## Abstract

The Lower Permian reservoirs in the western Sichuan Basin are ultra-deep with high temperature, high pressure and developed natural fractures. Leakage and contamination of drilling fluid is the main factor restricting reservoir stimulation effects, so the acidification will be the solution also as the first choice to enhance the gas recovery. In view of this, an acidification design was proposed to minimize the contamination skin factor to the highest degree. A model was first developed to calculate the critical pumping rate for opening natural fractures in deep beds. Then, the acidification model for the rock samples of natural fractures in the experimental scale was modified, and a model was established for predicting the effective penetration distance of acid and the fracture aperture in the conditions of wellbores.

#### Authors:

Guo Jianchun^{a}, Gou Bo^{a,b}, Wang Kunjie^{a}, Ren Jichuan^{a}, Zeng Ji^{c}

^{a}State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China. ^{b}Post-Doctoral Research Center, Southwest Petroleum University, Chengdu, Sichuan 610500, China. ^{c}Engineering and Technology Research Institute, PetroChina Southwest Oil & Gas Field Company, Chengdu, Sichuan 610017, China.

Received 13 March 2017; accepted 25 June 2017

Accordingly, a skin factor calculation model for network-fracture acidification was developed. It is indicated that when the acid pumping rate is 5.0 m^{3}/min, all natural fractures around Well S1-1 can be opened, regardless of their dip angles. Besides, the advantage of high-rate acid injection emerges gradually when the injected acid is more than 100 m^{3}. Moreover, for minimizing the skin factor, the network-fracture acidification in Well S1-1 was optimized by pumping 210 m^{3} acid at the rate of 4.5 m^{3}/min. According to the optimal design idea, network-fracture acidification has been successfully applied in Well S1-1, and a high-yield industrial gas flow was produced at the rate of 83.7 × 104 m^{3}/d. It is concluded that network-fracture acidification technology is a safest, most economical and effective mode for the stimulation of such ultra-deep reservoirs in the study area.

High-yield gas flow was successively obtained in the Lower Permian Maokou Fm and Qixia Fm in Jiulongshan, Daxingchang and Shuangyushi structures in the western Sichuan Basin. In particular, the high-yield gas flow obtained in Well Shuangtan 1 in the Shuangyushi structure in 2014 demonstrated huge prospects for natural gas exploration and development [1–3]. The Shuangyushi structure belongs to the front fold belt of Longmenshan at the northern margin of the upper Yangtze Craton, where the Lower Permian reservoirs are generally ultra-deep (>6000 m) with high temperature (>150 °C) and high pressure (bottomhole pressure >90 MPa) [1]. Natural fractures are developed in target reservoirs and a large amount of leakage of drilling fluid occurred in some producing intervals. The leakage and contamination are the main factors restricting reservoir stimulation. Acidification is a safe, effective and economical measure for the stimulation of such ultra-deep HTHP gas wells, the purpose of which is to completely remove the damage of drilling fluid, dredge the fracture network, minimize the reservoir skin factor and thus obtain relatively high gas well productivity [4].

Based on the geological features of the Lower Permian reservoirs in the Shuangyushi structure, the authors proposed the an acidification design to minimize the contamination skin factor specific to fracture-type reservoirs, namely, the natural fractures are reopened to drive the acid fluid flow and react along the natural fractures so as to realize deep-penetration blockage removal and acidification. Accordingly, a calculation model was developed for the opening of natural fractures, the critical pumping rate for opening natural fractures in the Qixia Fm in the western Sichuan Basin was determined and a model was established for predicting the effective penetration distance of acid in natural fractures. Based on this distance and the fracture aperture after acidizing, a skin factor calculation model for acidification was developed and the acid treatment parameters were optimized.

## 1 Geological features of reservoirs

The Lower Permian reservoirs in the Shuangyushi structure include Maokou Fm and Qixia Fm, which are mainly composed of gray–dark gray dolomite and dark–gray black limestone. The reservoirs are mostly buried between 6800 and 7500 m, with formation pressure coefficient of 1.4–1.9, formation temperature of 150–159 °C, porosity of 1.2–8.8% and thickness of 20–40 m. Core observation and image logging interpretation indicate that there are natural fractures and v_{ugs} in the target reservoirs (Figs. 1 and 2), which serves as the major reservoir space.

**Fig. 1.** Pictures of some coring sections in the Qixia Fm of Well S3.

Conventional logging interpretation and drilling shows indicate that there is severe drilling fluid leakage in the sections with natural fractures (Table 1). To open the natural fractures to eliminate the damage, dredge the natural fracture networks and realize the deep-penetration network fracture acidification of acid fluid is an economical and safe mode for the stimulation of such reservoirs [4,5].

**Fig. 2.** Electric image logging interpretation map for the Maokou Fm of Well S2 (1 in = 25.4 mm, 1 ft = 0.304 8 m, similarly hereinafter).

## 2. Network-fracture acidification design to minimize the skin factor

Leakage and contamination of drilling fluid in fracture-type reservoirs have certain characteristics. For example, a large amount of drilling fluid leakage along the natural fracture networks blocks them, and the “non-radial” contamination zone covers a wide range and causes more severe formation damage than that in conventional pore-type reservoirs [6,7]. Since the natural fracture networks contribute the most to reservoir productivity, it is inevitable to reopen the natural fractures and dredge the natural fracture networks in the stimulation of reservoirs [7].

**Table 1.** Drilling shows and logging interpretation of some wells in the Shuangyushi structure.

Practices have proved that conventional matrix acidification technology cannot effectively remove the contamination in the deep formation of such reservoirs. Conventional deep acid fracturing technique to make long fractures can reduce deep-formation contamination and connect the reservoirs far from the wellbore, but only communicate limited natural fractures, possibly leading to quick decline of production after acid fracturing. The volume acid fracturing technology for complicated acid fracturing networks with high liquid amount and a high pumping rate has gradually been applied in domestic fracture-type tight carbonate reservoirs in recent years [8]. However, the single-well acidification effect of the Lower Permian ultra-deep wells in the western Sichuan Basin in the earlier stage indicates that the wellhead pressure reached 95 MPa at an acid pumping rate of 3.0 m^{3}/min without obvious fracture shows in the formation, indicating relatively high engineering risks in high-pumping-rate volume acid fracturing technique.

Practices have proved that the network-fracture deep-formation acidification technology can effectively dredge the natural fracture network system of the reservoirs with natural fractures, so as to improve the flow conditions of formation and thus increase productivity [9]. Essentially in this technique, high injection rate is applied when engineering conditions permit, so as to increase the bottomhole pressure and open the natural fractures; the acid fluid flows into the reservoir in a non-radial form along the natural fractures and forces the acidizing fractures to expand in depth, so as to increase the permeability in the near wellbore zone, realize in-depth blockage removal, increase the gas drainage radius, minimize the skin factor and obtain high-yield gas flow (Fig. 3) [10].

**Fig. 3.** Diagram of network-fracture acidification.

In order to implement network-fracture acidification in the Lower Permian ultra-deep HTHP gas wells in the western Sichuan Basin, we should take measures first to: (1) define the critical pumping rate needed to open natural fractures under the condition of limited wellhead pressure; and (2)increase the effective penetration distance of acid fluid to connect more natural fractures under the condition of ultra-temperature where acid-rock reaction is extremely quick.

## 3 Optimal design of network-fracture acidification for ultra-deep gas wells in the western Sichuan Basin

The design of network-fracture acidification for ultra-deep gas wells in the western Sichuan Basin involves two key aspects: (1) critical conditions for opening natural fractures and effective penetration distance of acid fluid in them; and (2) minimization of the acidification skin factor.

### 3.1. Critical conditions for opening natural fractures

To realize the engineering goal that the acid fluid enters the reservoir along the natural fractures for non-radial in-depth acidification of the damage zone, it is necessary to determine the critical pumping rate for opening natural fractures in the conditions of reservoirs and then to judge whether it can be realized in engineering depending on the condition of wellhead pressure.

The stress that natural fractures bear depends on the total formation stress state and the position and the dip angle of the fractures. Even if the natural fractures in the formation are at the same depth, their normal effective stresses are different if they are developed in different directions and dip angles. Horizontal fractures and vertical fractures are only under the action of vertical effective stress and horizontal effective stress respectively. The approaching angle of natural fractures and wellbores or hydraulic fractures is θ, the normal stress σ_{n} and shearing stress τ_{n} on the natural fracture surfaces are [11]:

where, θ represents the approaching angle of natural fractures and wellbores or hydraulic fractures, (°); σ_{H} represents the maximum horizontal principal stress, MPa; σ_{h} represents the minimum horizontal principal stress, MPa.

Assuming that the acid fluid penetrates into the natural fractures and reservoirs before the natural fractures are open, if the pressure drop inside the natural fractures is neglected, the fluid pressure at the inlet and inside the natural fractures is p_{f}. The criterion for natural fracture opening is [11]:

pf>σ_{n } (3)

A simplified physical model was established to judge whether a close natural fracture can be opened under a certain acid injection rate. Under this model, acid fluid is injected into the wellbore at a certain rate, and when the injection rate is higher than the outflow rate, the internal wellbore pressure increases due to fluid compression.

According to the mass conservation law, increment of acid fluid inside the wellbore in unit time is:

ΔV=Q_{inj}-Q_{out} (4)

where, ΔV represents the variation of fluid volume in unit time, m^{3}; Q_{inj}: represents the injected fluid volume in unit time, m^{3}; and Q_{out} represents outflowing fluid volume in unit time, m^{3}.

Assuming the wellbore volume is constant, according to the definition of fluid compressibility, extra bottomhole pressure (Δp) needed by compressed fluid volume ΔV is:

The bottomhole pressure at this moment is:

p_{f} = p_{i} + Δp (6)

where, p_{f} represents the bottomhole pressure, MPa; p_{i} represents the initial bottomhole pressure, MPa; Δp represents the pressure increment, MPa; V represents the wellbore volume, m^{3}; Cacid represents the compressibility coefficient of acid fluid, MPa^{−1}.

When formula (6) meets formula (3), the natural fracture will be opened. Assuming the natural fracture is wellbore-centered and ring-like, and the leakage of acid fluid into the natural fracture and reservoir meets the Darcy law, if the improvement of reservoir permeability by acid fluid within a short time is neglected, then the leakage of acid fluid into the reservoir in unit time is [12]:

where, K represents the permeability of perforation interval, m_{D}; h represents the thickness of perforation interval, m; rf represents the length of natural fracture, m; r_{w} represents the wellbore radius, m.

The critical pumping rate for opening a natural fracture can be calculated by formulas (1)–(7). Given the wellhead pressure limit, wellhead pressure under different acid pumping rates shall also be determined by formula (8),

p_{t} = p_{f} +p_{F} – p_{h} (8)

where, p_{t} represents the wellhead pressure, MPa; p_{F} represents the friction of acid fluid in wellbore, MPa; p_{h} represents fluid volume pressure in wellhead, MPa.

Friction of acid fluid in wellbore is calculated by formula (9)[13]:

where, ρ represents the acid fluid density, kg/m^{3}; f represents the friction coefficient, dimensionless; L represents the tubing length, m; D represents the tubing diameter, m.

It can be judged whether the natural fracture can be opened and the critical pumping rate needed for opening by formulas (1)–(9). The Qixia Fm reservoir of Well S1-1 in the Shuangyushi structure was selected as an example to demonstrate the calculation process of critical pumping rate.

**Table 2.** In-situ stress in Well S1-1 and critical bottomhole pressure for opening natural fractures.

Based on the in-situ stress test data of Well S3 which is adjacent to Well S1-1, namely, the gradients of maximum horizontal principal stress, minimum horizontal principal stress and vertical stress of the Qixia Fm is 0.0229 MPa/m, 0.0199 MPa/m, and 0.027 MPa/m, respectively, the principal stresses of Well S1-1 in three directions are calculated (Table 2). The critical bottomhole pressure needed to open natural fractures of different dip angles (Table 2) can be calculated by formula (3).

**Table 3.** Basic data of Well S1-1.

Based on the basic data of Well S1-1 (Table 3), the bottomhole pressures under different acid pumping rates were calculated by formulas (4)–(7), and the bottomhole pressures of Well S1-1 under different acid pumping rates were calculated by formulas (8) and (9) (Fig. 4).

**Fig. 4.** Bottomhole and wellhead pressures under different acid pumping rates.

It can be known from Fig. 4 that under the condition of wellhead pressure limit, the critical pumping rate to fracture the reservoir is difficult to be reached, indicating that under the current wellhead condition of ultra-deep gas wells in the western Sichuan Basin, deep acid fracturing is difficult to be achieved and blockage removal and acidification is the necessary technique. When the acid pumping rate is above 3.5 m^{3}/min, the bottomhole pressure is higher than the minimum critical pressure for opening the natural fracture (dip angle of natural fracture is 0°); when the acid pumping rate is 5.0 m^{3}/min, the bottomhole pressure reaches 173.6 MPa.

It can be known from Table 2 that all natural fractures around Well S1-1 can be opened, regardless of their dip angles, which meets the condition for network-fracture acidification; when the acid pumping rate is above 5.0 m^{3}/min, the wellhead pressure exceeds the pressure limit and reaches its working limit. During acid injection, as the natural fracture is being opened, the acid fluid gradually dredges the natural fracture and the skin factor gradually decreases, and the wellhead pressure may decrease under the condition of certain acid injection [14].

### 3.2. Effective penetration distance of acid fluid in natural fractures

The effective penetration distance of acid fluid in natural fractures is another key element for realizing deep-formation acidification. Assuming that a natural fracture is round surrounding the wellbore, the leakage of acid fluid on its wall is neglected. This paper paid key attention to the effective penetration distance of acid fluid in natural fractures, the linear flow acidification model for the rock samples of natural fractures in the experimental scale was modified and an acidification model for acid fluid to flow into the natural fractures on the radial direction was established in the conditions of wellbores [14]. Therefore, the mass conservation equation of acid fluid on the length direction of natural fractures, the mass transfer equation and dynamic change equation of fracture width are as follows:

Initial conditions are:

Boundary conditions are:

The flow reaction model formulas (10)–(17) of acid fluid established were numerically solved by finite difference method. The impact of acid pumping rate on the effective penetration distance of acid fluid and the maximum fracture width after acidification was calculated based on the data of Well S1-1 (Table 3). Fig. 5 shows that the improvement of the acid pumping rate will speed up the flow of acid in the direction of natural fractures and make the acid move forward quickly, which is conductive to increasing the effective penetration distance of acid.

**Fig. 5.** Influence of acid pumping rate on the effective penetration distance of acid and the maximum fracture width after acidification (Acid injection volume of 100 m^{3}).

However, when the acid injection volume is unchanged, the improvement of the acid pumping rate means the contact reaction time between the acid and the rock will be reduced, resulting in the decrease of dissolution fracture width. The long effective penetration distance of acid is beneficial to interconnecting the far-well reservoirs.

### 3.3. Skin factor calculation model of network-fracture acidification

#### 3.3.1. Calculation of skin factor of contamination zone

At present, there is no calculation method for skin factor of drilling fluid contamination damage in fractured reservoirs, so the calculation method for skin factor of drilling fluid contamination damage in porosity reservoirs was used for reference:

where, r_{d} represents the drilling fluid contamination radius, m; K_{d} represents the average permeability of contamination zone, mD.

The contamination radius is calculated by the volume method according to formula (19) as follows.

where, V_{loss} represents the drilling fluid loss, m^{3}; ϕ represents the average porosity of reservoir.