Due to the limitation of actual shale gas reservoir conditions and fracturing technologies, artificial fracture networks are different greatly even in the same or similar stimulated reservoir volume. Deviations and even faults occur in evaluation and cognition if only the stimulated reservoir volume (SRV) is used to characterize and evaluate the effect of stimulation. In this paper, the spatial distribution of artificial fractures and natural fractures and the internal pressure state and degree of reserve recovery of stimulated shale gas reservoirs were studied by means of artificial fracture propagation numerical simulation and production numerical simulation.
Liu Yuzhanga,b, Yang Lifengb, Wang Xina,b, Ding Yunhonga,b, Wang Yonghui & Zou Yushi
aCNPC Key Laboratory of Reservoir Stimulation, Langfang, Hebei 065007, China. bPetroChina Petroleum Exploration and Development Research Institute, Beijing 100083, China. cChina University of Petroleum, Beijing 102249, China
Received 20 April 2017; accepted 25 July 2017
And three concepts were proposed, i.e., shale gas fracture network, ideal fracture network and appropriate-stimulation degree of fracture network. The study results indicate that, at the end of reservoir development, target zones can be classified into three types (i.e., relatively appropriate stimulation zone, transitional stimulation zone, and uncompleted stimulation zone) according to the recovery degree and production time of stimulated reservoirs; and that the final morphologic parameter of fracture networks and the reservoir characteristic are two main factors affecting the appropriate-stimulation degree of fracture networks.
As for a specific gas reservoir, the orientation, length, conduction, height and spatial location of its fracture network are the main factors influencing its appropriate-stimulation degree if the well trajectory is set. The proposal of the theory on the appropriate-stimulation degree of hydraulic fracture networks in shale gas reservoir enriches the theoretical system of shale reservoir stimulation technology, and it can be used as the reference for characterizing the fracture systems in other unconventional reservoirs, such as tight oil and gas reservoirs.
When fracturing optimization design and performance evaluation are conducted, the results of numerical simulation indicate that, given the same stimulated reservoir volume (SRV), artificial fracture conductivity and contacting area between artificial fracture and reservoir, individual well production, oil recovery and distribution of residual oil/gas are different if fracture distribution state is different.
Post-fracturing assessment is often based on micro-seismic events, while practical application shows that the performances after fracturing vary greatly even with similar physical properties of reservoir and micro-seismic event volume. This is because there are different distribution states of artificial fractures formed in fracturing. Since the final development effect depends on hydraulic fracture distribution state, it is essential to quantify fracture distribution state in fracturing design and post-fracturing evaluation.
Yin et al.  adopted the fractal method to characterize fracture development degree. Cipolla et al. , , ,  proposed injection pressure drawdown test to analyze fracture development degree in 2008, production matching method combined with numerical simulations and micro-seismic monitoring in 2009 and fracture complexity index in 2010. Xu et al.  analyzed fracture state by applying micro-seismic technology and mechanic fracture propagation analyzing software.
Wang et al.  proposed that parameters such as equivalent fracture amount, equivalent fracture width and equivalent leak-off coefficient can be used to characterize complex fractures. All these methods, either quantitative or qualitative, only describe fracture itself and their results cannot reflect the matching between fracture system and reservoir. Deviations and even faults occur in evaluation and cognition if only SRV or the intuitive sense of fracture morphology is used to characterize and evaluate the effect of stimulation.
In order to quantify the matching between artificial fracture and reservoir, the authors proposed the concept of appropriate-stimulation degree of fracture network in shale gas reservoir. Relatively appropriate stimulation zone, transitional stimulation zone and uncompleted stimulation zone were also put forward on the basis of recovery degree and non-dimensional production time (a specific time in a gas well life cycle divided by the total life cycle). And two types of factors influencing appropriate-stimulation degree of fracture network were analyzed.
Definition and connotation of fracture network appropriate-stimulation degree
After stimulation, artificial fractures and their connected natural fractures in shale gas reservoirs cut rocks in SRV into independent units with different shapes and sizes. Artificial hydraulic fracture simulation is carried out through artificial fracture propagation numerical simulation and production numerical simulation. Results show that the shape and size of units are different in varied process and reservoir conditions, thus the seepage state and production performance are different (Fig. 1).
Fig. 1. Pressure distribution of different gas reservoirs with various fracture morphologies but at the same development condition at the end of one-decade production (the matrix permeability is 100 nD).
Meanwhile, results of a large amount of micro-seismic show that production varies greatly even with similar physical properties of matrix and the same SRV because the number of influencing factors is large , , , . For example, there are two wells with the same borehole length and operation parameters in platform Y and both SRV of them is 0.7 × 108 m³. However, their production after stimulation is significantly different (Fig. 2, Fig. 3).
Fig. 2. Seismic interpretation of Wells Y-1 and Y-2 in Platform Y.
Fig. 3. Production curves of Wells Y-1 and Y-2 in Platform Y after fracturing.
In this paper, fracture network appropriate-stimulation degree was proposed to characterize the state of fracture network during hydraulic fracturing process and evaluate stimulation performance.
Fracture networks and ideal fracture networks
The following concepts are clarified before fracture network appropriate-stimulation degree is defined.
Fracture network of shale gas reservoir (or fracture network): a fracture system consisting of artificial fractures and natural fractures which connect with artificial fractures (Fig. 4).
Fig. 4. Schematic diagram of a fracture network in a shale gas reservoir.
An ideal fracture network: all points in fracture network matrix connecting a well almost reach a limited pressure at a specific time (Fig. 5-a). This definition has two meanings. First, an ideal fracture network is an ideal stimulation state without considering economic rationality and the possibility of engineering implementation. Second, all points in fracture network matrix have synchronous pressure drop. This means that the permeability of an ideal fracture network has improved greatly so that the average pressure in every matrix unit declines synchronously and reaches a certain value.
Fig. 5. Schematic diagram of ideal (a) and actual (b) fracture networks.
Appropriate-stimulation degree of shale gas reservoir fracture network
Based on ideal fracture network, the appropriate-stimulation degree of a shale gas reservoir fracture network is defined. It means the ratio of the recovery degree of an actual fracture network (Fig. 5-b) to that of an ideal fracture network. The appropriate-stimulation degree reflects a gap between the actual state and the ideal state of a fracture network, which can be considered as an important index for evaluating technological progress.
where, C0 is the fracture network appropriate-stimulation degree; similarly EC: the actual fracture network recovery degree, Emax: the ideal fracture network recovery degree.
Recovery degree of actual fracture network
Combined with production simulation software, the recovery degree of an actual fracture network under designated conditions can be achieved based on the geometric size and distribution state.
Recovery degree of ideal fracture network
Since an ideal fracture network is an ideal state, conventional numerical simulation cannot be used to calculate its recovery degree. In this paper, a material balance method was proposed for calculating the recovery degree.
1) Initial formation condition Molar quantity of free gas:
Volume of absorbed gas:
Molar quantity of absorbed gas:
2) The total molar quantity of gas in a formation when the formation pressure reaches a specific value (pd) at an ideal fracture network state.
Molar quantity of free gas:
Volume of absorbed gas:
The Molar quantity of absorbed gas:
3) According to the material balance principle, when formation pressure reaches a specific value, the gas recovery degree is:
Assuming the abandonment pressure of a gas reservoir at a given production is p’wf, the recovery degree of an ideal fracture network is:
Assuming gas reservoir temperature at the initial formation pressure is Ti, if Ti is equal to Td, then the recovery degree of an ideal fracture network is:
where, ni is the Molar quantity of free gas in initial formation conditions, mol; similarly nim: the Molar quantity of absorbed gas in initial formation conditions, mol; nimd: the Molar quantity of absorbed gas at a specific pressure at a state of ideal fracture network, mol; ηidea: the recovery degree of an ideal fracture network, dimensionless; Zi: the gas compressibility factor at an initial formation pressure, dimensionless; Zd: the gas compressibility factor at an abandonment pressure of gas reservoir, dimensionless; Ti: gas temperature at an initial formation pressure, K; Td: gas temperature at an abandonment pressure, K; pL: the Langmuir pressure of gas in an initial formation condition, Pa; pi: the initial formation pressure; Pa; pd: the specific pressure when production is conducting at the state of an ideal fracture network, Pa; p′wf: the abandonment pressure when production is conducting at the state of an ideal fracture network, Pa; Vi: the volume of free gas in gas reservoir at an initial formation pressure, m3; Vim: the volume of absorbed gas in gas reservoir at an initial formation pressure, m3; VL: the Langmuir volume, m3; Vimd: the volume of absorbed gas at a set formation pressure (pd), m3.
“Three partitions” of appropriate-stimulation degree of a fracture network
Target zones of stimulation are divided into several parts according to research purpose. At the end of reservoir development, target zones can be classified into three types (i.e. relatively appropriate stimulation zone, transitional stimulation zone and uncompleted stimulation zone, collectively referred to as “three partitions”) according to appropriate-stimulation degree (C0) and dimensionless production time (td, a specific time in a gas well life cycle divided by a total life cycle, td = t/tmax).
“Three partitions” are quantified as below (for appropriate-stimulation degree and dimensionless time, 95% is adopted as a critical point considering engineering error):
Relatively appropriate stimulation zone: 0.95 ≤ td ≤ 1.00, 0.95 ≤ C0 ≤ 1.00. The appropriate-stimulation degree of a specific part in target zones is nearly 1.00 while the dimensionless time reaches 0.95.
Transitional stimulation zone: td < 0.95, C0 ≈ 1.00. The appropriate-stimulation degree of a specific part in target zones is nearly 1.00 while the dimensionless time does not reach 0.95.
Uncompleted stimulation zone: td = 1.00, C0 < 0.95. At the end of reservoir development, the appropriate-stimulation degree of a specific part in target zones is still below 0.95.
Post-fracturing productivity of gas reservoirs with different fracture morphologies in Fig. 1 is stimulated using shale gas reservoir numerical simulation, in order to understand the appropriate-stimulation degree of fracture networks. Table 1 shows the basic parameters used in the simulation. Reservoir length is 600.0 m, reservoir width is 300.0 m, reservoir thickness is 33.3 m, reservoir temperature is 103 °C, matrix porosity is 4.2%, reservoir pressure is 66.8 MPa, the Langmuir pressure is 6.42 MPa, and the Langmuir volume is 0.00192 m3/kg.
Table 1. Evaluation of appropriate-stimulation degree (C0) of fracture network in different cases shown in Fig. 1
The final recovery efficiency of target zones with a size of 600.0 m × 300.0 m × 33.3 m is calculated to be 64% at an abandonment pressure of 10 MPa based on Eq. (10) and basic parameters.
If Cases ①, ② and ③ (shown in Fig. 1) are considered as a whole to evaluate the appropriate-stimulation degree of fracture networks, the appropriate-stimulation degree of Cases ①, ② and ③ with matrix permeability of 10 nD and 100 nD is shown in Table 1. The results show that corresponding to two formation permeabilities, the appropriate-stimulation degree of Case ② is higher, while the fracture network that is visually more complex in Case 1 actually does not have the highest appropriate-stimulation degree. Fracture networks with the same fracture geometry and different matrix permeabilities lead to different recovery degrees around fractures, resulting in various appropriate-stimulation degree of fracture networks.
Table 2. Evaluation results of appropriate-stimulation degree in the relatively appropriate stimulation zone.
The appropriate-stimulation degree of parts inside a fracture network varies depending on the objects of study. Case ② with a better appropriate-stimulation degree is chosen to be divided in order to further explain the state of target zones and thus the appropriate-stimulation degree of different parts in the fracture network is obtained, as shown in Table 2, Table 3, Table 4 and Fig. 6. The results show that, in Case ②, over-stimulation zone and the uncompleted stimulation zone take a relative high percent, so the total appropriate-stimulation degree is relatively low.
Table 3. Evaluation results of appropriate-stimulation degree in over-stimulation zone.
Table 4. Evaluation results of appropriate-stimulation degree in the uncompleted stimulation zone.