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Critical Parameters of a Horizontal Well in a Bottom Water Reservoir

Critical Parameters of a Horizontal Well in a Bottom Water Reservoir. Dr. Yue Ping. Email: yuepingaa@126.com Department: Southwest Petroleum University Address: No.8, Xindu Road, Chengdu, P. R. China. Layout. Background Experimental Program and Results Numerical Simulation Results

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Critical Parameters of a Horizontal Well in a Bottom Water Reservoir

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  1. Critical Parameters of a Horizontal Well in a Bottom Water Reservoir Dr. Yue Ping Email: yuepingaa@126.com Department: Southwest Petroleum University Address: No.8, Xindu Road, Chengdu, P. R. China

  2. Layout • Background • Experimental Program and Results • Numerical Simulation Results • Theoretical critical parameters models • Startup conditions of bottom water cresting/ Coning • Critical parameters of homogeneous reservoir • Critical parameters of heterogeneous reservoir • Impermeable barrier • Semi-permeable barrier • Semi-permeable barrier considering thickness • Conclusions

  3. Background Oil zone Bottom water zone Water coning & water cresting • The oil-water interface will deform and rise during the oil well producing in the bottom water reservoir (pressure drop and material balance relation) • Water coning in vertical wells • Water cresting in horizontal wells Fig. Water cresting in horizontal well

  4. Background • Normally, the calculated horizontal well critical rate is much smaller than the actual oil production rate ----This difference results due to two main reasons • Firstly, new critical (startup) conditions (Yue et al. 2009, 2012) should be applied • Secondly, geological conditions are far more complicated than assumptions of homogeneous models. reservoir barriers have great impact on the calculated results of critical rate. • It has been reported that reservoir barriers can significantly increase critical rate and delay water breakthrough time No quantitative investigations on barriers affecting the bottom water cresting in horizontal wells Formation with a barrier

  5. Experimental Program and result • Water coning experiment 突破井底 Developing water coning Developed water coning No water coning Water coning process • According to the description of the dynamic process of the water cresting in bottom water oil reservoir produced by horizontal wells, it is revealed that there is a startup state before the water can rise. • Produce rate is small, no water coning • Produce rate is bigger enough, developing water coning

  6. Numerical simulation of Water coning & cresting higher than initial critical rate smaller than initial critical rate VS • Water rises step by step in z direction • Small amount remained oil on both side • Water cresting develops fast • Water will flood the well quickly

  7. Theoretical critical parameters models • Startup conditions of bottom water cresting/ Coning • Critical parameters of homogeneous reservoir • Critical parameters of heterogeneous reservoir

  8. p2 ∆z p1 z w C C Bottom water Startup conditions of bottom water cresting/ Coning • Former scholars’ Critical condition • Derivation form static mechanics equilibrium Fig. Stress balance of water cresting Former Critical condition Eq.(1) Former Critical rate Eq.(2)

  9. p2 ∆z p1 z w C C Bottom water Startup conditions of bottom water cresting/ Coning • Derivation from seepage mechanics Fig. Stress balance of water cresting integral Also can get the Former Critical condition Eq.(1) The former critical condition are only fit for the calculation about the maintaining of certain water cresting height after the formation of water cresting

  10. rw 油区 z N h y W zw M bottom water C C Startup conditions of bottom water cresting/ Coning • Theory of Startup Condition ——New Critical condition No matter when W is at the highest point of N, or at least M,The condition of static equilibrium of the mass of a particle is Eq.(3) Eq.(4) Former Which? Water Cresting New critical condition Eq.(5) New critical condition focus on the condition of bottom water is beginning to rise

  11. Theoretical critical parameters models • Startup conditions of bottom water cresting/ Coning • Critical parameters of homogeneous reservoir • Critical parameters of heterogeneous reservoir

  12. zw z 0 • Critical parameters of homogeneous reservoir • Potential and potential gradient function of horizontal well The potential function of the of horizontal well production in bottom water reservoir is N Eq.(6) M Potential distribution on YZ profile Set y=0and Derivate above equation, the potential gradient function below the well borehole axis can be obtained N Eq.(7) M Potential gradient changes in different points on line MN Figs. Show the minimum value of potential gradientat M point

  13. Critical parameters of homogeneous reservoir • Critical parameters of horizontal well Combine equation (5) with (7) and let z = 0, the startup rate will be obtained: Eq.(5) Eq.(7) Eq.(8) New critical rate： We know productivity： Critical potential difference: here Critical pressure difference:

  14. Theoretical critical parameters models • Startup conditions of bottom water cresting/ Coning • Critical parameters of homogeneous reservoir • Critical parameters of heterogeneous reservoir

  15. b N N’ a Oil pay z M M’ h zw c y Water C C • Critical parameters of heterogeneous reservoir • impermeable barrier The entire flow process of this model is also divided into two stages. First stage, the fluid on the left side flows from the bottom to the MN plane. Set two virtual wells M and M΄, Equivalent well radius： The sketch of a horizontal well with a barrier in a bottom water reservoir The productivity of the image wells M or M΄ is ： Eq.(9) with A parameter γ is introduced to describe the relationship between the flow rate of the equivalent well Q1 and the total flow rate of the actual well Q2 Eq.(10)

  16. b N N’ a 油区 z M M’ h zw c y Water C C • Critical parameters of heterogeneous reservoir Second stage, the fluid flows from the MN plane into the wellbore. The rectangle region MNN΄M΄ is selected as the study area, which is equivalent to an Bottom-water-drive reservoir Rate of second stage ， Eq.(11) Eq.(12) New critical rate： With How can we get this empirical formula?

  17. b N N’ a Oil z M M’ h zw c y Water C C • Critical parameters of heterogeneous reservoir b=80m, c=20m, Rk=0 Did amount of numerical simulations

  18. Theory result Numerical result Theory result Numerical result Theory result Numerical result • Critical parameters of heterogeneous reservoir c=20m, b =0 ~100m b=60m, c = 5 ~ 25m c=5-25m, b=60m Use this empirical formula to match the simulation results

  19. Critical parameters of heterogeneous reservoir • Semi-permeable barrier ( ignoring thickness of barrier ) The pore space can be taken as the superposition of two parts pore spaces Fig. Sketch of the total formation divided into two parts • In the first part, partial pore space of the whole formation provides permeability of K1. • In the second part, the remaining part of the pore space provides zero permeability in the barrier area; while the permeability is K-K1 in the other area of the formation except the barrier area.

  20. Critical parameters of heterogeneous reservoir • Semi-permeable barrier ( ignoring thickness of barrier ) First part can be treated as the bottom water reservoir with permeability K1 Eq.(13) Second part can be treated as the bottom water reservoir with an impermeable barrier and the permeability of the formation is K-K1. Eq.(14) Superposition and coupling method can be used to determine the total critical potential difference for bottom water reservoir with semi-permeable barrier. Where RK = K1/K, Eq.(15) The critical rate Eq.(16)

  21. Critical parameters of heterogeneous reservoir • Semi-permeable barrier ( ignoring thickness of barrier ) The critical rate Eq.(16) • When K1=K, Eq. (16) becomes the critical rate of horizontal well in bottom water reservoir with no barriers. • When K1=0, Eq. (16) degrades to critical rate of horizontal well in bottom water reservoir with an impermeable barrier. • Eq. (7) is better to satisfy the formula for critical production.

  22. Critical parameters of heterogeneous reservoir • Semi-permeable barrier ( Considering thickness of barrier ) Fig. 2. The sketch of the total formation divided into two parts (Considering thickness of barrier ) If considering the thickness of the barrier, we found that Eq. (17) was more suitable when parameter d was restricted in 0 .2 to h/4. This means that the larger the thickness of the barrier, the higher is the parameters γ. It also means the larger the RK (the same to K1), the greater the thickness influence extent to parameters γ. Eq. (17) The critical rate

  23. Critical parameters of heterogeneous reservoir • Semi-permeable barrier ( Considering thickness of barrier ) Water rising process while the well produces below the initial critical rate Water rising process while the well produces above the initial critical rate Fig. . Formation with a thick semi-permeable barrier (b = 75m, c = 20m,d = 6m, Rk = 0.5) Also did a lot of numerical simulation

  24. Comparison between simulation and theory results Contrast theory and simulation results Use empirical formula Eq. (17) to match the simulation results Eq. (17) Fig. 12. Simulation and theoryQm comparison when c = 20m, d = 1m,Rk = 0 and 0.5, b range 0 to 100m Fig. 13. Simulation and theory Qm comparison when b = 60m, d = 1m,Rk = 0, c range 5 to 25m Fig. 14. Simulation and theory ΔФm comparison whenb = 60m, d=1m,Rk = 0, c range 5 to 25m

  25. Forecast, Analysis and Discussion Table. Basic information of reservoir, well and barrier Fig. 16. Critical rates with different RKand b • Fig. 16 shows that the critical rate monotonically linear decreases with the increase of RK when d is 1 m, but does not satisfy the linear decrease when d is 4 m. • Fig. 16 also presents that when RK = 1, all values are converged to the 41.74 m3/d, which is the critical rates of the formation without barrier

  26. Forecast, Analysis and Discussion Fig. 17.Comparison of critical rates with different RK, d and b • All the calculations show that the increase in b leads to better prevention of water cresting. • When b is close to zero, all values (Fig. 17) are converged to the 41.74 m3/d, which is the critical rate of the formation without barrier.

  27. Forecast, Analysis and Discussion Fig. 18 Comparison of critical rates with different RK, c and b • Both the Fig. 18 shows all curves for c = 20 are higher than the correspondent curves for c = 15 at the same value of RK. • This means that the closer the location of the barrier to the wellbore, the bigger the critical rate is. The same to the critical potential difference

  28. Conclusions New critical condition focus on the condition of bottom water is beginning to rise, and the result more reasonable. Barriers have significant impact on the production performance of horizontal wells developed in a bottom water drive reservoir. The bigger size and thickness, smaller permeability, higher position of semi-permeable barrier, the better the performance to prevent or resist the water cresting in a horizontal well producing from a reservoir with strong bottom water drive.

  29. Acknowledgement This work was supported by The National Natural Science Foundation of China (No. 51404201) The State Key Laboratory of Petroleum Resources and Prospecting of CUP (No. PRP/open-1501) Sichuan provincial science and Technology Department(No. 2015JY-0076) Sichuan Provincial Education Department (No.14ZB0045).

  30. What is the Next？ • Complex structural well Branched horizontal well (Liaohe Basin, China) Multi-lateral wells (Carmopolis, Brazil) Branched horizontal well (Qinshui Basin, China)

  31. z z Cover (closed boundary) y y x x 0 0 Bottom water (constant pressure) 底水区（恒压边界） What is the Next？ Multi branched wells with arbitrary distribution in 3D space

  32. …. … What is the Next？ • Branched horizontal well • Critical conditon The potential gradient of any point in the reservoir is Water cresting and coning Partial derivative of z Superposition of potential gradient

  33. Thank You !

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