Production-Performance Diagnostics Using Field Production Data and ...

Production-Performance Diagnostics Using Field-Production Data and Analytical Models: Method and Case Study for the Hydraulically Fractured South Belridge Diatomite Zhengming Yang, SPE, Aera Energy LLC

Summary Oil and water production data are regularly measured in oilfield operations and vary from well to well and change with time. Theoretical models are often used to establish the production expectation for different recovery processes. A performance surveillance understanding can be developed by comparing the field production data with the production expectation. This comparison generates quantitative or qualitative signals to determine whether the producer meets production expectations or the producer is underperforming and appropriate operational action is required to address the underperformance. The case study is for the South Belridge diatomite in California. This hydraulically fractured diatomite reservoir is currently under waterflood and steamflood. A methodology is proposed to establish the production expectation from historical production data. For primary depletion, the formation linear and bilinear flow models are applied to producers with vertical hydraulic fractures. For waterflood, an analytical method derived from the BuckleyLeverett displacement theory is used. Those analytical methods can predict production and provide surveillance signals for producers in the primary and waterflood recovery stages. For steamflood, a semiquantitative performance/surveillance criterion is proposed on the basis of understanding the mechanistic oil banking concept and reservoir simulation results for steamflood and waterflood. With those models representing expected production performance, an integrated flow regime diagram is proposed for production surveillance. A performance expectation can be developed for an individual producer. A significant overperformance relative to the expectation normally indicates changes in the recovery mechanism or improvement in sweep efficiency. A significant underperformance usually signifies an operational issue that requires correction to optimize the production performance. In the case study, the surveillance methodology for producers under primary depletion, waterflood, or steamflood is demonstrated by use of historical production data. In addition, water channeling between injectors and producers and its impact on production performance are discussed. On the basis of this surveillance methodology, some operational actions were proposed, and successful results are demonstrated. Examples of forecast for an individual producer in the primary depletion stage and field scale prediction in the waterflood stage are provided. Application indicates that the proposed methodology can serve as a convenient and practical tool for reservoir surveillance and operational optimization. Introduction The South Belridge diatomite is a 1,600-ft thick, low permeability (0.01 to 3 md), high porosity (60%) reservoir 45 miles northwest C 2012 Society of Petroleum Engineers Copyright V

This paper (SPE 153138) was accepted for presentation at the SPE Western North American Regional Meeting, Bakersfield, California, USA, 19–23 March 2012, and revised for publication. Original manuscript received for review 2 May 2012. Revised manuscript received for review 9 July 2012. Paper peer approved 3 September 2012.

712

of Bakersfield, California. Within the two order of magnitude range of permeability, the high value is attributed to the contribution of natural microfractures in the reservoir. Both injectors and producers are hydraulically fractured as a standard operating method because of the low permeability. Significant primary production started in 1977, and waterflood began in the late 1980s. Steamflood has been successfully tested since 1995, and it is now being expanded in some parts of the field. The primary production from producers with vertical hydraulic fractures follows linear flow behavior. On the basis of the analytical work by Cinco-Ley and Samaniego (1981) for pressure transient analysis (constant rate solution), the flow behavior follows the various linear flow models, depending on the fracture conductivity and storage capacity. For production data analysis (rate transient analysis with constant bottomhole pressure), Nott and Hara (1991) developed a formation linear flow formula for oil production rate by assuming infinite fracture conductivity. Azari et al. (1991) developed production rate formulas for both bilinear and formation linear flow with finite fracture conductivity. Plotting cumulative oil production vs. either the bilinear or the formation linear time scale can identify the linear flow type for a producer. The linear flow models can then be applied as a production decline analysis tool to forecast the oil production rate that is used as the production performance expectation for well surveillance purposes. For waterflood, a consistent analytical solution was developed on the basis of the Buckley-Leverett equation and the assumption of a semilog linear relationship between oil-to-water relative permeability ratio and water saturation (Yang 2009b). The method is applicable to unfavorable mobility ratio waterfloods and can be applied to diagnose the production performance and to predict the oil production rate for both an individual producer and a group of producers. One of the operational issues for the South Belridge diatomite waterflood is water channeling from injectors to producers. This is caused by closely spaced wells and variation in hydraulic fracture orientation caused by earth stress field changes that occur with production development. When fracture water channeling occurs, some of the injected water flows through intersecting hydraulic fractures. Although injected water is contained within the diatomite reservoir, as determined by an extensive monitoring program, the injection is not effectively displacing the oil in the matrix. In this instance, the oil production may behave similarly to either primary production or a mature waterflood, depending on the displacement and operational situation near the producer regardless of the producing water cut. The occurrence of fracture water channeling can be conveniently identified by the waterflood diagnostic analysis method (Yang 2009b). Some areas of the South Belridge diatomite have been converted from waterflood to steamflood. One of the operational issues for steamflood is the interaction of injection and production in the boundary of these two recovery processes. Another issue, as it relates to surveillance, is that steamflood response may start from a baseline of either a primary or waterflood production trend. December 2012 SPE Reservoir Evaluation & Engineering

Because of the complexity of the steamflood recovery process, there is currently no accurate analytical solution to forecast the production for surveillance purposes. Instead, reservoir simulation is used to forecast steamflood performance. However, on the basis of the mechanistic steamflood oil banking concept and the comparison of reservoir simulation results for steamflood and waterflood, semiquantitative surveillance criteria can be developed to analyze steamflood performance. In addition, other information (e.g., H2S concentration in the produced gas) is an indication of thermal response and can be used for surveillance of an individual producer. H2S is generated by the high-temperature aquathermolysis reaction of the sulfur compounds contained in the crude oil (Lamoureux-Var and Lorant 2005). An integrated flow regime diagram was developed on the basis of the analytical solutions of primary production and waterflood, as well as the mechanistic steamflood oil banking concept. The diagram has been successfully and conveniently applied to a production surveillance application in the South Belridge diatomite. With available field data, one can use the flow regime diagram to diagnose common operational issues. Two aspects are generally considered for the surveillance application: (1) The plot of the oilcut function Y vs. cumulative liquid production for diagnosing the flood displacement status (primary production; waterflood or steamflood response), for recognizing fracture water channeling in the waterflood, and for recognizing the interaction between waterflood and steamflood; and (2) the comparison of measured oil production with a calculated oil rate expectation vs. time to decide the potential and necessity of an operational intervention. The method is being successfully applied to field production surveillance for reservoir management and operational optimization. Analysis Waterflood. For a waterflood with an unfavorable mobility ratio between water and oil, Yang (2009b) developed an analytical method to diagnose production performance and to forecast oil production rate for either an individual well or a group of producers. The present paper further describes the application of the diagnostic method as a production surveillance tool. The method is valid when the volumetric sweep efficiency becomes stabilized in the unfavorable mobility ratio displacement. The waterflood analytical solution is as follows:   EV 1 . . . . . . . . . . . . . . . . . . . . . ð1Þ PV fo ð1  fo Þ ¼ QL B where fo is the oil fractional flow (oil-cut); B is a constant in the expression kro =krw ¼ AeBSw (Sw is water saturation, kro and krw are oil and water relative permeabilities, and A is a constant); EV is the volumetric sweep efficiency; PV is the total pore volume (PV) (bbl) in the subject area; and QL is the cumulative liquid production (bbl). The explicit determination of the parameters in Eq. 1 is generally unnecessary unless the purpose is to calculate the volumetric sweep efficiency. To generate an oil production rate forecast, the application is as follows. When the volumetric sweep efficiency is stabilized and becomes constant, the oil-cut function Y ¼ fo(1 – fo) can be extrapolated from a known reference point ‘0.’ Y¼

ðYQL Þ0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð2Þ QL

With the oil-cut function Y ¼ fo(1 – fo) forecast from Eq. 2, the future oil-cut and oil production rate qo can be calculated from liquid rate qL, as shown in Eqs. 3 and 4. The liquid rate can be estimated on the basis of known lift capacity or offset injection rates. pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 fo ¼ ð1  1  4Y Þ . . . . . . . . . . . . . . . . . . . . . . . . ð3Þ 2 qo ¼ fo qL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð4Þ Actually, Eq. 1 is applicable only after the producer experiences injection water breakthrough in the matrix. The South December 2012 SPE Reservoir Evaluation & Engineering

Belridge diatomite reservoir, however, is in the transition zone, and connate water is mobile. In this application, the plot of the oil-cut function Y vs. QL for the period before water breakthrough shows a generally constant value slightly less than 0.25. Due to the parabolic function form of the oil-cut function Y and the oilcut value range before water breakthrough [oil-cut at water breakthrough must be 1/2 or less, fo decreases, and (1 – fo) increases], Y ¼ fo(1 – fo) changes slowly and is nearly constant on the log-log scale. This nearly constant value behavior can be used to recognize the pre-breakthrough period, during which the oil flow behavior follows fracture-related linear flow models (detailed discussion in next subsection). After injection water breakthrough from the matrix occurs, the oil-cut function Y vs. the cumulative liquid production will decline with a slope of 1 on the log-log scale. Any significant deviation from either the Y value of 0.25 or the slope of 1 generally indicates abnormal water production due to fracture water channeling. This qualitative assessment has proved useful for surveillance of waterflood production performance.

Primary Production. In this paper, primary production is defined as the period before injected water breakthrough by means of displacement in the matrix. The waterflood diagnostic methods previously discussed can differentiate the primary production behavior from the post-breakthrough waterflood behavior. For pressure transient analysis (constant rate solution) in a well with vertical hydraulic fractures, Cinco-Ley and Samaniego (1981) demonstrated four possible flow regimes that depend on the dimensionless fracture conductivity and storage capacity: fracture linear flow; bilinear flow; formation linear flow, and pseudoradial flow, as shown in Fig. 1. The dimensionless fracture conductivity (kf bf)D and the dimensionless fracture storage capacity CfDf are defined as follows: ðkf bf ÞD ¼ CfDf ¼

kf b f kxf

. . . . . . . . . . . . . . . . . . . . . . . . . . . . ð5aÞ

bf /f cft . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð5bÞ pxf /ct

A value of (kf bf)D 300 was considered infinite conductivity by Cinco-Ley and Samaniego (1981). Except for fracture linear flow in the early time, there are three typical scenarios of linear flow regimes, as shown in Fig. 2: when (kf bf)D is small, the flow behavior is “bilinear” (slope of 1/4 in Case I, path A-B-C-D); when both (kf bf)D and CfDf are large, the behavior is formation linear flow (slope of 1/2 in the lower branch of Case II, Path L-IJ); and for large (kf bf)D and small CfDf, the flow behavior starts bilinear and changes to formation linear flow (upper branch of Case II, Path F-G-H-I-J). A well that produces at a constant bottomhole pressure (at either pumped-off or constant liquid level) satisfies the ratetransient analysis at constant pressure. The time frequency of field production measurements is generally weeks or months; it is longer than that for pressure transient analysis (in hours). Rate transient analysis, based on production data, is generally more extended into the reservoir than the early-time pressure transient analysis. As a result, the fracture linear flow period is generally too short to be seen. For South Belridge diatomite, the close well spacing (well spacing is less than hydraulic fracture half length) prevents the occurrence of pseudo-radial flow. Therefore, we observe only two flow regimes: bilinear flow and formation linear flow. Practically, bilinear flow is for fractures with finite conductivity and formation linear flow is for fractures with infinite conductivity. On the basis of field production data analysis (rate transient analysis) described in this paper, the purpose of analyzing primary production is to diagnose production performance rather than to interpret the reservoir and fracture parameters. For production data analysis, Azari et al. (1991) developed both the bilinear flow and formation linear flow formula with finite fracture conductivity. The bilinear formulas at a constant pressure condition were 713

Well Well

Fracture

Fracture

(a) FRACTURE LINEAR FLOW

(b) BILINEAR FLOW

Fracture

Fracture

Well

(c) FORMATION LINEAR FLOW

(d) PSEUDO RADIAL FLOW

Fig. 1—Flow regimes for a vertically fractured well (Cinco-Ley and Samaniego 1981).

derived by Azari et al. (1991) and can be rewritten (see Appendix A) as follows: Oil rate,

h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii pffiffiffi kFL ¼ 0:01417 ð4= pÞðPi  Pwf Þxf h /ct km =lo . . . .ð8bÞ

3 qo ¼ kBL t1=4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð6aÞ 4

Cumulative oil production,

Slope,

pffi Qo ¼ kFL t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ð9Þ 2

kBL

/lo ct x2f km h ¼ 40:001135 ðpi  pwf Þ Bo lo km

3 !1=4 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    kf bf hf 5 km xf h

                   ð6bÞ Cumulative oil production, Qo ¼ kBL t3=4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð7Þ Nott and Hara (1991) developed the formation linear flow model on the basis of an infinite fracture conductivity condition. The formation linear production rate formula derived by Nott and Hara (1991) is as follows: Oil rate, pffi 1 qo ¼ kFL = t . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð8aÞ 2 Dimensionless Pressure PWD

Slope,

102 E

D m=¼

1

B

CASE I

K

C J

(kf bf)D 0.1

m=¼

10–2 A

G

m=½

H

500

CASE II

F 10–4 10–10

L –8

10

10–6

10–4

10–2

1

102

Dimensionless Time tDxf Fig. 2—Log-log graph of typical cases for fractured wells (Cinco-Ley and Samaniego 1981). 714

The linear flow models for primary production are theoretically based on single-phase flow. The South Belridge diatomite is in the transition zone, and the connate water is mobile during primary production; therefore, oil and water two-phase flow exists. The unfavorable mobility ratio has an effect on the producing oil cut. Despite these conditions, we observe that the primary oil production is well characterized by the linear flow models. The effect of mobile water may be significant during early time (5), and the oil rate declines rapidly. Without a continuous supply of injected water near the producer, however, the formation mobile water partially exhausts, and then the oil-cut increases. Matrix water breakthrough occurs at approximately

135,187 bbl cumulative liquid production (October 2002), and the 1 slope for the oil-cut function Y begins. Fracture water channeling is not indicated by the Y function. Figs. 7b and 7d show the oil and liquid rates as functions of calendar time. Fig. 7c shows the cumulative oil production plotted on both the bilinear and formation linear time scales. The formation linear model with slope kFL ¼ 1,400 best fits the primary flow behavior. In August 2001, the formation linear flow behavior deviates from the established primary production trend and transitions to waterflood

(a) 985W-33: Y vs. QL

(b) 985W-33: Oil Rate Data and Forecast 100

1 Y data Y=0.25 Waterflood Forecast

Oil Rate (bbl/day)

Y 0.1

February 2000 mobility impact October 2002 QL = 135187 bbl slope = –1 starts

0.01 10,000

Oil Rate Primary Production Forecast Waterflood Forecast

80 60

August 2001 oil rate increases

40 20

100,000

0 1/1999

1,000,000

1/2004

(c) 985W-33: Primary Production With Formation Linear Flow 600

40,000

300

Q0 kBL

0 0

200 t¾

0 400

kFL = 1400

kFL

Q0 (bbl)

Q0 (bbl)

kBL

40,000

1,000

ΔQ0 kFL

0 0

1/2014

(d) 985W-33: Oil Rate Data and Forecast

Formation Linear Model Valid 80,000 2,000 August 2001

20 t½

40

0

400 Liquid Rate (bbl/day)

Bilinear Model Invalid 80,000

1/2009 Date

Cumulative Liquid Production (bbl)

Liquid Rate Future Liquid Rate

300

200

August 2001 liquid rate increase

100

0 1/1999

1/2004

1/2009

1/2014

Date

Fig. 7—Waterflood production performance investigation and forecast, 985W-33. December 2012 SPE Reservoir Evaluation & Engineering

717

(b) 586S1-33, Oil and Liquid Rates

(a) 586S1-33, Y vs. QL 1

40

240

30

180

20

120

10

60

Oil Rate (bbl/day)

Y 0.1

Liquid Rate (bbl/day)

Steamflood Response 1/2011

Water Channelling July 2006–May 2009

Y 0.01 10,000

Y=0.25

0 1/2000

1,000,000

Cumulative Liquid Production (bbl)

1/2002

Oil Rate Case A: qL=60

1/2004

1/2006 Date

1/2008

1/2010

0 1/2012

Case B: qL=110 Liquid Rate

Fig. 8—Water channeling investigation, 586S1-33.

response. Oil production forecasts are generated by use of the kFL ¼ 1,400 slope value and Eq. 8 during the primary production period and the oil-cut function Y that assumes a future 150 (B/D) total liquid production rate during the waterflood period. These forecasts are shown in Fig. 7B. The waterflood incremental oil response is approximately 10 bbl/day more than the extrapolated primary production forecast. Also shown is the expected production if the well were not abandoned for redevelopment purposes. Field Example 3: Fracture Water channeling, 586S1-33 and 974C-33. Two examples demonstrate the recognition of fracture water channeling by use of the oil-cut Y function and, in one case, how to develop an appropriate oil rate for both a mature waterflood (matrix water breakthrough) and fracture water channeling conditions. Producer 586S1-33 has operated from 1996 through the current time. The oil-cut function Y shown in Fig. 8a highlights the transition from primary production to mature waterflood behavior that is indicated by the Y function slope changing to 1. This transition from primary production behavior occurred in 2001. During the period of July 2006 through May 2009, fracture water channeling was evident by the Y function values, significantly less than the 1 slope trend. The fracture water channeling problem disappeared after May 2009 with the shut-in of the water injector and the conversion of the pattern to steamflood. This is indicated by the Y values returning to the previously established 1 slope trend. Fig. 8b shows the oil and total liquid rates since the matrix water breakthrough in 2000 and calculated oil rate expectation on the

TABLE 1—586S1-33: REFERENCE POINT FOR WATERFLOOD FORECAST

1 September 2005

fo

Y ¼ fo(1 – fo)

qL (B/D)

QL (bbl)

0.2290

0.1766

60

233,651

Field Example 4: Waterflood and Steamflood Flow Regimes, 542R2-29. This example demonstrates a typical and sustainable steamflood response for a producer that previously had been in a waterflood. Also discussed is the relationship between H2S concentration from produced gas composition measurements and the oil production performance. Producer 542R2-29 is on the boundary of the South Belridge Section-29 diatomite steamflood demonstration project and the surrounding waterflood, shown by the map in Fig. 10. The oil-cut function Y in Fig. 11a indicates that 542R2-29 has experienced

(a) 974C-33, Y vs. QL 1

(b) 974C-33, Oil and Liquid Rates 40

Oil Rate (bbl/day)

Y

0.1

0.01

0.001 10,000

400 Oil Rate Liquid Rate

Y Y=0.25

Cumulative Liquid Production (bbl)

100,000

30

300

20

200

10

100

0 9/1999

10/1999

11/1999 Date

12/1999

Liquid Rate (bbl/day)

Date

basis of the use of the prechanneling waterflood trend. September 2005 was selected as the reference date (Table 1) for the waterflood forecast. To generate a waterflood oil production rate forecast by use of the oil-cut function Y, the total liquid production rate must be assumed. Producer 586S1-33 had demonstrated mature waterflood behavior (slope of 1 on the Y plot) with a liquid production rate of 60 to 110 B/D before water channeling. A range of oil production expectations can be developed on the basis of two cases: Case A, qL ¼ 60 B/D; Case B, qL ¼ 110 B/D by use of the parameters shown in Table 1 and the waterflood analytical solution (Eqs. 2 through 4). The results plotted in Fig. 8b indicate that oil production rate was within 5 B/D of the expectation during the period of fracture water channeling and that oil production most recently is at waterflood expectation. An example of extreme water channeling is demonstrated by Producer 974C-33. This well was completed in September 1999. Fig. 9a shows the oil-cut function Y vs. cumulative liquid production. The extremely low Y value (0.005) indicates a high degree of fracture water channeling from the onset of production. Fig. 9b shows the corresponding oil and liquid production rate. At South Belridge, this behavior is presumed to be a result of direct communication between the closely spaced injector(s) and producer(s) through intersecting hydraulic fractures. In this case, the decision was made to shut in the producer. Fortunately, these extreme cases are infrequent.

0 1/2000

Fig. 9—Extreme water channeling, 974C-33. 718

December 2012 SPE Reservoir Evaluation & Engineering

Fig. 10—Section 29, steamflood demonstration project area.

primary production, waterflood, and steamflood flow regimes. The steamflood flow regime is indicated by Y values that trend flatter than the 1 slope, consistent with the oil banking conceptual model previously discussed. Fracture water channeling in either the waterflood or steamflood periods is not evident. Fig. 11b shows the historical liquid and oil production rates, the

forecast of the primary production by the bilinear flow model, and the forecast of waterflood production by the analytical method (Eqs. 2 through 4). The bilinear flow model was chosen after plotting cumulative oil primary production on both the bilinear and formation linear time scales shown in Fig. 11c. The bilinear slope of kBL ¼ 225 was used to generate the primary production (b) 542R2-29: Oil Rate 100

Y Y=0.25 Steamflood Response Waterflood Forecast

Oil Rate (bbl/day)

Y 0.1 Slope = –1: Waterflood Forecast 0.01 10,000

100,000

75

150

50

100

25

50

0 1/2003

1,000,000

March 2007 1/2005

1/2007

(c) 542R2-29: Primary Production With Bilinear Flow

kBL = 225

40,000

80,000

2,000

kBL

60,000

kFL

40,000

1,000

300

20,000 0 0

200 t¾

0 400

400 300 200 100

20,000 Q0 kBL

0 1/2013

500

H2S (PPM)

Q0 (bbl)

60,000

400

Q0 (bbl)

80,000

1/2011

(d) 542R2-29: H2S Indicates Steamflood Response

Formation Linear Model Invalid 100,000

120,000

1/2009 Date

Cumulative Liquid Production (bbl)

Bilinear Model Valid

200

Oil Rate Bilinear Forecast Waterflood Forecast Steamflood Response

March 2007 Steamflood Response

Liquid Rate (bbl/day)

(a) 542R2-29: Y vs. QL 1

Q0 kFL

0 0

20

t½

40

0 60

0 1/2003

1/2005

1/2007

1/2009

1/2011

1/2013

Date

Fig. 11—Steamflood production performance investigation, 542R2-29. December 2012 SPE Reservoir Evaluation & Engineering

719

forecast. The waterflood oil production expectation was forecast from the oil-cut Y-function slope of 1, a reference date of April 2007, and an assumed future total liquid rate of 140 B/D. The steamflood incremental oil production beyond the waterflood baseline is significant and can be quantitatively evaluated by use of this approach. Fig. 11d shows the H2S concentration in the gas produced from 542R2-29. In June 2006, the H2S concentration begins to consistently exceed the background value of 20 to 50 ppm. The oil response, on the other hand, begins 10 months later in April 2007, as indicated by the increasing oil-cut function Y in Fig. 11a and oil production rate more than waterflood baseline in Fig. 11b. We consistently observe that the H2S concentration (from gas phase) and the oil banking (from oil phase) do not reach a producer simultaneously, and the H2S arrives first. We theorize this could be caused by H2S in the gas phase that flows through the reservoir faster than the oil phase. The H2S response is a good leading indicator of thermal response and supplements the oil-cut Y function trend analysis for steamflood.

represented by Group 1 was converted from waterflood to steamflood in October 2010. The steamflood response began in March 2011, as observed by the increase of the oil-cut function Y in Fig. 12a. From a surveillance perspective, the sustainability of the steamflood performance can be assessed by the future monitoring of the oil-cut function Y that relates to the waterflood baseline and quantified incremental oil production. Figs. 12c and 12d show the oil-cut function Y and production rate plots for Group 2. Fracture water channeling was observed on a larger scale (approximately 30% of producers) after 2000, which is indicated by the oil-cut function Y being significantly less than Y ¼ 0.25. Only after 2007 did the waterflood reach maturity (matrix water breakthrough), which is indicated by the 1 slope. A program to improve injection conformance was implemented during 2009 and reduced fracture water channeling by approximately 20,000 B/D. A new waterflood forecast, shown in Fig. 12d, was established by assuming a 50,000 B/D total liquid rate and a reference date of October 2011. Ongoing monitoring of the oil-cut function Y and oil rate that is related to expectation provides a simple means to assess waterflood performance in this area.

Field Example 5: Establishing Waterflood Expectations for Two Well Groups. The previous examples demonstrate flow regimes in individual wells; the same techniques can be applied to groups of wells (Yang 2009a). In this example, two diatomite producing areas in the South Belridge field were selected. Group 1. A waterflood area consisting of 314 producers. The waterflood started in April 1989 and was converted to steamflood in October 2011. Group 2. A waterflood area consisting of 1,178 producers. The waterflood started in May 1998. Figs. 12a and 12b show the historical oil-cut function Y and production rate plots for Group 1. The waterflood reached maturity in 2000, and the Y function transitioned to a 1 slope. In 2003 and 2006, infill drilling programs were implemented, significantly improving the sweep efficiency as indicated by shifts in the Y function trend. After 2006, the 1 slope resumed. The areawide effect of fracture water channeling was not pervasive in this group (approximately 20% of producers). The Y function was extrapolated, and it forms the basis for the waterflood forecast shown in Fig. 12b by assuming a constant total liquid rate of 15,000 B/D, with December 2011 as a reference date. The area

Surveillance Case Studies The purpose of the three case studies described next is to demonstrate the application of the flow regime models at the South Belridge waterflood and steamflood areas in a surveillance situation. In all cases, the oil production expectations were developed, production underperformance was recognized, and diagnosis was performed to decide whether operational interventions were warranted. In two cases, several years of field production data are available to verify the response to those actions. Case Study 1: Production Expectation Redefined After Matrix Water Breakthrough, 542L1-29. Well 542L1-29 started production in February 2009. Fig. 13a shows the oil-cut function Y vs. the cumulative liquid production. Primary flow regime is indicated by the relatively constant Y value of 0.22, and fracture water channeling does not occur. Figs. 13b and 13d show the measured oil and total liquid production rates. Fig. 13c shows cumulative oil and gross applied to both the bilinear and formation linear time scales. In this case, the oil bilinear flow (slope kBL ¼ 212) (b) Group 1: Waterflood Baseline Forecast 6,000

March 2011 Steamflood Response

Y

Oil Rate (bbl/day)

5,000

0.1

Waterflood

0.01 10

100

15,000 12,000

3,000

9,000

2,000

6,000

1,000

3,000

0

1,000

0

1/1978 1/1983 1/1988 1/1993 1/1998 1/2003 1/2008 1/2013 1/2018 1/2023

Cumulative Liquid Production (MM bbl)

Date

(c) Group 2: Y vs. QL

(d) Group 2: Waterflood Forecast 16,000

1

Y

Oil Rate (bbl/day)

Water Channelling after 2000

0.1

2000 2007 Waterflood

0.01

12,000

80,000 Oil Rate Waterflood Forecast Liquid Rate Future Liquid Rate

60,000

6,000

4,000

4000

2,000

0 10

100

Cumulative Liquid Production (MM bbl)

1,000

Liquid Rate (bbl/day)

2003–2006 Infill Drilling

4,000

18,000

Oil Rate Waterflood Forecast Liquid Rate Future Liquid Rate

Liquid Rate (bbl/day)

(a) Group 1: Y vs. QL 1

0

1/1978 1/1983 1/1988 1/1993 1/1998 1/2003 1/2008 1/2013 1/2018 1/2023

Date

Fig. 12—Field scale production performance diagnosis and forecast. 720

December 2012 SPE Reservoir Evaluation & Engineering

(a) 542L1-29: Y vs. QL

(b) 542L1-29: Oil Rate Data and Forecast 80

1

Pre-7/2010 Oil Rate Data Oil Bilinear Forecast on 7/2010 Post-7/2010 Oil Rate Data

Y Data

Y

Oil Rate (bbl/day)

Y Forecast Y=0.25

60

40 Case B 20

Slope=–1: Water Breakthrough 0.1 1,000

10,000

Case A

100,000

0 1/2009

1,000,000

1/2010

1/2011

Cumulative Liquid Production (bbl)

(c) 542L1-29: Primary Production with Bilinear Flow

Q0, QL (bbl)

Q0 QL kFL

400

kBL = 212

40,000

200

kFL 1,600

80,000 kFL

800

40,000

Q0 = 212t¾ 0 0

60

t¾

120

0 180

1/2015

1/2016

Pre-7/2010 Liquid Rate Liquid Rate Forecast on 7/2010 Case B: 150 (bbl/day) Post-7/2010 Liquid Rate Data

2,400

120,000

kBL

QL = 605t¾

80,000

200

Liquid Rate (bbl/day)

600

Q0 QL kBL

Q0, QL (bbl)

120,000

1/2014

(d) 542L1-29: Liquid Rate Data and Forecast

Formation Linear Model Invalid

Bilinear Model Invalid

1/2012 1/2013 Date

150

100

Case A: 85 (bbl/day)

50

Q0 0

0 0

10

t½

20

30

0 1/2009

1/2010

1/2011

1/2012 1/2013 Date

1/2014

1/2015

1/2016

Fig. 13—542L1-29: Surveillance Case Study 1, recognizing transition to waterflood regime.

and liquid (bilinear slope ¼ 605) were selected on the basis of the constant slope indications. The formation linear flow model is invalid. Figs. 13b and 13d show the oil and liquid rate forecasts derived in July 2010 from extrapolation of the bilinear model (Eq. 6a). We theorize the smooth decline of gross liquid rate in Fig. 13d, and the oil rate fluctuation in the first few months is the effect of mobility ratio. The field production data agree satisfactorily with the forecasts, and minimal surveillance effort is required until June 2011, the time at which oil production rate trends below expectation. The surveillance workflow detects this underperformance and prompts further analysis. Review of the Y function plot indicates that injection water matrix breakthrough has occurred by mid-2011, indicated by the transition to a 1 slope (Fig. 13a). After water breakthrough, the linear flow model does not apply, and the waterflood analytical method must be used to generate an oil rate forecast. October 2011 is selected as the reference date, and two total liquid rate cases are selected (Fig. 13D). Case A represents a constant gross scenario at 85 (B/D), and Case B represents a case in which the liquid production rate is increased to 150 (B/D). The basis for the Case B liquid rate value is from pattern water injection to production ratio and field experience. The calculation of future oil rate, shown in Fig. 13b, is from Eqs. 2 through 4. If the future liquid rate remains at 85 B/D (Case A), the oil rate will decline rapidly below the previously established bilinear flow trend. The field measurements of oil production since mid-2011 are consistent with the oil rate expectation in Case A. A review of the well was completed, and it was determined that the well was pumped off. Further work is required to review offset injection to ensure that the effective liquid production rate can reach a level similar to that of Case B. This example demonstrates the importance of recognizing the change in flow regime so that oil production from the pattern can be optimized through the surveillance process. Case Study 2: Well-Test Equipment Repaired and Artificial Lift Optimization, 533D1-29. Producer 533D1-29 has operated in a waterflood area since 2007. Fig. 14a shows the oil-cut function Y vs. the cumulative liquid production. By comparison with the schematic in Fig. 5, fracture water channeling is indicated from the onset of production. Fig. 14c shows the historical cumulative December 2012 SPE Reservoir Evaluation & Engineering

production plotted against both bilinear and formation linear time scales. Primary oil production behavior is evident despite the fracture water channeling. The bilinear slope value of kBL ¼ 171 is selected as most representative on the basis of the linear trend and constraint that the linear fit passes through the origin (Fig. 14c). This oil rate forecast, based on the bilinear flow model, was generated in February 2009 (Fig. 14b). In comparison, a forced fit on the basis of formation linear flow without honoring the initial condition was also made, and that forecast is also shown in Fig. 14b. The difference between the two oil rate forecasts and the comparison with historical production data demonstrate the importance of selecting the correct linear flow model. In the bilinear flow case, production is underperforming to expectation. If the linear flow model had been incorrectly used to establish the expectation, uplift opportunities would not have been recognized. On the basis of the comparison of measured oil production with the bilinear rate forecast, several periods of underperformance were recognized through the surveillance workflow. Starting in August 2008, the total liquid production suddenly declined from 200 to 110 140 B/D, and measured oil production declined 10 to 15 B/D less than forecast. Diagnosis of well equipment revealed low pump efficiency. The oil rate measurements returned to expected values after pump repair. By the end of 2009, the oil rate was again below expectation by 10 B/D. An analysis of downhole pump performance and comparison with oil and gross liquid testing data, as shown in Fig. 15, revealed a decline in efficiency and a required minimum lift capacity of 170 B/D. This analysis resulted in a recommendation to service the well and to upsize the pump to increase displacement. This work was completed in October 2010, and oil production increased by 12 B/D. This example demonstrates the importance of establishing the correct linear flow model from which to establish an oil rate expectation. In this case, bilinear flow behavior was evident despite fracture water channeling. Surveillance monitoring was successful on two occasions to recognize underperformance that resulted in corrective actions and significantly increased production. Case Study 3: Injection and Artificial Lift Optimization, 933H-29. Producer 933H-29 is located, as shown in Fig. 10, on the boundary of the Section-29 diatomite steamflood demonstration 721

(a) 533D1-29: Y vs. QL

(b) 533D1-29: Oil Rate Data and Forecast 80

1

Oil Rate History Before 2/2009 BiLinear Linear Model Forecast Forced Formation Linear Fit Oil Rate Data After 2/2009 10/2010 2/2009 Pump Upsize Pump Repair

Y

Oil Rate (bbl/day)

Y

Y=0.25

0.1

0.01 1,000

10,000

100,000

60

40

20

0 1/2007

1,000,000

1/2008

1/2009

(c) 533D1-29: Primary Production with Bilinear Flow

400

Q0 = 171t¾

12,000 8,000

300 kBL Damaged Productivity 200

4,000

100

0 0

50

t¾

100

Q0 (bbl)

Q0 (bbl)

16,000

0 150

12,000

280

1,200 kBL

8,000

800

4,000

400

0 0

10

1/2012

320

Liquid Rate (bbl/day)

500

1/2011

(d) 533D1-29: Liquid Rate Data

Formation Linear Invalid Initial Condition Not Honored 20,000 2,00 Q0 = 800 t½ –3211 16,000 1,600

Bilinear Flow Valid 20,000

1/2010 Date

Cumulative Gross Production (bbl)

t½

20

2/2009 Pump Repair

240

10/2010 Pump upsize

200 160 120 80 Liquid Rate

40 0 1/2007

0 30

170 (bbl/day) 1/2008

1/2009

1/2010

1/2011

1/2012

Date

Fig. 14—533D1-29: Surveillance Case Study 2, addressing pump deficiencies.

project and adjacent to waterflood patterns in the surrounding area. The oil-cut function Y in Fig. 16a indicates that the producer had experienced primary production and waterflood flow regimes without fracture water channeling. Fig. 16c shows that primary production is best modeled by use of the bilinear flow equations, with slope kBL ¼ 172. The mature waterflood production expectation was determined by the waterflood analytical method (Eqs. 2 through 4), which is based on an average pre-steamflood liquid rate of 70 B/D.

This surveillance case study occurred during the steamflood time period. The H2S concentration in the produced gas, as shown in Fig. 16d, starts to rise from the base value of approximately 50 ppm to a value of 500 ppm on April 2006. The increase of the oilcut function Y values from the 1 slope in April 2007 indicated the arrival of the oil bank and a typical steamflood response. However, in March 2008, the tangent of the function Y in Fig. 16a became steeper than 1 and gradually approached the waterflood baseline. During this same time, H2S concentration declined.

533D1-29 Well Test Gross

190

Well Test Oil

Pump Efficiency

PUMP CAPACITY 170 BBL/DAY

180 170 160 150 140 130 120 110 100 90

PUMP EFFICIENCY=71%

80

PUMP EFFICIENCY=61%

70 60 50

TEST STATION PROBLEM

40

PRODUCITIVITY LOSS DUE TO LOW PUMP EFFICIENCY

30 20 10 4/27/2009

5/27/2009

6/26/2009

7/26/2009

8/25/2009

9/24/2009 10/24/2009 11/23/2009 12/23/2009 1/22/2010 Date

2/21/2010

3/23/2010

Fig. 15—533D1-29: Production testing and pump condition diagnosis. 722

December 2012 SPE Reservoir Evaluation & Engineering

(a) 933H-29: Y vs. QL

(b) 933H-29: Oil and Liquid Rate 80

1

Oil and Liquid Rate (bbl/day)

Primary and Waterflood Y=0.25 Steamflood Response Waterflood Forecast

Y

May 2009 Operational Intervention

Waterflood Forecast

April 2007 0.01 10,000

100,000

Liquid Rate

60

40

20

0 1/2000

1,000,000

Primary Production and Waterflood Steamflood Response BiLinear Forecast Waterflood Forecast (qL=70 bbl/day)

1/2002

1/2004

Cumulative Liquid Production (bbl)

(c) 933H-29: Primary Production with Bilinear Flow Q0 kBL

Q0 (bbl)

80,000

400 kBL

60,000

300

40,000 kBL = 172

200

20,000

100

0

0 0 150 200 300 400 500 t¾

kFL 1,500

40,000

1,000

200

20,000

500

100

0

20

40 t½

60

0 80

1/2010

1/2012

(d) 933H-29: H2S Indicates Steamflood Responses

400

60,000

0

1/2008

500

H2S (PPM)

500

100,000

600

Formation Linear Model Invalid 100,000 2,500 Q0 kFL 80,000 2,000 Q0 (bbl)

Bilinear Model Valid

1/2006 Date

300

0 1/2000

1/2002

1/2004

1/2006 Date

1/2008

1/2010

1/2012

Fig. 16—933H-29: Surveillance Case Study 3, addressing loss of steamflood response.

Both were surveillance signals that steamflood response was diminishing, and this prompted further analysis. It was determined that the pump was losing efficiency, and it was also suspected that offset water injection was suppressing the oil bank. In April 2009, the well was serviced, and the worn pump was repaired. At the same time, offset water injection rates were reduced. Since then, the steamflood response has recovered, indicated by the increasing oil-cut function Y (Fig. 16a). The H2S concentration increased from 50 to more than 200 ppm (Fig. 16d), and the oil production rate increased from 10 to 22 B/D and is above the waterflood baseline (Fig. 16b). This example demonstrates how the combination of the oil-cut function Y and H2S concentrations signaled a degradation of steamflood response. Corrective actions were taken that increased oil production. Conclusions A production surveillance methodology has been proposed based on the analytical solutions for primary and waterflood production and a mechanistic model for steamflood. The methodology involves the use of the oil-cut function Y vs. the cumulative liquid production to identify the flow regime experienced by individual producers or groups of producers. The flow regimes are (1) primary production; (2) mature waterflood, here defined as the period after injected water breakthrough from the matrix; (3) water channeling, defined as injection through the reservoir but bypassing the matrix from injector to producer; and (4) steamflood, a followup recovery process to waterflood. An integrated flow regime diagram is provided to recognize the flow regime. Field examples demonstrate the various flow regimes. With the flow regime identified, the expected oil production rate vs. time can be calculated for both primary production and waterflood. For the hydraulically fractured South Belridge diatomite, linear flow models determine the primary oil production expectation by use of rate transient analysis principles. Both bilinear and formation linear flow behavior exist and can be determined on the basis of the field production data. The presumption of the existence of only one linear flow type or extended use in the waterflood flow regime will introduce error to the forecast. December 2012 SPE Reservoir Evaluation & Engineering

For waterflood, the oil-cut function Y plot in conjunction with an assumption of total liquid rate is used to generate a production expectation. The total liquid rate assumption is informed by injection policy and available artificial lift capacity. If water channeling is present, the method enables the quantification of reduced oil rate that may occur in this flow regime. For steamflood, the mechanistic oil banking model does not provide a basis for forecasting oil production. However, for steamflood surveillance in the South Belridge diatomite, the technique provides a qualitative assessment of the sustainability of the recovery process and a method to determine the incremental oil production that is realized to date. On the basis of this method, surveillance efforts can focus on investigating the differences between the predetermined production expectation and field measured oil and water rate data. Case studies describing these investigations and the resultant actions show the benefit of the method in terms of optimized oil production. Nomenclature bf ¼ fracture width, in. B ¼ constant in the semilog oil-to-water relative permeability ratio c ¼ compressibility, 1/psi EV ¼ volumetric sweep efficiency, fraction f ¼ fractional flow, fraction h ¼ formation thickness, ft hf ¼ fracture height, ft k ¼ permeability, md kBL ¼ bilinear flow slope, B/D3/4 kFL ¼ formation linear flow slope, B/D1/2 PV ¼ formation pore volume, bbl Q ¼ cumulative production, bbl q ¼ production rate, B/D S ¼ saturation, fraction t ¼ time, days xf ¼ fracture half length, ft Y ¼ fo fw, the oil-cut function, fraction / ¼ porosity, fraction l ¼ viscosity, mPas 723

Subscripts 0 ¼ reference point for waterflood forecast f ¼ fracture L ¼ liquid (oil plus water) m ¼ matrix O ¼ oil phase W ¼ water phase Acknowledgments The author wishes to thank Aera Energy LLC for permission to publish this work and many engineers for their comments, especially Brent Carnahan for reviewing the manuscript, Alfredo Urdaneta for helpful comments, and Indar Singh for implementing this surveillance methodology. References Azari, M., Soliman, M.Y., Wooden, W.O. et al. 1991. Performance Prediction for Finite Conductivity Vertical Fracture. Paper SPE 22659 presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 6–9 October. http://dx.doi.org/10.2118/22659-MS. Cinco-Ley, H., and Samaniego-V., F. 1981. Transient Pressure Analysis for Fractured Wells. J. Pet. Tech. 33 (9): 1749–1766. http://dx.doi.org/ 10.2118/7490-PA. Hong, K.C. 1994. Steamflood Reservoir Management. Tulsa, Oklahoma: PennWell Books. Lamoureux-Var, V. and Lorant, F. 2005. H2S Artificial Formation as a Result of Steam Injection for EOR: A Compositional Kinetic Approach. Paper SPE 97810 presented at the SPE/PS-CIM/CHOA International Thermal Operations and Heavy Oil Symposium, Calgary, Alberta, Canada, 1–3 November. http://dx.doi.org/10.2118/97810-MS. Nott, D.C. and Hara, S.K. 1991. Fracture Half-Length and Linear Flow in the South Belridge Diatomite. Paper SPE 21778 presented at the SPE Western Regional Meeting, Long Beach, California, 20–22 March. http://dx.doi.org/10.2118/21778-MS. Yang, Z. 2009a. Analysis of Production Decline in Waterflood Reservoirs. Paper SPE 124613 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 4–7. http://dx.doi.org/ 10.2118/124613-MS. Yang, Z. 2009b. A New Diagnostic Analysis Method for Waterflood Performance. SPE Res Eval & Eng 12 (2): 341–351. http://dx.doi.org/ 10.2118/113856-PA.

Appendix A: Rewrite the Bilinear-Flow Formulas Azari et al. (1991) derived the dimensionless cumulative production (Eq. 11 in Azari et al. 1991). By inserting the dimensionless

724

fracture conductivity, dimensionless fracture height, and the dimensionless time, we obtain the following:  QwD ¼ 0:49

kf bf hf km xf h

1=2

0:0002637km /lo ct x2f

!3=4 t3=4 . . . . ðA–1Þ

The dimensionless cumulative oil production (Eq. 6a in Azari et al. 1991) by definition is QwD ¼

0:8936Bo Qo . . . . . . . . . . . . . . . . . . . . ðA–2Þ /ct hx2f ðPi  Pwf Þ

Equalizing Eq. A–1 with Eq. A-2 and grouping all the parameters into a slope result in 2

kBL

/lo ct x2f km h ¼ 40:001135 ðpi  pwf Þ Bo lo km

3 !1=4 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    kf bf hf 5 km xf h

                   ðA-3Þ The cumulative oil production is Qo ¼ kBL t3=4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . ðA–4Þ Taking the derivative of the cumulative oil production vs. time gives the oil production rate: 3 qo ¼ kBL t1=4 . . . . . . . . . . . . . . . . . . . . . . . . . . ðA–5Þ 4 Zhengming Yang is a senior staff reservoir engineer with Aera Energy LLC (a Shell and ExxonMobil joint venture) in Bakersfield, California, USA. He works on integrated reservoir study and simulation projects, as well as performance diagnoses and forecasts based on field production data. Before joining Aera Energy LLC, Yang worked on integrated reservoir study and simulation projects for heavy and conventional oils in the US, Venezuela, and China. He holds a diploma in chemical engineering from Tianjin University in Tianjin, China; an MS degree in petroleum engineering from the Research Institute of Petroleum Exploration and Development in Beijing; and a PhD degree in petroleum engineering from the University of Southern California in Los Angeles.

December 2012 SPE Reservoir Evaluation & Engineering