Study on Productivity Numerical Simulation of Highly Deviated and Fractured Wells in Deep Oil and Gas Reservoirs

This paper establishes the model of sandstone, porosity and permeability on single well in allusion to 10 highly deviated and fractured wells in deep oil and gas reservoirs of Jidong Oilfield, which forms a numerical simulation method of highly deviated and fractured wells in deep oil and gas reservoirs of Jidong Oilfield. The numerical simulation results of highly deviated and fractured wells productivity in deep oil and gas reservoirs are given out under different layers (layer ES1, layer ES3, layer ED2,and layer ED3), different deviation angles(60°and 75°), different fracture parameters and producing pressure drops. Through the comparison with testing data getting from exploration wells, we know that the calculation results of numerical simulation are consistent with practical testing results.


Introduction
Large-scale hydraulic fracturing of highly deviated and horizontal wells is the most effective method to develop low permeability sandstone and carbonate reservoir, tight oil and gas reservoir, unconventional oil and gas reservoir [1][2][3].The productivity simulation and influencing factor analysis of highly deviated and fractured wells are the scientific basis of fracturing design and productivity prediction [4][5].The computational difficulties of numerical simulation of highly deviated and fractured wells are mainly reflected in deviation angle, long-term flow conductivity, the processing of natural fracture, etc [6][7][8].At present, the researches on highly deviated fracturing issues mainly focus on the mechanism of fracture initiation and propagation, deviated well fracturing, indoor simulation experiments, field tests and so on [9][10][11].There are few researches on the productivity numerical simulation of highly deviated and fractured wells [12][13][14].This paper forms a deviated and fractured wells productivity numerical simulation method of natural fracture development formation in deep oil and gas reservoirs, which provides a basis for the optimization design of the fracturing construction parameters and the evaluation of fracturing effect on highly deviated wells, so as to guide the actual field work for oilfield.

Establishment of representative well geological models
For 10 representative highly deviated wells of different layers in deep oil and gas reservoirs of Jidong Oilfield, on the basis of porosity and permeability deriving from single well logging interpretation, establish the geological models based on single well sandstonesection distribution, which provides the basis for numerical simulation.
For 10 representative highly deviated wells of different layers in deep oil and gas reservoirs of Jidong Oilfield, on the basis of porosity and permeability deriving from single well logging interpretation, establish the geological models based on single well sandstone section distribution, which provides the basis for numerical simulation.The sample well is located in layer ED 3 of Jidong Oilfield deep reservoirs, and the log interpretation profile is shown in Figure 1.The plane grid number of the sample well is set to 54 *44, with a step length of 30m, and the number of vertical grid is set to 59.There is no interference between the sample well and the surrounding wells, so a rectangle boundary can approximatively be used as the boundary of a single well model.Figure 2 shows the plane grid graph of the sample well, and Figure 3-Figure 6 respectively represent for the structure model, porosity model, permeability model and sandstone model of the sample well.
The geological model shows that the single well model is faithful to the single well data, and the goodness of fit is more than 95%.

Simulated horizons and the treatment of natural fracture development
Table 1 shows the testing and log interpretation results, natural fracture development and some others of the target layer section of 10 representative wells, and we can get the following conclusions from Table 1: layer ES 3 of deep oil and gas reservoirs in Jidong Oilfield is natural fracture development, while the fractures of layer ES 1 , layer ED 2 and layer ED 3 do not develop.Through practical experience and the analysis of calculation results, for the intervals of natural fracture development, the goodness of fit is higher when the effective permeability is dealt with logging permeability, and for the intervals that do not develop, when the effective permeability is calculated according to 1/8 of the logging permeability, the result is more reliable.

Experiment of long-term flow conductivity
The experiment of long-term flow conductivity can reflect the true flow conductivity of the fracture under the condition of oil and gas reservoir, and provide reliable reference for fracturing design and construction.The Fracturing Center of PetroChina Research Institute of Petroleum Exploration gives the experimental result of long-term flow conductivity (20-40 mesh ceramic), which is shown in Figure 7. where w f is fracture closure width (cm), k f is fracture permeability (D), t is time (d).
According to the model, the flow conductivity is about 5.0 D.cm at 22 -20 days (Table 2).

Skin factor caused by well deviation
The highly deviated well is different from vertical and horizontal wells.In the process of production, the well deviation will cause formation fluid disturbance and generate additional pressure drop, which can be represented by the skin factor.Figure 8 is a schematic diagram of partially perforated deviation well.Where T is deviation angle (°), r w is well diameter (m), z w is the central coordinate of deviation well (m), h w is the perforation length (m), h is reservoir thickness (m).
Define the dimensionless quantity: At this point, the skin factors of different deviation angles are shown in Table 3.Where s θ+p is the skin factor caused by well deviation and perforation, s p is the skin factor caused by perforation, and s θ is the skin factor caused by well deviation.
Table 3 shows that when all the intervals are perforated, the skin factor caused by perforation is 0, that is to say, the skin factor is only related with the deviation angle.In this paper, the skin factor caused by well deviation is integrated into the grid computing of numerical simulation.

Analysis of Calculation Results
The numerical simulation results of highly deviated and fractured wells productivity in deep oil and gas reservoirs is given out under different layers, different deviation angles, different fracture parameters and producing pressure drops.When the producing pressure drop is 24MPa, the production estimation ranges of different layers are shown in Table 4.When the producing pressure drop is 24MPa, the production estimation ranges of different layers and production parameters are obtained through the statistical results of numerical simulation: for the oil wells in layer ES 1 , when the permeability is about 2.6 mD, the initial production is between 3 and 4.5 m 3 /d, and for the gas wells in layer ES 1 , when the permeability is about 0.26 mD, the initial production is between 1.5×10 4 and 3×10 4 m 3 /d.For the oil wells in layer ES 3 , when the permeability is about 0.5 mD, the initial production is between 5 and 25 m 3 /d, and for the gas wells, the initial production is between 5×10 4 and 10 5 m 3 /d.For the oil wells in layer ED 2 , when the permeability is about 0.68 to 1.5 mD, the initial production is between 1 and 4 m 3 /d.For the oil wells in layer ED 3 , when the permeability is about 6.2 to 13.2 mD, the initial production is between 8 and 12 m 3 /d.The results of this research have an important significance for the optimization design of the fracturing construction parameters and the evaluation of fracturing effect on highly deviated wells.

Figure 7 .
Figure 7. Experimental result of long-term flow conductivity.The long-term flow conductivity fitting model of core plate is shown as following according to the experimental

Figure 8 .
Figure 8. Schematic diagram of partially perforated deviation well.

Table 1 .
Simulation horizons and natural fracture development situation.

Table 2 .
Predicting results of long-term flow conductivity.

Table 3 .
Skin factors of different deviation angles(Cinco-Ley)

Table 4 .
Production estimation ranges of different simulation schemes