аааааааааа. томск. Оценка перспектив использования технологий создания газогидратных барьеров при
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3.1.4. CSMHYD CSMHYD is a special computer program that is able to predict not only hydrate formation conditions (P and T) but also the hydrate Type (I or II) basing on certain natural gas composition. The results of calculations are presented at Fig.3.2: Figure 3.2. CSMHYD calculation results 55 As a conclusion, the following Tab. 3.6 represents the results of hand and computer calculations. Although, the difference is not so great in terms of formation and bottomhole temperature values, anyway, it exists. Thus, in the following chapters, CSMHYD calculation results will be taken as a base [25]. 3.1.5. Results Table 3.6. Overall results Method Temperature, °C Hydrate formation pressure P hform, atm Gas Gravity 9 27 Skhaliakho and Makogon 23.2 Ponomarev 21.07 CSMHYD 29.65 3.2. Critical rate estimation Except the stable conditions of hydrate formation and existence it is necessary to evaluate the producer performance in the presence of the barrier. This evaluation can be made by analytical comparison of the critical rates in without barrier and with it [26]. In the field D case, large gas cap exists over the oil-saturated part of oil rim. This fact is proved by fluid sampling and well-logging interpretation results. Thus, it can be considered that gas coning phenomenon may be observed later during production. The coning considerably limits oil production and make profitable production of oil rim oil is particularly questionable. Such problem has been, therefore, studied previously both in laboratories and on fields. However, it is clear that field results are difficult to interpret due to uncertainties in bottomhole conditions of wells, cement jobs results, reservoir heterogeneity, etc. Moreover, it is hard in practice to vary completion conditions. In laboratories, the presence of 2 phases is also problematic to simulate. On the other hand, due to involvement of a great number of parameters, hand theoretical calculations are difficult to achieve without drastic simplifications assumption. That is why a lot of existent theoretical models are too partial, inconclusive and approximate to be reliable. Some of 56 them do not take into account reservoir anisotropy, some – flow curvature near the wellbore because of partial perforation of well, some – the perforation interval length and its location, etc. 3.2.1. Vertical Producers One of the first works published on the phenomena of coning was by Wyskoff and Muskat. Their technique involves Laplace’s equation solution for single phase, steady-state and incompressible flow that is the basis of approximate solution of the critical flow rate in isotropic formations presented by them [27]. Muskat and Wyskoff method was simplified by other researchers – Meyer and Garder[28] for radial flow while Chierici et al [29] and Chaney et al [30] applied potentiometric model approach to receive the value of critical flow rate. Schols [31] found an empirical critical rate expression from conducted on Hele-Shaw models experiments. Schols method can be applied to both water and gas coning; however, only when water or gas coning exists separately. Also, Wheatley [32] presented an approximate theory for estimation of critical oil rate in reservoirs with anisotropy considering an OWC interface as a streamline. Then, in the same way, Chaperon [33] derived an expression of a critical rate in anisotropic reservoirs in a closed system and proved that if the vertical permeability value decreases, the value of critical rate slightly increases and the critical cone elevation changes insignificantly. Then analytical and numerical method was proposed by Hoyland et al [34] for critical rate prediction in the case of water coning in homogeneous anisotropic formations. Here, the basis for analytical solution composes an assumption that wellbore is infinitely conductive. The results of Hoyland et al work were presented in the form of dimensionless critical rate vs dimensionless radius graphic graph, as a function of partial penetration of the well for isotropic and anisotropic reservoirs. Addington [35] derived generalized critical rate and post-breakthrough GOR correlations basing on the Prudhoe Bay simulation study. Then Sobocinski and Cornelius [36] developed correlation for water cone rise prediction in no-gas cap incompressible homogeneous system. Other references 37-43 also represent different results of coning study for vertical wells. 57 3.2.1. Technology Firstly, vertical producers were considered. In the case of vertical well the first step is drilling of the vertical well and perforating of it some distance above GOC level. The second step is lowering of heating unit through the well for the purpose of hydrate formation prevention in the wellbore during the injection of water if occasionally gas from gas cap enters the wellbore. The third step is injection of certain volume of fresh water at the temperature above the hydrate formation temperature in order to increase the area of water distribution in reservoir without premature hydrates formation. Subsequent well shutoff is necessary for injected water and reservoir temperature equalization. Then the well is brought into production and gas cap gas enters the well starting to displace water from pore space. Residual fresh water and gas interaction activates hydrate formation under reservoir conditions. Decrease of the gas rate indicates the hydrate barrier formation [37]. Hydrate crystals specific volume is twenty percent larger than water specific volume allowing hydrates to plug all the pore space. Afterwards, existent perforations are plugged and new perforations are made below, in oil-saturated part. Then the well can be brought into permanent productions of the oil rim reserves (Fig. 3.3). Figure 3.3. Hydrate barrier creation technology in vertical well 3.2.1.2. Critical rate without barrier Estimation of the critical rate without barrier was made applying seven theoretical models of Meyer-Garder, Chierici-Ciucci, Hoyland et al, Chaney et al, Chaperon, Schols [45] and modified method of Muskat that includes skin for partial penetration by Brons and Marting [46]. 58 Trying to find the most accurate model, the last approach was taken as a basis because it accounts for reservoir anisotropy and flow curvature near the wellbore due to partial perforation of well. However, all the calculations are presented below. Table 3.7. Input data Input data Oil density ρ o, g/cc 0.83 Water density ρ w , g/cc 1.249 Gas density ρ g , g/cc 0.000768 Oil column thickness h, ft 53.8 Perforated interval h p , ft 6.56 Oil formation volume factor B o , RB/STB 1.119 Wellbore radius r w , ft 0.246 Drainage radius r e , ft 656.17 Absolute permeability k h , mD 899.1 Oil phase permeability k o , mD 584.415 Oil viscosity, μ o , cp 10.6 Anisotropy, k v /k h 0.01 Meyer-Garder Method Meyer and Garder suggest that coning development is a result of the radial flow of the oil and associated pressure sink around the wellbore. In their derivations, Meyer and Garder assume a homogeneous system with a uniform permeability throughout the reservoir, i.e., k h = k v . It should be pointed out that the ratio k h /k v is the most critical term in evaluating and solving the coning problem. Consider the schematic illustration of the gas-coning problem shown in Figure 3.4. 59 Figure 3.4. Gas coning Meyer and Garder correlated the critical oil rate required to achieve a stable gas cone with the following well penetration and fluid parameters: difference in the oil and gas density; depth Dt from the original gas-oil contact to the top of the perforations; the oil column thickness h. The well perforated interval h p , in a gas-oil system, is essentially defined as: ℎ 𝑝 = ℎ − 𝐷 𝑡 (3.2.1.2.1) Meyer and Garder propose the following expression for determining the oil critical flow rate in a gas-oil system: 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 [ 𝜌 𝑜 − 𝜌 𝑔 𝑙𝑛 𝑟 𝑒 𝑟 𝑤 ] ( 𝑘 𝑜 𝜇 𝑜 𝐵 𝑜 ) [ℎ 2 − (ℎ − 𝐷 𝑡 ) 2 ] (3.2.1.2.2) where q cg – critical oil rate, STB/day; ρ g ,, ρ o – density of gas and oil, respectively, lb/ft 3 ; k o – effective oil permeability, md; r e , r w – drainage and wellbore radius, respectively, ft; h – oil column thickness, ft; D t – distance from the gas-oil contact to the top of the perforations, ft. Thus, inserting the values into the expression (3.2.1.2.2): 60 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 [ 0.83 ∙ 62.428 − 0.000768 ∙ 62.428 𝑙𝑛 656.17 0.246 ] ( 584.415 10.6 ∙ 1.119 ) [53.8 2 − (53.8 − 47.24) 2 ] = 22.68 𝑆𝑇𝐵/𝑑𝑎𝑦 22.68 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟐. 𝟗𝟗 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 Chierici-Ciucci Method Chierici and Ciucci used a potentiometric model to predict the coning behavior in vertical oil wells. The results of their work are presented in dimensionless graphs that take into account the vertical and horizontal permeability. The authors introduced three dimensionless parameters that can be determined from a graphical correlation to determine the critical flow rates [38]. The first dimensionless parameter that the authors used to correlate results of potentiometric model is called the effective dimensionless radius and is defined by: 𝑟 𝐷𝑒 = 𝑟 𝑒 ℎ 𝑝 √ 𝑘 ℎ 𝑘 𝑣 (3.2.1.2.3) 𝑟 𝐷𝑒 = 6.56√0.01 = 10 where h p – perforated interval, ft; r e – drainage radius, ft; k v , k h – vertical and horizontal permeability, respectively. The second dimensionless parameter that the authors used in developing their correlation is termed the dimensionless perforated length and is defined by: 𝜀 = ℎ 𝑝 ℎ (3.2.1.2.4) 𝜀 = 6.56 53.8 = 0.12 The authors introduced the dimensionless gas cone ratio as defined by the following relationship: 𝛿 𝑔 = 𝐷 𝑡 /ℎ (3.2.1.2.5) where D t is the distance from the original GOC to the top of perforations, ft. 61 𝛿 𝑔 = 𝐷 𝑡 ℎ = 47.24 53.8 = 0.88 Chierici and coauthors proposed that gas-oil contact is stable only if the oil production rate of the well is not higher than the following: 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 ∙ ℎ 2 (𝜌 𝑜 − 𝜌 𝑔 ) 𝐵 𝑜 𝜇 𝑜 𝑘 𝑜 𝑞 𝐷𝑐 (3.2.1.2.6) where Δρ – density difference (lb/ft 3 ); B o – average oil formation volume factor (FVF); μ o – average oil viscosity (cp); k o – oil permeability (md); q Dc – dimensionless critical producing rate; h – pay thickness (ft); q c is given in STB/day. The authors provided a set of working graphs for determining the dimensionless function q Dc from the calculated dimensionless parameters r De , ɛ, and δ. Figure 3.5. Dimensionless critical rate chart for r De =10 62 From the plot: 𝑞 𝐷𝑐 = 0.15 Thus, 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 ∙ 53.8 2 (0.83 ∙ 62.428 − 0.000768 ∙ 62.428) 1.119 ∙ 10.6 584.415 ∙ 0.15 = 27.2 𝑆𝑇𝐵/𝑑𝑎𝑦 27.2 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟑. 𝟔 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 Hoyland et al Method Hoyland, Papatzacos, and Skjaeveland presented two methods for predicting critical oil rate for coning in anisotropic, homogeneous formations. The first method is an analytical solution, and the second is a numerical solution to the coning problem. The Analytical Solution Method Using the expressions from previous method (3.2.1.2.3; 3.2.1.2.4): 𝑟 𝐷𝑒 = 10 𝜀 = 0.12 Figure 3.6. Critical rate correlation 63 𝑞 𝑐𝐷 = 0.21 Then, applying formula (3.2.1.2.6), obtain: 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 ∙ 53.8 2 (0.83 ∙ 62.428 − 0.000768 ∙ 62.428) 1.119 ∙ 10.6 584.415 ∙ 0.21 = 38.1 𝑆𝑇𝐵/𝑑𝑎𝑦 38.1 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟓 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 The Numerical Solution Method 𝑟 𝐷𝑒 = 10 Table 3.8. q cD vs h p relationship q cD1 (0.905) 0.025 h p1 0.905 q cD2 (0.714) 0.09 h p2 0.714 q cD3 (0.476) 0.18 h p3 0.476 q cD4 (0.238) 0.22 h p4 0.238 q cD5 (0.048) 0.23 h p5 0.048 Figure 3.7. Plot q cD vs h p 𝑞 𝑐𝐷 = 0.22 𝑞 𝑐𝑔 = 0.246 ∙ 10 −4 ∙ 53.8 2 (0.83 ∙ 62.428 − 0.000768 ∙ 62.428) 1.119 ∙ 10.6 584.415 ∙ 0.22 = 40 𝑆𝑇𝐵/𝑑𝑎𝑦 0.01 0.1 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Dim en sion less Cr itical R at e Fractional Well Penetration 64 40 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟓. 𝟐𝟕 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 Chaney et al Method Chaney et al developed a set of working curves for determining oil critical flow rate. The authors proposed a set of working graphs that were generated by using a potentiometric analyzer study and applying the water coning mathematical theory as developed by Muskat-Wyckoff [39]. 𝑄 𝑐𝑢𝑟𝑣𝑒 = 570 𝑞 𝑐𝑔 = 0.2676 ∙ 10 −4 [ 𝑘 𝑜 (𝜌 𝑜 − 𝜌 𝑔 ) 𝜇 𝑜 𝐵 𝑜 ] 𝑄 𝑐𝑢𝑟𝑣𝑒 (3.2.1.2.7) 𝑞 𝑐𝑔 = 0.2676 ∙ 10 −4 [ 584.415(0.83 ∙ 62.428 − 0.000768 ∙ 62.428) 1.119 ∙ 10.6 ] 570 = 38.22 𝑆𝑇𝐵/𝑑𝑎𝑦 38.22 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟓. 𝟎𝟒𝟑 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 65 Figure 3.8. Critical production rate curves Chaperon Method Chaperon proposed a simple relationship to estimate the critical rate of a vertical well in an anisotropic formation. The relationship accounts for the distance between the production well and boundary [40]. 𝑞 𝑐𝑔 = 0.0783 ∙ 10 −4 [ 𝑘 𝑜 (ℎ − ℎ 𝑝 ) 2 𝜇 𝑜 𝐵 𝑜 ] ∆𝜌𝑞 𝑐 ∗ (3.2.1.2.8) 570 66 𝑞 𝑐 ∗ = 0.7311 + ( 1.943 𝛼 ′′ ) (3.2.1.2.9) 𝛼 ′′ = ( 𝑟 𝑒 ℎ 𝑝 )√ 𝑘 𝑣 𝑘 ℎ (3.2.1.2.10) 𝛼 ′′ = ( 656.168 6.56 ) √0.01 = 10 𝑞 𝑐 ∗ = 0.7311 + ( 1.943 10 ) = 0.92 𝑞 𝑐𝑔 = 0.0783 ∙ 10 −4 [ 584.415(53.8 − 6.56) 2 1.119 ∙ 10.6 ] (0.83 ∙ 62.428 − 0.000768 ∙ 62.428) ∙ 0.92 = 41.24 𝑆𝑇𝐵/𝑑𝑎𝑦 41.24 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟓. 𝟒𝟒 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 Schols Method Schols developed an empirical equation based on results obtained from numerical simulator and laboratory experiments. His critical rate equation has the following form: 𝑞 𝑐𝑔 = 0.0783 ∙ 10 −4 [∆𝜌 𝑘 𝑜 (ℎ − ℎ 𝑝 ) 2 𝜇 𝑜 𝐵 𝑜 ] ∙ [0.432 + 3.142/ln ( 𝑟 𝑒 𝑟 𝑤 )]( ℎ 𝑟 𝑒 ) 0.14 (3.2.1.2.11) 𝑞 𝑐𝑔 = 0.0783 ∙ 10 −4 [(0.83 ∙ 62.428 − 0.000768 ∙ 62.428) 584.415(53.8 − 6.56) 2 10.6 ∙ 1.119 ] ∙ [0.432 + 3.142/ln ( 656.17 0.246 )]( 53.8 656.17 ) 0.14 = 33.3 𝑆𝑇𝐵/𝑑𝑎𝑦 33.3 𝑆𝑇𝐵 𝑑𝑎𝑦 ∙ 0.159 ∙ 𝜌 𝑜 = 𝟒. 𝟒 𝒕𝒐𝒏𝒆𝒔 𝒅𝒂𝒚 67 Muskat Method This method is based on relatively simple hydrostatic considerations and critical coning rate here is the rate of oil production at which the gas cone rises to a point just above the nearest perforations but stabilizes and no gas is produced (Fig. 3.9) [41]. Figure 3.9. Gas Hydrostatic Equilibrium For the case of single gas coning, 𝑝 𝑤 − 𝜌 𝑔 𝑔ℎ 𝑎𝑝 = 𝑝 𝑒 − 𝜌 𝑜 𝑔ℎ 𝑎𝑝 (3.2.1.2.12) i.e. 𝑝 𝑒 − 𝑝 𝑤 = (𝜌 𝑜 − 𝜌 𝑔 )𝑔ℎ 𝑎𝑝 and critical rate in the case of single gas coning will be equal to: 𝑞 𝑐𝑔 = 2𝜋𝑘 𝑜 ℎ(𝑝 𝑒 − 𝑝 𝑤 ) 𝐵 𝑜 𝜇 𝑜 (𝑙𝑛 𝑟 𝑒 𝑟 𝑤 + 𝑆 𝑝𝑝 ) (3.2.1.2.13) consequently, 𝑞 𝑐𝑔 = 2𝜋𝑘 𝑜 ℎ(𝜌 𝑜 − 𝜌 𝑔 )𝑔ℎ 𝑎𝑝 𝐵 𝑜 𝜇 𝑜 (𝑙𝑛 𝑟 𝑒 𝑟 𝑤 + 𝑆 𝑝𝑝 ) (3.2.1.2.14) However, to delay gas coning maximally, it is necessary to find primarily the location of optimum perforation. In the case of field D with inactive aquifer, the perforation should be located at the bottom of oil-saturated part for the purpose of maximum breakthrough time [25, 26]. The next step is to estimate S pp – Brons and Marting pseudo-skin for partial penetration which is the function of 𝑏 = ℎ 𝑝 ℎ and ℎ 𝐷 = √𝑘 𝑣 /𝑘 ℎ ∙ ℎ 𝑠 𝑟 𝑤 (h s is illustrated at the Fig.3.10). 68 Figure 3.10. h s variations 𝑏 = ℎ 𝑝 ℎ = 6.56 53.8 = 0.12 ℎ 𝑠 = ℎ = 53.8 𝑓𝑡 ℎ 𝐷 = √𝑘 𝑣 /𝑘 ℎ ∙ ℎ 𝑠 𝑟 𝑤 = √0.01 ∙ 53.8 0.492 = 21.9 Then, the value of S pp from the plot can be found: Figure. 3.11. Pseudo-skin due to partial penetration 69 𝑆 𝑝𝑝 = 7 Consequently, water and gas free oil critical rate can be estimated using formulae ( 3.2.1.2.14): 𝑞 𝑐𝑔 = 2𝜋𝑘 𝑜 ℎ(𝜌 𝑜 − 𝜌 𝑔 )𝑔ℎ 𝑎𝑝 𝐵 𝑜 𝜇 𝑜 (𝑙𝑛 𝑟 𝑒 𝑟 𝑤 + 𝑆 𝑝𝑝 ) = 2 ∙ 3.14 ∙ 584.415 ∙ 10 −15 ∙ 53.8 ∙ 0.3048 ∙ (0.83 ∙ 1000 − 0.000768 ∙ 1000) ∙ 32.174 ∙ 0.3048 ∙ 53.8 ∙ 0.3048 1.119 ∙ 10.6 ∙ 10 −3 (𝑙𝑛 656.17 ∙ 0.3048 0.246 ∙ 0.3048 + 7) = 0.00004 𝑚 3 𝑠𝑒𝑐 = 3.45 𝑚 3 𝑑𝑎𝑦 Converting m 3 to tones: 𝑞 𝑐𝑔 = 2.46 ∙ 𝜌 𝑜 = 2.46 ∙ 0.83 = 2.86 𝑡𝑜𝑛𝑒𝑠 𝑑𝑎𝑦 The results of other estimations are presented in the Table 3.9. Table 3.9.Critical rates Method Meyer and Garder Chierici- Ciucci Hoyland et al Chaney et al Chaperon Schols Muskat Critical rate, t/day 2.99 3.6 5 5.27 5.04 5.44 4.4 2.86 |