SPE-173481-STU

Exploring the Diagnostic Capability of RTA Type Curves

Siddharth Mishra, MIT Pune

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE international Student Paper Contest at the SPE Annual Technical Conference and Exhibition held in Amsterdam,The Netherlands, 27–29 October 2014.

This paper was selected for presentation by merit of placement in a regional student paper contest held in the program year preceding the International Student PaperContest. Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). Thematerial, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members.Electronic reproduction, distribution,or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted toan abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

The cost intensive oil and gas industry dictates the use of techniques which maximize quality informationwhile minimising rig time. Continuous improvement in data acquisition techniques as well as datainterpretation methods has been seen in the recent past. One such modern data interpretation method isthe “Rate Transient Analysis (RTA)”.

Pressure Transient Analysis (PTA) and Rate Transient Analysis (RTA) has been the industry practicefor analysis of pressure data. PTA is mainly used for analysis of short-term conventional well test whileRTA is used mainly for analysis of pressure and rate data over a long time span. RTA can also be termedas a modern Decline Curve Analysis (DCA) method. Traditional DCA deals with pseudo steady state flowregime and is an empirical / semi empirical method. However RTA deals with transient state flow and theRTA flow equations have analytical origin. RTA is known to give convincing estimates of reservoirparameters when low frequency (weekly or monthly) production data is available. However recently,considerable amount of work has been done to study the applicability of RTA on high frequency well testdata.

The utility of PTA for well test interpretation is well known among reservoir engineers and it has a richliterature base. However there exists several “complex scenarios” where conventional PTA interpretationbecomes non feasible. Under these scenarios RTA proves to be a promising interpretation tool.

Also a large pool of literature is available on the diagnostic capabilities and sensitivity analysis of thePTA type curves. What is not available in literature is the diagnostic power and sensitivity analysis ofRTA diagnostic plots. Owing to the need of RTA as a modern data interpretation tool, this paper discussesthe diagnostic capability of RTA type curves by generating synthetic models of complex reservoir systems(numerical well test modelling & simulation) and studying the sensitivity of various reservoir parameterson the RTA type curves.

BackgroundThere are two most important components essential for optimum reservoir characterization. The first is“data acquisition techniques” and second is “data interpretation methods”. With the advancement intechnology and solid state electronics, the data acquisition part has reached its own great heights. Howeverthe data interpretation part seems to be lagging behind. The scenario is something like this, “we have

collected the best possible data, but we do not have good enough tools to do justice with it.” The reasonbeing that conventional Pressure Transient Analysis (PTA) has served us so well in the past, that we donot think of any other interpretation methods other than PTA. But what if a situation arise where theconventional PTA will become “non feasible”?

It is not like alternate interpretation tools don’t exist. The only problem is that, not much work has beendevoted to explore such alternate interpretation tools. One such alternate interpretation tool is RateTransient Analysis (RTA).

Pressure Transient Analysis (PTA) and Rate Transient Analysis (RTA) has been the industry practicefor analysis of pressure data. PTA is mainly used for analysis of short-term conventional well test whileRTA is used mainly for analysis of pressure and rate data over a long time span. Traditional Decline CurveAnalysis (DCA) is an empirical procedure used mainly to predict recoverable reserves and futureproduction rates, based on boundary dominated flow. With this preconception in mind, the applicabilityof RTA has been hardly checked for analysis of short-duration well tests. However recently, considerableamount of work has been done to study the applicability of RTA on high frequency well test data.

This is the reason for undertaking this work. In this paper, our aim is to answer couple of importantquestions. First is, Can we provide the industry with an alternate interpretation tool, called RTA,when conventional PTA fails? And if yes, then how effective is it?

As already mentioned, there are several scenarios where conventional PTA becomes “non feasible”. Itis interesting to note these cases.

The first case is “tight reservoirs”, where the permeability value is typically in nanodarcies. Here theradius of investigation or the pressure transient will take a very long time to show radial regime or willtake infinite amount of time to reach the boundary (Figure 1). Hence it is not feasible to depend on anexpensive operation like a well test, to interpret the permeability or the boundary of these reservoirs. Thiscalls for another alternative interpretation tool, which is feasible under the above conditions. Here comesRTA, which can give you the same parameters that PTA gives you, and moreover you need not wait forinfinite build up time, as RTA works well on monthly production data. So you can produce your well,collect the data while producing, and later interpret the data. But make sure you have your gauges fittedand make proper data recording for the pressures and the rates!

The next case is “small reservoirs”. Now one may ask if we are detecting a small reservoir, then whyto waste our time and money in characterizing it? After all we are not going to produce from a smallreservoir right? Yes of course we are not going to produce from such a small reservoir. By small reservoirwe mean that if we look at a mini DST (Dual Packer) scale of observation, we may see smallheterogeneities as boundaries. And hence we can see a boundary effect in our derivative. Here conven-

Figure 1—Tight reservoir derivative plot

2 SPE-173481-STU

tional PTA won’t work, as our radial regime will be masked by boundary and wellbore storage effects(Figure 2). Here again we will call RTA for rescue.

In the present scenario, where we encounter lots of marginal small structures, it is no more a surpriseto see depletion during short span of a DST (Figure 3). The same depletion is also seen in Dual-Packerassisted mini-DSTs which are being widely used nowadays. They see flow barriers on a smaller scale, astheir radius of investigation is limited. In these cases of depletion where boundary effects are seen, RTAwas attempted, as it qualifies the condition of boundary dominated flow.

Short-duration well tests or more popularly known as Drill Stem Tests (DST) usually get affected bywellbore segregation effect during build-up phase. This build-up phase pressure transient data serves asbackbone of PTA. In this case, either the well test is rendered useless in terms of determination ofreservoir and boundary properties or only drawdown data is history matched for determination of reservoirproperties qualitatively.

Apart from these scenarios where PTA doesn’t work, there are several other scenarios where RTA mayprove to be a promising option.

One such scenario is when we have surveillance data but we don’t know what to do with it. Ifsurveillance/monitoring can provide you with the luxury of reservoir characterization then why do you

Figure 2—Small reservoir derivative plot

Figure 3—Pressures and rates (Depletion Case)

SPE-173481-STU 3

need to go for some of the expensive controlled experiments like well testing? (However the level ofcharacterization provided by testing or PTA cannot be ignored).

TheoryThis paper talks about one recently evolved data interpretation technique i.e. RTA and the diagnosticcapability of RTA type curve. So at this point it is important for us to know “What is RTA?” and whatare “RTA type curves?”

What is RTA?Because most of the reservoir engineers have a preliminary knowledge about PTA and decline curve

analysis, it will be really easy for them to understand RTA by correlating it with PTA. So let us understandRTA by comparing it with PTA. RTA basically deals with rates and the entire analysis of RTA is basedon rates (or some function of rates) whereas PTA deals with pressures or some function of pressure onthe y-axis. Moreover for PTA, rate is the correcting factor, whereas for RTA we have pressure as thecorrecting factor. The same parameters of permeability, drainage area, skin etc. can be estimated usingRTA like we do it in PTA. We are familiar with the Bourdet derivative, Horner plot, MDH plot etc. whichare diagnostic/interpretation plots in PTA. Likewise we have Blasingame plot, RNI plot, Agarwal-Gardener plot in RTA which are used for diagnosis and interpretation. The typical data sources for PTAare well test data, whereas RTA works well with production data. The period of investigation for PTA maytake from hours, days or weeks. However for RTA we need production data which may range from weeks,months or years.

Now since we have got an idea of what RTA is, let’s look back at the history of RTA and then we willsee the modern methods of RTA. The history begins with Arps analysis in the year 1945 which was givenby J.J.Arps, famously known as decline curve analysis (DCA). Traditional Decline Curve analysis is anempirical procedure used mainly to predict recoverable reserves and future production rates, based onboundary dominated declining rate. When sufficient production data are available and production isdeclining, a curve fit of the past production performance can be done using certain standard curves. Thiscurve fit is then extrapolated to predict future performance. This procedure is called decline curve analysisin which all factors influencing the curves in the past are assumed effective (unchanged) throughout theproducing life. Due to empirical nature, traditional decline curve analysis can be used for almost anysituation, on single fluid streams or multiple fluid streams, on reservoirs with pressures below or abovebubble point and on constant or variable bottom hole pressures. The modern type curve analysis, however,are partially or fully derived analytically, based on reservoir fluid flow equations and assuming somesimplifying conditions. Such type curves are generally used for predicting reserves and future productionrates as well as reservoir parameters. Since decline curves represent production from the reservoir underboundary flow conditions, it cannot be expected to give expected result in the early life of the well, i.e.when it is still in the transient flow and the reservoir boundaries have not been reached.

Basically three types of decline curves have been identified, namely, exponential, hyperbolic andharmonic. When analyzing rate decline, two sets of curves are normally used. The flow rate is plottedeither against time or against cumulative production. These curves provide a direct estimate of the ultimaterecovery at a specified economic limit.

Next came the analytical type curves by Fetkovich during 1980’s. Fetkovich used analytical flowequations to generate type curves for transient flow, and he combined them with the Arps empiricaldecline curve equations. Accordingly, the Fetkovich type curves are made up of two regions, the righthand side, which is identical to the Arps type curves and the left hand side, derived from the analyticalsolution to the flow of a well in the centre of a finite circular reservoir producing at a constant wellboreflowing pressure.

The production decline analysis techniques of Arps and Fetkovich are limited in that they do notaccount for variations in bottom-hole flowing pressure in the transient regime, and only account for such

4 SPE-173481-STU

variations empirically during boundary dominated flow. Since it is not possible to keep constant BHPduring the transient period, this assumption would give incorrect results. Blasingame and McCray notedthat using a pressure normalized flow rate when the bottom-hole pressure varies significantly did notremedy the problem. They sought functions that would transform the variable pressures/variable ratessolution into an equivalent constant pressure or constant rate solution. They introduced two specific timefunctions (also known as material balance time functions), tcr the constant rate time analogy, and tcp forconstant pressure. For the liquid case, the constant rate analogy time function is defined as the ratio of thecumulative and the flow rate:

Blasingame and others plotted this time function versus several y-axis functions. These functions aredesigned in such a manner that they will reflect the change in BHP while doing interpretation. Followingare some of these y-axis functions: -

Now the question is how to use these functions to interpret reservoir parameters? Well in simple terms,the analysis technique is entirely same as in PTA, but instead of analyzing pressure, we are analyzingrates. Instead of using Bourdet derivative, which we use as a diagnostic plot in PTA, we are using theabove function for diagnosis and interpretation. Since all the above functions have BHP term in it, anychanges in BHP will be reflected in the plot and we need not worry about the constant BHP assumption.Several flow regimes could be identified using the above functions as plots, which will help us understandthe reservoir and further interpret its properties. Following table shows the flow regimes that can be seenusing the above plotting functions:-

Experimentation/WorkflowThe following is the general workflow implemented for the work presented in this paper: -

● Generate numerical models for complex reservoir systems in Ecrin Saphir.● Generate their PTA type curves (Bourdet derivative) and see their diagnostic power.● Simulate a synthetic well test for the complex reservoir system and generate rate and pressure data

on which RTA is to be done.● In order to run simulation, there exists two possibilities: -

a. Generate Pressures at a constant step rate (Typical Well Test Scenario)b. Generate Rates at constant BHP (Production Scenario)

● Generate the RTA type curves using the generated pressure and rate data.● Study the diagnostic capability of the generated type curves.● Perform required sensitivity analysis on the generated type curves by varying various reservoir

parameters.

This part of experimentation and workflow, deals with Numerical Modelling & Simulation for generatingsynthetic well test data. Now the question arises, “Why to go for Numerical Modelling & Simulation?”

SPE-173481-STU 5

The reason for undertaking this work on Numerical Simulation was because of a particular limitation ofthe analytical technique. The numerical technique has several advantages as compared to that of theanalytical technique. The advantage of using a numerical simulator is that complex geometries, PVT /compositional changes, relative permeability changes, saturation changes etc. while testing, can bemodeled using a numerical simulator, but these are not possible to model using an analytical simulator.In the context of this work, the challenge was to generate the type curves for some of the complexreservoir systems. Thus the Numerical Modelling & Simulation facility provided by Ecrin4.3 wasexplored.

So by using Numerical Modelling & Simulation, type curves for complex reservoir systems like thoseof a T-shaped channel, L-shaped channel etc. were generated. This process has now added a few more“ready-made” models available for interpretation. It was also desired to do some sensitivity analysis onsome of the reservoir parameters in these geometries, so that if anyone goes for model matching, it wouldbe easy for them if they know beforehand which parameter influence the type curve in what way. Figurebelow shows the entire workflow.

ResultsThe objective of this work is to understand the diagnostic power of RTA type curves. As alreadymentioned, the available RTA type curves are those of Rate Normalized Integral (RNI), Blasingame,Agarwal-Gardner (AG). As can be seen from table 1, the flow regime identification capability of RNI typecurve is the best. So this work will focus mostly on RNI type curve. First we will explore the diagnosticcapability of RTA type curves for various complex geometries and heterogeneous reservoir systems, andthen we will run some sensitivity analysis of various reservoir parameters on the type curves.

It is to be noted that, while running simulations for every single case, the rock and the fluid propertiesare assumed to be the same, except the reservoir property on which sensitivity is to be run.

Figure 4—Workflow used to perform Experimentation

6 SPE-173481-STU

Exploring Diagnostic Capabilitya) Complex Reservoir Geometries: -

River channels can be straight, high-energybraided streams or low energy meandering chan-nels. This distinction is critical to reservoir geome-try. Let us look into two reservoir geometries andtheir flow regime diagnosis using RTA type curves.

➢ L – Shaped ChannelFor an L-shaped channel, the flow regimes that

we could expect because of the reservoir geometryare: radial flow, followed by channel flow, followedby radial again, followed by boundary dominatedflow. The RNI plot (Figure 7) clearly shows all theexpected flow regimes and hence has an excellentdiagnostic capability (almost of the same order asthat of Bourdet Derivative).

This encouraged us to introduce few more complications into the model and the diagnostic capabilitywas reviewed. The following figures (Figure 8 to 14) shows the Bourdet Derivative and the RNI Plot forthese complex reservoir systems.

➢ L – Shaped Channel � Fractured Well: -➢ T – Shaped Channel➢ T – Shaped Channel � Fractured Wellb) Different Reservoir Types: -Here we have the option to run simulation in two different ways: -

1. Generate Pressures at a constant step rate (Typical Well Test Scenario)2. Generate Rates at constant BHP (Production Scenario)

Table 1—Flow regimes for various RTA type curves

Figure 5—L-Shaped Channel 2-D Model

SPE-173481-STU 7

Figure 6—Log-Log Plot: dp and dp’ [psi] vs dt [hr]

Figure 7—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 8—Log-Log Plot: dp and dp’ [psi] vs dt [hr]

8 SPE-173481-STU

Figure 10—T-Shaped Channel 2-D Model

Figure 11—Log-Log Plot: dp and dp’ [psi] vs dt [hr]

Figure 9—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

SPE-173481-STU 9

Figure 12—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 13—Log-Log Plot: dp and dp’ [psi] vs dt [hr]

Figure 14—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

10 SPE-173481-STU

➢ Dual Porosity Reservoirsa) Const. BHP Solution: -b) Const. Rate Solution: -The double-porosity model assume that the reservoir is not homogeneous, but made up of rock matrix

blocks, with high storativity and low permeability, connecting to the well by natural fissures of lowstorativity and high permeability. Once the fissure system has started to produce, a pressure differentialis established between the matrix blocks, still at initial pressure pi, and the fissure system, which at thewellbore has a pressure Pwf. The matrix blocks then start to produce into the fissure system, effectivelyproviding pressure support, and the drawdown briefly slows down, creating a transitional ‘dip’ in thederivative. This is the characteristic signature for a dual porosity reservoir. As can be seen from the abovefigures (Figure 16 and 17), RNI plot successfully identifies this characteristic dip.

➢ Two Layered Reservoirsa) Const. BHP Solution: -b) Const. Rate Solution: -

Figure 15—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 16—Log-Log Plot: Normalized Pressure and derivative [psi] vs te [hr]

SPE-173481-STU 11

➢ Radial Composite Reservoirsa) Const. BHP Solution: -b) Const. Rate Solution: -With composite models, the reservoir is divided into 2 regions of different mobilities and/or storativi-

ties. Above two figures (Figure 19 and 20) clearly shows two radial stabilizations at different levelsbecause of different mobility and storativity of the two regions, thereby providing successful diagnosis.

Running Sensitivity Analysis

● Skin● Permeability● Reservoir Size

Figure 17—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 18—Log-Log Plot: Normalized Pressure and derivative [psi] vs te [hr]

12 SPE-173481-STU

Figure 19—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 20—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

SPE-173481-STU 13

Figure 21—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

Figure 22—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

14 SPE-173481-STU

ConclusionSo we just viewed the results of RTA done under two possible simulations i.e. well test scenario andproduction scenario. From this we can conclude that, RTA type curves have a very good diagnosticcapability if we use it on well test data. The Rate Normalized Integral (RNI) type curve gives excellentresults and can identify all the expected flow regimes. Its diagnostic capability is comparable to that ofthe Bourdet derivative. However Blasingame type curve can diagnose boundary only. So it is not of muchuse as far as reservoir characterization is concerned.

Even for production data, RTA type curves prove to have good diagnostic capability. However in thecase of production data, what really matters is the quality of data collected. Although pressure transientand production data analyses have the same governing theory (and solutions), we must recognize thatpressure transient data is acquired as part of a controlled “experiment,” performed as a specific event [e.g.,a pressure buildup (or PBU) tests]. In contrast, production data are generally considered to be surveillance/monitoring data — with little control and considerable variance occurring during the acquisition of theproduction data. We can separate the analysis of production data into two separate initiatives — theestimation of reservoir properties from transient flow data and the estimation of reservoir volume fromboundary dominated flow data. Perhaps the most important issue for the estimation of reservoir propertiesis to acknowledge that legacy production data (i.e., data which are 20� years old) may contain neither thequality, nor the frequency sufficient to produce competent estimates of reservoir properties. In short, it isnecessary to have accurate and frequent estimates of rate and pressure data. The expectation that lowquality/low frequency data can yield highly accurate results is simply unrealistic.

Probably the utilization of Permanent Downhole Gauges (PDG) is a feasible alternative to collect highfrequency/good quality production data on which RTA will prove to be an excellent tool. With continuousimprovement of modern day data acquisition techniques, this problem of data quality is expected to befade away.

AcknowledgementI would like to thank Mr. Nitish Kumar and Mr. Vaibhav Deshpande (Schlumberger) for guiding methroughout this work.

Figure 23—Log-Log Plot: Normalized Pressure Int. and derivative [psi] vs te [hr]

SPE-173481-STU 15

I would also like to thank Mr. Samarth Patwardhan for his guidance and the department of petroleumengineering, MIT Pune for providing me the software packages used to complete this paper.

Nomenclature

English Symbols

k � permeability, mdPdi � pressure integralPdid � pressure integral derivativepi � initial pressure, psipwf � flowing bottomhole pressure, psiq � flowrate, STB/dQ � produced oil, STBqDd � dimensionless flowrate based on decline rateqi � initial flowrate, STB/ds � skin factortc � superposition time (Q/q), daytDd � dimensionless time based on decline rate

Subscripts

c � superpositiond � derivativeD � dimensionlessDA � dimensionless based on areaDd � dimensionless based on decline rate (D)i � initial

References1. Agarwal, R.G., Gardner, D.C., Kleinsteiber, SW., and Fussell, D.D.: “Analyzing Well Production

Data Using Combined-Type-Curve and Decline-Curve Analysis Concepts,” SPEREE (Oct. 1999)478–486.

2. Arps, J.J: “Analysis of Decline Curves,” Trans., AIME (1945) 160, 228–247.3. D.M. Anderson, G.W.J. Stotts, and L. Mattar, Fekete Assocs. Inc., and D. Ilk and T.A. Blasin-

game, Texas A&M U: “Production Data Analysis–Challenges, Pitfalls, Diagnostics”, SPE 1020484. Dominique Bourdet, “Well Test Analysis: The Use of Advanced Interpretation Models”, Hand-

book of Petroleum Exploration & Production, Elsevier Publications, 2002, Vol. 3, 1–45.5. Fetkovich, M.J.: “Decline Curve Analysis Using Type Curves,” JPT (June 1980) 1065–1077.6. Fetkovich, M.J, Vienot, M.E, Bradley, M.D, and Kiesow, U.G. 1087. Decline Curve Analysis

Using Type Curves – Case Histories. SPEFE, 637.7. Lee, John, “Well Testing”, Society of Petroleum Engineers of AIME, New York, USA, 1982,

1–71.8. M. Ebrahimi, SPE, ACECR-Production Technology Research Institute, “Enhanced Estimation of

Reservoir Parameters Using Decline Curve Analysis”, SPE 133432.9. Olivier Houze, Didier Viturat, Ole S. Fjaere, “Dynamic Data Analysis”, Kappa Publication,

133–167.

16 SPE-173481-STU

10. Palacio, J.C. and Blasingame, T.A.: “Decline Curve Analysis Using Type Curves – Analysis ofGas Well Production Data,” paper SPE 25909 presented at the 1993 Joint Rocky MountainRegional/Low Permeability Reservoirs Symposium, Denver, CO, 26-28 April.

11. ZHOU Wentao, WANG Yinli and FANG Peng, LI Ji, “Advanta Operation Reference Manual”,Schlumberger, 2012.

SPE-173481-STU 17