrix to the fracture.

In a block, the hydraulic fracture is explicitly modeled; moreover, the matrix is described as some subcells whose size increases logarithmically, while moving away from the hydraulic fracture to properly simulate the large pressure drop between the matrix and the fracture. In addition, a dual permeability grid is used to allow simultaneous matrix-to-matrix and fracture-to-fracture flows. This method can accurately and efficiently model transient gas production from hydraulic fractures of the horizontal wells in shale gas reservoirs [14, 15]. The reservoir is assumed to be homogeneous and the fractures evenly spaced, with stress-independent porosity and permeability.

It is assumed that there is no water flow in the reservoir modeling of shale gas. In our simulation, gas is only flowing into the wellbore through the hydraulic fractures, that is, no matrix-wellbore communication. The turbulent gas flow due to high gas flow rate in hydraulic fractures is modeled as non-Darcy flow. The non-Darcy Beta factor, used in the Forchheimer number, is determined using a correlation proposed by Evans and Civan [16] as follows:

where the unit of K is md and the unit of β is ft^{−1}. The β(f) correlation was obtained using over 180 data points including those for propped fractures and was found to match the data very well with the correlation coefficient of 0.974 [14]. This equation is implemented into the numerical model and used for accounting for non-Darcy flow in hydraulic fractures. Figure 1 is a diagram of typical shale gas completion design with a multistage hydraulic fracture treatment, which illustrates several important geometric fracture parameters, such as outer fractures, inner fractures, fracture spacing, and fracture half-length.

**Figure 1:** A sketch of multiple hydraulic fractured horizontal shale gas well.

## 3. Economic Model

NPV is one of the most common methods used to evaluate the economic viability of investing a project. It is referred to the sum of all cash flows discounted to a specific point in time at the investor’s minimum discount rate. The correlation between the present value P and the future value F is

where i is the currency escalation rate or interest rate; n is the number of periods.

The NPV is calculated using the following expression:

where V_{F} is future value of production revenue for a fracture reservoir; V_{0} is future value of production revenue for an unfractured reservoir; FC is the total fixed cost; C_{well} is the cost of one horizontal well; C_{fracture} is the cost of hydraulic fracture in a horizontal well; N is the number of horizontal wells. The costs of well and fracture used in the economic analysis are based on the work of Schweitzer and Bilgesu [17], as shown in Table 1.

**Table 1:** Economic data for NPV calculation.

## 4. Langmuir Isotherm

Gas shales are organic-rich formations. Gas storage in the shale is mainly divided into free gas in natural fractures and matrix pore structure and adsorbed gas in organic materials. Langmuir isotherm is widely used to describe the gas adsorption phenomenon. The amount of gas stored in shale is often described by Langmuir equation:

where Gs is the gas content in scf/ton, V_{L} is the Langmuir volume in scf/ton, P_{L} is the Langmuir pressure in psi, and P is pressure in psi. The bulk density of shale (ρ_{B}) is needed to convert the typical gas content in to scf/ton. Langmuir pressure and Langmuir volume are two key parameters. Langmuir volume is referred to as the gas volume at the infinite pressure representing the maximum storage capacity for gas; Langmuir pressure is referred to as the pressure corresponding to one-half Langmuir volume. As the reservoir pressure is decreased, gas is desorbed from the surface of the matrix.

**Figure 2:** Adsorption isotherms for Barnett Shale core samples [4].

Figure 2 shows a graph of gas content with pressure for the adsorbed gas and total gas used for Barnett Shale [4]. Both free gas and adsorbed gas add together to generate the total gas content. In Barnett Shale, the adsorbed gas is approximately 46% of the total gas. Contrary to conventional gas reservoirs, the amount of gas desorption in the matrix is commonly described by the Langmuir isotherm in a range of reservoir pressures. The Langmuir isotherm of the Barnett Shale used in this study is illustrated in Figure 3.

**Figure 3:** Langmuir isotherm curve for Barnett Shale (V_{L}=96 scf/ton, P_{L}=650 psi, and ρ_{B}=2,58 g/cm^{3}).

It is clearly shown that higher Langmuir pressure releases more adsorbed gas and results in higher gas production. Generally, in early stage of production, when reservoir pressure is high, the gas desorption contribution to the gas production is insignificant; however, for long-term production, it is necessary to account for gas desorption, based on a laboratory measured isotherm due to the more substantial pressure depletion, resulting in more gas desorption. CMG [18] was used to model the effect of gas desorption from a shale gas reservoir in a black oil model with a technique developed by Seidle and Arri [19]. A Langmuir isotherm is replicated by a black oil model’s solution gas ratio to include the effect of gas desorption in shale.

## 5. History Matching for Barnett Shale

Published average reservoir data for a Barnett Shale well were used for history matching [20]. In this case, the well was stimulated by a multistage fracturing with a single, perforated interval for each stage. In this simulation study, we set up a reservoir with a volume of 3000ft x 1500ft x 300ft. The fracture spacing and half-length are set at 100 ft and 150 ft, respectively, and the number of fractures is 28. Detailed reservoir information about this section of the Barnett Shale is listed in Table 2.

**Table 2:** Parameters used in history matching.

The reservoir is assumed to be homogeneous and the fractures evenly spaced, with stress-independent porosity and permeability. Only gas is flowing in the reservoir, which is assumed to behave as non-Darcy flow. The history matching of field data is presented in Figure 4(a). It shows a more reasonable match between the numerical simulation results and the actual field gas flow data, considering the effect of gas desorption, contributing to 15.6% of total gas production at around 4.5 years of gas production. In addition, Figure 4(b) shows the forecasting of gas production for a 30-year period with and without considering gas desorption. As shown, with the gas production, the gas desorption contributes more due to substantial pressure depletion and larger gas drainage area and finally contributes to 20.7% of the total gas production at 30 years of gas production.

**Figure 4:** History matching of Barnett Shale with and without gas desorption effect.

Thus, the impact of gas desorption cannot be ignored when performing history matching and assessing production forecast of gas production in Barnett Shale formation. Hence, this study takes into account gas desorption effect for the subsequent optimization of multiwell placement in Barnett Shale.

## 6. Multiwell Modeling

Two scenarios describing multiple horizontal well placement were studied, as illustrated in Figure 5. Scenario 1 is referred to as aligning fracturing, where hydraulic fracturing is between two wells in an aligned pattern, and Scenario 2 is referred to as alternating fracturing, where hydraulic fracturing is between two wells in a staggered pattern.

**Figure 5:** Two scenarios of multiple horizontal well placement.