EFFECT OF GAS-OIL-RATIO ON OIL PRODUCTION MASTER OF SCIENCE

Transcription

1 EFFECT OF GAS-OIL-RATIO ON OIL PRODUCTION A THESIS Presented to the Faculty of the African University of Science and Technology in Partial Fulfilment of the Requirements for the Degree of MASTER OF SCIENCE By PARKER, Ebenezer Sekyi Abuja, Nigeria November, 2010

2 ABSTRACT Maximum production from an oil well can be achieved through proper selection of tubing size. The selection of optimum tubing size must be evaluated when completing a well in any type of reservoir especially solution gas drive reservoir since there is likelihood of producing more gas as the reservoir pressure declines. The most widely used methods such as Tarner, Muskat and Tracy methods for predicting the performance of a solution gas drive reservoir were discussed and used to estimate the behaviour of producing GOR. A comparison was made between the results from each method. System analysis approach was adopted for this study. The future IPR curves were determined by a combination of Vogel and Fetkovich correlation. Beggs and Brill multiphase spreadsheet was used to produce the TPR curves by estimating flowing bottomhole pressure for several tubing size using the predicted GOR produced and a range of flowrates. The effect of water production was also considered in this study. The results showed that for IPR5 as GOR increased from 1052 to 1453 scf/stb, oil production rate for 2 7/8-in increased by 17.6% and 3.3% for a further increase in GOR at 2610 scf/stb. At a GOR of 2610 scf/stb oil production decreased by 3.17% at water-cut of 5% and 9.5% at water-cut of 25%. All things being equal, the percentage reduction in production reduces as GOR increases from 2610 to 5635 scf/stb for all the tubing sizes used. i

3 ACKNOWLEDGEMENT I thank the Almighty God for giving me the strength and ability to complete my master programme successfully. I would also like to thank the members of my graduate committee for their earnest contribution, support and time. I would like to acknowledge the advice, supervision, guidance and financial support of Professor Dulu Appah throughout my entire work. I thank the African University of Science and Technology for providing and making available the necessary facilities which facilitated my research with much less stress. Finally, I would like to thank my parents, Mr and Mrs Parker and my siblings, Adelaide, Benjamin and Nancy for their unceasing prayers and encouragement. ii

4 TABLE OF CONTENTS Content Page ABSTRACT... i ACKNOWLEDGEMENT... ii TABLE OF CONTENTS... iii LIST OF FIGURES... v LIST OF TABLES... vi CHAPTER INTRODUCTION Vertical Lift Problems relating to tubing Pressure Drop across Production System Inflow Performance Relationship Single Phase Inflow Performance Two Phase Inflow Performance Relationship Construction of IPR using Test Points Future inflow performance relationship for an oil well Tubing Performance Relationship Behaviour of Produced GOR Statement of Problem Objectives Methodology CHAPTER LITERATURE REVIEW Overview of System Analysis Approach Applications of System Analysis Approach iii

5 2.3 Optimization Approach CHAPTER METHODOLOGY Prediction of produced GOR Tarner s method Tracy s Method Muskat Method Future inflow performance relationship (IPR) for an oil well Construction of TPR curves CHAPTER RESULTS AND DISCUSSION Results Discussion Behaviour of Tubing curves at LGOR Behaviour of Tubing curves at HGOR Production profile of the various tubing sizes Effect of water cut in HGOR condition CHAPTER CONCLUSION AND RECOMMENDATION CONCLUSION RECOMMENDATION APPENDIX A APPENDIX B NOMENCLATURE REFERENCES iv

6 LIST OF FIGURES Page Figure 1.1 Pressure Losses in a Simple Production System Figure 2.1 Node flow rate and pressure Figure 4.1 Variation of GOR with Pressure using Tracy, Tarner and Muskat Methods Figure 4.2 GLR vrs GOR at varying water cut ratios. (Tracy s method) Figure 4.3 GLR vrs GOR at varying water cut ratios. (Tarner s Method) Figure 4.4 GLR vrs GOR at varying water cut ratios. (Muskat s Method) Figure 4.5 Variation of GOR with reservoir pressure Figure 4.6 Future Inflow Performance Relationships Curves Figure 4.7 Effect of tubing size on production rate at a constant GOR (840 scf/stb) Figure 4.8 Effect of tubing size on production rate at a constant GOR (1052 scf/stb) Figure 4.9 Effect of tubing size on production rate at a constant GOR (1453 scf/stb) Figure 4.10 Effect of tubing size on production rate at a constant GOR (2610 scf/stb) Figure 4.11 Effect of tubing size on production rate at a constant GOR (3444 scf/stb) Figure 4.12 Effect of tubing size on production rate at a constant GOR (5653 scf/stb) Figure 4.13 Production profile for 2 3/8-in tubing size Figure 4.14 Production profile for 2 7/8-in tubing size Figure 4.15 Production profile for 3 1/2-in tubing size Figure 4.16 Production profile for 4-in tubing size Figure 4.17 Effect of water cut on flowrate at a GOR of 2610 scf/stb Figure 4.18 Effect of water cut on flowrate at a GOR of 3444 scf/stb Figure 4.19 Effect of water cut on flowrate at a GOR of 5635 scf/stb Figure A.1 Log-log graph of K ro vrs S g Figure A.2 Log-Log graph of K rg vrs S g Figure B.2 Variation of pressure and instantaneous GOR calculated by Tarner smethod Figure B.4 Variation of pressure and instantaneous GOR calculated by Muskat method v

7 LIST OF TABLES Page Table 4.2a Available PVT Data for predicting oil reservoir performance Table 4.2b Data generated from PVT data in table 4.2a Table 4.2c Continuation of Data generated from PVT data in table 4.2b Table 4.3a Operating point for various tubing diameters at a GOR of 840 scf/stb Table 4.3b Operating point for various tubing diameters at a GOR of 1052 scf/stb Table 4.3c Operating point for various tubing diameters at a GOR of 1453 scf/stb Table 4.3d Operating point for various tubing diameters at a GOR of 2610 scf/stb Table 4.3f Operating point for various tubing diameters at a GOR of 5635 scf/stb Table 4.4a Variation in production rate and pressure with GOR range of scf/stb Table 4.4b Variation in production rate and Pressure with GOR range of scf/stb Table 4.4c Variation in production rate and Pressure with GOR range of scf/stb Table 4.4d Variation in production rate and pressure with GOR range of scf/stb Table B.1 Data generated from PVT data in table 4.2a using Tarner method Table B.3a Data generated from PVT data in table 4.2a using Muskat method Table B.3b Continuation of data generated from PVT data in table B.3a vi

8 CHAPTER 1 INTRODUCTION Production optimization identifies the opportunities to increase production and reduce operating costs. The overall goal is to achieve the optimum profitability from the well. To achieve and maintain this, it is essential to evaluate and monitor different sections of the production system including, the wellbore sandface, reservoir, produced fluids, production equipment on surface and downhole. Several methods are being used for production optimization. The most common and widely used method is the system analysis approach commonly known as nodal analysis. Optimization of the wellbore is considered mainly during well completion stages. Tubing joints vary in length from 18 to 35 feet although the average tubing joint is approximately 30 feet. Tubing is available in a range of outer diameter sizes. The most common sizes are 2 3/8-in, 2 7/8-in, 3 1/2-in and 4 1/2-in. The API defines tubing as pipe from 1-in to 4 1/2-in OD. Larger diameter tubulars (4 1/2-in to 20-in) are being termed casing. (Schlumberger, 2001) The flow rate per well is the key parameter. It governs the number of wells that need to be drilled to achieve the optimum economic output of the field. The first parameter that needs to be considered in the tubing string selection is the nominal tubing diameter. The grades of steel and nominal weight are chosen based on the stress the tubing will have to withstand during production. Thirdly, depending on the how corrosive the existing and future effluents, the type of connection and the metallurgy are selected. In fact the different stages mentioned above overlap and sometimes make the choice of tubing a difficult job. In the determination of the nominal pipe diameter, the nominal diameter through the weight governs the inside through diameter of the pipe. The flows that can pass through it depend on the acceptable pressure losses but are also limited by two parameters: the maximum flow rate corresponding to the erosion velocity and the minimum flow rate necessary to achieve lifting of water or condensate. Tubings with diameter less than 2 7/8-in are mostly reserved for operations on well using concentric pipe and are termed macronic string. Note also that the space required by couplings of the tubing limits the nominal tubing diameter that can be run into the production casing. (Perrin, et al., 1999) 1

9 1.1 Vertical Lift Problems relating to tubing In lieu of the usefulness of tubing strings in oil and gas production, it can have some limitations. Tubing wear occurs most often in pumping wells. It depends little upon whether the hole is vertical or slanting, but it is much worse in dog-legged holes regardless of the deviation. It may either be external or internal. If external, it is usually the couplings which are affected and the cause is the rubbing against the inside of the casing in phase with the reversing strokes of the sucker rods. If the wear is internal, it is caused by the sucker rods. There can be leakage from the inside to the outside or vice versa. This can be attributed to the API thread shape used (the V- shaped or round thread shape.) The tubing string can be flattened from wall to wall by either having a higher hydrostatic pressure or as a result of diastrophic shifting of formation caused by an earthquake. Since some 90 percent of all oil-well tubing is upset design, practically all failures are in the body of the pipe. However, any tension failures are rare because tubing is almost always run inside of casing and except for occasional trouble of unseating packers; it seldom becomes stuck and therefore needs not be pulled on. As with upset casing, upset tubing will stretch before failing. The tubing will burst when the pressure inside the tubing string is higher than the pressure in that annulus. This tubing trouble is commonly seen in high pressure wells and can be exceeding serious. (Hexter, 1955) 2

10 1.2 Pressure Drop across Production System P wh 4 Gas Sales Line P sep STOCK TANK ΔP T P wf 2 P wfs 1 Figure 1.1 Pressure Losses in a Simple Production System. 3

11 Integrating the production system component helps to design a well completion or predict the production ratio properly. Since the tubing section in Figure 1.1 contributes to about 80% of the total pressure drop in the production system, much research should be carried out in that area in order to reduce the pressure drop. The pressure drops in the tubing section are mainly frictional pressure drop and hydrostatic pressure drop. The last pressure drop which is due to acceleration is usually neglected because it is negligible. The general pressure gradient equation for a vertical well is: (1.1) Equation (1.1) can be written as the composite of the three component as (1.2) Many correlations have been developed in the last 30 and 40 years for predicting two-phase flowing pressure gradient in producing wells. Due to the limitations and the availability of some for these correlations, Beggs and Brill was used for prediction in this study. (Beggs, 2003) The optimization process requires the knowledge of inflow performance relationship, the tubing performance relationship and the behaviour of the produced gas-oil-ratio. 1.3 Inflow Performance Relationship The inflow performance relationship of a well is a relationship between its producing bottomhole pressure and it corresponding production rates under a given reservoir condition. The preparations of inflow performance relationship curves for oil and gas wells are extremely important in production system analysis. Unless some idea of the productive capacity of a well can be established the design and optimization of the piping system of the well becomes difficult. 4

12 1.3.1 Single Phase Inflow Performance In a single phase liquid flow, the pressure is above the bubble point pressure. The inflow performance relationship is usually depicted by a straight line. The IPR equation for this phase is given as: (Clegg, 2007) (1.3) Two Phase Inflow Performance Relationship Solution gas escapes from the oil and becomes free gas when the reservoir pressure falls below the bubble point pressure. During this state of pressure decline, oil and gas (two phase flow) exists in the whole reservoir. The presence of free gas leads to reduced relative permeability and increased oil viscosity. The synergies of these two effects result in lower oil production rates. This makes the IPR curve deviate from linear trend below the bubble point pressure. The two main widely used empirical correlations for modeling IPR of two phase reservoir are; Vogel (1968) equation. (1.4) The can be theoretically estimated based on the reservoir pressure and productivity index above the bubble point pressure. (BOYUN, et al., 2007) The pseudo-steady state flow follows that (1.5) Fetkovich equation is written as (1.6) 5

13 Where n is an empirical constant related to Construction of IPR using Test Points Due the unavailability of reservoir parameters for the determining productivity index in the IPR model, test points are frequently used for constructing IPR curves. Constructing IPR curves using test points involves back calculation of the constant in the IPR model for single phase (under-saturated oil) reservoir. The model constant can be determined by using equation (1.3) Where is the tested production rate at tested flowing bottomhole pressure For a partial two-phase reservoir, the model constant in the generalized Vogel equation (equation 1.4) must be determined on the range of tested flowing bottomhole pressure. If the range of tested flowing bottomhole pressure is greater than bubble point pressure, the model constant should be determined by equation (1.3). (Boyun, 2007) If the tested flowing bottomhole pressure is less than bubble point pressure, the model constant J* should be determined using (1.7) 6

14 1.3.4 Future inflow performance relationship for an oil well For saturated conditions many approximate methods to simulate the effects of depletion on productivity index for saturated conditions. Usually those methods provide an equation relating changes in the productivity index J* as a function of reservoir average pressure. In essence the methods for future reservoir prediction express changes in J* as a function of changes in average reservoir pressure. In this study a combination of Fetkovich and Vogel equations were used to predict the future IPRs. (Prado, 2009) Fetkovich expressed changes in productivity index as a function of changes in average reservoir pressure as; (1.8) Fetkovich also expressed Absolute Open Flow (AOF) as a function of the average reservoir pressure. (1.9) For under-saturated conditions, when the bottom hole flowing pressure is higher than the bubble point pressure, the flow of fluids in the reservoir is single phase and the linear IPR is valid. (Prado, 2009) When the bottom hole flowing pressure is below the bubble point pressure, a modified parabolic equation is used for the IPR. (1.10) (1.11) 7

15 (1.12) Productivity index for the saturated part of the IPR is defined as: (1.13) (1.14) (1.15) 1.4 Tubing Performance Relationship A tubing performance may be defined as the behaviour of a well in giving up the reservoir fluids to the surface. The performance is commonly showed as a plot of flowrate versus bottomhole flowing pressure. This plot is called the tubing performance relationship (TPR). For a specified wellhead pressure, the TPR curves vary with diameter of the tubing. Also, for a given tubing size, the curves vary with wellhead pressure. For single-phase liquid flow, pressure loss in tubing can be determined using a simple fluid flow equation for vertical pipe, or using some graphical pressure loss correlations where available with GLR = 0. Tubing performance curves are used to determine the producing capacity of a well. By plotting IPR and TPR on the same graph paper, a stabilized maximum production rate of the well can be estimated. (Lyon, 2010) 1.5 Behaviour of Produced GOR Increasing GOR lightens the mixture density and thereby reduces the pressure loss due to hydrostatic forces. Larger gas quantities usually result in larger pressure losses due to friction. 8

16 The GOR is considered critical when the producing GOR is equal to or greater than three times the solution GOR (R si ), that is (GOR 3R si ) for producing oil well that is not on gas lift. (Slider, 1983) The relationship between GLR and GOR can be expressed as (1.16) The produced GOR is constant above the saturation pressure. However, once the gas saturation has reached a point that the free gas in the reservoir begins to flow, the behaviour of the gas-oil - ratio becomes more complicated. The produced gas-oil-ratio, R at any particular time is the ratio of the standard cubic feet of gas being produced at any time to stock-tank barrels of oil being produced at that same instant. (Slider, 1983) (1.17) The term can be expanded using the radial flow equation as: (1.18) Writing and in terms of the above equation applied at the wellbore with the rates corrected from reservoir volumes to scf and stb, respectively, yields an expression for reservoir flowing GOR and the produced GOR: (1.19) 9

17 (1.20) (1.21) The ratio of the effective permeabilities in the above equation is the same as the ratio of the relative permeabilities which is a function of the liquid saturation. In order to determine the relative permeability ratio and the produced gas oil ratio, it is necessary to evaluate the oil saturation corresponding to any cumulative oil production. (Slider, 1983) The oil saturation is the remaining reservoir barrels of oil in the reservoir,, divided by the reservoir pore volume in barrels. The pore volume can be determined from the initial oil saturation, and the original reservoir barrels of oil in the reservoir,. Thus the material balance expression for the oil saturation is written as: (1.22) 1.6 Statement of Problem The proper selection, design, and installation of tubing string are critical parts of any well completion. Tubing strings must be sized correctly to enable the fluids to flow efficiently or to permit installation of effective artificial lift equipment. The optimum tubing size is selected to obtain the desired production rates at the lowest capital and operating costs. This usually means at the maximum initial flow rate and maintaining it as long as possible. Whatever the case, the selection process inevitably involves analysis of the gross fluid deliverability and flow stability under changing reservoir conditions to confirm that the production forecast can be met. A tubing string that is too small causes large friction losses and limits production. It also may severely restrict the type and size of artificial lift equipment. A tubing string that is too large may 10

18 cause heading and unstable flow, which results in loading up of the well and can complicate workover operations. As previously mentioned, the changing conditions over the life of the well must be considered when selecting tubing size. These changes are normally declining reservoir pressure, increasing water cut and Gas Oil Ratio which will reduce flow rates. Water production is rarely observed in the early and mid-stages of production. However GOR production is likely to occur during the early stage as well as throughout the life of the well. High Gas Oil Ratio (HGOR) is a situation where the produced GOR is equal to or three times higher than the initial GOR. When this occurs it will lead to unstable flow and thus hinder production forecast. This trend is downwards towards cessation of flow and, obviously the tubing selected for the start of production will not be the optimum size after some period of time. 1.7 Objectives 1. To examine the effect of Low and High GOR on tubing performance. 2. To identify the critical points beyond which production begins to decline. 3. To observe the effect of water production at HGOR condition on production rate. 1.8 Methodology 1. Generation of GOR profile with respect to decreasing reservoir pressure. 2. Sensitivity Analysis (based on the GOR profile). 3. Determination of critical point of GOR. 4. Analysis of the effect of water production at HGOR condition on oil flowrate. 11

19 2.1 Overview of System Analysis Approach CHAPTER 2 LITERATURE REVIEW Systems analysis, which has been applied to many types of systems of interacting components, consists of selecting a point or node within the producing system (well and surface facilities). Equations for the relationship between flow rate and pressure drop are then developed for the well components both upstream of the node (inflow) and downstream (outflow). The flow rate and pressure at the node can be calculated since flow into the node equals flow out of the node and only one pressure can exist at the node. Furthermore, at any time, the pressures at the end points of the system (separator and reservoir pressure) are both fixed. Thus: P R - (Pressure loss upstream components) = P node (2.1) P sep + (Pressure loss downstream components) = P node (2.2) Figure 2.1 Node flow rate and pressure 12

20 Typical results of such an analysis are shown in Figure 2.1 where the pressure-rate relationship has been plotted for both the inflow (Equation 2.1) and outflow (Equation 2.2) at the node. The intersection of these two lines is the (normally unique) operating point. This defines the pressure and rate at the node. This approach forms the basis of all hand and computerized flow calculation procedures. It is frequently referred to as Nodal analysis. 2.2 Applications of System Analysis Approach The use of systems analysis to design a hydrocarbon production system was first suggested by Gilbert (1954). Gilbert performed a sensitivity analysis to determine an approximate solution for natural flow and gas-lift problems for 1.9-in, 2 3/8-in, in and 3 1/2-in API tubing sizes and crude oils with API gravity ranging from 25 to 40 API. He also explains the hydraulics of natural flow as well as summarizing the methods for estimating individual well capabilities using the same set of API tubing sizes. The author has prepared a very useful tool for the solution of problems relative to flow of oil, gas, and water in a tubing string. Brown and Lea run a production optimization using a computerized well model. This computerized well model has contributed to improving completion techniques, for better efficiency and higher production with many wells. The optimization was carried out for gravel packed well as well as perforated wells. Tubings were evaluated for a well to gravel packed. The IPR curve was prepared using Darcy s law including the additional turbulence pressure drops. The Gulf Coast well was considered for this experiment. Tubing sizes of 2 7/8-in 3 1/2-in and 4 1/2-in are evaluated at the wellhead pressure of 1200 psi needed to flow gas into the sales lines. From the analysis 4 ½-in tubing is selected. For the perforated well a sample oil well with low GOR, a low bubblepoint pressure, and assumed single-phase liquid flow across the completion was analyzed. The reason for this selection is that current technology has offered solutions only for single-phase flow across such completions. When two-phase flow occurs across a gravel-packed or a standard perforated well, relative permeability effects must be considered. The IPR curve was prepared with Darcy s law, 13

21 assuming no pressure drop across the completion. Tubing performance curve was plotted for 2 3/8-in, 2 7/8-in and 3 1/2-in- -in tubing. Assuming 3 1/2-in-in tubing is selected, transfer it pressure drop curve. Using the appropriated equations from Mcleod and as discussed by Brown et al., the pressure drops across the available completions were determined. A final plot is constructed to show the importance of perforating underbalanced. Rafiqul Awal et al develop a new nodal analysis technique which helps improve well completion of matured oil field. They proposed the use of a simple, tapered tubing string completion (using larger internal diameter ID tubing pipes in the upper sections) that can be customized for specific reservoirs. They employed nodal analysis technique to develop an equivalent tubing diameter (ETD) concept. The ETD allow for comparing the well performance for single ID tubing. The procedure also seeks an optimum length for the larger tubing ID in the upper section. This method had limitations as it was suitable for wells with moderate to high open flow potential. It is suited for low GOR wells with high future water-cut. The technique was to reduce or eliminate the high capital cost of investing into waterflooding or any other Enhanced oil recovery method. The experiment was carried out by firstly using a mono tubing completion using five tubing ID sizes: in, in, in, in and in. The well performance graphs produced showed that for water-cut ranging from 50% to 60%, the stabilized gross liquid rate increase with tubing size until in. The reserve at in indicating the optimum tubing diameter lies between the in and in Next, we show the nodal analysis results for the Duplex Tapered Internal Diameter Tubing Completion TIDC realizations. The TIDC realizations shown were very simple, i.e., the depth intervals for various tubing sizes in a TIDC completion are equal. The result showed that the Duplex TIDC gives significantly higher gross liquid rates at all three water-cut values. The optimization process was carried out by choosing several values for length of the upper tubing section, and comparing the stabilized flow rates. It reveals the optimum length of the upper section (larger ID, in.) to be 3,600-ft, which much shorter than the smaller ID (3.476-in.), lower section: (9,990 3,600) ft = 6,390-ft. In the foregoing duplex TIDC optimized solution, the economic gains are significant, given the high oil price. The duplex TIDC gives increased gross fluid rates as follows: 14

22 10 to 15% compared to the in. mono tubing completion, and 10 to 30% compared to the in. mono tubing completion, over the water-cut range of 50 to 70% 2.3 Optimization Approach This work looks closely at the application of nodal analysis to oil wells with high GOR. Analysis of the behaviour of GOR produced on production rate is coupled with variation of water-cut at HGOR conditions. 15

23 CHAPTER 3 METHODOLOGY 3.1 Prediction of produced GOR Planning the development of a reservoir with respect to sizing equipment and planning for artificial lift as well as evaluating the project form an economics point of view, requires the ability to predict reservoir performance in the future. The reservoir PVT data must be available in order to predict the primary recovery performance of a depletion-drive reservoir in terms of Np and Gp. These data are: initial oil-in-place, hydrocarbon PVT, initial fluid saturation, and relative permeability. All the methods used to predict the future performance of a reservoir are based on combining the appropriate material balance equation (MBE), with instantaneous GOR using a proper saturation equation. However the prediction is narrowed only to the instantaneous GOR. The calculations are repeated at a series of assumed reservoir pressure drops. There are several techniques that were specifically developed to predict the performance of the solution gas drive reservoir. These methods include Tarner s method, Tracy s method and Muskat method, Tarner s method Tarner (1944) pointed out that the N p1 and G p1 are set equal to zero at the initial reservoir pressure that is at bubble point pressure. He computed based on the assumed using equation (3.1) (3.1) For each of N pn assumed, a corresponding S o was determined using equation (2.7). From the S o determined, calculate S g using equation (3.2) and using the field data S g versus k g /k o in appendix A determine k g /k o (3.2) 16

24 Calculate the instantaneous Gas Oil ration (R n ) using equation (2.6) Checking the validity of the assumed Np necessitates the need to calculate the Gp again using equation. (3.3). if the new calculated G p agrees with the previous G p then the assumed N p is correct. This sequence is repeated for the subsequent pressures. (3.3) If there are difficulties in the guessing of the cumulative oil production equation (3.4) can be used. (3.4) Tracy s Method Tracy (1955) suggests that the general material balance equation can be rearranged and expressed in terms of two functions of PVT variables for depletion drive reservoir without water influx. Following equation is based on an initial oil in place of 1 STB (3.5) Where (3.6) (3.7) The following Procedure was adopted for the prediction 1. Select an average reservoir pressure 2. Calculate values of the PVT functions 3. Estimate the GOR at assumed reservoir pressure from PVT data 17

25 4. Calculate the average instantaneous GOR using equation (3.8) (3.8) 5. Calculate the incremental oil production from equation 3.9 (3.9) 6. Calculate the cumulative oil production using equation (3.10) (3.10) 7. Calculate the oil and gas saturation at selected average reservoir pressure 8. Obtain relative permeability ratio K rg /k ro at S g 9. Calculate the Instantaneous GOR from equation (2.6) 10. Compare the estimated GOR in step (3) with the calculated GOR in step (10). If the values are within acceptable tolerance proceed to next step. If not within the tolerance set the estimated GOR equal to the calculated GOR and repeat the calculation from step (2). 11. Calculate the cumulative gas production (3.11) 12. Since results of the calculations are based on 1 STB of oil initially in place, a final check on the accuracy of the prediction should be made on the MBE and repeat the calculation from step 1 = 1±Tolerance (3.12) 18

26 3.1.3 Muskat Method Muskat (1946) expressed the material balance equation for a depletion-drive reservoir in following differential form: (3.13) Craft, Hawkins, and Terry (1991) suggested the calculations can be greatly facilitated by computing and preparing in advance in graphical form the following pressure dependent groups: (3.14) (3.15) (3.16) Introducing the above pressure dependent terms into Equation (3.14) gives (3.17) 19

27 Craft et al, 1991 proposed the following procedure for solving Muskat s equation for a given pressure drop. The following procedure was adopted 1. Prepare a plot of k rg /k ro versus gas saturation 2. Plot R s, B g and (1/B g ) versus pressure and determine the slope of each plot at selected pressures, that is db o /dp, dr s /dp and d(1/b g )/dp 3. Calculate the pressure dependent terms X(p), Y(p) and Z(p) that correspond to the selected pressures in step Plot the pressure dependent terms as a function of pressure. 5. Graphically determine the values of X(p), Y(p) and Z(p) that corresponds to the pressure p. 6. Solve equation (3.17) for (dso/dp) by using the oil saturation S o * at the beginning of the pressure drop interval p* 7. Determine the oil saturations So at the average reservoir pressure using equation (3.18) (3.18) 8. Using the So from Step 7 and the pressure p, recalculate (ds o /dp) from equation Calculate the average value for (ds o /dp) from the two values obtained in step 6 and 8 or; (3.19) 10. Using solve for oil saturation S o from (3.20) This value of S o becomes for the next pressure drop interval. 20

28 11. Calculate gas saturation Sg by (3.21) 12. From equation (2.7), solve for the cumulative oil production (3.22) 13. Calculate the cumulative gas production G p using equation (3.22) and repeat steps 5 through 13 for all pressure drops. (3.23) These prediction methods were compared and series of graphs were constructed to select the best method. A plot of GLR versus GOR was constructed using various water cut ratios (15%, 20 % and 25%). 3.2 Future inflow performance relationship (IPR) for an oil well Several correlations have been developed for predicting future inflow performance relationships curves (IPRs). In this study a combination of Fetkovich and Vogel Equation was used to predict the future IPRs. The following steps were used to construct the IPRs. 1. Using Beggs and Brill (1978 ), estimate the bubble point pressure, P b for the current GLR 21

29 2. Calculate and it corresponding using the equations (3.24) and (3.25) respectively at the average reservoir pressure. (3.24) (3.25) The q b below the bubble point pressure and at the bubble point pressure is zero. Above the bubble point pressure, is determined by using equation (3.24). Below the bubble point pressure the is based on previous and pressure and determined by using equation (3.25) 3. Calculate for the average reservoir pressure (3.26) 4. Calculate for the productivity index J* and for the bubble point pressure P b (3.27) 5. Generate a pressure profile below the bubble point pressure and calculate the corresponding and J* using Fetkovich correlations. 6. Plug in the first average reservoir pressure and it corresponding in the IPR program.xls to generate the IPR. 7. Repeat steps 6 and 7 for all the generated in 5 to generate their IPR s. 22

30 3.3 Construction of TPR curves Using the Beggs and brill spreadsheet, the generated flowrates and it corresponding pressures were used to construct the outflow performance relationship (OPR) or TPR curve. To achieve that, a range of tubing sizes (2 3/8-in, 2 7/8-in, 3 1/2-in and 4 -in) were selected. The tubing diameter, estimated GOR, depth of the well, wellhead pressure, reservoir pressure and fluid properties were kept constant while changing the oil flowrate. The watercut was assumed to be zero in the first instance and later varied with equal interval. For each flowrate used a pressure is recorded at the node. This method was used to construct TPR curves for all the tubing string sizes considered in this study. 23

31 CHAPTER 4 RESULTS AND DISCUSSION In this chapter the nodal analysis described in chapter two is applied for various instantaneous GORs and water cuts. The results obtained from the sensitivity analysis are presented in this chapter. 4.1 Results Tables 4.4a to 4.4e show the variation in oil production rate as well as pressure for a particular range of GOR. The red coloured numbers in Tables 4.3a to 4.3f signify an increase in either the production rate or bottomhole flowing pressure. The blue coloured numbers in Tables 4.3a to 4.3f signify a decrease in either the production rate or bottomhole flowing pressure. Tables 4.3a to 4.3f show the operating points of the various tubing sizes at specific reservoir pressure and GOR. 24

32 GOR (SCF/STB A comparison of GOR estimated by the three predictive methods as described in chapter 3 is presented in Figure Tracey Tarner Muskat Pressure, Psi Figure 4.1 Variation of GOR with Pressure using Tracy, Tarner and Muskat Methods. 25

33 GLR (SCF/STB) GLR (SCF/STB) Tracy wc (15%) wc (20%) 4000 wc (25%) Tracy 15% 20% GOR (SCF/STB) 25 Figure 4.2 GLR vrs GOR at varying water cut ratios. (Tracy s method) Tarner wc (15%) wc (20%) 4000 wc (25%) Tarner 15% 20% GOR (SCF/STB) Figure 4.3 GLR vrs GOR at varying water cut ratios. (Tarner s Method) 26

34 GLR (SCF/STB) Muskat wc (15%) wc (20%) wc (25%) Muskat 15% 20% 25% GOR (SCF/STB) Figure 4.4 GLR vrs GOR at varying water cut ratios. (Muskat s Method) Table 4.1 Estimated GLR at varying water cut with all the prediction methods Tracy Tarner Muskat Calculated Difference wc (%) GOR (scf/stb) GLR (scf/stb) 25% % % % % % From Table 4.1 all the prediction methods yielded approximately the same GLR at a specific GOR and water cut. The results presuppose that either of the methods can be used to predict the instantaneous gas oil ratio for the oil well with much accuracy. Tracy method was selected due to the fact, the error margin between the estimated and calculated GOR was very small and a zero 27

35 tolerance was observed for each pressure drop. The only exception is that Muskat method predicted a much higher GOR of 6304 scf/stb as opposed to the 5800 and 5635 scf/stb of Tarner and Tracy methods respectively. Following Tracy s steps in Chapter three for prediction of produced GOR, the GOR was estimated. Table 4.2b shows the generated data based on input PVT data in Table 4.2a. A plot of the produced or instantaneous GOR versus pressure is also showed in Figure 4.3 The following data applies to a solution gas drive reservoir Initial oil in place is 3.7 MMSTB Connate Water Saturation is 35% Oil Saturation is 0.65 Bubble Point Pressure is 2500 psi Abandonment Pressure is 700 psi Table 4.2a Available PVT Data for predicting oil reservoir performance P B o B g R s U o /U g psi bbl/stb bbl/scf scf/bbl

36 Table 4.2b Data generated from PVT data in table 4.2a P Psi Фo Фg Rav ΔNp Np ΔGp

37 Table 4.2c Continuation of Data generated from PVT data in table 4.2b Gp So Sg kro krg krg/kro GOR (Scf/stb) 840 Tolerance E

38 GOR SCF/STB The produced GOR using Tracy s method in Table 4.2c is plotted against it respective bottomhole pressure pressure in Figure Pressure Psi Figure 4.5 Variation of GOR with reservoir pressure The data generated for Muskat and Tarner methods using the same data in Table 4.1a are presented in appendix B. Plots of GOR versus pressure for both methods are also presented in appendix B. 31

39 Preesure, psi The Inflow performance relationship curves in Figure 4.4 were produced by following the procedure in section Production rate, stb/day IPR 1 IPR 2 IPR 3 IPR 4 IPR 5 IPR 6 IPR 7 IPR 8 IPR 9 IPR 10 IPR 11 Figure 4.6 Future Inflow Performance Relationships Curves 32

40 Bottomhole Flowing Pressure psi Figure 4.7 to 4.12 shows plots of IPR and TPR for various tubing sizes at specific GOR at a water cut of zero. GOR of 840 scf/stb " 2.875" 3.5" 4" IPR 1 IPR 2 IPR 3 IPR 4 IPR 5 IPR 6 IPR IPR Flowrate, stb/day IPR 9 IPR 10 IPR 11 Figure 4.7 Effect of tubing size on production rate at a constant GOR (840 scf/stb) Table 4.3a Operating point for various tubing diameters at a GOR of 840 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

41 Bottomhole Flowing Pressure,psi GOR at 1052 scf/stb " IPR 1 IPR " 3.5" 4" IPR 3 IPR 4 IPR 5 IPR 6 IPR IPR Flowrate,stb/day IPR 9 IPR 10 IPR 11 Figure 4.8 Effect of tubing size on production rate at a constant GOR (1052 scf/stb) Table 4.3b Operating point for various tubing diameters at a GOR of 1052 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

42 Bottomhole Flowing Pressure,psi GOR at 1453 scf/stb " IPR " IPR 2 IPR 3 IPR " IPR 5 IPR " IPR 7 IPR 8 IPR 9 0 IPR IPR 11 Flowrate,stb/day Figure 4.9 Effect of tubing size on production rate at a constant GOR (1453 scf/stb) Table 4.3c Operating point for various tubing diameters at a GOR of 1453 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

43 Bottomhole Flowing Pressure,psi GOR at 2610 scf/stb " 2.875" IPR 1 IPR 2 IPR " 4" IPR 4 IPR 5 IPR 6 IPR 7 IPR 8 0 IPR IPR 10 Flowrate, stb/day IPR 11 Figure 4.10 Effect of tubing size on production rate at a constant GOR (2610 scf/stb) Table 4.3d Operating point for various tubing diameters at a GOR of 2610 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

44 Bottomhole Flowing Pressure,psi GOR at 3444 scf/stb " 2.875" 3.5" 4" IPR 1 IPR 2 IPR 3 IPR 4 IPR 5 IPR 6 IPR Flowrate, stb/day IPR 8 IPR 9 IPR 10 IPR 11 Figure 4.11 Effect of tubing size on production rate at a constant GOR (3444 scf/stb) Table 4.3e Operating point for various tubing diameters at a GOR of 3444 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

45 Bottomhole Flowing Pressure,psi GOR at 2610 scf/stb " 2.875" IPR 1 IPR 2 IPR " 4" IPR 4 IPR 5 IPR 6 IPR 7 IPR 8 0 IPR IPR 10 Flowrate, stb/day IPR 11 Figure 4.12 Effect of tubing size on production rate at a constant GOR (5653 scf/stb) Table 4.3f Operating point for various tubing diameters at a GOR of 5635 scf/stb IPR/OD 2 3/8-in 2 7/8-in 3 1/2-in 4-in Q P Q P Q P Q P

46 Table 4.4a Variation in production rate and pressure with GOR range of scf/stb Production Increase % ( scf/stb) Pressure reduction psi OID/IPR ID/IPR / N/A 2 3/ N/A 2 7/ N/A 2 7/ N/A 3 1/ N/A 3 1/ N/A N/A N/A Table 4.4b Variation in production rate and Pressure with GOR range of scf/stb Production Increase % ( scf/stb) Pressure reduction psi OD/IPR ID/IPR / / / / / / N/A N/A Table 4.4c Variation in production rate and Pressure with GOR range of scf/stb Production decrease % ( scf/stb) Pressure increase psi ID/IPR ID/IPR / / / / / / N/A N/A Table 4.4d Variation in production rate and pressure with GOR range of scf/stb Production decrease % ( scf/stb) Pressure increase psi ID/IPR ID/IPR / N/A 2 3/ N/A 2 7/ / / /

47 Flowrate, stb/day Table 4.4e Variation in production rate and Pressure with GOR range of scf/stb Production decrease % ( scf/stb) Pressure increase psi ID/IPR ID/IPR / N/A 2 3/ N/A 2 7/ / / / /8" TUBING SIZE IPR1 IPR2 IPR GOR, scf/stb Figure 4.13 Production profile for 2 3/8-in tubing size 40

48 Flowrate, stb/day Flowrate, stb/day /8" TUBING SIZE GOR, scf/stb IPR1 IPR2 IPR5 Figure 4.14 Production profile for 2 7/8-in tubing size /2" TUBING SIZE IPR2 IPR5 IPR GOR, scf/stb Figure 4.15 Production profile for 3 1/2-in tubing size 41

49 Flowrate stb/day Flowrate, stb/day " TUBING SIZE IPR1 IPR2 IPR5 IPR GOR, scf/stb Figure 4.16 Production profile for 4-in tubing size scf/stb and IPR wc = 0 wc = 20% wc = 5% wc = 25% Tubing diameter, in Figure 4.17 Effect of water cut on flowrate at a GOR of 2610 scf/stb 42

50 Flowrate, stb/day Flowrate, stb/day scf/stb and IPR wc = 0 wc = 5% wc = 20% wc = 25% Tubing diameter, in Figure 4.18 Effect of water cut on flowrate at a GOR of 3444 scf/stb scf/stb and IPR Tubing diameter, in wc = 0 wc = 5% wc = 20% wc = 25% Figure 4.19 Effect of water cut on flowrate at a GOR of 5635 scf/stb 43

51 4.2 Discussion The two major components of production optimization (cost and reduction in pressure losses) can be positively influenced by acting on the analysis and recommendation of this study. In the analysis of the behaviour of the produced GOR on tubing performance, equal numbers of Low and High GOR values were selected Behaviour of Tubing curves at LGOR From Figure 4.5, tubing performance curves for (2 3/8-in, 2 7/8-in, and 3 1/2-in) tubing sizes intersect IPR1 and IPR4 curves making tubing selection feasible. The 4-in tubing performance curve intersect IPR1 to IPR3 curves. Moving closer to IPR5, the TPR curves for (2 3/8-in, 2 7/8- in, and 3.1/2-in) tubing sizes converge. The bigger tubing size (4-in) cannot be used to produce the well at lower IPR curves (IPR4 and IPR5). Considering the IPR1 curve, the 4-in tubing size can produce as high as 2100 stb/day at a bottomhole pressure of 1375 psi whereas the 2 3/8-in produces 1310 stb/day at a much higher bottomhole pressure of 2090psi. The bottomhole pressure tends to decrease with increasing tubing diameter. As GOR increases from 840 scf/stb to 1052 scf/stb in Figure 4.6, a shift in the tubing curves to the right is observed associated with an increase in oil production. From table 4.4a it can be seen that for all the tubing sizes used the more bottomhole pressure reduces the greater the percent increase in oil production rate. Considering the IPR1 curve, 2 7/8-in tubing size experienced the highest pressure drop associated with the highest percent increment in production. The same trend was observed when the GOR increased from 1052 to 1453 scf/stb. The only exception was 1.5% reduction in production rate at for 2.3/8-in tubing size when it intersect the IPR1 curve. Considering IPR2 and for the same range of GOR, 4-in has the highest production rate increase followed by 3 1/2-in with a corresponding pressure drop of 80psi and 130psi respectively. There was no pressure drop using 2 7/8-in yet there was a potential gain in production. 44

52 From table 4.4a to 4.4b, it was observed that as GOR increases, bottomhole pressure decreases associated with an increase in oil production rate. This phenomenon is mainly valid for low GOR cases Behaviour of Tubing curves at HGOR From Figure 4.8, a slight shift of the tubing curves to the left side is observed. This is associated with decrease oil production. At a GOR of 2610 scf/stb, production can be feasible and extended to the IPR5 curve. Moving from the region of LGOR to HGOR a decrease in production rate is observed due to the increase in bottomhole pressure. For a GOR range of 1453 to 2610 scf/stb and IPR5 curve, there is a percent decrease in production using 2 3/8-in, 2 7/8-in and 3 1/2-in tubing sizes. As the GOR increases further, the more the rise in bottomhole pressure causing much more decrease in production. For a GOR ranges of 2610 to 3444 scf/stb and 3444 to 5635 scf/stb, the 4-in tubing size can be still be used to produce a substantial quantity of the oil at lower reservoir pressures. From table 4.4d to 4.4e, it is observed that as GOR increases, bottomhole pressure increases with an associated decrease in oil production rate. This phenomenon is mainly valid for HGOR cases Production profile of the various tubing sizes The analysis of the two cases of GOR condition shows that there is a point for each tubing size where production rate begins to decline. Considering IPR1 and IPR 2 in Figure 4.13 there is a sharp gradual increase in production rate. The production rate tends to decrease when the GOR increases beyond 1500 scf/stb. The production rate beyond the critical point for IPR5 seems to be fairly constant. From Figure 4.14, the same trend in Figure 4.13 was observed for 2 7/8 tubing size. From Figures 4.15 and 4.16 the critical point for 3 1/2 and 4 tubing sizes varies for different IPR curves and the critical point is also not distinct. Production using 4 tubing size with the Lower IPR curves (IPR5 and IPR6) will be only possible beyond a GOR of 2600 scf/stb. 45