Optimization Well-Type on the Conditions of Basal Groundwater

For optimization well-type on the conditions of basal groundwater, inasmuch as an analogy exists between electrical and fluid flow, the electrolytic analogy experiments have been conducted, which made a series of comparisons and evaluations between 9 types of complex well configurations and vertical well in terms of production. Taking into account the boundary condition of basal groundwater, we conducted 3×3×10 experiments in totally, including vertical well, horizontal well, radial well, snaky well, 3 types of fishbone well and 3 types of multilateral well. The experiment of every well mentioned above was conducted on the voltage values of 2V, 3V, 4V and conductibility values of 90μs/cm, 200μs/cm, 350μs/cm respectively. And then, specific settings were made for the stimulated well-types and reservoirs in order to make evaluations. The results indicate that production range in a diminishing sequence from horizontal well, 60°-fishbone well, 90°-fishbone well, 30°-fishbone well, 4-lateral Well, snaky well, radial well, 3-lateral Well, 2-lateral Well to vertical well. In the meantime, proposed the conception of radio of production and that even if changed the voltage value, the radio of production changed little for some specific well-types under the condition of the same resistivity. Utilizing the conclusion above, the production of complex well configurations’s transformed from vertical wells can be calculated in specific conditions of the reservoir. The obtained experimental conclusions are useful for engineers and researchers to verify their analytical production model exactly and computer codes.


INTRODUCTION
At present, sorts of well-types could be drilled successfully.Complex well configurations mean welltype which has multiple branches or arbitrary well track.It includes horizontal well, multilateral well, fishbone well, snaky well and others differing from vertical well.Flow into the complex well configurations geometries is mostly three-dimensional and requires analytical treatment of 3D diffusivity equation.It is not readily to calculate the production of every well-type by analytical methods.Analytical production solutions for these wells require use of advanced mathematical technique.In published relevant literature, complex functions, double or triple infinite series, even improper integrals were utilized in the model.Also, the analytical solutions for complex well configurations geometries require considerable computational effort and time.
Although physical law of which fluid flow in the differs from current law of which current flow in the fluid medium, the differential equations which describe steady state fluid flow in the porous medium can be considered identical to that describe current flow in the fluid medium by introducing several dimensionless variables.Single-phase fluid problems may be simulated by electrolytic analogy experiment based on hydroelectricity similarity principle.Experimental studies on electrolytic models are cost effective, fast and easier to control.
Electrolytic analogy experiments have been used to investigate many previous problems involving fluid flow in the porous medium.The earliest electrolytic analogy experiment was used to model flow into perforation.
McDowell and Muskat (1950) estimated the effects by the length, diameter and phase angle of borehole.In their conclusion, if the length of borehole was long enough, the production of perforated completion would be greater than that of barefoot completion.Howard and Watson (1950a, b) came to a similar conclusion.Huskey and Crawford (1967) investigated the influence of symmetrically distributed multiple fractures on well flow capacity and effective permeability by carrying out experiments.Aiyin et al. (1988) constructed electrolytic model to investigate drilling damage zone and perforation pollution.Yildiz and Langlinais (1991) verified their 3dimensional model for flow across gravel packs based on the experimental results from an electrolytic apparatus.Abu-Elbashar et al. (1992) simulated the flowing in shale with low permeability by electrolytic analogy experiments.Suprunowicz et al. (1998) investigated convergent flow to horizontal wells by carrying out electrolytic analogy experiments.
Turhan and Deniz (1998) used conducted electrical analog experiments to measure production of complex well configurations.Guoqing et al. (2004), Yildiz (2005), Zhan-Qing et al. (2007), Guo and Huang (2009) and Fan et al. (2006) investigated respectively the seepage law of near-wellbore area including multilateral well, fishbone well and other complex well configurations s and optimized the branch patterns including length, angle, amount and interval, finally established production formulas of symmetrical branch well by carrying out electrolytic analogy experiment.Mei et al. (2005), Haihong et al. (2006), Jinde et al. (2009), Fenxi et al. (2009), Wu et al. (2009), Chen et al. (2006) and Meng et al. (2007) investigated the production influencing factors of hydraulicallyfractured horizontal wells and the optimization of fracture patterns.Pang et al. (2006) investigated the production law of combination placing of vertical and horizontal wells.
Found through research, comprehensive comparisons of complex well configurations s have not been drawn a nd that the optimal well-type of specific reservoir conditions has not been proposed as well.This study extended the application range of electrolytic analogy experiment and the calculations of the production of the multilateral well-types were made based on the experimental date for the first time.
Accordingly, the evaluations of the exploitation effect about 10 well-types were made under the conditions of basal groundwater.T he obtained experimental conclusions are useful for engineers and researchers to verify their analytical production model exactly and computer codes.

EXPERIMENTAL RPINCIPLES
The differential equation which describes steady state fluid flow in the porous medium can be considered identical to that describes current flow in the fluid medium, namely hydroelectricity similarity principle.
Single variable approach is adopted in the experiment.Table 1 illustrates the parameters of the simulated reservoir.
The relationship between production of practical well and formation pressure in the reservoir can be obtained by similarity coefficient conversion, according to the experimental data including potential drop, current resistivity and so on.
Table 2 illustrates the corresponding relationships between resistivity of solution and viscosity of crude (1) Pressure similarity coefficient: Flow similarity coefficient: Resistance similarity coefficient: Flux similarity coefficient: If the value of current is given, then: Similarity criterion of the modeling is Table 3 illustrates similarity coefficients based on Eq. (1-5).
The practical production can be calculated by Eq. ( 6) based on the experimental data.

EXPERIMENTAL DESIGN
A schematic of the experimental setup is given in Fig. 1.Electrolytic analogy experimental apparatus is basically composed of simulation module of reservoir, low-voltage current module, positioning measurement system and data acquisition system (Fig. 1).In the  The length of completion section is 8 cm by barefoot well completion.

Horizontal well
The horizontal section is completed by barefoot completion , and the length of drilling is 40 cm.

Snaky well
The snaky section is completed by barefoot completion , and the length of drilling is 40 cm.
30°-fishbone well Both of the horizontal section (30 cm) and branches (5 cm) are completed by barefoot completion and the total length of drilling is 40 cm.The branches locate on the trisection points of horizontal section.The angle between chief wellbore and branch is 30 °.

60°-fishbone well
Both of the horizontal section (30cm) and branches (5 cm) are completed by barefoot completion and the total length of drilling is 40cm.The branches locate on the trisection points of horizontal section.The angle between chief wellbore and branch is 60°.
90°-fishbone well Both of the horizontal section (30 cm) and branches (5 cm) are completed by barefoot completion and the total length of drilling is 40 cm.The branches locate on the trisection points of horizontal section.The angle between chief wellbore and branch is 90°.

2-lateral well
Both of the two simulated branches (10 cm) are completed by barefoot well completion and the angle between them is 180°.

3-lateral well
All of the three simulated branches (10 cm) are completed by barefoot well completion and the angle between every two of them is 120°.

4-lateral well
All of the four simulated branches (10 cm) are completed by barefoot well completion and the angle between every two of them is 90°.

Radical well
The real displacement is 40 cm completed by barefoot well completion.
NaCl solution was used to simulate the porous medium, copper plate electrodes were used to simulate supply boundary and copper wire was for simulating the wellbore.The size of the organic glass tank is 800 mm×800 mm×200 mm.In the low-voltage current module, the potential drop was kept below 36 V for the reasons of safety.And then, the reduced potential drop was conveyed to well model or supply boundary with the frequency of 600 Hz which avoided polarization.The organic glass tank was filled with NaCl solution of known salinity and conductivity.The boundary condition of basal groundwater or the boundary condition of edge water was simulated by connecting the positive pole of power supply with copper plates located on the edge or bottom.Well model made by copper wire was connected with negative pole of power supply.The well model was placed in the center of the tank.
To examine the effect of hysteresis and polarization, experiments were repeated with different salinities and potential drops.The resistivity of the solution was measured by a commercial resistivitymeter.
The height of the liquid level was 10 cm and the diameter of the well model was 1 mm.The experimental consequences are showed in Fig. 2. Practical production of simulated well-type is not given, because the similar work has been done previously.
Figure 2 illustrates the current comparisons on the condition of basal groundwater with the resistivity values of 90, 200, 350 µs/cm, respectively.According to the Fig. 2, the sequence of exploitation effects for different well-types ranging from good to poor is: horizontal well, 60°-fishbone well, 90°-fishbone well, 30°-fishbone well, 4-lateral Well, snaky well, radial well, 3-lateral Well, 2-lateral Well , vertical well.The exploitation effect of horizontal well is best on the condition of homogeneous basal groundwater.There is an optimal angle between horizontal section and branch for fishbone well, rather than that the bigger angle is, the better exploitation effect is.

CONCLUSION
• An electrolytic analogy experiment was conducted: Evaluations and optimizations of complex well configurations were made by electrolytic analogy experiment.• The exploitation effects comparisons of 10 welltypes were made: The sequence of exploitation effects for different well-types ranging from good to poor is: horizontal well, 60°-fishbone well, 90°fishbone well, 30°-fishbone well, 4-lateral Well, snaky well, radial well, 3-lateral Well, 2-lateral Well , vertical well.• The conception of radio of production is proposed: For the specific reservoir, the radio of production changes little by changing the voltage value with the same resistivity.Utilizing the conclusion, the production of the well transformed from vertical well can be calculated under the conditions of specific reservoir.

Fig. 1 :
Fig. 1: Scheme of experimental apparatus simulation module of reservoir, organic glass tank simulated the area of reservoir, particular concentration

L
= Geometric dimension of formation or well, m Q = Production of well, m 3 /d R m = Resistance of solution R f = Resistance of formation fluid ΔU = Potential drop in the modeling, V ∆P = Pressure drop in the reservoir, MPa K = Permeability of reservoir, 10 -3 µm 2 ρ = Resistivity of solution, µs/cm µ = Viscosity of crude oil, mPa/s I = Current through solution, mA C p = Pressure similarity coefficient C q = Flux similarity coefficient C l = Geometrical similarity coefficient C ρ = Flow similarity coefficient Subscripts: m = Parameters of modeling o = Parameters of reservoir

Table 1 :
Parameters of modeling and reservoir Parameters of model

Table 5 :
Current and radio of production on the conditions of basal groundwater (a) The resistivity value is 90µs/cm