Pump Fillage Calculation (PFC) Algorithm for Well Control

Transcription

1 6 th Annual Sucker Rod Pumping Workshop Wyndham Hotel, Dallas, Texas September 14 17, 2010 Pump Fillage Calculation (PFC) Algorithm for Well Control Victoria Ehimeakhe, Ph.D. Weatherford

2 Introduction For many producing wells assisted by beam pumping, the rate at which the reservoir fluids are produced (pump displacement) can exceed the rate at which the formation is supplying fluids into the wellbore. This leads to what is commonly known as pump off or fluid pound. Fluid pound can cause rod compression / buckling, leading to rod and tubing damage. In order to maximize production and minimize costs, a well can be controlled using calculated pump fillage by slowing or stopping the well. Pump fillage is obtained from the downhole position and load data. Pump fillage can be an illusive value to find especially when dealing with gas compression, viscous fluids, deviated wells The pump fillage calculation (PFC) is a method comprised of four algorithms that use only downhole data to compute the pump fillage for a given pumping unit stroke Sucker Rod Pumping Workshop 2

3 The Pumping Cycle Top of stroke (TOS) corresponds to the end of the pumping unit upstroke. Bottom of stroke (BOS) corresponds to the end of the pumping unit downstroke. The transfer point corresponds to the point at which the TV opens on the downstroke Sucker Rod Pumping Workshop 3

4 Method of Positions Let p(t), t = 1,, N be the downhole position data comprised of N points. The transfer point (TP) is characterized by a plateau, i.e. a change in concavity. The top of stroke (TOS) is located by finding the critical point of the downhole position data, i.e. finding the point where the 1 st derivative of the downhole position data intersects the x- axis. The change in concavity is linked to the 2 nd derivative. If f (x)>0, the graph of f(x) will be concave up, while if f (x)<0, the graph of f(x) will be concave down. Therefore, finding the transfer point is the same as finding the maximum of p (t) in between the critical point and the absolute minimum. This means finding the point where the graph is concave up between the top of stroke and the part of the graph where the graph is concave down Sucker Rod Pumping Workshop 4

5 Method of Loads Let f(t), t = 1,,N be the downhole load data. The transfer point is characterized by a sharp drop in the load values. This sharp drop in load corresponds to the points at which the slope of the data is the most negative, i.e. the 1 st derivative of the downhole load is at its minimum. Therefore, locating the transfer point is equivalent to computing the 1 st derivative of the downhole load and finding its absolute minimum Sucker Rod Pumping Workshop 5

6 Method of Ordering The downhole load data is organized into top points and bottom points by taking the top eighth and bottom eighth section of the downhole card. The average middle value is calculated from the intersection of the card with the imaginary half line. The position value corresponding to these average values can be calculated by finding the position point nearest to the intersection of the horizontal average lines with the graph of the downhole card. The current pump fillage value is taken to be the combination of the ratios of the position corresponding to the average bottom value and the average middle value to the position corresponding to the average top value of TOS Sucker Rod Pumping Workshop 6

7 Pump Fillage Calculation (PFC) The pump fillage calculation (PFC) is composed of the three methods presented previously. Under certain operating conditions such as gas compression, viscous fluids, deviated wells and wells with a worn pump or tagging bottom, the pump fillage value for a given stroke might prove more difficult to compute. Under these conditions, the method of Positions, Loads and Ordering may output different results for the calculated pump fillage value. A fourth method is therefore needed to approximate the pump fillage range for a given downhole card Sucker Rod Pumping Workshop 7

8 Method of Multiple Pump Fillage (MPF) The load span of the downhole card is divided into M segments, yielding a set of M load values, L i, i = 1,,M. The position at each segment is calculated by finding the (position, load) pair closest to the intersection of the horizontal load segment with the downhole card. The pump fillage at each segment L i, is computed by taking the ratio of each of the corresponding position value to the top of stroke, yielding a set of M pump fillage values, Pf i, i = 1,,M : Pf i = position(l i ) / position(tos) Sucker Rod Pumping Workshop 8

9 Method of Multiple Pump Fillage (continued) A set of M pump fillage values Pf i, i = 1,,M are output from the above method. The values can be plotted. The MPF graph shows plateaus where the pump fillage is the same for several load segments. The range of the Pf i is 0 Pfi 100. This range is split into K increments. Sorting the Pf i into the K intervals by number of occurrences creates a probability density function, PDF. The maximum of the PDF represents the interval in which the pump fillage value is most likely to lie Sucker Rod Pumping Workshop 9

10 Overview of PFC algorithm 2010 Sucker Rod Pumping Workshop 10

11 Delta Program Historically, pump fillage has been calculated by various beam pumping analysis programs. LOWIS is Weatherford s artificial lift host software package. The beam analysis module in LOWIS is used to analyze rod pumped wells and determine pump fillage from the resulting downhole cards. The Delta program is a complete analysis program used in LOWIS, which contains a method for pump fillage approximation. The Delta program has been used in the industry since the 1960 s. In the following slides results from PFC are compared to the pump fillage values output by the Delta program Sucker Rod Pumping Workshop 11

12 Full Card Example 1: Delta pump fillage 96.45, PFC pump fillage 100, pump fillage interval [100, 101]. Description: Full pump fillage 2010 Sucker Rod Pumping Workshop 12

13 Full Card Example 2: Delta pump fillage 97, PFC pump fillage 100, pump fillage interval [100, 101]. Description: Full card tagging bottom 2010 Sucker Rod Pumping Workshop 13

14 Gas Compression Example 3: Delta pump fillage 16.06, PFC pump fillage 8.3, pump fillage interval [7,10 ]. Description: Pumped off well with gas compression 2010 Sucker Rod Pumping Workshop 14

15 Gas Compression Example 4: Delta pump fillage 100, PFC pump fillage 2.5, pump fillage interval [1,4 ]. Description: Pump barrel completely filled with gas Sucker Rod Pumping Workshop 15

16 Gas Compression Example 5: Delta pump fillage 94.59, PFC pump fillage 1.79, pump fillage interval [1,4 ]. Description: Pump barrel almost completely filled with gas Sucker Rod Pumping Workshop 16

17 Unusual Card Shape Example 6: Delta pump fillage 82.98, PFC pump fillage 100, pump fillage interval [100, 101]. Description: Unexplained card shape 2010 Sucker Rod Pumping Workshop 17

18 Tight Spot During Downstroke Example 7: Delta pump fillage 31.84, PFC pump fillage 97.61, pump fillage interval [97,100 ]. Description: Load loss on downstroke 2010 Sucker Rod Pumping Workshop 18

19 Pump Tagging Bottom Example 8: Delta pump fillage 16.03, PFC pump fillage 98.38, pump fillage interval [97, 100]. Description: Almost full pump - tagging bottom 2010 Sucker Rod Pumping Workshop 19

20 Statistics: 1000 wells 2010 Sucker Rod Pumping Workshop 20

21 Conclusions PFC is a robust algorithm capable of calculating reliable and accurate pump fillage values regardless of well conditions. The multi-method approach guarantees that each method is utilized according to its strength. Using PFC results in combination with a methodology to control the well from the pump fillage maximizes well production while minimizing the operating costs Sucker Rod Pumping Workshop 21

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