INVESTIGATION OF THE EFFECT OF STIMULATION TREATMENT AND CERTAIN PARAMETERS ON GAS WELL DELIVERABILIITY BY USING DIFFERENT ANALYSIS APPROACHES

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1 ISSN IJAETCS (214) Vol.1, No.1, 1-19 Research Article International Journal of Advancement in Engineering, Technology and Computer Sciences INVESTIGATION OF THE EFFECT OF STIMULATION TREATMENT AND CERTAIN PARAMETERS ON GAS WELL DELIVERABILIITY BY USING DIFFERENT ANALYSIS APPROACHES Abdelrahman Elkhaiat I & Sayed Gomaa II* I The British University in Egypt, Cairo, Egypt II* Al Azhar University, Cairo, Egypt ABSTRACT: This paper assesses the impact of a stimulation treatment on a gas well deliverability. Modified isochronal test is conducted on a gas well prior to and after a stimulation treatment. The stimulation treatment has increased the deliverability of the well as expected and the treatment is proven justified. This work also compares between the different analysis approaches, empirical, pressure, pressure squared, and pseudo-pressure approaches. This comparison is conducted on modified isochronal test data for several wells to check the accuracy of each analysis approach. The pseudo-pressure approach is the most accurate one as it takes into account the variation of fluid properties with varying reservoir pressure. The results obtained by other approaches are compared to the pseudo-pressure approach and their error percentages are presented. The effect of several parameters on well deliverability is also investigated. The results obtained by both empirical and pressure squared approaches are compared for the parameters. A spreadsheet programwas developed to analyze deliverability tests data by the different analysis approaches. The validity of the developed spreadsheet program was checked by comparing its results with both analytical solution and the results obtained by commercial software. Increasing reservoir temperature would affect gas viscosity and gas compressibility and result in an overall decrease in well deliverability. Decreasing skin factor would increase the deliverability but Darcy s equation tends to overestimate deliverability at high negative skin values. KEYWORDS: Deliverability, stimulation. Modified isochronal, viscosity, temperature, pressure squared INTRODUCTION: Gas well deliverability is the ability of a well to flow or to deliver gas to the surface. Estimation of the stabilized absolute open flow potentials (AOFPs) is required by regulatory agencies in order to set the maximum allowable rates of production. In addition, it helps make sales contracts. It is also important as it aids in the design of pipelines systems and in making the field development plan. In this paper, the modified isochronal test is carried out both prior to and after a stimulation job for a gas well. The deliverability of the well is calculated in both cases to assess the success of the stimulation job. Both empirical and theoretical analyses of the test are illustrated. The results of each calculation approach are compared for the stimulated well and six other wells in order to assess the accuracy of each method. This helps to identify the easiest calculation approach that yields reasonable accurate results under a given condition (i.e. reservoir pressure) for rapid analytical calculation if no software is available. Any change in some parameters would affect the deliverability of gas wells. A sensitivity study is carried out for reservoir temperature, net pay thickness and skin to assess their impact on well deliverability. 2. LITERATURE REVIEW: To measure the maximum deliverability, which is absolute open flow potential, primitive techniques were used back before 192 s. The gas well was allowed to produce to the atmosphere with no restrictions. Such techniques had several disadvantages and caused severe problems to the formation (1). In 1929, Pierce and Rawlins published their study in two parts (2). This work was further improved by Rawlins and Schellhardt in 1936 in their famous monograph(1). However, because gas flow rate and pressure at the sand face has to stabilize at each step during the conventional backpressure test of Rawlins and Schellhardt, Cullender developed the isochronal test technique in 1955 to

2 Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No shorten the duration of deliverability test (3). In order to shorten the test duration further, Katz and his colleagues developed the modified isochronal test in 1959 (4). One main important factor in designing and selecting a deliverability test is the stabilization time, i.e. the time required to reach the pseudo-steady state. Stabilization time could be known either from the production characteristics of the well or from previous deliverability tests conducted on the concerned well (5). If stabilization time is not known, it can be assumed relative to the neighboring wells whose data are available and which are located in the same formation type. The stabilization time can also be calculated from the following equation The conventional backpressure test is conducted only if the time of stabilization is estimated to be few hours. If not, either isochronal or modified isochronal test will be preferred. Isochronal test should be selected if a greater accuracy is required. However, modified isochronal tests provide reliable results and can save time and money (6). Different deliverability tests are analyzed either theoretically or empirically. The theoretical analysis of transient data obtained during deliverability tests is based on the exact solutions to the general diffusivity equation for radial flow developed by Houpeurt in 1959(7). On the other hand, empirical analysis of stabilized deliverability tests is based on the empirical equations developed by Rawlins and Schellhardt in 1936(1). There are several assumptions for both analyses. For instance, homogeneous and isotropic reservoirs are assumed. They are also applicable to radial flow only. Therefore, they cannot be applied in layered or fractured reservoirs or any other heterogeneities. Furthermore, both empirical and theoretical analysis assume that wellbore storage effect has ended which may be not applicable in short duration tests especially in low-permeability reservoirs (8). The Empirical analysis is based on Rawlins and Schellhardt equation Where (1) (2) (3) The theoretical analyses of deliverability tests are based on the diffusivity equation in the radial form. After introducing the pseudo-pressure term to the equation by Al-Hussainy et al. in 1966(9), the following equation has been reached The first analysis based on theoretical basis was first mentioned in literature by Houpeurt (7). The author found out that it is convenient to put the solution to the diffusivity equation in the form The previous equation is commonly known as Laminar-Inertial-Turbulent (LIT) equation. There are three different approaches for the left hand side in the previous equation, the pressure, the pressure-squared, and the real gas pseudo-pressure approaches. The third approach (i.e. pseudo-pressure approach) is the most accurate approach as it takes into account the change in gas properties (i.e. gas viscosity and gas deviation factor) with respect to pressure. The pressure-squared approach assumes that the product (μz) is constant which is valid only at pressure values less than 2 psi (1). The pressure approximation approach, however, assumes that the product (μβ g) is constant which is, according to Fetkovich, valid only at pressure values greater than 3 psi (11). For the right hand side, the value of (aq) represents the drop in pressure due to laminar flow and the term (a) is the laminar flow coefficient, while the second term (i.e. bq 2 ) represents the pressure drop as a result to turbulent flow with (b) being the inertial turbulent flow coefficient (1). (4) (5)

3 Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No The pressure-squared equation in the form of the LIT equation will be (6) Where, (7) (8) The pressure equation in the form of the LIT equation will be (9) Where, (1) (11) The pseudo-pressure equation in the form of the LIT equation will be (12) Where, (13) (14) 3. METHODOLGY: A spreadsheet program was developed to analyze deliverability tests data by the different analysis approaches. The validity of the developed spreadsheet program was checked by comparing its results with both analytical solution and the results obtained by commercial software. The data of modified isochronal test for eight different wells are used in the study. The effect of certain parameters, i.e. changing reservoir temperature, net pay thickness and skin on well productivity is examined.the methodology adopted in this paper to evaluate the temperature effect is changing the reservoir temperature, and monitoring the corresponding change in gas viscosity. Moreover, the gas compressibility factor is affected by changing the reservoir temperature. Hence, this resultant change in Z-factor has to be taken into consideration as well. By varying the aforementioned three parameters, the combined effect of their variation on absolute open flow potential is evaluated. For assessing the skin impact, the skin value is varied from -7 to 7. However, higher negative skin values are less frequent, but they are deliberately chosen to show the overestimation of AOFP in some cases. 4. RESULTS AND DISCUSSION: 4.1. THE EFFECT OF STIMULATION TREATMENT: Modified Isochronal Test is carried out on a gas well (well x) before and after hydraulic fracturing job. The deliverability test data is analyzed prior to and after the stimulation job for the well (x). The absolute open flow is expected to increase significantly due to stimulation (Fig:I).

4 ERROR PERCENTAGE COMPARED TO LIT, % Bottomhole Flowing Pressure (psia) Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No Pre-Fracturing Post-Fracturing Gas Flow Rate (MMSCF/Day) Fig I: IPR curves before and after stimulation treatment Fig. I shows the IPR curves for both cases (i.e. prior to and after hydraulic fracturing). It is obvious that the absolute open flow has increased greatly due to the hydraulic fracturing treatment. It has increased from MMSCF/Day to 25 MMSCF/Day, which accounts for 83% increase. In other words, the absolute open flow almost doubled due to stimulation job. This proves that the stimulation job was successful and that it was justified. 4.2.COMPARISON BETWEEN DIFFERENT ANALYSIS APPROACHES: Post-fracturing modified isochronal test data of well x along with modified isochronal tests data of 6 wells published in Brar and Aziz paper (12)is analyzed using empirical and theoretical analyses approaches (i.e. pressure, pressure squared, and pseudo-pressure methods). The error percentages between the obtained values of AOFPs by different approaches are compared to the values obtained by the most accurate approach, i.e. the pseudo-pressure approach as shown in Fig. II no.1 no.2 no.3 no.4 no.5 no.6 x Pressure Squared Empirical Pressure Fig II: Error percentages of different approaches compared to LIT approach By investigating the results, it is evident that the pressure-squared approach yields the most reasonably acceptable results and the pressure approach to yield highly erroneous results. The values obtained by pseudo-pressure approach were taken as the base accurate values to which the results of other approaches are compared. By looking into values obtained

5 Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No by empirical analysis, the error percentages range from.12 % in well x to 8.91 % in well no. 3. For the pressure-squared approach, the highest error percentage is 3.83 % for well no. 4 and the least error percentage is.28% error only in well x. On the other hand, for pressure approach, the error percentages range from 15.9 % in well x to as much as % in well no. 4. From the previous discussion, it can be concluded that the pressure-squared approach yields a reasonable estimate of the absolute open flow, while the pressure approach gives the most erroneous inaccurate results. The pressure approach cannot be used under any circumstances for gas wells if average reservoir pressure is within the range of cases investigated. The empirical analysis also yields satisfying results to some point. However, the most accurate method, i.e. pseudo-pressure method, is not very complicated. The only additional data required is specific gravity, reservoir temperature, and CO 2 & H 2 S mole fraction. A simple spreadsheet can be created and used to provide accurate results INVESTIGATION OF THE EFFECT OF SEVERAL PARAMETERS ON WELL DELIVERABILITY: Any change in some parameters, fluid parameters and reservoir parameters, would affect the deliverability of gas wells. The effect of changing reservoir temperature, net pay thickness and skin on well productivity is examined. Table I shows the variation range of the parameters used in the study. Parameter Base case Variation range Reservoir Temperature, o F 283 8: 3 Skin Factor -4-7 : 7 Net Pay Thickness, ft 5 1 : 1 Table I: Variation ranges of investigated parameters THE EFFECT OF RESERVOIR TEMPERATURE ON WELL DELIVERABILITY: The impact of changing the reservoir temperature on the productivity of gas wells is investigated. However, this effect cannot be studied solely as certain parameters must change when the reservoir temperature varies, i.e. gas viscosity and gas compressibility factor must be changed. The methodology adopted in this paper is changing the reservoir temperature, and monitoring the corresponding change in gas viscosity. Moreover, the gas compressibility factor is affected by changing the reservoir temperature. Hence, this resultant change in Z-factor has to be taken into consideration as well. By varying the aforementioned three parameters, the combined effect of their variation on absolute open flow potential is evaluated. The reservoir temperature is varied from 8 o F to 3 o F with the base case being at 283 o F. The gas viscosity is evaluated using Lee, Gonzalez, and Eakin semi-empirical correlation. On the other hand, the gas compressibility factor is calculated using Dranchuk and Abou-Kassem (DAK) analytical solution. The reservoir pressure is not varied neither the gas specific gravity in order not to complicate the calculations. Table:II summarizes the effect of reservoir temperature on both gas viscosity and gas compressibility factor for well x. Reservoir temperature( o F) Z µ g, cp Table II: Temperature effect Z-Factor and gas viscosity for well (X) The effect upon absolute open flow is evaluated by two different analytical approaches; the pressure squared and the empirical analysis methods. After obtaining the corresponding values of gas viscosity and gas compressibility factor, parameters C, a, and b are varied by manipulating equations (3), (7), and (8) respectively. The results are compared and depicted in Fig. III.

6 Absolute Open FLow, MMscf/day Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No Pressure Squared Empirical Reservoir Temperature, F Fig III: Effect of changing reservoir temperature on well deliverability As it can be noticed in the Fig:III, the combined effect of increasing reservoir temperature on gas viscosity and gas compressibility factor would result in a lower absolute open flow potential. Usually, an increase in temperature would result in a corresponding increase in gas viscosity at reservoir conditions. This increase in viscosity will make the gas more resistant to flow, and hence the inflow performance is impaired. Therefore, the absolute open flow will decrease as well. By comparing the two curves obtained from the two different approaches (i.e. pressure-squared and empirical), it is found out that the empirical simplified analysis tends to result in higher values of AOFP away from the point of the base case. However, in case the reservoir temperature is varied higher than the base case, the opposite of this behavior would result, i.e. the empirical correlation will result in lower AOFP values compared to that obtained by pressure squared. This argument is shown in Fig:IV, whose values are obtained from modified isochronal test of well no. 4 published by Brar and Aziz (12). Table III summarizes the effect of reservoir temperature on both gas viscosity and gas compressibility factor for well no. (4). Reservoir Temperature ( o F) Z µ g, cp Table III: Temperature effect on Z-factor and gas viscosity for well no. (4) From Table III, it can be seen that for gas viscosity to increase, the reservoir temperature must increase for the same reservoir pressure and gas specific gravity. The accompanied change in gas compressibility factor is also shown in the Table III. However, the effect of reservoir temperature on absolute open flow is shown in the following Fig. IV.

7 Absolute Open Flow, MMscf/day Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No Pressure Squared Empirical Reservoir Temperature, F Fig IV: Effect of temperature on deliverability with low temperature base case In the previous chart, the base reservoir temperature is around 1 o F. At higher temperatures, the empirical method tends to result in lower AOFP as expected. This erroneous behavior resulting from applying empirical equation can be attributed to the assumption of the parameter (n) being constant. Hence, the change in rate dependent skin due to the change in gas viscosity resulting from changing temperature was not taken into consideration. In the first case, the parameter (n) was determined from the analysis based on a relatively high viscosity compared to viscosity values at lower temperatures. However, at lower temperatures when viscosity becomes less, the constant parameter (n) neglects the increase in pressure drop in the vicinity of the wellbore due to the lower new value of gas viscosity. On the contrary, if the base case is of low temperature, the parameter (n) accounted for the high turbulence due to the low viscosity. However, increase the temperature in this case while assuming constant (n) would result in lower AOFP. As the parameter (n) is not changed to account for the increase in viscosity at higher temperatures THE EFFECT OF SKIN ON WELL DELIVERABILITY: Skin is a dimensionless parameter that describes the condition in the vicinity of the wellbore. A positive skin factor is an indication of an increase in pressure drop. Different causes could result in such positive skin values, such as; formation damage, turbulent flow and partial penetration. In contrast, a negative skin value is an indication of a better condition around the wellbore that resulted in a less pressure drop than normal. This negative skin is obtained after a stimulation treatment such as hydraulic fracturing and acidizing jobs. The effect of skin on well deliverability is investigated by varying the skin value from -7 to 7. However, higher negative skin values are less frequent, but they are deliberately chosen to show the overestimation of AOFP in some cases. Fig:V shows the effect of skin factor variation on absolute open flow potential. From the Fig:V, it is obvious that lowering the skin factor value results in an increase in well productivity. This increase in well deliverability is due to the reduction in pressure drop for the same flow rate due to the enhancement of the near wellbore region condition. Moreover, pressure-squared Houpeurt equation is compared with Darcy s equation of compressible fluids to assess their accuracy. AOFP values exhibit very similar trends for both equations at positive skins and low negative skin values as well. It is obvious from the Fig:V that Darcy s equation overestimates absolute open flow drastically in case of higher negative skin values. This unexpectedly high estimation of AOFP is because the skin parameter is included in the denominator of Darcy s equation, which results in the division by a small number less than unity.

8 Slope (n) AOFP, MMSCF/Day Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No Pressure-Squared Darcy Skin Fig V: Effect of skin variation on well deliverability Because the parameter (C) of Rawlins and Schellhardt empirical equation is a parameter dependent on drainage area and independent of near wellbore condition, simplified empirical analysis could not be used to assess the effect of varying skin on well deliverability, as the only way to obtain slope (n) is by isochronal or modified isochronal testing. However, changing the skin factor value will result in a change in the characteristic slope (n) of the equation. Iterations are made to calculate the characteristic slope (n) for each value of skin factors that would yield the same corresponding AOFP value already obtained by pressure squared Houpeurt analysis. The values of slope (n) are plotted versus the corresponding skin factors in Fig.VI to monitor the change in slope due to varying skin values. By inspection of the Fig.VI, it is obvious that decreasing the skin factor value results in an increase in the slope value, the more the slope value approaches unity, the more laminar is the flow. On contrast, an increase in skin factor value in the positive direction results in reduction of slope value towards the.5 value, which means that the flow becomes more turbulent Skin Fig VI: Effect of skin variation on slope (n) of the deliverability equation THE EFFECT OF NET PAY THICKNESS ON WELL DELIVERABILITY: In this section, net pay thickness effect on the productivity of the well is investigated. Net pay thickness is varied from 1 to 1 feet. It can be seen from Fig. VII that the relationship between net pay thickness and well deliverability is a linear relationship. The thicker the net pay, the more space available for the gas to flow to the wellbore, and hence, a higher AOFP is expected. Another point to

9 AOFP, MMSCF/Day Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No be observed from the Fig. VII is that both approaches (i.e. empirical and pressure squared) yield identical values for AOFP for different net pay thickness values. The empirical approach yields accurate results in this case because net pay thickness is a reservoir rock property and it has nothing to do with the near wellbore condition. Therefore, the assumption of the slope (n) to be constant when net pay thickness is changed is valid here. Pressure Squared Empirical Net Pay Thickness, ft 5. CONCLUSION: It can be concluded that: Fig VII: Effect of net pay thickness variation on well deliverability a) If a stimulation treatment is applied to a gas well, the deliverability of the well should be measured after the treatment to assess its success and to prove whether it is justified or not. b) Pseudo-pressure (LIT) approach should be used when analyzing gas well deliverability test data, while the pressure-squared approach yields the best approximation for LIT approach. c) If the reservoir temperature is found to be different than assumed, the parameters of either pressure squared or pseudo-pressure equations can be adjusted by modifying the value of temperature, gas viscosity, and gas compressibility factor in pressure squared equation, or the value of temperature only in pseudo-pressure equation. It is not recommended to adjust the parameters of the empirical equation, as the assumption of constant (n) is inaccurate. d) If all the terms within the parameters (a) and (b) of the deliverability equations are known and the skin factor is changed, the parameters of pressure squared, pseudo-pressure, and Darcy s equations can be adjusted. However, Darcy s equation cannot be used at high negative skin values as it tends to overestimate the well deliverability drastically. e) A spreadsheet program was developed to analyze deliverability tests data by the different analysis approaches. NOMENCLATURE a Laminar Flow Coefficient, psia 2 /Mscfd AOFP Absolute Open Flow Potential, MMSCF/Day b Inertial Turbulent flow coefficient, (psia/mscfd) 2 C Coefficient in the deliverability equation, MMSCF/Day/psia 2n c t Total isothermal Compressibility, psi -1 D Non-Darcy skin coefficient, (MMSCF/Day) -1 k Reservoir permeability, md kh Permeability thickness or flow capacity, md.ft n Reciprocal slope of deliverability line, dimensionless p Pressure, psia

10 Elkhaiat & Gomma/International Journal of Advancement in Engineering, Technology and Computer Sciences, Vol.1, No P R Q r e r w s t Z Φ μ β g Average Reservoir pressure, psia Flow rate, MMSCF/Day Drainage radius, ft bore radius, ft Skin factor, dimensionless Time, hr Gas deviation factor, dimensionless Porosity, fraction Viscosity, cp Pseudo-Pressure corresponding to, psia 2 /cp Gas formation volume factor, cu.ft/scf REFERENCES 1. Rawlins, E. L., & Schellhardt, M. A., 1936,Back-Pressure Data on Natural-Gas s and Their Application to Production Practices, United States Bureau of Mines, Pierce, H. R., & Rawlins, E. L., 1929,The Study of a Fundamental Basis for Controlling and Gaging Natural-Gas s, The United States Bureau of Mines. 3. Cullender, M. H., 1955, The Isochronal performance Method of Determining the Flow Characteristics of Gas s,petroleum Transactions, AIME, 24, Katz, D. L., Cornell, D., Vary, J. A., Kobayashi, R., Elenbaas, J. R., Pettmann, F. H., & Weinaug, C. F., 1959,Handbook of Natural Gas Engineering. United States of America: McGraw-Hill Book Company, Inc, Energy Resources Conservation Board, 1978,Theory and Practice of The Testing of Gas s. Calgary, 3, Chaudhry, A. U., 23,Gas Testing Handbook. Elsevier, Houpeurt, A., 1959,The Flow of Gases in Porous Media,Revue de L'Institut Francais du Petrole, XIV(11), Lee, J., & Wattenbarger, R. A., 1996,Gas Reservoir Engineering, Socity of Petroleum Engineers, Al-Hussainy, R., Ramey, H., & Crawford, B. P., 1966,The Flow of Real Gases Through Porous Media,Journal of Petroleum Technology, Ahmed, T., & Meehan, D. N., 212,Advanced Reservoir Management and Engineering, Elsevier, 2, Fetkovich, M. J., 1973, The Isochronal Testing of Oil,Fall Meeting of the Society of Petroleum Engineers of AIME. Las Vegas, Nevada. 12. Brar, G. S., & Aziz, K., 1978,Analysis of Modified Isochronal Tests to Predict the Stabilized Deliverability Potential of Gas s without Using Stabilized Flow Data,Journal of Petroleum Technology, 3,

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