pump fillage calculation (pfc) algorithm for well control files/2... · 6th annual sucker rod...

6th Annual Sucker Rod Pumping Workshop

Wyndham Hotel, Dallas, TexasSeptember 14 – 17, 2010

Pump Fillage Calculation (PFC) Algorithm for Well Control

Victoria Ehimeakhe, Ph.D.Weatherford

Sept. 14 - 17, 2010 2010 Sucker Rod Pumping Workshop 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.

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.


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 1st derivative of the downhole position data intersects the x-axis.

• The change in concavity is linked to the 2nd 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.


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 1st derivative of the downhole load is at its minimum.•Therefore, locating the transfer point is equivalent to computing the 1st derivative of the downhole load and finding its absolute minimum.

Method of Ordering

• 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.


•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.

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.


Method of Multiple Pump Fillage (MPF)

• The pump fillage at each segment Li, 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, Pfi, i = 1,…,M:

Pfi = position(Li) / position(TOS).


•The load span of the downhole card is divided into M segments, yielding a set of M load values, Li, 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.

Method of Multiple Pump Fillage (continued)

• A set of M pump fillage values Pfi, 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 Pfi is 0 ≤ Pfi ≤ 100.•This range is split into K increments.•Sorting the Pfi 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.

Overview of PFC algorithm


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.


Full Card

Example 1: Delta pump fillage ‘96.45’, PFC pump fillage ‘100’, pump fillage interval [100, 101].

Description: Full pump fillage


Full Card

Example 2: Delta pump fillage ’97’, PFC pump fillage ‘100’, pump fillage interval [100, 101].

Description: Full card tagging bottom


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


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.


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.


Unusual Card Shape

Example 6: Delta pump fillage ‘82.98’, PFC pump fillage ‘100’, pump fillage interval [100, 101].

Description: Unexplained card shape


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


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


Statistics: 1000 wells


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.



Copyright

Rights to this presentation are owned by the company(ies) and/or author(s) listed on the title page. By submitting this presentation to the Sucker Rod Pumping Workshop, they grant to the Workshop, the Artificial Lift Research and Development Council (ALRDC), and the Southwestern Petroleum Short Course (SWPSC), rights to:

– Display the presentation at the Workshop.– Place it on the www.alrdc.com web site, with access to the site to be as

directed by the Workshop Steering Committee.– Place it on a CD for distribution and/or sale as directed by the Workshop

Steering Committee.

Other use of this presentation is prohibited without the expressed written permission of the author(s). The owner company(ies) and/or author(s) may publish this material in other journals or magazines if they refer to the Sucker Rod Pumping Workshop where it was first presented.


DisclaimerThe following disclaimer shall be included as the last page of a Technical Presentation or Continuing Education Course. A similar disclaimer is included on the front page of the Sucker Rod Pumping Web Site.The Artificial Lift Research and Development Council and its officers and trustees, and the Sucker Rod Pumping Workshop Steering Committee members, and their supporting organizations and companies (here-in-after referred to as the Sponsoring Organizations), and the author(s) of this Technical Presentation or Continuing Education Training Course and their company(ies), provide this presentation and/or training material at the Sucker Rod Pumping Workshop "as is" without any warranty of any kind, express or implied, as to the accuracy of the information or the products or services referred to by any presenter (in so far as such warranties may be excluded under any relevant law) and these members and their companies will not be liable for unlawful actions and any losses or damage that may result from use of any presentation as a consequence of any inaccuracies in, or any omission from, the information which therein may be contained.The views, opinions, and conclusions expressed in these presentations and/or training materials are those of the author and not necessarily those of the Sponsoring Organizations. The author is solely responsible for the content of the materials.The Sponsoring Organizations cannot and do not warrant the accuracy of these documents beyond the source documents, although we do make every attempt to work from authoritative sources. The Sponsoring Organizations provide these presentations and/or training materials as a service. The Sponsoring Organizations make no representations or warranties, express or implied, with respect to the presentations and/or training materials, or any part thereof, including any warrantees of title, non-infringement of copyright or patent rights of others, merchantability, or fitness or suitability for any purpose.

pump fillage calculation (pfc) algorithm for well control files/2... · 6th annual sucker rod...

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