Analysis of shale gas production performance by SGPE

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3 Kanji Kato, Mahmood Ahmadi, Carlos Pereira and Oscar Gonzalez 449 obtained by dividing GIP by lateral length equivalent to reservoir thickness in vertical wells. A value, Spacing K, is easily calculated by dividing pseudo area calculated in the previous step by the thickness of shale reservoir. The back ground theory for PE and SGPE is same. SGPE estimates the following values where K denotes values calculated by SGPE. Since physical meaning of each parameter is slightly different from definitions in reservoir engineering terminology, it is necessary to distinguish them clearly. Permeability K Spacing K GIP K Usually permeability and other parameters are obtained by using history matching approach. However, simulation model assumes value of all parameters before any calculation and tremendous effort is required to obtain a good match. In addition, excellent history match, even if they are achieved, sometimes they bring different long term cumulative gas production. On the other hand, SGPE does not require any specific assumption as required in the simulation model but does derive information from only gas rate and FWHP. Fig. 4 schematically shows relationship among input data, SGPE and its results. It is very straight forward and it takes a half an hour to calculate result. simulation was used to answer this question. FBHP was calculated by simulation for assumed gas rate in order to obtain a pair of input data which is physically correct a certain shale gas model. Since simulation model requires all parameters, we know all value of parameters when we have assumed simulation model. This is key point since we do not know all parameters dealing with field data, however we know them in advance if we use synthetic data. The concept of procedure is depicted in Fig. 5. and is similar with what has been explained for validity check of PE in Fig. 1 but much more complex in assumptions and its results. First, five synthetic gas production rate patterns were generated using hyperbolic decline equation as shown in Fig. 6 and they are named as Well 1 to Well 5, respectively. Second, FBHP was calculated using numerical simulation. Detail of simulation model is out of scope of this paper but outlines of the simulation mode are as follows; Dual-porosity / dual-permeability system Element of symmetry and fine cell grid(5 to 40 ) Shape factor was used to capture fracture density distribution Gas sorption was deactivated Natural fractures were neglected 4 hydraulic fracture(fracture hereaer)density patterns 4. Objective of the study and its procedure As explained, SGPE assumes that flow in fractured shale is approximated with pseudo- steady radial flow. The question in here is what these values derived by SGPE imply? The objective of this paper is to answer to this question. Numerical Fig. 6 5 synthetic gas rates Fig. 5 Procedures to examine implication of values derived from SGPE Fig. 7 Fracture density patterns for individual well penetration J. Japanese Assoc. Petrol. Technol. Vol. 77, No

4 450 Analysis of shale gas production performance by SGPE Fig. 8 Permeability K for 20 individual cases were considered(f1, F2, F3, and F4) Common fracture permeability of 0.7 md is assumed FBHP constraints of 1500 psig Specific values of main parameters are presented in Table 1. It should be noted that different matrix permeability and fracture penetration are assigned to individual wells; higher gas rate well considers higher matrix permeability and deeper fracture penetration and vice versa. This assumption was based on our previous experience of analyzing many field wells in order to generate realistic FBHP for synthetic gas rate. Fracture density distribution is one of the main unknown in shale gas reservoirs. In the simulation model four fracture density distribution patterns are assumed for each gas rate or well respectively. We believe that fracture density distribution through the Stimulated Rock volume(srv)or along fracture penetration depth is not uniform. It is assumed that the number of fractures is exponentially decreasing along the fracture penetration. Specifically it is assumed that fracture density or number of fractures per stage(400 was assumed)at a horizontal well is between 50 and 1000 and decrease along distance from well to 1 at end of fracture penetration. Fig. 7 shows these fracture density patterns which were named as F1 to F4 for five wells respectively. F1 has more fractures than F2 and F4 has the least fractures or the least fracture density. As described above, 20 cases(5 wells 4 fracture patterns)were generated and 20 sets of FBHP corresponding to 20 cases were calculated by numerical simulation, It means 20 well data, a pair of gas rate and FBHP which shall be put into SGPE, have been synthesized. It should be noted that each set of data can be considered as a real data and that perfect history match can be achieved with parameters descrived if someone tried history matching. 6. Result and discussion 6.1 Permeability K Permeability K of 20 cases are presented in Fig. 8. Values range between 1.4 and 0.2 md. As explained each well has same gas rate and other parameters except fracture patterns (F1 to F4). It can be seen that Permeability K is decreasing along fracture density descending. It means Permeability K is Fig. 9 Matrix permeability and Permeability K Fig. 10 Spacing K for 20 individual cases reflecting fracture density. Permeability K shown in Fig. 8 is plotted against matrix permeability in Fig.9. It is demonstrating a linear correlation between Permeability K and matrix permeability in logarithmic scale for the same fracture pattern. It is likely that Permeability K is reflecting matrix permeability under certain fracture permeability although longer fracture penetration is assumed for larger matrix permeability. It is concluded that Permeability K is reflecting average property of hydraulically fractured shale including matrix permeability, fracture permeability and fracture density distribution under certain fracture penetration. 6.2 Spacing K Spacing K of twenty cases are presented in Fig. 10. The values range from 500 to 100. It ranges wide but please remember the penetration depths of fractures are assumed between 500 and 200. It shows that the influence of fracture density distribution to Spacing K is generally minor. However, the ratio of Spacing K between F1 and F4 for each is different. The ratio of F1/F4 in Well 1 with matrix permeability of 500nD is smaller than Well 5 with matrix permeability of 20 nd. This suggests that the effect of fracture job is smaller for a high matrix permeability shale at least in terms of Spacing K. Twenty Spacing K in Fig. 10 are cross-plotted for fracture penetration as shown in Fig. 11. It should be noted that Spacing K and fracture penetration is similar in Well 1(fracture penetration of 500 )where matrix permeability is 500nd. The difference between Spacing K and fracture penetration is coming lager with decreasing fracture penetration or decreasing

5 Kanji Kato, Mahmood Ahmadi, Carlos Pereira and Oscar Gonzalez 451 Fig. 14 Schematic concept of EDA(for tight shale or low fracture density) Fig. 11 Relationship between fracture penetration and Spacing K Fig. 12 Pressure distribution in shale aer 1 year period for various wells(f2 fracture pattern)with fracture penetration(arrow)and Spacing K(star) matrix permeability but please note the difference is less than 100 at most. Fig. 12 shows pressure distribution in shale aer one year which is calculated by simulation for five wells of F2 fracture pattern. It corresponds to pressure distribution at the day of last production. Fracture penetration and Spacing K are also indicated in the figure by arrow and star respectively. Fig. 12 shows us shale pressure at location of Spacing K. It is a point of about 1000 psi below initial pressure or closer to well from point of initial pressure. Why is shorter than fracture penetration? One reason is that flow in fractured shale is believed to be quite complex and the assumption under SGPE does not properly represent such flow in shale. It is true. However, we think about another reason. Fig. 13 is part of independent simulation work which carried out in early stage of this study. In this model, flow from matrix to fracture was examined with fine grid cells of 1 under Darcy flow. Fracture spacing was assumed 50 and some matrix permeability was examined. Fig. 13 is suggesting that the un-drained matrix would remain even in SRV when matrix permeability is small or fracture spacing is large at the time of one year. Such a situation is believed likely in shale in field since fracture development in shale is also believed not homogeneous and fracture permeability is not unique. Fig. 14 is a schematic diagram which depicts situation in shale as described above. When un-drained matrix is le behind in tight matrix shale or in less fracture densities shale, rock volume drained in SRV is less than SRV based on defined by fracture penetration. We call this length Effective Drainage Area(EDA)conceptually. Since Spacing K is reflecting drained shale rock volume(recall that SGPE is handling observed gas rate which comes from drained shale matrix), Spacing K is consequently shorter than fracture penetration if un-drained matrix exists and is indicating EDA. For higher matrix permeability shale, un-drained matrix shale does not exist. Fig. 15 shows schematic concept of EDA for higher matrix permeability shale. Fracture penetrated area is equivalent to stimulated rock volume(srv). Aer some Fig. 13 Pressure distribution of shale block surrounded by fractures J. Japanese Assoc. Petrol. Technol. Vol. 77, No

6 452 Analysis of shale gas production performance by SGPE Fig. 15 Schematic concept of EDA(higher matrix permeability) Fig. 18 GIP K for 20 individual cases Fig. 16 Result of SGPE for real field data, it suggests that there might be correlation between Spacing K and Permeability K Fig. 17 Exactly same plot with Fig. 16 for results obtained by this study period of production, part of gas in shale matrix which flows into SRV yields pressure depletion from initial pressure to some distance from SRV or from end of fracture penetration. By introducing this hypothesis of EDA, Spacing K is considered to be a measure of EDA for any type of shale, tight or permeable and is indicating fracture penetration length and also seems to explain result of calculation shown in Fig. 11. It should be noted that Spacing K is close to fracture penetration for high permeability matrix case and 100 less than fracture penetration as shown in Fig. 11. In operational point of view, this is valuable information. If operator proposed shorter spacing for field development than half of Spacing K, in-fill wells will be redundant and just additional capital investment. We faced such a situation and run very sophisticated simulation study and proved that calculation of SGPE was true. Now operator is considering optimum development plan. On the other hand, if the current half spacing in developing area is larger than Spacing K plus 100, the current spacing is not optimum and much gas will be le in-between wells. Spacing K would be a good tool to diagnose optimal spacing design. 6.3 Spacing K and Permeability K SGPE was applied on real field data and the results of Spacing K and Permeability K were cross-plotted as shown in Fig. 16. Fig. 16 may suggest a relationship between Spacing K and Permeability K but nothing is certain on what actually means since this was real field data at that time. Fig. 17 is same plot as Fig. 16 but for the results obtained by this study. These two graphs look quite similar on the relationship between Spacing K and Permeability K. The difference between Fig. 16 and Fig. 17 is that we have known in advance what has been assumed for these results in Fig. 17. As explained in section 4, a tight matrix shale with shorter fracture penetration and vice versa is assumed in this study. Similarity of these two figure means that the shale model assumed in this study could be a one explanation on why relationship between Spacing K and Permeability K in Fig 16 was found. This may suggest another hypothesis that longer fracture penetration will develop in high matrix permeability shale and shorter fracture penetration will develop in lower matrix permeability shale. 6.4 GIP K GIP K is calculated by material balance concept in SGPE under assumption that pseudo steady radial flow in shale reservoir. The results of GIP K for all twenty cases are presented in Fig. 18. Since Spacing K is derived from GIP K, this results that Fig.18 is similar with Fig. 10. Here again that the influence of fracture density pattern is generally minor and even smaller in Well 1 where matrix permeability is high. Fracture density should be a function of fracture job. Between F1 and F4, the numbers of fracture are different by 20 times. It suggest that there might be optimum fracture job on cluster spacing, especially for high matrix permeability shale. GIP K is also compared with cumulative gas production calculated by simulation for 5 wells with F2 fracture pattern (Fig. 19). It is quite clear that GIP K is showing excellent one to one correspondence with cumulative gas calculated by

7 Kanji Kato, Mahmood Ahmadi, Carlos Pereira and Oscar Gonzalez 453 GIP K could be a good indicator for recoverable gas. It is also suggested that the optimum fracture job could exist for shale with good matrix permeability. SI Metric conversion factors bbl E-01=m E-01=m E-02=m 3 md E-16=m 2 nd E-22=m 2 psi E+03=Pa Fig. 19 Cumulative gas production calculated by simulation for 10 and 20 years was cross plotted against GIPK with F2 fracture pattern for 5wells simulator. Obviously cumulative gas production should be smaller than GIP according to recovery factor. In other words, GIP K is too small in value. There could be three reasons why GIP K is smaller than cumulative gas production; 1)Static reservoir pressure is approximated under-pseudo steady radial flow which may not capture the fluid flow in shale gas accurately 2)Production period for synthetic gas production of only one year yields un-drained matrix shale inside the SRV. The un-drained matrix in SRV does not contribute to gas production in one year period. SGPE considers drained matrix only and these un-drained matrix may be drained in 10 years. 3)Drainage area could expand further even beyond SRV during 10 years of production. GIP K does not express the exact GIP but it could be a good indicator of recoverable gas. 7. Conclusions This paper suggests that much more information on shale reservoir can be derived from daily gas rate and FWHP data which are quite common data in shale gas operation. SGPE calculates Permeability K, Spacing K and GIP K from these data. SGPE does not require any specific assumption which is required in simulation model but does derive information from production data itself. This paper examined the implication of these three parameters. Permeability K is reflecting average property of hydraulically fractured shale including matrix permeability, fracture permeability and fracture density distribution under certain fracture penetration. Spacing K is considered to be a measure of EDA for any type of shale, tight or permeable and is a good measure of fracture penetration length. It would be a good tool to diagnose optimal spacing design. Reference Kato, K., 1987:Estimation of Initial Gas in Place and apparent Permeability using Suface measured Well Production Data, JAPT, 52(5), 要 旨 加藤完司 マムートアマディ カルロスペレイラ オスカーゴンザレス 孤立したガス層の日産ガス量と坑口圧から浸透率と原始埋蔵量を計算するアルゴリズムは筆者により発表されている (Kato, 1987) 今回このアルゴリズムをシェールガス用に拡張,SGPE と名付けシェールガスの生産データに適用した SGPE により, 生産データから以下の値を計算することができる Permeability K Spacing K OGIP K 本法は均質なガス層を前提にしている シェールガスが水平坑井であること, 内部に密度分布が不明なフラクチャーを含み極めて不均質なこと, それに伴うフローが複雑なことから, 得られた値は 厳密な油層工学の意味する値とは異なる 本論では, 任意の日産ガス量を仮定し, シミュレーションモデルにより坑底圧を計算, これらをフィールドデータとして SGPE に与え, 上記の意味するところを明らかにする 結論は下記のとおり ; Permeability K : フラクチャーされたシェール層の, マトリクス浸透率, フラクチャー浸透率, フラクチャーの分布を反映した物性の平均 Spacing K : 排ガスエリアを示す指標であり, 操業上の見地においてフラクチャー深度の良好な指標となる OGIP K :10~20 年で回収できるガス量の良い指標となる可能性がある J. Japanese Assoc. Petrol. Technol. Vol. 77, No

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