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Yatay kuyuların verimliliği

Horizontal well productivity

  1. Tez No: 14134
  2. Yazar: KUBİLAY MENEKŞE
  3. Danışmanlar: PROF.DR. ABDURRAHMAN SATMAN
  4. Tez Türü: Yüksek Lisans
  5. Konular: Petrol ve Doğal Gaz Mühendisliği, Petroleum and Natural Gas Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1990
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 67

Özet

ÖZET Bu çalışmada yatay kuyuların verimliliği incelenmiş ve yatay kuyuların düşey ve düşey çatlaklı kuyulara göre verimlilik artışı sağlayacağı koşullar araştırılmıştır. Sonsuz bir rezervuarda yer alan yatay kuyuların basınç davranışlarının incelenmesi sonucunda yatay kuyu verimliliğinin kuyu uzunluğunun artması, formasyon kalınlığının azalması ve düşey yöndeki geçirgenliğin artmasıyla artacağı gösterilmiştir. Elde edilen bir başka Önemli sonuç da kuyunun delinmesi sırasında oluşacak yataydan sapmaların verimliliği önemli ölçüde etkilememesidir. Bu çalışmada bulunan en önemli sonuç sınırlı bir rezervuarda yer alan yatay ve düşey çatlatılmış kuyuların verimliliğinin akış koşullarının bir fonksiyonu olduğunun gösterilmesidir. Elde edilen sonuçlar rezervuardaki akış koşullarının doğru olarak tanımlanmaması ve bu akış koşulları için geçerli bağıntıların kullanılmaması durumunda kuyu verimliliğinin üç kata varan oranlarda hatalı belirlenebileceğini göstermektedir. iv

Özet (Çeviri)

SUMMARY HORIZONTAL WELL PRODUCTIVITY...1 Some well completion types have been developed to gain higher production rates for the same pressure drop as conventional types. Principally, we need larger surface area for fluid entry to obtain this increment in productivity. Vertically fractured wells are a common example for this purpose. Some technical developments in drilling technology made it practical to drill horizontal wells during the last decade. Having some advantages such as low water and gas coning tendency or effective drainage of possible natural fractures in the reservoir, horizontal wells compete with vertically fractured wells while operational costs and difficulties limit the feasibility of horizontal wells in this competition. In this work, horizontal well performance was evaluated regarding pseudoskin and productivity index concepts. Horizontal well pressure behavior is rather complex to obtain comparing to vertical wells or vertically fractured wells. A reservoir produced by a horizontal well has different flow regimes (even three dimensional during particular time periods) and no simplification can be made due to symmetry as we made for a cylindrical reservoir with a fully penetrating vertical well at the center. Pressure equations for horizontal wells that were obtained and presented in literature by Özkan et al. [2] were used for the comparison of horizontal wells and vertical wells. Pseudoskin function concept is one of the methods for this comparison. Horizontal well pseudoskin function is simply the difference between horizontal well and vertically fractured well dimensionless pressures and can be shown as follows: F = PmD' P to Where pwo and p to are horizontal well and vertically fractured well dimensionless pressures respectively. To obtain pseudoskin functions, pressure equations need to be derived first. Subtracting these equations, common terms cancel each other and what remains is the pseudoskin function. Pseudoskin function of a vertically fractured well with respect to a vertical well is as follows [2] :a{xü y k / k x L ^ J ~P[xDiZwD,ruD,LB) where.. 1 y“ cos nn(z wD + r wD)cosnjT z aD n LDyj K/ kxn-i ”? Since the pseudoskin function represents an extra pressure drop to produce at the same flowrate, larger pseudoskin function values mean smaller productivity. In this work, it is shown that pseudoskin function depends strongly on horizontal well length and weakly on vertical location of horizontal well. Two inner boundary conditions can be taken into consideration for a horizontal well; infinite conductivity and uniform flux. Infinite conductivity condition which assumes uniform pressure throughout the horizontal well is more realistic to represent the actual flow conditions in the wellbore and it was used throughout this work. But since the analytical solutions for this condition were difficult to derive, two different methods using the uniform flux equation were utilized to obtain infinite conductivity results. One of them is called the 'equivalent pressure point'' method which is based on the assumption that pressure values of the infinite conductivity and the uniform flux solutions are identical at some particular distance from the midpoint of the horizontal well. This distance was suggested to be about three fourths of the half vilength of a horizontal well by some authors in the literature [5]. Regarding this method, the uniform flux solution evaluated at that particular distance gives the infinite conductivity results. The other method is called 'pressure averaging' [4]. This riiethod, assumes that the arithmetic average value of the uniform flux solution is equal to the infinite conductivity solution. This averaging is made by integrating the uniform flux solution along the horizontal well length and dividing by the horizontal well length. But this second method was found to yield erroneous results. Horizontal and vertical well performances, were compared using productivity index concept for both steady state and pseudosteady state conditions. Productivity index is the ratio of the flow rate to the pressure drawdown. Productivity index equations for vertical wells are well known in the literature. To calculate the productivity index ratio of horizontal well to vertical well, productivity index equations for horizontal wells were needed. These equations were derived substituting the horizontal well effective wellbore radius in the productivity equation of a vertical well. Horizontal well effective wellbore radius represents the equivalent vertical well radius that gives the same flowrate as a horizontal well does. Productivity of a horizontal well can be calculated using these equations. Horizontal well length is the most important parameter that affects the horizontal well productivity. Horizontal well productivity increases as the well length increases. This increment is sharper in pseudosteady state flow conditions. Horizontal well location in the vertical direction between reservoir top and bottom does not affect the productivity increment considerably. Reservoir thickness is a very important reservoir parameter limiting the use of horizontal wells. Ratio of horizontal well productivity to vertical well productivity decreases as the reservoir thickness increases. The reason for this inverse relationship is that vertical well productivity increases more than horizontal well productivity does as the reservoir thickness increases. Anisotropy does have significant effect on productivity. Horizontal well productivity decreases as the ratio of vertical permeability to horizontal viapermeability decreases. Horizontal wells are more effective in reservoirs with high vertical permeabilities. However most reservoirs have low vertical permeability comparing to horizontal permeability. Studies in the literature related to pseudosteady state performance of a horisontal well are for cylindrical reservoirs. This work also contains the productivity of a horisontal well in different reservoir geometries. The Shape factor equation for rectangular reservoirs given by Özkan et al. [9,10] was used to evaluate the productivity of a horizontal well at any location in a rectangular reservoir of various dimensions. The values of the shape factor for both vertical fracture and horizontal wells were calculated for the same set of drainage area values for each reservoir geometry shown in tables. Pseudosteady state flow equation for a horizontal well located in a rectangular reservoir is given by the following equation: 0.0\416kh[p-pw/) q = - B^\ where C A is the shape factor. As can be seen in this equation, higher shape factor values mean higher flow rates. Regarding the shape factor values obtained, it can be shown that a horisontal well at the center of a square reservoir performs better than the one at the center of a rectangular reservoir of 2:1 aspect ratio while both have the same drainage area (and therefore the same drainage volume). Also, a horisontal well at the center of a square reservoir produces more than that located off the center. Deviations from these conclusions are cases of small drainage area values that allows the horizontal well length to be comparable to the reservoir dimensions and causes the flow geometry to become linear. The vertical fracture shape factor shows the similar behavior as horizontal well does. However, higher shape factor values of vertically fractured wells represent their higher performance comparing to horisontal wells assuming that horisontal well and < vertical fracture lengths are the same. The specific conclusions of this work are: Horisontal wells were found advantageous in thin and high vertical permeability reservoirs. viii- Productivity of a horisontal well is insensitive to the location of the well in the vertical plane. Therefore, any deviation occured in the reservoir during drilling of a horisontal well has no significant effect on productivity. - Horizontal well length is the most effective factor on the productivity augmentation, and the productivity of a horisontal well increases as the well length increases. - Horisontal well productivity is a function of flow conditions in the reservoir. The ratio of horisontal well productivity to vertical well productivity is greater in pseudosteady state flow as compared to steady state flow. - Shape factors of horizontal wells and vertically fractured wells were calculated. Regarding this values Horisontal wells in a closed rectangular reservoirs were found to produce at higher flowrates if they were located at the center and if the aspect ratio of the reservoir gets closer to unity. - To obtain infinite conductivity results from both pseudoskin function and shape factor equations, equal pressure point and pressure averaging methods were applied to the uniform flux solution and equal pressure point method was found more reasonable and reliable. IX

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