Production System Analysis

Size: px

Start display at page:

Download "Production System Analysis"

Dorthy Sullivan
5 years ago
Views:

1 Production System Analysis

2 Production System Analysis Nodal Analysis An analytical tool used in forecasting the performance of the various elements comprising the completion and production system. This concept is based on the a well having one flow rate implied by fixed end pressures.

3 Nodal Analysis This procedure consist of selecting a division point (node) in the well and dividing the system at this point. The locations of the most commonly used nods are shown:

4 Nodal Analysis Once a node is selected, i.e. bottom hole pressure, the pressure is calculated from both directions (upstream and downstream from the node). Inflow to the node: p p (upstream components) = r p node Outflow from the node: p + p (downstrea m components) = FWH p node

5 Nodal Analysis The pressure drop, Δp, in any component varies with flow rate, q. Therefore, a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements 1 and 2, given previously. The procedure is illustrated graphically in Fig. 1-3.

6 Determination of Flowing Capacity

7 Nodal Analysis Using a simple producing system and selecting the wellheadas the node Inflow to the node: p r p res p tbg = p wh Outflow from the node: p sep + p flowline = p wh

8 node

9 The effect of the flow capacity of changing the tubing size and the effect of a change in flowline size.

10 Nodal Analysis Frequently used is the procedure to select the node between the reservoir and the piping system. Inflow to the node: p r p res = p wh Outflow from the node: p sep + p flowline + p tbg = p wf

11 The effect of a change in tubing size on the total system producing capacity when p wf is the node pressure.

12 A case in which the well performance is controlled by the inflow is below. In this case, the excessive pressure drop could be caused by formation damage or inadequate perforations.

13 A qualitative example of selecting the optimum tubing size for a wellthat is producing both gas and liquids is shown below

14 Procedure for Apply Nodal Analysis 1. Determine which components in the system can be changed. Changes are limited in some cases by previous decisions. For example, once a certain hole size is drilled, the casing size and, therefore, the tubing size is limited. 2. Select one component to be optimized. 3. Select the node location that will best emphasize the effect of the change in the selected component. This is not critical because the same overall result will be predicted regardless of the node location.

15 Procedure for Apply Nodal Analysis 4. Develop expressions for the inflow and outflow. 5. Obtain required data to calculate pressure drop versus rate for all the components. This may require more data than is available, which may necessitate per- the analysis over possible ranges of conditions. 6. Determine the effect of changing the characteristics of the selected component by plotting inflow versus outflow and reading the intersection. 7. Repeat the procedure for each component that is to be optimized.

16 Reservoir Performance

17 WELL PERFORMANCE EQUATIONS To calculate the pressure drop occurring in a reservoir, an equation that expresses the energy or pressure losses due to viscous shear or friction forces as a function of velocity or flow rate is required. Although the form of the equation can be quite different for various types of fluids, the basic equation on which all of the various forms are based is Darcy's law.

18 Linear Flow (constant area flow) Oil p 1 p 2 = q o µ obol q 3 o koa A 13 2 B 2 o βρ L o Gas p 2 1 p 2 2 = q sc Zµ glt βztlγ L 2 g + q sc 2 kga A p 1 = upstream pressure, psia Z = gas deviation factor p 2 = downstream pressure, psia T = flowing temperature, o R μ o = oil viscosity, cp γ g = gas gravity (air=1) B o = oil formation volume factor, bbl/stb q sc = gas flow rate, scf/day L = Length of flow path, ft μ g = gas viscosity, cp K o = permeability of oil, md K g = permeability of gas, md = velocity coefficient, ft -1 A = area open to flow, ft 2 q o = oil flow rate, stb/day β

19 Radial Flow Oil q o = k µ B o o o ln( r h( e / p r e w p wf ) + S ) Gas q sc = µ ZT 6 k g h( p p e = pressure at r=r e, psia Z = gas deviation factor p wf = well flowing pressure, psia T = flowing temperature, o R μ o = oil viscosity, cp p R = avg. reservoir pressure, psia B o = oil formation volume factor, bbl/stb q sc = gas flow rate, scf/day k o = permeability of oil, md μ g = gas viscosity, cp r w = wellbore radius, ft K g = permeability of gas, md r e = well drainage area, ft h = reservoir thickness, ft q o = oil flow rate, stb/day q sc = gas flow rate, Mscfd S = skin factor g R ln(. 472r e / r p w wf ) )

20 Linear Flow Radial flow

21 Productivity Index (J) The relationship between well inflow rate and pressure drawdown has often been expressed in the form of a Productivity Index J, J = p R q o p wf q o = oil flow rate, stb/day p R = avg. reservoir pressure, psia p wf = well flowing pressure, psia

22 Permeability Alteration and Turbulence The magnitude of the pressure change due to the skin and turbulence, defined as: p skin = q µ B S A value for S (skin factor due to permeability change) can be obtained from analysis of various types of pressure transient tests. k o o h o o

23 Factors Affect Productivity Index Phase Behavior in Reservoirs Relative Permeability Behavior Oil Viscosity Behavior Oil Formation Volume Factor Behavior B o = Volume of oil plus its dissolved gas at p, T Volume of oil at stock tank conditions, psc, T sc

24 Phase Behavior Diagram

25 Relative Permeability Behavior

26 Oil Viscosity Behavior

27 Oil Formation Volume Factor Behavior

28 Factors Affecting Inflow Performance For oil reservoirs 1. Decrease in k ro as gas saturation increases. 2. Increase in μ o as pressure decreases and gas is evolved. 3. Shrinkage of the oil as gas is evolved when pressure on the oil decreases. 4. Formation damage or stimulation around the well bore 5. An increase in the turbulence as oil flow rate increases.

29 Drive Mechanisms The source of pressure energy to cause the oil and gas to flow into the well bore has a substantial effect on both the performance of the reservoir and the total production system

30 Dissolved Gas Drive A dissolved-gas-d rive reservoir is closed from any outside source of energy, such as water encroachment. Its pressure is initially above bubblepointpressure, and, therefore, no free gas exists. The only source of material to replace the produced fluids is the expansion of the fluids remaining in the reservoir.

31 Dissolved Gas Drive

32 Gas Cap Drive A dissolved-gas-d rive reservoir is closed from any outside source of energy, such as water encroachment. Its pressure is initially above bubblepointpressure, and, therefore, no free gas exists. The only source of material to replace the produced fluids is the expansion of the fluids remaining in the reservoir. Some small but usually negligible expansion of the connate water and rock may also occur.

33 Gas Cap Drive

34 Water Drive A dissolved-gas-d rive reservoir is closed from any outside source of energy, such as water encroachment. Its pressure is initially above bubblepointpressure, and, therefore, no free gas exists. The only source of material to replace the produced fluids is the expansion of the fluids remaining in the reservoir. Some small but usually negligible expansion of the connate water and rock may also occur.

35 Water Drive

36 Combination Drive In many cases, an oil reservoir will be both saturated and in contact with an aquifer. In this case, all three of the previously described mechanisms may be contributing to the reservoir drive. As oil is produced, both the gas cap and aquifer will expand and the gas/oil contact will drop as the oil/water contact rises, which can cause complex production problems.

37 Drawdown The difference between the average reservoir pressure and the flowing bottomhole pressure. The effects of drawdown on inflow performance differs for a well with zero skin factor. The effects of both positive and negative skin factors will then be discussed.

38 Positive Skin

39 Negative Skin

40 Effect of Depletion In any reservoir in which the average reservoir pressure is not maintained above the bubble point pressure, gas saturation will increase in the entire drainage volume of the wells. This will cause a decrease in the pressure function in the form of decreased k ro, which will cause an increase in the slope of the pressure profile and the IPR. Therefore to maintain a constant inflow rate to a well, it will be necessary to increase the drawdown as p R declines from depletion

41 Depletion on the Pressure Profile

42 Depletion on the IPR

43 Predicting Present Time IPR s Vogel Method Vogel developed and empirical equation for the case of a depletion drive reservoir, in which the reservoir pressure is everywhere below the bubble point pressure. He arrived at the the following relationship between dimensionless flow rate and pressure: 2 q q o o(max) = p p wf R 0.8 p p wf R

44 Vogel s Equation q q o o(max) = p p wf R 0.8 p p wf R 2 p wf = well flowing pressure, psia p R = avg. reservoir pressure, psia q o = oil flow rate, stb/day Note: q o(max) is a fictitious value of production representing a maximum drawdown, corresponding to p wf =0.

46 Constant Productivity Index The dimensionless IPR for a well with a constant productivity index can be calculated from: q q o o(max) = 1 p p p wf R

47 Vogel Method The tangent of the curve represents 1/J. Therefore, the Jis the negative derivative of q with respect to P. The negative sign is due to the fact that the slope of the curve is negative but the Jis a positive quantity. (At P wf =P r ) J q = 1.8 max P r Vogel s equation should approximate Darcy s equation at very low flow rates. = K µ o o H B o

48 Vogel Method One may want to predict a well s behavior at some future time when the reservoir pressures deplete. future o o o future r future B K P q J = = µ max 1.8 Simply solving for (q max ) future we obtain present o o o present r present B K P q J = = µ max 1.8 ( ) ( ) ( ) ( ) = present r future r present o o o future o o o present future P P k B B k q q µ µ max max

49 Predicting Future IPR s for Oil Wells As the pressure in an oil reservoir declines from depletion, the ability of the reservoir to transport oil will also decline. This is caused from the decrease in the pressure function as relative permeability to oil is decreased due to increasing gas saturation. Planning the development of a reservoir with respect to sizing equipment and planning for artificial lift, as well as evaluating the project from an economics standpoint, requires the ability to predict reservoir performance in the future.

50 Standing Method Standing published a procedure that can be used to predict the decline in the value of q o(max) as gas saturation in the reservoir increases from depletion. q = q wf 0. 8 o( F ) o(max) F p p RF p p wf RF 2

51 FetkovichMethod The method proposed by Fetkovichto construct future IPR's consists of adjusting the flow coefficient C for changes in ( ) 2 2 p p n for changes in f(p r ). He assumed that f(p r )was a linear function of p r and, therefore, the value of C can be adjusted as C =C F q o = C p R wf ( prf / prp )

52 FetkovichMethod A value of C p is obtained from present time production tests, that is, tests conducted when p R = p RP. Fetkovichassumed that the value of the exponent nwould not change. Future IPR's can thus be generated from q = o( F ) C p ( p RF / p RP )( p 2 RF / p 2 RP ) n

53 Well Completion Effects There are basically three types of completions that may be made on a well depending on the type of well, well depth, and type of reservoir or formation. Open Hole Completions Perforated Completions Perforated, Gravel Packed Completions

54 Open Hole Completions The casing is set at the top of the producing formation and the formation is not exposed to cement. Also, no perforations are required The only effect of the completion on inflow The only effect of the completion on inflow performance of an open hole completion will be caused by alteration of the reservoir permeability by damage or stimulation.

55 Perforated Completions The most widely used completion method is one in which the pipe is set through the formation, and cement is used to fill the annulus between the casing and the hole. This, of course, requires perforating the well to establish communication with the producing formation. This type of completion permits selection of the zones that are to be opened.

56 Perforation

57 Perforated, Gravel Packed Completions In some reservoirs, the lack of cementing material in the reservoir allows sand to be produced into the well. When completing wells in which the formation is incompetent or unconsolidated, a gravel pack completion scheme is frequently employed. In this type of completion, a perforated or slotted liner or a screen liner is set inside the casing opposite the producing formation.

58 Gravel-Pack

59 Well Flow Correlations One of the most important components in the total well system is the well tubing. As much as 80 percent of the total pressure loss can be consumed in lifting the fluids from the bottom of the hole to the surface. The flow may exist in tubing or in the annulus between the tubing and the casing. The wells may be vertical of can be drilled at large deviation angles, especially in the case of offshore wells or wells drilled in urban areas.

60 Well Flow Correlations Many correlations have been developed over the years to evaluate the pressure drop resulting from the multiphase flow of fluids in a vertical or deviated well.

61 Well Flow Correlations 1. Establish stable flow conditions at particular values of q L, q g, pipe diameter, pipe angle, etc. 2. In a test section of length ΔL, measure H and 2. In a test section of length ΔL, measure H L and Δp. Methods for measuring H L include nuclear densitometers, capacitance devices, quick closing valves, etc. Flow pattern may be observed if the test sectionis transparent.

62 Well Flow Correlations 3. Calculate mixture density and elevation component. ρ = ρ H + ρ (1 H ) s dp dl L L g ρ g sin Θ 4. Calculate and acceleration and friction component. dp p dp dp = dl L dl dl el el = s g c el L acc

63 Well Flow Correlations 5. Calculate a two phase friction factor 2gcd dp ftp = 2 ρvm dl f 6. Change test conditions and return to step 2.H L, f TP, and flow pattern should be obtained over a wide range of conditions. 7. Develop empirical correlations for H L, F TP and flow pattern as a function of variables that will be known for design cases. These variables include v sl, v sg, d, fluid properties, pipe angle, etc.

64 Choke Sizing

65 Choke Sizing for Liquid Flow Critical velocity is the velocity of sound in that medium. This velocity is a limiting factor, so the fluid cannot be accelerated to a large velocity. The critical of any fluid is given by: V = 68.1 ρc ρ= fluid density, lbm/ft 3 C = isothermal compressibility of the fluid, psi

66 Choke Sizing Single Phase Liquid Flow Calculating the pressure drop across a choke is relatively easy. However, flow through the choke is liquid and gas since tubing pressure is usually below the bubble point. If the exit velocity is below critical, the flow is: q = 22800Cd c P ρ d c = choke throat diameter, in ΔP = differential pressure across the choke, psi C is given from the Flow Coefficient Graph

67 Graph of Flow Coefficients for flow through chokes (Crane, 1957) h-valves-pipes-and-fittings Accessed Feb 24, 2010 Reynolds number is given by Re = 928ρVd µ

68 Choke Sizing In the case of gas exiting an open-ended flow line, the sonic velocity is given by: V g = 41.4 kzt γ g T = temperature, o R γ g = gas specific gravity relative to air Z = compressibility factor k = ratio of gas specific heat at constant volume to constant pressure (k=c p /c v ) or obtained from Specific Heat Ratios for Hydrocarbon Vapors Graph

69 Choke Sizing The gas flow rate at critical velocity is given by Q = g V g d 2 PT e e sc 2122TZP sc Q = Gas flow rate, MMSCFD T = Gas temperature, o R P = Pressure, pisa D = Pipe diameter, in V * g= Sonic velocity in gas at P and T, ft/s Z = Gas compressibility factor at P and T

70 Choke Sizing for Gas Flow Gas flow through a small diameter exit can be described by below. q 155.5C AP k + γ T k 1 d up 2/ k ( k 1)/ k = 2 g [ r r ] g C d = Choke discharge coefficient A = Choke throat area, in 2 T = Inlet temperature, o R P up = Upstream gas pressure, psia k = gas specific heat ratio, c p /c v r = P dn /P up if r o

71 Choke Sizing for Two Phase Flow Choked flow for a gas liquid mixture is difficult to mode, and only empirical correlations are available. Two presently available are the Gilbert and the Ros correlations, give as P up = Aq ( R ) L d C 64 P up = upstream pressure, psig (Gilbert), psia(ros) q L = liquid flow rate, bbl/day d 64 = choke diameter in 64ths Correlation A B C Gilbert Ross p B

72 Choke Sizing To ensure the flow is critical, the equation by Wallis can be used to calculate the critical velocity. 2 1/ ( ) 2 * *2 + + = L L L g g g g g L L V V V ρ λ ρ λ λ ρ λ ρ V* = critical velocity γ = in-situ volume fraction of each phase ρ = density of gas and liquid, lbm/ft 3

73 Flow in Pipes and Restrictions (vertical wells)

74 Two Phase Flow Variables Liquid Holdup-fraction of an element of pipe that is occupied by liquid at some instant. H L = volume of liquid in a pipe element volume of the pipe element Gas Holdup-relative in-situ volume of liquid and gas expressed in terms of the volume fraction. H g = 1-H L

75 Two Phase Flow Variables No-Slip Liquid Holdup-the ratio of the volume of liquid in a pipe element that would exist if the gas and liquid traveled at the same velocity (no slippage) divided by the volume of the pipe element.. γ L = q L ql +q g q L = sum of the in-situ oil and water q g = the in-situ gas flow rate

76 Two Phase Flow Variables No-Slip Gas-gas void fraction can be defined as γ g = 1 λ L = q L q g +q g q L = sum of the in-situ oil and water q g = the in-situ gas flow rate

77 Two Phase Flow Variables Density-The density of an oil/water mixture may be calculated from the oil and water densities and flow rates if no slippage between the oil and water phases is assumed. ρ = ρ f + ρ L o o w f w where f o = q o q + o q w and f w = 1-f o

78 Two Phase Flow Variables Velocity-the velocity that phase would exhibit if it flowed through the total cross sectional area of the pipe alone. v L = qg The actual area through which the gas flows is reduced by the presence of the liquid to AH g. Therefore, the actual gas velocity is calculated from: v g = q g AH g A

79 Two Phase Flow Patterns Whenever two fluids with different physical properties flow simultaneously in a pipe, there is a wide range of possible flow patterns. By flow pattern, reference is made to the distribution of each phase in the pipe relative to the other phase.

80 Two phase vertical flow patterns

81 93-96 Effects of Variables on Well Performance During the producing life of a well or field many conditions can change that will affect the well's flowing performance. Also, conditions can change from well to well in a field at a given time, and conditions can certainly vary among fields.

82 Effects of Variables on Well Performance Some of these variables that can change are 1. Liquid Flow Rate 2. Gas/Liquid Ratio 3. Water/Oil Ratio or Water Cut 4. Liquid Viscosity 5. Tubing Diameter and Slippage

83 Liquid Flow Rate The effect of increasing liquid rate will be an increase in both H L and fluid velocity. This will cause an increase in both the hydrostatic and friction. The effect may be seen graphically in Figure 3-22 that was constructed by choosing some general well conditions and holding everything constant except q L.

85 Gas/Liquid Ratio The GLR has more effect on two-phase flowing pressure gradients than any other variable. In a depletion-type field the gas/oil ratio will usually increase with time until late in the life of the reservoir. The GLR may decrease if water cut increases. The GLR has the most effect on the hydrostatic component of the pressure gradient equation because H L will decrease as GLR increases. However, the total flow rate will increase, and the friction loss depends on the flow rate squared.

87 Water/Oil Ratio or Water Cut The total pressure gradient in the well will increase as f w increases. This results from an increase in liquid density if the water is heavier than the oil and also from a decreasing GLR, since the free gas in the tubing comes primarily from the oil only. The effect may be expressed graphically in Figures 3-25 and 3-26.

88 Figure 3-25 shows only the effect of increased liquid density while the total effect is shown in Figure 3-26.

89 Liquid Viscosity The effects of liquid viscosity on pressure drop are very difficult to isolate. This results from the fact that the concept of a gas/liquid mixture viscosity has no physical meaning. The liquid viscosity will affect H L to some degree and will also increase the shearing stresses in the liquid and, therefore, the friction pressure drop. If an oil/water mixture is present, dispersions or emulsions may form and cause a very large increase in the pressure gradient. At the present time, there is no method to accurately predict the viscosity of an oil/water mixture, much less the viscosity of a gas/oil/water mixture.

90 Liquid Viscosity The combined effects of decreasing API gravity and increasing viscosity for a gas/oil mixture are shown qualitatively in Figure If water were present, the effects would probably be even more pronounced.

91 Tubing Diameter and Slippage The selection of the proper tubing size to install in a well is one of the most critical and the most neglected functions of a production engineer. In many cases the tubing size will be selected based on such criteria as what has been used in the past or what is available on the pipe rack. A total system analysis, which combines the reservoir and piping system performance, is required to select the proper tubing size, but the effects of tubing size on velocity and slippage will be discussed.

92 As the tubing size increases, the velocity of the mixture decreases and eventually the velocity will be too low to lift the liquids to the surface. The well will then begin to load up with liquids and may eventually die. The tubing size at which a well will begin to load or the maximum tubing size which will sustain flow can be determined from a plot such as Figure 3-29.

93 Tubing Diameter and Slippage The effect of declining production rate and, therefore, velocity for a particular tubing size can be shown qualitatively in Figure For a particular tubing size, well depth, wellhead pressure and as/liquid ratio, there will exist a minimum production rate that will keep the well unloaded. Figure 3-31 shows the effect of tubing diameter on the minimum rate. This type of information is valuable in determining at what rate a well will begin to load for various tubing sizes.

94 Use of Prepared Pressure Traverse Curves In some cases it is not feasible for the field engineer to conduct an involved computer study to calculate a traverse or to calculate the pressure drop in a tubing string for give field conditions. In some cases, it may be advantageous to construct a set of pressure traverse curves for hypothetical values of the variables such as q L,GLR, d, f w, etc. These curves can then be used to estimate the pressure drop that would occur in a well producing under similar conditions.

Reservoir Flow Properties Fundamentals COPYRIGHT. Introduction

Reservoir Flow Properties Fundamentals Why This Module is Important Introduction Fundamental understanding of the flow through rocks is extremely important to understand the behavior of the reservoir Permeability