## Abstract

As unconventional tight oil reservoirs are currently a superior focus on exploration and exploitation throughout the world, studies on production performance analysis of tight oil reservoirs appear to be meaningful. In this paper, on the basis of modern production analysis, a method to estimate dynamic reserve (OOIPsrv) for an individual multistage fractured horizontal well (MFHW) in tight oil reservoir has been proposed. A model using microseismic data has been developed to calculate fracturing network parameters: storativity (ω) and transmissivity ratio (λ).

#### Authors:

Hongwen Luo^{1}, Haitao Li^{1}, Jianfeng Zhang^{1}, Junchao Wang^{2}, Ke Wang^{1}, Tao Xia^{1}, Xiaoping Zhu^{3}

^{1}State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China. ^{2}Xinjiang Oilfield Company of Petro China, Karamay 834000, China. ^{3}The First Primary School of Xi Yong, Chongqing 401132, China

Received: 26 August 2016 / Accepted: 12 March 2017 / Published online: 23 March 2017

© The Author(s) 2017.

There main focuses of this study are in two aspects: (1) find out effective methods to estimate OOIP_{SRV} for an individual MFHW in tight oil reservoir when there is only production data available and (2) study the relationship between productivity and fracturing network parameters (ω and λ) so as to estimate the productivity for individual MFHW from microseismic data. In order to demonstrate and verify the feasibility of developed methods and models, 5 filed wells and 2 simulated wells have been analyzed. The proposed method to calculate OOIP_{SRV} proves to be applicable for MFHW in tight oil reservoirs. From the calculated results of ω and λ for example wells, it has been found that there exists linear relationship between the value of ω/λ and average production (Q_{ave}) for an individual MFHW completed in this actual tight oil reservoir. On the basis of derived linear relationship between ω/λ and Q_{ave}, the productivity for more individual MFHWs can be directly estimated according to microseismic interpretation.

## Introduction

In order to achieve economical exploration, hydraulic fracturing stimulation has been widely used to enhance the production performance of tight reservoirs because of its low or ultra-low permeability (Bello and Wattenbarger 2010). A successful fracturing stimulation can directly improve the deliverability and productivity of an individual well. The significance of production performance analysis is that dynamic reserves and reservoir parameters can be determined.

Often, linear flow is the dominant flow regime in tight reservoirs and production takes place at high drawdowns because of the low permeability. On the basis of linear flow characteristic for MFHW in unconventional reservoirs, modern production analysis method (MPA) has been developed obtain reservoir parameters and perform flow regime identification (Cheng 2011; Song and Ehlig-Economides 2011; Clarkson 2013). Log–log normalized rate versus time plot and square root time plot are two useful tools of MPA to identify flow regime change and obtain characteristic parameters which are available for the estimation of reservoir permeability and effective fracture half length (Clarkson and Beierle 2010; Poe et al. 2012). Ibrahim et al. (2006) derived Ac(k_{SRV}) ^^{1/2 }and OOIP_{SRV} according to the slope of square root time plot and the end of the linear flow (T_{elf}).

A correction factor which corrects the slope of the square root time plot and improves the accuracy of Ac(k_{SRV})^^{1/2 }was presented (Clarkson et al. 2012). OOIP_{SRV} and reservoir parameters could also be calculated from advanced production decline analysis methods (APDA) which is based on the boundary dominated flow regime (Tang et al. 2013). The Arps-Fetkovich-type curves were used to identify the transient versus depleting stages and to estimate the reservoir parameters and future decline paths (Abdelhafidh and Djebbar 2001).

A comprehensive presentation of all the methods available for analyzing production data, highlighting the strengths and limitations of each method has been finished (Mattar and Anderson 2003). These methods include Arps, Fetkovich, Blasingame and Agarwal–Gardner (A–G), normalized pressure integrative (NPI) as well as a new method called the Flowing Material Balance. Li et al. (2009) and Qin et al. (2012) performed the production analysis on unconventional gas reservoirs and presented the limitations and the range of application of different curves.

As the indexes of fracturing stimulation effectiveness, fracturing network parameters (ω and λ) are widely studied by many scholars. Moghadam et al. (2010) generated dual-porosity-type curves for various Lambda and Omega values, and converted them to a single curve that is equivalent to Wattenbarger’s linear flow-type curve. Al-Ajmi et al. (2003) presented a practical method to estimate the storativity of a layered reservoir with cross-flow from pressure transient data. An estimate of the transmissivity ratio may be obtained from production logs.

The storativity on the other hand needs to be determined from the pressure transient data or by independent means (Brown et al. 2011). Lian et al. (2011) derived the collaborative relationship between storativity and transmissivity ratio during the decrease in reservoir pressure. Few works have been done to study the direct relationship between fracturing network parameters (ω and λ) and productivity. However, Sander (1986) proposed a method to estimate the ratio of transmissivity (λ) and storativity (ω) from decline analysis using streamflow data that provides a useful reference when researchers are seeking for the relationship between productivity and fracturing network parameters.

Modern production analysis (MPA) and advanced production decline analysis (APDA) methods are commonly used to evaluate shale gas reservoirs in the previous studies. In this work, we demonstrate the availability of these two approaches in tight oil reservoirs, and we have introduced a solution to estimate OOIP_{SRV} directly on the basis of MPA. As a validation of our introduced method, three APDA techniques (Blasingame A–G and NPI) have been used to calculate OOIP_{SRV} as well. For the purpose of finding out the inside relationship between productivity and fracturing network parameters, a model has been developed to calculate ω and λ for an individual fracturing stage or for the whole MFHW in tight oil reservoir on the basis of microseismic data. Once ω and λ are figured out for an individual MFHW, it becomes easy to find the relationship between productivity and fracturing network parameters.

In order to demonstrate the feasibility and applicability of developed methods and models, 5 filed wells and 2 simulated wells have been analyzed. It has been found that there exists linear relationship between ω/λ (the ratio of storativity and transmissivity ratio) and average production of a single MFHW(Q_{ave}) for target tight oil reservoir. On the basis of derived linear relationship, the productivity for more individual MFHW can be directly estimated according to microseismic interpretation. The results of analysis and calculation for actual cases have validated the applicability of proposed solution for OOIP_{SRV} estimation and verified the convenience of developed models for fracturing network parameters calculation. From this study, it provides a method to estimate productivity directly from macroseismic data which is meaningful to be applied to more tight oil reservoirs.

## Methodology

MPA is one of the most commonly used methods to conduct production performance for multistage fractured horizontal well (MFHW) completed in unconventional reservoirs. Reservoir parameters and fracture properties can be obtained from production performance analysis using linear flow plot and square root time plot (Clarkson and Beierle 2010; Anderson et al. 2010; Clarkson 2013). Log–log normalized rate vs time plot is use to perform flow regime identification for MFHW in this paper, and a method based on square root time plot analysis to estimate OOIP_{SRV} has been introduced.

As modern production performance analysis technique, advanced production decline analysis (APDA) expands the range of application of decline analysis methods. APDA has been applied to carry out reservoir parameters calculation and OOIP_{SRV} evaluation in this study. What’s more, methods to calculate fracturing network parameters (ω and λ) for MFHW according to microseismic interpretation have been developed. With the knowledge of relationship between fracturing network parameters and productivity, it is convenient to estimate the productivity for a new MFHW on the basis of microseismic data.

### Modern production analysis method (MPA)

Oil/gas reservoir performance describing methods are based on the high-accuracy pressure data from transient well tests. MPA and well test are the basic facilities which were utilized to evaluate the characteristics and performances of unconventional reservoirs. As for tight oil reservoirs, well test needs very accurate pressure data from transient pressure tests which is time-consuming due to the very low pressure conductivity in tight layers. MPA has been widely adopted to accomplish production performance analysis to obtain useful reservoir parameters and OOIP_{SRV}.

### Log–log normalized rate versus time plot analysis

As for MFHW completed in tight oil reservoirs, two dominant flow regimes, transient linear flow regime which may last for several months or years, even several decades and boundary dominated flow, are widely agreed on in this industry. According to previous researches (Clarkson and Beierle 2010) or case studies (Clarkson and Williams-Kovacs 2013; Anderson et al. 2012) for tight oil or shale gas wells, the flow regime identification is performed to determine which model (corresponding to specific flow regime) to be used for reservoir parameters estimation.

Many theories and methods have been set up to capture the flow regime changes. In this paper, log–log normalized oil rate versus time plot has been used to identify flow regime. This plot has proven to be useful to perform flow regime identification for fractured horizontal wells completed in tight oil reservoirs (Clarkson 2013; Pinillos and Rong 2015).

During linear flow period, the slope of Log q/(P_{i} − P_{wf}) vs log time plot is equal to −0.5. During the boundary dominated flow, it equals to −1. The most significant contribution of Log–log normalized rate versus time plot in this paper is to identify the linear flow regime and find out the end time of linear flow (T_{elf}) directly. In order to decrease the production data fluctuation led by the change of production systems, the dimensionless rate and dimensionless time have been brought into use in this work, which are defined as follow (Bello and Wattenbarger 2010):

Generate Eqs. (2) and (3) into Eq. (1) (derivation refers to “Appendix 1”):

Equation (4) indicates that there exists linear relationship between normalized pressure and square root time (Δp_{q} versus t^^{1/2}).

### Square root time plot analysis

Considering the characteristics of linear flow regimes, we can draw the normalized pressure versus square root of material time plot to figure out the slope (m) of characteristic straight line. Once T_{elf} and m have been determined, the effective permeability (k_{SRV}) and effective fracture half length (X_{f}) of SRV zone can be estimated from Eqs. (5) and (6) (Qin et al. 2012; Chu et al. 2012; Ye et al. 2013).

Based on the straight-line behavior of linear flow on the square root time plot, the simplest form of the linear flow equation is (Clarkson et al. 2012):

Considering the interference of adjacent wells, skin factor and finite conductivity, the slope of plot is defined as Eq. (8).

The equations presented above are based on the assumption of a constant flowing pressure. While the flowing pressure of oil well is variable, the slope of square root time plot was given by Anderson et al. (2010):

The product of effective permeability and fracturing half length is as follows:

_{elf}, reservoir parameters (k

_{SRV}and X

_{f}) and OOIP

_{SRV}can be estimated.

It is assumed that a multistage fractured horizontal well (MFHW) is made up of a series of individual fracture stage, every stages of a MFHW are identical and the number of hydraulic fractures equals the number of fracture stage (Fig. 1).

**Fig. 1** Scheme of single fracture stage

Once the slope of square root time plot (m) is determined, the arithmetic product of total contacted matrix surface areas (A_{c}) for a multistage fractured horizontal well (A_{c} is sum of contacted matrix surface areas for each individual fractures (A_{c1}); every fracture has two contacted surfaces) and effective permeability can be detected from square root time plot analysis (derivation refers to “Appendix 2”):

The right part of Eq. (11) is determined by the slope of square root time plot (m) which is derived from actual production data. Combining with known or measured formation parameters, Ac(k_{SRV})^^{1/2 }is easy to be figured out. Then, the dynamic reserve (OOIP_{SRV}) can also be calculated from Eq. (12). The detailed derivations of Eq. (12) are presented in Appendix 2.

### Advanced production decline analysis (APDA)

Many decline analysis curves and models have been established during the history of oil/gas exploration and exploitation. The most typical one is Arps decline curve analysis method which is under the assumption of constant bottom pressure and permeability (Ibrahim et al. 2006). Arps decline curve can only be used to analyze production performance in steady flow regimes. Traditional decline analysis (Arps) gives reasonable answers to many situations except for that it completely ignores the flowing pressure data (Mattar and Anderson 2003). As a result, it may underestimate or overestimate the reserves.

Advanced production decline analysis (APDA) method (including Fetkovich, Blasingame, Agarwal–Gardner, NPI, transient, etc.) breaks the limitations of Arps decline curve, and it can be used to perform the production analysis even if the flow is not steady for a single well (Zhu et al. 2009). APDA can not only be applied to evaluate OOIP_{SRV}, but also be utilized to determine the reservoir parameters (k_{SRV}, r_{eD} et al.). APDA approached to realize the standardization of production analysis curves. Furthermore, it provides a new facility to analyze the storage and drainage characteristics of oil/gas wells qualitatively and quantitatively on the basis of large amount of daily rate and pressure data (Liu et al. 2010).

Type curve matching (TCM) is the main manner to obtain reservoir parameters and OOIP_{SRV} using advanced production decline analysis (APDA). Many scholars and researchers have done a lot of works on APDA and developed many standard charts (Fetkovich 1980; Palacio and Blasingame 1993). In order to decrease calculation error, three kinds of APDA methods (Blasingame, Agarwal–Gardner and NPI) have been adopted to calculate OOIP_{SRV} for MFHWs in this work.

For each kind of TCM, there are three types of curves on the standard chart, namely normalized rate curve, normalized rate integral curve and normalized rate integral derivative curve defined as Eqs. (13), (14) and (15). (Zhu et al. 2009; Liu et al. 2010; Sun 2013).

Normalized rate:

Normalized rate integral:

Normalized rate integral derivative:

As for each kind of APDA method, the steps to perform the production analysis are similar. Due to the fact that the focus of this paper is not to study the differences between different individual APDA methods, not all of the adopted APDA methods have been discussed in detail. Here, we take the Blasingame analysis method as an example to explain how to figure out the OOIP_{SRV} for a MFHW, and for more details about Agarwal-Gardner and NPI methods refer to previous works (Zhu et al. 2009; Liu et al. 2010; Sun 2013).

Firstly, the actual production data are used to draw the log normalized rate vs log time curve [log (q/△p] versus log t_{ca}), log normalized rate integration versus log time curve [log (q/△p)_{i} vs logt_{ca}] and log normalized rate integration derivation versus log time curve [log (q/△p)_{id} vs logt_{ca}]. Taking any two of the three types of curves or all of the three curves, a TCM log–log chart is established. Subsequently, the actual TCM log–log chart for target well is applied to fit the developed standard chart to determine the dimensionless borehole radius (r_{eD}). The detailed steps to obtain r_{eD} are presented in “Appendix 3”; once r_{eD} have been figured out, the OOIP_{SRV} and more relevant reservoir parameters can be estimated.

Effective wellbore radius (r_{wa}):

The drainage radius (r_{e}) could be calculated from Eq. (16) as r_{eD} and r_{wa} have been obtained:

As shown in “Appendix 3”, we have introduced how to determine the variables which are used to calculate dynamic reserve (OOIP_{SRV}):

Fracturing network parameters calculation

Network fracturing technique is an important method to improve the production for tight oil reservoirs. Fracturing network parameters (ω and λ) are the indexes of fracturing stimulation effectiveness.

Storativity (ω) is defined as the ratio of elastic storage ability of fracture system to the total storage ability of the pay zone. It indicates the relative size of elastic storage ability of fracture system and matrix system (Lian et al. 2011). Resources exchanged between fractures and matrix blocks can be characterized by transmissivity ratio (λ) which reflects how easy or difficult the fluid medium flows into fracture from matrix (Wang 2015).

Due to the fact that the main purpose of fracturing stimulation for tight oil reservoir is to develop larger stimulated reservoir volume (SRV), the focus of network fracturing is to connect as many natural fractures as possible based on the shear slide of secondary fracture system. Most proppants are used to support hydraulic fractures, and very few proppants (even if there is some, the proppant size is very small and the volume of those proppants can be ignored comparing the total volume of secondary fractural system in SRV) can be brought into natural fractures. Then, the volume of secondary fracture system can be estimated from the volume of fracturing fluid injected into reservoir layer. Assuming the matrix block is divided into plats by secondary fracture (Fig. 2), the porosity of connected natural fractures is 100% and the system compressibility of secondary fracturing networks is homogeneous, ω and λ are defined as (Warren and Root 1963; Wang 2015):

**Fig. 2** Scheme of fractured layer (natural fractures refer to as secondary fractures)