## Abstract

Hydraulic extended-reach limit (HERL) model of horizontal extended-reach well (ERW) can predict the maximum measured depth (MMD) of the horizontal ERW. The HERL refers to the well’s MMD when drilling fluid cannot be normally circulated by drilling pump. Previous model analyzed the following two constraint conditions, drilling pump rated pressure and rated power. However, effects of the allowable range of drilling fluid flow rate (Q_{min}≤Q≤Q_{max}) were not considered. In this study, three cases of HERL model are proposed according to the relationship between allowable range of drilling fluid flow rate and rated flow rate of drilling pump (Q_{r}). A horizontal ERW is analyzed to predict its HERL, especially its horizontal-section limit (L_{h}).

#### Authors:

##### Xin Li^{1,2}, Deli Gao^{1,2} & Xuyue Chen^{1,3}

^{1}State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum, Beijing, 102249, P.R. China. ^{2}MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249, P.R. China. ^{3}Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78705, USA.

Received: 23 February 2017, Accepted: 28 April 2017, Published: 08 June 2017

© The Author(s) 2017

Results show that when Q_{min} ≤Q_{r} ≤Q_{max} (Case I), L_{h} depends both on horizontal-section limit based on rated pump pressure (L_{h1} ) and horizontal-section limit based on rated pump power (L_{h2} ); when Q_{min} < Q _{max} < Q_{r} (Case II), L_{h} is exclusively controlled by L_{h1}; while L_{h} is only determined by L_{h2} when Q_{r}< Q_{min} <Q_{max} (Case III). Furthermore, L_{h1} first increases and then decreases with the increase in drilling fluid flow rate, while L_{h2} keeps decreasing as the drilling fluid flow rate increases. The comprehensive model provides a more accurate prediction on HERL.

## Introduction

Longer horizontal-section length of horizontal extended-reach well (ERW) often means higher oil and gas output, and is also an economical choice for oil field development1. However, drilling engineers have no idea how far the horizontal ERW can extend. The hydraulic extended-reach limit (HERL) theory of the horizontal ERW can be used to predict the maximum measured depth (MMD) of horizontal ERW from the perspective of hydraulics, especially the bearing capacity of drilling pump.

Wang and Guo (2008) first proposed the concept and the computational model of HERL theory^{2}. The HERL theory of the horizontal ERW can be summarized as follows. The horizontal ERW cannot extend without limitation. Drilling pump will stop circulating drilling fluid when the total pressure losses of circulation system exceed the rated pressure of drilling pump, which is a critical point. The measured depth of the horizontal ERW at the critical point is defined as the HERL of the horizontal ERW. In other words, the HERL of the horizontal ERW refers to the well’s MMD when the drilling fluid cannot be normally circulated by drilling pump. The HERL is mainly related to the total pressure losses of circulation system and the rated pressure of the drilling pump. Later in 2009, Guo and Wang (2009) applied the HERL theory to the Liuhua field in the South China Sea^{3}.

They analyzed the ERW’s HERL based on the established HERL model. Gao et al. (2009) also introduced and analyzed the concept and influence factors in the HERL model for horizontal ERW^{4}. Sun (2013) further developed the HERL model, he regarded the rated power of drilling pump as a new constraint condition^{5}. The HERL model based on new constraint condition is also introduced. However, these studies only consider the effects of rated pressure of drilling pump and rated power of drilling pump on the HERL model; the allowable range of drilling fluid flow rate, an important hydraulic parameter range, was not taken into consideration.

Each drilling pump has a maximum output power, known as the rated power of drilling pump P_{r}. Meanwhile, each drilling pump also possesses several cylinders with different diameters, and every cylinder has a certain allowable pressure, which is called the rated pressure of drilling pump pr. The drilling fluid flow rate Q under the conditions of P_{r} and pr is called the rated flow rate of drilling pump Q_{r}. In general, P_{r}, pr and Q_{r} have the following relationship.

When Q≤ Q r , the pump pressure is restricted by the allowable pressure of cylinder, the maximum pump pressure can only reach the rated pump pressure of drilling pump *p*_{ r }. Then the pump power keeps increases with the increase in drilling fluid flow rate *Q* until Q= Q r , namely the rated power of drilling pump *P*_{ r }is reached, and the drilling fluid flow rate *Q* at this time is the rated flow rate of drilling pump *Q*_{ r }. In brief, *p*_{ r }is the major constraint condition when Q≤ Qr. In contrast, the pump power is maintained at *P*_{ r }when Q> Q r , the pump pressure keeps decreasing as drilling fluid flow rate *Q* increase. In other words, *P*_{ r }becomes the main constraint condition when *Q* > *Q*_{ r }^{6}.

As mentioned above, the rated pump pressure of drilling pump *p*_{r }and the rated power of drilling pump *P*_{r }as two constraint conditions of HERL model for horizontal ERW are provided under the conditions of *Q* ≤ *Q*_{r }and *Q* > *Q*_{ r }respectively. However, the effects of allowable range of drilling fluid flow rate on the HERL model are not considered. During the drilling process, the drilling fluid flow rate *Q* has a theoretical range, namely the allowable range of drilling fluid flow rate. Specifically, too small *Q* cannot meet the needs of hole cleaning; however, if *Q* is too large, the bearing capacity of the drilled formation may be threatened. The allowable range of drilling fluid flow rate is expressed in Eq. (2).

where *Q*_{min} is the lower limit of drilling fluid flow rate, L/s; *Q*_{max} is the upper limit of drilling fluid flow rate, namely the upper limit considering the bearing capacity of drilled formation, L/s.

The main purpose of this paper is to establish a more comprehensive and accurate model of HERL for horizontal ERW according to the relationship between the above allowable range of drilling fluid flow rate and the rated flow rate of drilling pump *Q*_{r }. Moreover, the bearing capacity of existing hydraulic equipment can also be evaluated based on the established HERL model, avoiding the situation that the designed horizontal-section length exceeds the limit extension ability provided by the available drilling pump.

## Results

### HERL model

For a horizontal ERW, the lengths of vertical section and deviated sections can be obtained by an inclinometer before drilling into the horizontal section. Therefore, we mainly analyze the well’s horizontal-section limit *L*_{h }, which can be expressed in Eq. (3).

where *L*_{h }is the horizontal-section limit, m; *L*_{h1} is the horizontal-section limit based on rated pump pressure, m; L_{h2} is the horizontal-section limit based on rated pump power, m; *p*_{ r }is the rated pressure of drilling pump, MPa; *P*_{r }is the rated power of drilling pump, kW; Δp_{g} is surface pipeline pressure drop, MPa; Δp_{b} is bit pressure drop, MPa; Δp_{stv} is the drill string pressure losses of vertical section, MPa; Δp_{std} is the drill string pressure losses of deviated sections, MPa; Δ p_{av} is the annular pressure losses of vertical section, MPa; Δp_{ads} is annular pressure losses of small-inclination section, MPa; Δp_{adl} is annular pressure losses of large-inclination section, MPa; ( Δp/ΔL)_{sth} is drill string pressure loss gradients in horizontal section, MPa/m; ( Δp/ΔL)_{ah} is annular pressure loss gradients in horizontal section, MPa/m.

According to the relationship between the allowable range of drilling fluid flow rate Q min ≤Q≤ Q max and the rated flow rate of drilling pump *Q*_{ r }, the Eq. (3) can be divided into the following three Cases, including Q min ≤ Q_{r} ≤ Q_{max}, Q_{min} < Q_{max} < Q_{r} and Q_{r} <Q_{min} <Q_{max} . They are expressed in Eqs (4)–(6).

where *Q*_{r }is rated flow rate of drilling pump, L/s.

### Application example

For a horizontal ERW, the established HERL model is used to predict the well’s HERL, especially the horizontal-section limit. The specific data of this well is listed in Tables 1 and 2^{7}, and schematic overview of the horizontal ERW is illustrated in Fig. 1.

**Table 1:** Design table of casing program.

**Table 2:** List of input data for modeling.

First of all, the authors assume that the fracture pressure in the horizontal section is identical, otherwise inconsistent comparison conditions will occur when the parameters sensitivity analysis is carried out. Meanwhile, the bearing capacity of drilled formation and the needs of hole cleaning should be considered to determine the allowable range of drilling fluid flow rate.

**Figure 1 **Schematic overview of the horizontal extended-reach well.

The specific calculation results show that the lower limit based on the needs of hole cleaning Q_{hc} is 29.6 L/s, the lower limit considering the bearing capacity of drilled formation Qmin – d_{f} is 27.1 L/s, and the upper limit of drilling fluid flow rate Q max is 39 L/s. Therefore, the allowable range of drilling fluid flow rate ranges from 29.6 L/s to 38.5 L/s. Moreover, according to the conditions given in Tables 1 and 2, the rated pressure of drilling pump *p*_{ r }is 39 MPa, the rated power of drilling pump *P*_{r }is 1323 kW, so the rated flow rate of drilling pump *Q*_{ r }is 34 L/s. Depending on the relationship between allowable range of drilling fluid flow rate and the rated flow rate of drilling pump *Q*_{ r }, the HERL model belongs to Case I, which can be determined by Eq. (4). Effects of drilling fluid flow rate on the horizontal-section limit based on rated pump pressure *L*_{ h1} and the horizontal-section limit based on rated pump power *L*_{ h2} are shown in Fig. 2a, which is also the schematic overview of the situation of Q min ≤ Q r ≤ Q max (Case I).

**Figure 2 **Effects of drilling fluid flow rate on L_{h1} and L_{h2} & the schematic overview of the situation Q_{min} ≤ Q_{r} ≤ Q_{max} (Case I). (**a**) Effects of drilling fluid flow rate on L_{h1} and L_{h2} ; (**b**) Effects of different ROPs on L_{h1} and L_{h2} ; (**c**) Effects of different drill pipe rotation speeds on L_{h1} and L_{h2} .

As shown in the Fig. 2a, the horizontal-section limit based on rated pump pressure L h 1 first increases and then decreases with increase in drilling fluid flow rate; meanwhile, the horizontal-section limit based on rated pump power L h 2 keep decreasing as drilling fluid drilling fluid flow rate increases when Q min ≤ Q r ≤ Q max . The abscissa value of the intersection between these two curves is the rated flow rate of drilling pump *Q*_{r }(34 L/s). The HERL, especially the horizontal-section limit is mainly dependent on L h 1 when *Q* ranges from Q min to *Q*_{ r }( Q min ≤Q≤ Q r ), which is indicated by the yellow dotted area in the Fig. 2a. However, the HERL especially the horizontal-section limit mainly depends on L h 2 if *Q* ranges from *Q*_{ r }to Q max ( Qr<Q≤ Q max), which is indicated by the blue dotted area in the Fig. 2a. Furthermore, both L h 1max (the maximum horizontal-section limit based on rated pump pressure) and L h 2 max (the maximum horizontal-section limit based on rated pump power) are larger than L h max (the maximum horizontal-section limit). L h max can be obtained at Q r (34 L/s). Specifically, L h 1max is 5270 m, L h 2max is 5955 m, while L h max is 5068 m. Considering the lengths of vertical section and deviated sections, each drilling fluid flow rate corresponds to a well’s HERL, and the maximum HERL of the horizontal ERW is 7463 m, which can also be obtained at *Q*_{ r }(34 L/s).

## Discussion

In order to analyze the effects of different parameters on the HERL especially the horizontal-section limit of horizontal ERW, parameters sensitivity analysis is discussed. Furthermore, results simulated by the established model are also compared with the results of the previous model that did not consider the allowable range of drilling fluid flow rate.