Study on Optimization of Stimulation Technology of Heterogeneous Porous Carbonate Reservoir

Abstract

Mishrif (M) reservoir of Faihaa (F) oilfield in Iraq is a heterogeneous porous carbonate reservoir. The reservoir properties of each reservoir unit differ greatly, and the distribution of porosity and permeability is non-uniform. Some reservoir units have the problem that the expected production cannot be achieved or the production decline rate is too fast after matrix acidification. This work optimized and compared the process of acid fracturing and hydraulic fracturing techniques. The Mishrif B (MB) and Mishrif C (MC) layers are selected as the target units for fracturing and the perforation intervals are optimized. The acid fracturing process adopted the acid fracturing technology of guar gum pad fluid and gelled acid multi-stage injection. According to the wellhead pressure limit and fracture propagation geometry, the pumping rate is optimized. The recommended maximum pumping rate of acid fracturing is 5.0 m³/min, and the optimized acid volume is 256.4 m³. The pressure changes during hydraulic fracturing and acid fracturing are different. It is recommended that the maximum hydraulic fracturing pump rate is 4.5 m³/min for MB and MC layers, and the amount of proppant in MB and MC layers is 37.5 m³ and 43.7 m³, respectively. The production prediction of two optimized processes is carried out. The results showed that the effect of acid fracturing in MB and MC layers is better than hydraulic fracturing, and it is recommended to adopt acid fracturing technology to stimulate MB and MC layers. Acid fracturing operation is carried out in the X-13 well, and better application results are achieved. The results of this study provide optimized reference ideas for reservoir stimulation in heterogeneous porous reservoirs.

1. Introduction

It is estimated that more than 60% of the world’s oil reserves are contained in carbonate reservoirs [1]. Taking the Middle East as an example, the region is dominated by carbonate reservoirs, with about 70% of oil and 90% of nsatural gas distributed in these reservoirs [2,3,4]. However, the non-uniform porosity and permeability distribution and strong heterogeneity of the reservoir are the main factors affecting the stimulation effect of carbonate reservoirs [5]. Matrix acidification has always been the main stimulation technology for eliminating near-well damage and restoring natural productivity in carbonate reservoirs [6,7,8]. The carbonate reservoir is affected by sedimentation and diagenesis during the formation process, which shows strong heterogeneity. General acidification is often unable to effectively stimulate low-permeability areas, resulting in the improvement of single well production when matrix acidification is not obvious [9]. The diverting agent is added to the acid fluid system to block the high-permeability layer and make the acid fluid flow to the low-permeability area [10,11,12]. Due to the small scale of matrix acidification and the limited flow range of acid fluid, it cannot be further improved in the reservoir, and only the matrix near the wellbore has a good improvement effect. At present, some reservoir units of the M reservoir in the F oilfield are unable to achieve the expected effect of increasing production after acidification. On the basis of fully understanding the reservoir characteristics and stimulation potential, the field stimulation process optimization is carried out to explore the effective method of low-permeability reservoir stimulation in the Middle East M reservoir.

Carbonate reservoirs in the Middle East have high calcite content, so acid treatment is generally used to improve the porosity and permeability distribution [13]. The common treatment method for low-permeability carbonate reservoirs is acid fracturing. The evaluation indexes of acid fracturing effect mainly include acid etched fracture length and acid etched fracture conductivity [14]. The M carbonate reservoir has strong heterogeneity and mineral homogeneity. Reducing acid fluid filtration and acid rock reaction rate can effectively increase fracture length and conductivity. Most of the existing studies have evaluated the adaptability and process optimization of acid fracturing operations from two aspects: acid fluid combination [15] and acid fluid systems [16]. By adding a variety of additives to the acid fluid, the rheology of the acid fluid system is changed, and the liquid filtration and acid–rock reaction rate are reduced. Liu et al. [17] experimentally tested the reaction rates of three different acid fluid systems: conventional acid, diverting acid, and gelled acid. The experimental results show that the gelled acid with better reaction rate delay effect and lower friction can produce longer acid etched fractures and conductivity. Wang et al. [18] prepared a low-viscosity microlactic acid suitable for the field based on the characteristics of carbonate reservoirs in the Middle East. Compared with hydrochloric acid, emulsified acid, and surface-active acid by rotating disk and core displacement experiments, it is proved that the acid has the ability to etch the surface of the fracture to form high-conductivity fractures and has good field applicability. The above research focuses on the optimization of acid performance, and there are relatively few studies on acid fracturing treatment parameter optimization. In the process of acid fracturing, the influence of treatment parameters on the length and conductivity of acid etched fractures is very important.

In the process of carbonate reservoir stimulation, Iraq’s Halfaya oilfield has successfully adopted hydraulic fracturing operation and achieved good stimulation effect [19,20]. This provides a new idea for optimizing the stimulation process of carbonate reservoirs in the Middle East. The hydraulic fracturing process of carbonate reservoirs is affected by many factors, which makes the fracture propagation mechanism complex [21,22], and it is difficult to control fracture propagation. Liu et al. [23] modeled the distribution of natural fractures and cavities in carbonate reservoirs using the element partition method to study the interaction law of hydraulic fractures and cavities under different injection conditions. In order to clarify the mechanism of hydraulic fracture extension in carbonate reservoirs, some scholars have used the extended finite element method to establish a fully coupled model to study the effects of natural fractures and cavities on fracture extension in carbonate reservoirs [24,25].

At present, most of the studies on carbonate reservoir stimulation are related to fracture extension. Fewer scholars optimize the specific parameters in the operation process. The aim of this paper is to establish a set of stimulation technology optimization processes for heterogeneous porous carbonate reservoirs. We use numerical simulation to optimize the operation parameters of acid fracturing and hydraulic fracturing. In the optimization of acid fracturing process parameters, we will take the rate of change in dimensionless conductivity as an evaluation index. The final choice of acid fracturing or hydraulic fracturing technology will be decided based on the production change after stimulation. The field application further verifies the accuracy of the optimization results.

2. Reservoir Characteristics

The M reservoir is the most important bearing carbonate reservoir in the Mesopotamian basin in southeastern Iraq [26,27]. The oil reserves of the reservoir account for 30% in Iraq’s total oil reserves. The M reservoir depth in the F oilfield is about 2800 m, and the continuity of reservoir thickness is good, with an overall thickness of about 300 m. The reservoir is a porous carbonate reservoir, which is characterized by medium porosity (Φ = 4~10%) and low permeability (Kg = 0.01~25 mD), with wide distribution of porosity and permeability. Figure 1 shows the diversity of pore types, mainly composed of moldic pores, interparticle pores, and dissolution pores, with a small amount of microfractures. Although the M reservoir contains many pore types in the vertical direction, the pores are filled with microcrystalline calcite cement, resulting in poor connectivity between pores and low reservoir permeability. According to the analysis of reservoir minerals, the M reservoir is mainly composed of calcite, as the content of calcite is more than 95%, containing a small amount of dolomite, quartz, etc., and the content of clay minerals is less than 5%. Due to the high content of calcite, additives such as corrosion inhibitors, diverting agents, and gelling agents are often added during the acid treatment process to slow down the acid–rock reaction rate, increasing the effective distance of the live acid and improving the acid etched fracture conductivity [28].

Based on GR/Sonic/DEN logging response, the M reservoir in the Faihaa (F) oilfield can be divided into four reservoir units: Mishrif B (MB), Mishrif C (MC), Mishrif D (MD), and Mishrif E (ME), as shown in

Table 1. Core rock mechanics test results of different reservoir units.

Layer	Depth/m	Compressive Strength/MPa	Young’s Modulus/MPa	Poisson’s Ratio	Vertical Stress/MPa	Horizontal Stress/MPa
						Maximum	Minimum
MB	2860.55	185.61	18.81 × 103	0.26	75.76	71.63	66.69
MC	2915.21	117.63	22.38 × 103	0.24	77.27	72.15	67.21
MD	2958.98	223.51	16.22 × 103	0.23	78.46	72.81	67.02
ME	3024.50	94.20	16.33 × 103	0.23	80.00	75.04	69.87

. The thickness of the MB layer is the largest and the MC layer is the smallest. The reservoir reserves of the MB and MC layers account for about 70% of the total reserves of the M reservoir, the MD layer accounts for 23%, and the ME layer accounts for 6%. The physical properties of the four reservoir units are quite different. In the MB layer, there is only a thin stable layer in the shallower section, and the pore permeability distribution is poor in the deeper position. The results of a triaxial stress compression test show that the overall performance of the M reservoir includes a low Young’s modulus and medium Poisson’s ratio. The fracture initiation and propagation mechanism in the reservoir is complex, and it easily forms short fractures.

3. Selection of Target Layers

Reasonable selection and evaluation of the treatment interval are critical steps in the success of fracturing. From the perspective of the overall reservoir physical properties of the M reservoir, the overall gas permeability of MB, MC, MD, and ME layers is about 1.95, 4.31, 10.31, and 15.6 mD, respectively. On the whole, the permeability of MB and MC layers is lower than that of MD and ME layers. Based on stimulation history analysis, the MD and ME layers of the X-5 well are acidified after drilling and completion. The production of MD and ME layers reached a good level after acidification, and the stable yield effect is better. In the X-10 well, the production of MB and MC layers cannot reach the expected level after acidification, and the production decreases rapidly. It is believed that the low-permeability layer cannot be effectively utilized. Therefore, it is recommended to use fracturing stimulation for MB and MC layers in low-permeability areas. For MD and ME layers with good permeability distribution, acidification is still used to stimulate.

In addition, in the edge area of the reservoir structure, edge and bottom water are developed. For the M reservoir, there are four reservoir units from top to bottom: MB, MC, MD, and ME layers (Figure 2). The crude oil is marked as green and the water is marked as blue. From the vertical distribution position of the reservoir unit, the ME layer is located at the bottom and close to the edge and bottom water. When the ME layer is stimulated by fracturing, there is a risk of fractures communicating with edge and bottom water, resulting in wellbore flooding. Therefore, acid fracturing or hydraulic fracturing is not recommended for the ME layer. In summary, MB and MC are the target layers for reservoir stimulation. The above is the process of selecting the target layers for the Mishrif reservoir. Figure 3 shows the detailed flow chart of the target layers selection, which contains three parties.

4. Optimization of Stimulation Process Parameters

Well X-13 is selected as a test well for acid fracturing and hydraulic fracturing. The well is a new drilling well, and the target layers of MB and MC are not formally put into production. The reservoir thickness of the MB layer is 102 m, the average porosity is 15%, and the permeability is 0.9 mD. The minimum stress is 44.5~46.5 MPa, and the API weight of crude oil is about 21.5. The reservoir thickness of the MC layer is 39 m, the average porosity is 17%, and the permeability is 3.52 mD. The minimum principal stress is 44~46 MPa, and the API weight of crude oil is about 20. In the acid fracturing operation of carbonate reservoirs in the Middle East, viscous pad fluid acid fracturing technology is often used to effectively improve the conductivity of acid etched fractures. The effect of the pad fluid is to generate sufficient scale fracture geometry, reduce the temperature of the fracture wall surface, reduce the acid filtration, and form a longer action distance. Subsequently, acid fluid is injected into the formation. Because the viscosity of the pad fluid is higher than that of the acid fluid, the acid fluid will produce “fingering” during the displacement of the fracturing fluid, which helps the acid fluid to carry out non-uniform etching on the fracture wall [29,30]. Alternate injection of pad fluid and acid fluid will reduce the filtration rate of subsequent injection of acid fluid. At the same time, multiple “fingering” is formed in the displacement stage, which increases the action distance of acid fluid and is more conducive to the formation of longer and higher-conductivity acid etched fractures. Figure 4 shows the mechanism of etching the fracture surface by retarded acid (gelled acid) during acid fracturing. This can effectively control the acid filtration, so that the acid fluid fully etches the fracture surface to form a non-uniform etching cake to prevent fracture closure. This acid fracturing operation adopts a multi-stage injection acid fracturing process.

In carbonate oil and gas reservoirs, the main minerals are calcium carbonate and calcium magnesium carbonate. Carbonate oil and gas reservoirs are usually acidified with hydrochloric acid, and their acid–rock reaction equations are:

2HCl + CaCO₃ = CaCl₂ + CO₂↑ + H₂O

(1)

4HCl + MgCa(CO₃)₂ = CaCl₂ + MgCl₂ + 2CO₂↑ + 2H₂O

(2)

The rate of acid–rock reaction can be expressed by the reduction of acid concentration per unit of time, according to the law of mass action: when the temperature and pressure are constant, the rate of chemical reaction is proportional to the product of the reactant concentration to the power of n. Since the acid–rock reaction is a complex-phase reaction, the rock reactant concentration can be regarded as a constant value. Therefore, the acid–rock reaction rate can be expressed as:

$$J=K{C_w}^n$$

(3)

where J is the reaction rate, mol/s∙cm²; K is the reaction rate constant (mol∙L)⁻ⁿ∙mol/(cm²∙s); C_w is the acid concentration, mol∙L⁻¹; n is the reaction order.

The effects of temperature on the proppant reaction rate constant K are described by the Arrhenius equation:

$$K=K_0\exp [E_a-\left(RT\right)]$$

(4)

where K₀ is the pre-exponential factor, which is the reaction rate constant at an infinitely high temperature, (mol/L)⁻ⁿ∙L/(cm²∙s); E_a is the activation energy, J/mol; R is the gas constant; J/mol∙K; T is the absolute temperature, K.

The fracture conductivity principles of acid fracturing and hydraulic fracturing are different. During the acid fracturing process, the acid fluid etches the surface of the fracture to form non-uniform corrosion, which can support the fracture to prevent closure, form an oil flow channel, and achieve the effect of increasing the fracture conductivity. Hydraulic sand fracturing prevents the fracture from closing by injecting proppant fillers into the fracture. Figure 5 and Figure 6 show the two different processes.

The proppant transport modeling during hydraulic fracturing is based on computational fluid dynamics methods. The fluid/proppant flow model simulates the flow of fluid and proppant in a two-dimensional vertical fracture. The properties of the fluid and proppant are allowed to vary along the fracture length and in its height. The width can vary spatially and temporally.

The mass conservation equation for the fracturing fluid is:

$$\frac{\partial m_l}{\partial t}+\frac{m_l}{V}\frac{\partial V}{\partial t}+\frac{1}{W}(\frac{\partial }{\partial x}{m}_l{u}_{l}W+\frac{\partial }{\partial z}{m}_l{w}_{l}W)={\rho }_l\left(q_{lI}-q_{lL}\right)$$

(5)

and for each proppant it is:

$$\frac{\partial m_p}{\partial t}+\frac{m_p}{V}\frac{\partial V}{\partial t}+\frac{1}{W}(\frac{\partial }{\partial x}{m}_p{u}_{p}W+\frac{\partial }{\partial z}{m}_p{w}_{p}W)={\rho }_p{q}_{pI}$$

(6)

where m_l is the local liquid mass per unit fracture volume, kg; m_p is the proppant mass per unit volume, kg; V is the fracture volume, m³; W is the fracture width, m; u_l and w_l are the liquid velocities in the x- and z-directions, m/s; u_p and w_p are the proppant velocities in the x- and z-directions, m/s; ρ_l and ρ_p are the material densities of the liquid and proppant, respectively, kg/m³; q_lI is the volume injection rate of clear liquid, m³/min; q_lL is the volume loss rate of liquid due to leakoff, m³/min; q_pI is the volume injection rate of proppant, m³/min.

The momentum conservation of the liquid in the x-direction is given by:

$$m_l\frac{\partial u_l}{\partial t}=-{\alpha }_l\frac{\partial p}{\partial x}-{\alpha }_l\frac{\partial \tau }{\partial x}-\sum _i{C}_{d_i}(u_l-u_{p_i})-m_l{g}_x$$

(7)

The momentum equation for the proppant is:

$$m_{pi}\frac{\partial u_{pi}}{\partial t}=-{\alpha }_{pi}\frac{\partial p}{\partial x}-{\alpha }_{pi}\frac{\partial \tau }{\partial x}-\sum _i{C}_{di}(u_{pi}-u_l)-m_{pi}{g}_x$$

(8)

where p is the pressure, MPa; τ represents the wall friction stress, MPa; C_d is the drag coefficient between the liquid and proppant, g_x is the acceleration due to gravity in the x-direction, m/s².

During fracturing, the proppant particles are carried by the fluid and the force of the fluid acting on the particles is expressed as:

$$F=\frac{1}{2}{C}_d{\rho }_l{u}_{rel}^{2}A$$

(9)

where u_rel is the relative velocity between the fluid and particle, m/s; A is the frontal area of the particle, m².

Friction on the walls of the fracture can lead to a decrease in pressure within the fracture. The pressure drop arising from the shear stress at the wall can be related to the friction factor:

$$\frac{\mathsf{\Delta }p}{\mathsf{\Delta }x}=\frac{1}{2}f{\rho }_l{u}^2\frac{1}{D}$$

(10)

where f is friction factor.

The resultant friction factor f_p is modeled as:

$$f_p=f\times CF$$

(11)

The proppant multiplier factor is:

$$CF={\mu }_r^{0.55}{\rho }_r^{0.45}$$

(12)

where µ_r is dimensionless relative slurry viscosity, Pa∙s; ρ_r is relative slurry density, kg/m³.

4.1. Perforation Intervals

In acid fracturing, the selection of perforation position has a great influence on the scale of the fracture. The following aspects need to be considered in the selection process of perforating well section: ① in the selection process of perforation section, the interval with lower in situ stress should be selected, which is conducive to fracture initiation. ② Considering the distribution of crude oil in the reservoir, the position with high oil abundance should be selected as far as possible for perforation to ensure the maximum economic benefit of production increase. ③ The perforation length is controlled between 10 and 15 m. If the perforation length is too long, the stress distribution of the reservoir will be destroyed, which will easily cause the fracture height to be out of control and communicate with the upper and lower adjacent layers.

Based on the above criteria, the perforation position is adjusted and optimized by the fracturing simulation software, and the perforation interval of the MB layer is finally determined to be 2868.0~2883.0 m, and the perforation interval of the MC layer is 2913.0~2923.0 m, as shown in Figure 7. Perforation at the upper perforation position is conducive to fracture initiation and can effectively control the fracture height to achieve a better fracture scale.

4.2. Optimization of Acid Fracturing Process Parameters

The acid fluid system and fracturing fluid system should be determined before the optimization. In this optimization, gelled acid is used as the main acid fluid [31,32], and guar gum fracturing fluid is used as the pad fluid. The volume ratio of fracturing fluid and gelled acid is 1:2. After determining the fluid system and fluid ratio for treatment, the optimization of acid fracturing process parameters mainly considers the optimization of treatment pumping rate and acid volume. Before the fracturing design, it is often necessary to combine the well structure and wellhead device to determine the reasonable treatment pressure range. The reasonable pumping rate range is determined by injection pressure prediction. Next, Fracpro PT (CARBO Ceramics Inc., Houston, TX, USA. Version: 10.10.13) is used for optimization simulation of treatment parameters.

4.2.1. Pumping Rate

The wellhead device pressure is limited to 55.16 MPa during field treatment. The pressure prediction in

Table 2. Surface pressure and horsepower forecast.

Breakdown Pressure Gradient	2900 m Downhole Pressure Prediction	Wellhead Pressure with Different Pumping Rate (MPa)
(MPa/m)	(MPa)	3 m3/min	4 m3/min	5 m3/min
0.017	49.39	31.99	40.69	46.49
0.018	52.19	34.79	43.49	49.29
0.019	55.19	37.79	46.49	52.28
1000 m ID2.75″ tubing friction gradient estimation, MPa		4.00	7.00	9
2900 m total tubing friction, MPa		11.60	20.30	26.10
2900 m hydrostatic pressure, MPa		29.00	29.00	29.00
Wellhead device pressure limitation, MPa		55.16

shows that the surface pressure will be close to 55.16 MPa when the pumping rate is 5 m³/min. Therefore, it is recommended that the reasonable treatment pumping rate is 5 m³/min. However, the fracturing pumping rate of the same reservoir in adjacent blocks in the Middle East is up to 6 m³/min. In order to ensure the comprehensive optimization of treatment parameters, the pumping rate optimization range is set to 3~7 m³/min. The change trend of fracture geometry and fracture conductivity in the simulation process is shown in Figure 8 and Figure 9.

The fracture width in Figure 8 refers to the fracture width of the pad fluid stage. The acid etched fracture width is the fracture width after the closure. MB layer simulation results show that when the pumping rate is less than 6 m³/min, as the pumping rate increases, the fractures mainly propagate along the fracture length direction. Hindered by the stress interlayer, the fracture height development is not obvious. When the pumping rate reaches 7 m³/min, the fracture breaks through the stress barrier, the fracture height breaks through the limit, and the fracture half-length becomes shorter. The change in fracture width is consistent with the change in fracture half-length. Therefore, it is considered that the pumping rate should not exceed the critical value of 6 m³/min. When the pumping rate exceeds the critical value, the risk of interlayer channels increases sharply. In the process of fracturing in low-permeability reservoirs, increasing fracture length is more beneficial to increase production than increasing fracture conductivity. When the pumping rate is 6 m³/min, the maximum surface pressure will reach 62.17 MPa, which is much higher than the pressure limiting condition of the wellhead device. During the treatment process, the pumping rate needs to be appropriately reduced. Therefore, the recommended pumping rate is 5 m³/min, at which time the acid corrosion fracture half-length has reached the expected requirements. The optimization process of pumping rate in the MC layer is basically the same as that in the MB layer. The fracture height of the MC layer is well controlled in the process of changing the pumping rate. The fracture half-length and fracture width of the MC layer increase with the increase in pumping rate, and the fracture height is within the controllable range. The recommended pumping rate of the MC layer is also 5 m³/min. When the pumping rate is 5 m³/min, the surface pressure reaches 51.89 MPa, which is close to the maximum pressure limit of the wellhead device.

The acid etched fracture conductivity is another important index to evaluate the effect of acid fracturing. With the gradual increase in pumping rate, the acid etched fracture conductivity and dimensionless conductivity decrease. In the process of optimization simulation, the total amount of liquid and the amount of acid fluid are unchanged. With the increase in acid pump rate, the fracture length and fracture height gradually increase, and the fracture surface area increases. The contact area between the acid fluid and the fracture surface increases, resulting in a decrease in the etching degree of the acid fluid on the fracture wall. After the pump is stopped, some of the etching cakes on the surface of the fracture cannot withstand the closure stress, resulting in a decrease in the width of the acid etched fracture, which further leads to a decrease in the fracture conductivity. Figure 10 shows the principle that the conductivity of acid etched fracture decreases with the increase in pumping rate.

4.2.2. Acid Volume

After determining the pumping rate, the reasonable volume of acid fluid is optimized. In the process of acid fracturing, the acid fluid mainly plays the role of etching the fracture surface. The acid fluid reacts with the fracture surface to form a non-uniform etching surface, so that the fracture surface can withstand greater closure stress and increase the fracture conductivity. Figure 11 and Figure 12 show the changes in fracture scale and fracture conductivity in the process of acid fracturing optimization.

The simulation results (Figure 11) show that under the condition of keeping the amount of pad fluid unchanged and only changing the volume of acid volume, the acid etching fracture half-length, fracture height, and average fracture width mostly do not change. It is considered that the amount of acid fluid has little effect on the fracture scale. The amount of pad fluid mainly affects the fracture scale. After increasing the amount of acid volume, the acid fluid contact per unit fracture area increases. The amount of rock dissolved by acid increases, resulting in a large number of non-uniform convex bodies on the fracture surface, preventing the fracture from closing, increasing the etching fracture width, and improving the conductivity after the fracture is closed. In order to accurately describe the influence of changing the amount of acid fluid on fracture conductivity, a dimensionless conductivity change rate is established to evaluate the contribution of acid to fracture conductivity as shown in Figure 13.

The change rate of fracture dimensionless conductivity is defined as:

$$r_{Fcd}=\frac{{Fcd}_{x_1}-{Fcd}_{x_2}}{V_{x_1}-V_{x_2}}$$

(13)

where ${Fcd}_{x_1}$ is the dimensionless conductivity when the volume of acid is $x_1$,${Fcd}_{x_2}$ is the dimensionless conductivity when the volume of acid is $x_2$,$V_{x_1}$ and $V_{x_2}$ are acid volumes $x_1$ and $x_2$, respectively.

4.3. Optimization of Hydraulic Fracturing Process Parameters

4.3.1. Pumping Rate

During hydraulic fracturing, the proppant carried by the fracturing fluid continuously enters the formation and accumulates, resulting in different pressure changes during hydraulic fracturing and acid fracturing. There are few cases of hydraulic fracturing in carbonate reservoirs. With reference to the treatment parameters of hydraulic fracturing successfully implemented in Tarim oilfield in China and Halfaya oilfield in the Middle East under similar conditions, the maximum pumping rate is no higher than 5.5 m³/min. Combined with the previous prediction of pumping pressure (Table 2), the optimal range of hydraulic fracturing pumping rate is selected as 3.5–5.5 m³/min. The changes in fracture geometry and fracture conductivity under different pumping rates are shown in Figure 14 and Figure 15.

The simulation results in Figure 14 show that fracture length and fracture height increase as pumping rate increases. The width of the propped fracture tends to decrease under the influence of the fracture height and fracture length. In Figure 15, the fracture conductivity decreases as the pumping rate increases, keeping the total proppant volume constant while the pumping rate is optimized. With the increase in pumping rate, fracture half-length, fracture height, fracture surface area, and fracture volume increase. As the total amount of proppant is constant, the effective proppant placement area increases, which results in a decrease in propped fracture width. The change in fracture conductivity is affected by the width of the propped fracture, so the fracture conductivity also shows a decreasing trend.

Pumping rate also needs to be further combined with treatment pressure changes to optimize. Considering the limited pressure of 55.16 MPa on the wellhead device, when the pumping rate is 4.5 m³/min, the maximum treatment surface pressure on the MB layer is 51.30 MPa, the treatment surface pressure on the MC layer is 53.23 MPa, and the surface pressure is close to 55.16 MPa. Continuing to increase the pumping rate will exceed the wellhead pressure limit and is not recommended. Therefore, it is recommended to have a reasonable pumping rate of 4.5 m³/min for hydraulic fracturing. The optimization process of MC layer pumping rate is similar to that of MB, and it is recommended that the hydraulic fracturing pumping rate of the MC layer is also 4.5 m³/min.

4.3.2. Proppant Dosage

During the fracturing process, proppant mainly plays a role in supporting fractures to prevent closure, expanding oil flow channels, and increasing fracture conductivity. In the process of fracturing scale optimization, it is necessary to adjust and optimize the amount of fracturing fluid and proppant. There is often a correlation between fracturing fluid and proppant usage. The two parameters generally need to be adjusted at the same time and cannot be quantitatively analyzed. Therefore, the amount of fracturing fluid and proppant can be adjusted simultaneously by setting the proppant concentration in the fracture during the simulation. Figure 16 and Figure 17 show the change in propped fracture geometry and fracture conductivity as a function of proppant concentration in the fracture.

According to the simulation results (Figure 16), the change in proppant dosage has little effect on the fracture half-length and fracture height, while the proppant dosage mainly affects the propped fracture width, that is, the width of the fracture after closure. Increasing the proppant concentration within a certain range means increasing the amount of proppant in the fracture. The proppant fills the fracture sufficiently to support the fracture and prevent it from closing. When the proppant concentration in MB is greater than 4 kg/m² and the proppant concentration in MC is greater than 5 kg/m², sand plugging occurs during fracturing. The surface pressure rises sharply after sand plugging. Therefore, the recommended optimal proppant dosages for the MB layer and MC layer are 37.5 m³ and 43.7 m³, respectively.

4.4. Comparison of Different Stimulation Measures

The optimized treatment parameters are simulated for fracture extension, and the simulation results are imported into the reservoir simulator to predict the production changes after different stimulation techniques. Figure 18 shows the comparison of stimulation effects after different stimulation processes in MB and MC layers. The results show that the accumulated oil production of the MB layer after acid fracturing is 18.9~19.7% higher than that of hydraulic fracturing, and that of the MC layer after acid fracturing is 10.9~15.9% higher than that of hydraulic fracturing. After comprehensive analysis, it is concluded that the stimulation effect of acid fracturing is better than that of hydraulic fracturing. The M carbonate reservoir of the F oilfield in Iraq is more suitable for acid fracturing, which is conducive to acid–rock reaction to form acid etched fractures and improve low-permeability conditions. Although hydraulic fracturing can have a certain improvement effect, considering that the porous carbonate reservoir has high filtration loss, sand plugging easily occurs, and the fracture height is not easy to control, which affects the stimulation effect after fracturing. Therefore, hydraulic fracturing is not the preferred stimulation method.

The optimal treatment parameters were imported into the fracture analysis module of Fracpro PT to simulate fracture propagation. For the MB layer, the reservoir pressure is 31.80 MPa, porosity is 15%, water saturation is 22%, the total compressibility is 1.15 × 10⁻³ 1/MPa, and the fluid viscosity is 1.64 mPa∙s. For the MC layer, the reservoir pressure is 33.2 MPa, porosity is 20%, water saturation is 23%, the total compressibility is 2.25 × 10⁻³ 1/MPa, and fluid viscosity is 1.51 mPa∙s. The rock mechanical parameters of the reservoir are imported into the well logging curve. Figure 19 and Figure 20 show fracture propagation profiles designed for fracturing parameters. Fracture scale meets the requirements and fracture conductivity distribution is good.

5. Field Application

The field stimulation well is the X-13 well, which is not perforated after completion. MB and MC are undeveloped layers. The depth range of the MB layer is 2807.2~2906.9 m, and the depth range of the MC layer is 2906.9~2949.1 m. The optimized perforation parameters are used for the perforation interval, with a perforation interval of 2868.0~2883.0 m for the MB layer and 2913.0~2923.0 m for the MC layer. The field treatment adopts segmented acid fracturing, which involves performing acid fracturing on the MC layer, followed by inserting a packer, and then perforation and acid fracturing on the MB layer. Before the main acid fracturing operation, a Mini Frac test and a diagnostic fracture injection test were conducted, as shown in

Table 3. DFIT and Min Frac result.

Parameter	MB		MC
	DFIT	Mini Frac	DFIT	Mini Frac
Frac Gradient	0.025 MPa/m	0.012 MPa/m	0.013 MPa/m	0.016 MPa/m
Closure Gradient	0.018 MPa/m	0.013 MPa/m	0.012 MPa/m	0.014 MPa/m
Fluid Efficiency	51.45%	69.77%	34.72%	36.83%
Reservoir Pressure	33.07 MPa	33.32 MPa	32.37 MPa	33.63 MPa
Permeability	0.65 mD	-	3.75 mD	-

. The test results provide optimization guidance for the main acid fracturing treatment.

The MB and MC layers adopt the pad–acid fluid multi-stage injection acid fracturing process. The target reservoir temperature is 96 °C. The pad fluid uses guar gum fracturing fluid, which has good viscoelasticity and fluid loss reduction properties. Basic formula of pad fluid: 0.27% SRG-1 (guar gum) + 0.3% ADN-1 (claim stabilizer) + 0.1% ADB-1 (non-emulsifier) + 0.01% ADS-1 (highly concentrated fungicide) + 0.1% ADPJ-1B (cross-linking regulator) + 0.3% ADPJ-1A (cross-linking agent). As the main acid system, gelled acid can effectively reduce acid–rock reaction rate and increase the effective action distance of acid fluid. Acid fluid system formula: 20% HCl + 0.6% ADJ-1 (gelling agent) + 1.0~1.5% ADH-1 (corrosion inhibitor) + 1.5% ADT-1 (multi-function). Indoor experiments were conducted to test the viscosity, temperature resistance, shear resistance, and acid fluid etching rate of the pad and acid fluid systems. The experimental results indicate that the pad and gelled acid systems meet the performance requirements for acid fracturing fluids.

The main acid fracturing operation adopts three-stage alternating injection. The total liquid consumption is 382.2 m³, of which the amount of gelling acid is 254.3 m³, and the maximum pumping rate is 5 m³/min. During the first stage of alternate injection, the pumping rate is first raised to 4 m³/min, at which time the maximum surface pressure did not exceed the wellhead pressure limit. When the wellbore is fully filled with fracturing fluid, the pressure begins to stabilize and geometric fracture shapes begin to be induced at net pressure. After acid injection, the pressure gradually decreases, mainly due to differences in hydrostatic pressure and friction between fracturing fluid and acid, as well as the reaction between acid and carbonate rocks in the reservoir. In the second stage of alternate injection, the fracturing fluid is still injected at the pumping rate of 4 m³/min, and the pumping rate is increased to 5 m³/min when the acid is injected. Increasing the pumping rate can effectively extend the acid action distance and deeply improve reservoirs. In the third stage of alternate injection, the fracturing fluid is initially injected at the same pumping rate of 5 m³/min, and the pumping rate is reduced to 4.5 m³/min as the surface pressure gradually approaches the maximum pressure limit of the wellhead device. Subsequent acid injection continued at a displacement of 4.5 m³/min. The subsequent acid fluid will continue to be injected at a pumping rate of 4.5 m³/min. After the acid fracturing is completed, the pump is stopped for a period of time. After the fracture is closed, 15% HCl solution is used for closed fracture acidizing, which can effectively improve the conductivity of acid eroded fractures after closure.

As shown in Figure 21 and Figure 22, the wellhead pressure is maintained above 2.42 MPa during the production process after the acid fracturing test, and the initial production after fracturing of the MB layer is 271.1 m³/d in 32/64 “choke conditions”. The MC layer produced 306.8 m³/d at 38/64 “choke”. The daily production is much higher than that of other acid wells in the same region. After continuous production for four months, the wellhead pressure is stable, the production decline is small, and the effect of reservoir stimulation is significant.

In addition, according to the company’s production requirements, further reservoir stimulation measures are required when the daily production is below the critical value of 40 m³/d. The results of the program simulations indicate that further operations will be considered after 4 years of continuous production after stimulation. Such production is maintained for a longer period of time.

6. Conclusions

In order to solve the problem of poor stimulation effect after acidification in some reservoir units, this paper takes the M reservoir of the F oilfield in Iraq as a study object, the feasibility is analyzed, and the treatment parameters of different stimulation processes in low-permeability reservoirs are optimized. In addition, they have been successfully applied to the X-13 well in the field. The main conclusions are as follows:

(1)

Heterogeneous porous carbonate reservoirs have poor general acidification effect. Reservoir porosity and permeability distribution are non-uniform. After a comprehensive study of the M reservoir, it is considered that MB and MC layers with poor porosity and permeability distribution and physical property conditions are target layers for fracturing. The ME layer is close to the edge and bottom water, and MD and ME layers have good porosity and permeability distribution, so it is recommended to continue matrix acidizing operations.

(2)

The high filtration loss during hydraulic fracturing and the sensitivity of carbonate rock to sand concentration can easily cause sand plugging. The variation of hydraulic fracturing operation pressure is higher than that of acid fracturing (taking the MB layer as an example, when the pump rate is 5 m³/min, the operation pressure of acid fracturing is 52.38 MPa, and the hydraulic fracturing operation pressure is 55.93 MPa). Generally, the hydraulic fracturing treatment pumping rate (4.5 m³/min) is slightly lower than the acid fracturing pumping rate (5 m³/min). Combined with the analysis of the changes in production after different stimulation measures, the maximum daily oil production after acid fracturing reaches 557.90 m³, and the daily oil production after hydraulic fracturing is 441.97 m³, so acid fracturing is more recommended for heterogeneous porous carbonate reservoirs.

(3)

The “guar gum fracturing fluid + gelled acid multi-stage alternating injection + closed fracture acidizing” process is tested in the field. The results show that this technology can effectively increase the distance of acid action, which is conducive to generating high conductivity fractures.