_{2}Geological Storage Projects

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The existing investigations on the maximum allowable wellhead injection pressure have found the upper limit of wellhead injection pressure, which, however, cannot provide a practical operational designing scheme of wellhead injection parameters for CO_{2} geological storage projects. Therefore, this work firstly proposes the complete constraint conditions of wellbore injection to realize the whole process of forward and inverse calculations of wellbore pressure and then applies it to explore the relationship between wellhead injection pressure and injection rate. The results show that the wellhead injection pressure and the injection rate are a pair of mutually constrained physical quantities. For a certain injection project, the allowable wellhead injection pressure and injection rate separately form a continuous interval. Change of one quantity within its allowable interval will also change the other within its interval, both jointly forming a closed region. Thus, controlling the wellhead injection parameters in this closed region can simultaneously ensure the effectiveness and safety of injection. Subsequently, this work further studies the factors of impacting the relationship between wellhead injection pressure and injection rate and finds that all the temperature of injected fluid, the parameters of saturation, and the characteristic parameters of reservoirs only change their upper and lower limits to some extent but have no essential effects on their relationship. Application of this theory and method in Shenhua CCS demonstration project obtained the relationship diagram of wellhead injection pressure and injection rate, which found that its actual injection parameters just fall into the closed region of the relationship diagram, effectively verifying the reliability of this work.

In the China-US joint announcement on climate change, 2014, China intended to achieve the peaking of CO_{2} emissions around 2030 and to make best efforts to peak early [_{2} level in the atmosphere [_{2} geological storage includes site selection, well drilling, injection, monitoring, and evaluation [_{2} injection. Therefore, it is very important to control wellbore injection parameters [_{2} injection (resulting complex two-phase flow in pores and cracks), and the complexity and uncertainty of geological conditions, a great challenge to the effectiveness and safety of CO_{2} injection is induced [

Currently, it is widely accepted by engineers that controlling the maximum bottom hole pressure is practical and reliable to avoid the strata fracturing [

Thus, as to a determined target injection flow, the above methods of designing wellhead injection pressure can only provide the maximum allowable wellhead injection pressure. However, the actual wellhead injection pressure must be less than its maximum value in consideration of safety, so how much should the applicable wellhead injection pressure be? Could any wellhead injection pressure bellowing the maximum allowable wellhead injection pressure ensure that the target injection flow will enter the reservoirs completely? Of course, the answer is no. That is to say, the applicable wellhead injection pressure not only has an upper limit but also has a lower limit. Only the pressure of ranging from the lower limit to the upper limit can ensure that the target injection flow will enter the reservoirs completely. Another question is how does the applicable wellhead injection pressure change when the target injection flow changes? It would be transferred to the schema of constant pressure controlling; thus the problem is how to determine the applicable target injection flow under knowing the wellhead injection pressure. Apparently, to answer these questions exactly, it is necessary to investigate the wellhead injection pressure and the injection rate simultaneously and to master the internal relationship between wellhead injection pressure and injection rate clearly. In addition, to facilitate the application in projects, it is worthy to study their influential factors.

Therefore, this work will firstly improve the constraint conditions of wellbore injection from the perspective of flow rate to realize the whole process of forward and inverse calculations of wellbore pressure and then explore the relationship between wellhead injection pressure and injection rate and its influential factors. Finally, we apply this method to Shenhua CCS demonstration project to find the feasible ranges of wellhead injection pressure and injection rate and to verify the reliability of this work simultaneously.

Figure

Schematic of the injection well and its related reservoirs.

As described in Bai et al. [_{2} is injected at a given wellhead injection pressure

Hence, the complete constraint conditions of wellbore injection are

The first inequality of (

As mentioned above, inverting wellhead parameters based on the bottom hole conditions only can find their maximum value, which, however, can only be used as the upper limit of injection control. Therefore, in practical operation, it is necessary to directly calculate the wellbore pressure and flow rate distribution according to the given wellhead injection parameters and then to judge whether the injection is safe and effective. It is a forward calculation process. The fast explicit finite difference model (EFDM) from wellhead to bottom can be derived based on the continuity equation of steady flow, the motion equation of vertical wellbore, and the state equation of fluid [^{2}/s); ^{2});

CO_{2} is injected from wellhead through wellbore into the reservoirs; due to the presence of brine in the reservoir pores, the flow changes into two-phase flow [_{2} plume at the bottom and top of the reservoir (m), respectively; ^{2}); _{2} (kg/m^{3}); _{2} (m·s/kg); and

On the basis of (_{2} equals the sum of outflow to the next well segment and inflow into the

When (

There are two basic control models on fluid injection, namely, the constant pressure and the constant flow rate. For constant pressure, the allowable interval of flow rate should be solved; and as for constant flow rate, the problem is how to obtain the allowable interval of pressure. However, the results under different control models are the same. Therefore, this work chooses the control model of constant pressure as an example to explore the relationship between wellhead injection pressure and injection rate. The calculation procedures of forward calculation process are listed as follows:

Set

Set the initial

Compute the wellbore pressure according to (

Judge whether the computed results at the equivalent node meet the constraint condition of (

Renew

Renew

Plot the relationship diagram between

In the following, this work supposed an analysis case to explore the relationship between

The parameters of reservoir-caprock combination units.

Reservoir number | Reservoir thickness | Caprock thickness | Reservoir permeability ^{−3} ^{2}) | Reservoir porosity | Fracturing pressure | Formation pressure |
---|---|---|---|---|---|---|

1 | 10 | 1400 | 6 | 12 | 35 | 15 |

2 | 10 | 200 | 5 | 11 | 38 | 17 |

3 | 10 | 200 | 4 | 10 | 41 | 19 |

4 | 10 | 200 | 3 | 9 | 44 | 21 |

First, it is necessary to present the wellbore pressure distribution for a determined

Distribution of wellbore pressure at different injection rates.

It is clear from Figure

Table

The simulation injection design schemes.

Injection design schemes | (a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) |
---|---|---|---|---|---|---|---|---|

| 15 | 14.49 | 14 | 13 | 6 | 5 | 4.83 | 4.5 |

| 0∼9 | 0∼9 | 0∼9 | 0∼9 | 0∼2.5 | 0∼2.5 | 0∼1.1 | 0∼2.5 |

Curves of pressure and flow rate on the interface of wellbore and reservoir along with injection rate.

There are two types of curves shown in Figures

_{2} injection; if greatly expanding the time, even a tiny _{1} could not be used as the design scheme of the gas injection projects. Moreover, whether _{2} can be used as the design scheme still needs to be determined by the constraint conditions about flow rate, which can be judged by the flow rate curves of the last reservoir. Apparently,

Figures

The two above-mentioned types of injection schemes represent two limit zones in the relationship diagram between _{2} fluid is just able to be injected into the reservoir completely. And the right one represents the upper limit of constraint conditions about pressure, in which just no reservoir would fracture. The feasible flow rate corresponding to these two intersections is unique and determined. Therefore, the wellhead injection parameters should be away from the intersections and close to the middle region as much as possible when designing the injection schemes, which will bring a greater allowable interval for pressure and flow rate, and then the projects will be safer.

Relationship diagram between wellhead injection pressure and injection rate.

The influential factors can be classified into two parts: the human-controllable factors and the engineering geological factors, as shown in Figure

The influential factors of the relationship between wellhead injection pressure and injection rate.

As for the geothermal gradient, it was studied by Lui et al. [

Take the situation of

Relationship diagram between wellhead injection pressure and injection rate at different temperature of injected fluid.

According to Figure

In the above cases, the saturation parameters

The values of parameters

A | B | C | D | E | F | G | H | I | J | |
---|---|---|---|---|---|---|---|---|---|---|

| 0.55 | 0.55 | 0.55 | 0.55 | 0.55 | 0.40 | 0.50 | 0.55 | 0.60 | 0.70 |

| 0.9999 | 0.999 | 0.99 | 0.97 | 0.95 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 |

Relationship diagram between wellhead injection pressure and injection rate at different

Relationship diagram between wellhead injection pressure and injection rate at different

Figures _{2} domain and brine domain of two-phase flow are mutually restrictive.

The thickness, permeability, and porosity of reservoirs as their inherent characteristic parameters are invariant for a given storage site, but they directly determine the capacity of the reservoir. Thus their influence that aims to generalize the above obtained conclusions to other projects is analyzed. Secondly, with CO_{2} injected into the reservoir, this will cause a series of physical and chemical reactions. However, a change in load and chemical reactions with minerals will generally cause changes in the permeability and porosity of reservoirs [

The values of reservoir thickness.

Reservoir number | Reservoir thickness (m) | |||
---|---|---|---|---|

A | B | C | D | |

1 | 10 | 10 | 20 | 20 |

2 | 10 | 13 | 16 | 20 |

3 | 10 | 16 | 13 | 20 |

4 | 10 | 20 | 10 | 20 |

The values of reservoir permeability.

Reservoir number | Reservoir permeability (×10^{−3} ^{2}) | |||
---|---|---|---|---|

A | B | C | D | |

1 | 6 | 6 | 8 | 8 |

2 | 5 | 5 | 7 | 7 |

3 | 4 | 6 | 4 | 6 |

4 | 3 | 5 | 3 | 5 |

The values of reservoir porosity.

Reservoir number | Reservoir porosity (%) | ||
---|---|---|---|

A | B | C | |

1 | 12 | 17 | 22 |

2 | 11 | 16 | 21 |

3 | 10 | 15 | 20 |

4 | 9 | 14 | 19 |

Relationship diagram between wellhead injection pressure and injection rate at different reservoir thickness.

Relationship diagram between wellhead injection pressure and injection rate at different reservoir permeability.

Relationship diagram between wellhead injection pressure and injection rate at different reservoir porosity.

On the basis of Figures

The formation pressure in essence also affects the capacity of reservoirs; therefore it has some similarity to the five above-mentioned parameters. However, it is also different from them because it also determines the lower limit of constraint conditions about pressure. Thus, it is discussed together with the fracturing pressure. Table

The values of formation pressure and fracturing pressure.

Reservoir number | Formation pressure (MPa) | Fracturing pressure (MPa) | |||
---|---|---|---|---|---|

A | B | C | D | E | |

1 | 15 | 15.5 | 16 | 35.5 | 36 |

2 | 17 | 17.5 | 18 | 38.5 | 39 |

3 | 19 | 19.5 | 20 | 41.5 | 42 |

4 | 21 | 21.5 | 22 | 44.5 | 45 |

Relationship diagram between wellhead injection pressure and injection rate at different formation pressure and fracturing pressure.

Comparison of curves A, B, and C shows that, with the formation pressure increasing, both allowable

In Section

The calculation parameters of the reservoir-caprock combination units in Shenhua CCS demonstration project are listed in Table _{2}-brine flow in the reservoirs, although the actual reservoirs have strong heterogeneity.

The parameters of reservoir-caprock combination units in Shenhua CCS project [

Reservoir number | Reservoir thickness | Caprock thickness | Logging permeability ^{−3} ^{2}) | Logging porosity | Fracturing pressure | Formation pressure |
---|---|---|---|---|---|---|

1 | 9 | 1699 | 2.81 | 10.6 | 35.29 | 17.45 |

2 | 5 | 57 | 5.47 | 12.4 | 37.53 | 17.89 |

3 | 40 | 191 | 1.431 | 9.7 | 38.95 | 20.15 |

4 | 8 | 43 | 6.58 | 12.9 | 42.60 | 21.43 |

5 | 4 | 119 | 5.99 | 12.6 | 47.00 | 22.94 |

6 | 26 | 114 | 2.738 | 12.5 | 43.47 | 23.1 |

7 | 8 | 52 | 5.1 | 11.9 | 46.03 | 23.84 |

8 | 12 | 178 | 0.039 | 5.2 | 45.68 | 22.75 |

Figure _{2} was injected at a constant injection rate about 4.0 kg/s. Inputting the actual injection parameters into Figure

Relationship diagram between wellhead injection pressure and injection rate in Shenhua CCS project.

The monitoring records of wellhead injection pressure.

In addition, according to the conclusions of Section

To improve the control theory of the wellhead injection parameters, this work firstly developed the complete constraint conditions of wellbore injection and then studied the relationship and its influential factors between

_{2} injection.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was sponsored by the National Natural Science Foundation of China (Grant no. 41672252).

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