SPE 159400

Dynamic Delumping of Reservoir Simulation Arif Kuntadi, SPE, NTNU, Petrostreamz AS, Curtis H. Whitson, SPE, NTNU, PERA AS, Mohammad Faizul Hoda, SPE, Petrostreamz AS

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 8-10 October 2012. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material 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 to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Integrated modeling is becoming a necessary tool in the petroleum industry to manage the value chain of different models. Reservoir models commonly utilize a simple fluid model to reduce computational time. However, the downstream models often require a more detailed EOS fluid model to perform surface-process facility modeling. This paper presents a dynamic delumping method to generate detailed compositional streams from either black-oil or compositional (lumped-EOS) reservoir simulations, performed as a simple post-processing step.

A set of phase-specific, pressure-dependent split factors are used to perform dynamic delumping. The split factors are generated from simulated depletion PVT experiments using a detailed-EOS model. Delumping is performed phase-wise at the well-connection level, for each time step of the reservoir simulator. For gas injection processes, the amount of injection gas is estimated from stream information and, accordingly, removed from the stream before applying the phase-specific pressure-dependent split factors. Different split factor sets are used when the reservoir model has multiple PVT regions.

We have run many reservoir simulation cases using different production mechanisms and reservoir fluids. Compared with detailed-EOS simulations, the proposed method gives near-exact results for depletion, and excellent agreement in gas injection cases. Dynamic delumping also works with complex fluid systems exhibiting large in-situ compositional (GOR) variations. For injection gas cases, improved accuracy is obtained using a tracer option in the reservoir simulator, to better estimate injection-gas quantity. This approach requires negligible cpu compared with detailed-EOS reservoir simulation.

Dynamic delumping is applied as an automated post-processing for any reservoir simulator. The results of our work provide a key technology for integrating subsurface and surface petroleum models, ensuring greater consistency in the complete value chain and enabling engineers to optimize assets, both locally and globally.

Introduction In the last few years, integrated modeling has become a preferred tool in the petroleum industry to manage the value chain of different assets. It is slowly replacing the traditional modeling approach that treats each petroleum asset model separately. Having different discipline models and applications in a single platform will ensure more consistency of the value chain from one asset to another. Integrated modeling also enables engineers to optimize assets, both locally and globally, using an automatic approach. Coupling of different petroleum assets entails transferring and combining petroleum streams from one asset to the others. Stream conversion is a key requirement in integrated modeling because petroleum assets usually have their own fluid model, and it is rare to have a single common fluid model in both the subsurface and surface simulation models.

Integrated modeling in reservoir and production management typically couples the reservoir, production network and process simulations. Reservoir simulation usually utilizes a simple fluid model to reduce the computational time due to the large numbers of grid cells being used in the reservoir model. The fluid model becomes more detailed as it moves downstream. Translating from a more detailed fluid description to a simpler description is usually a trivial process, but the converse does not hold true.

Dynamic Delumping

This paper presents a dynamic delumping method to generate detailed compositional streams from either black-oil or compositional (lumped-EOS) reservoir simulations, performed as a simple post-processing step using a set of phase-specific, pressure-dependent split factors. The split factors are generated from simulated depletion PVT experiments using a detailed-EOS model. Delumping is performed phase-wise at the well-connection level, for each time step of the reservoir simulator.

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The dynamic delumping behaves like “a linker” between subsurface and surface petroleum models; therefore it enables reservoir engineers to build a complex and detailed reservoir model and requires low computational time due to the use of the simple fluid model. The process engineers will get sufficiently detailed fluid information from the results of the dynamic delumping conversion. The dynamic delumping provides a key technology in the integrated modeling discipline.

Black-oil Delumping Whitson and Brulé (2000) introduced a black-oil delumping concept by presenting a procedure to calculate gas and oil compositions at reservoir conditions from surface phase properties (compositions and densities) combined with the black-oil properties. Hoda (2002) extended this concept to develop the first black-oil delumping method, called BOz delumping, based on a set of split factor tables generated from a depletion PVT experiment. The split factors define the conversion parameter from a surface phase rate of the reservoir simulation output to the mole amount of the reservoir phase. The split factors are set up as a lookup table using pressure as the variable. Each reservoir phase has one set of conversion table as well as the injection gas (if exists in the simulation). To recognize the presence of the reservoir phases, Hoda utilized the comparison between the producing gas-oil ratio (Rp) and the black-oil properties (solution gas-oil ratio (Rs) and oil-gas ratio (rs)). Table 1 summarizes the presence of the reservoir oil (RO), reservoir gas (RG), and injection gas (IG) for depletion and injection gas recovery processes on the black-oil delumping implementation.

Table 1 — Reservoir phases identification on the Hoda BOz delumping implementation

Condition Simulation Case

Depletion Gas Injection

Rp < Rs RO RO

Rs ≤ Rp ≤ 1/rs RO+RG RO+RG

Rp > 1/rs RG RG+IG

Ghorayeb and Holmes (2005) proposed another black-oil delumping method which is also based on a depletion PVT

experiment. Their delumping method requires the surface phase properties (mass amount and density) from reservoir simulation and a lookup table generated from a depletion PVT experiment to obtain composition and mole amount of the reservoir phase. The lookup table is set up using specific variable that depends on the simulation case. The total composition of the wellstream is calculated from the composition and mole amount of the reservoir phases. Ghorayeb and Holmes also addressed black-oil delumping during gas injection recovery process but their approach did not consider the effect of the free gas that might exist in the reservoir. Vignati et al. (2010) modified the Ghorayeb and Holmes black-oil delumping scheme to recognize the nature of the free gas (liberated gas from reservoir oil, gas cap and injection gas). They proposed a procedure to re-estimate the composition of reservoir gas entering a completion by utilizing the tracer tracking feature available in most commercial reservoir simulators.

We found that the Hoda black-oil delumping procedure is simple for the implementation and also consistent, mainly, because the conversion factors are generated using the same procedure as for the black-oil table. However, this delumping procedure has a potential problem in the gas injection case, for which Hoda assumed that the production stream of the given well-connection consists of reservoir oil and gas for a producing GOR in the range of Rs ≤ Rp ≤ 1/rs. However, we found that this scenario is not always the case. From both the compositional and black-oil reservoir simulations with tracer tracking, we found that the production stream might contain injection gas for a producing gas-oil ratio in the range of Rs ≤ Rp ≤ 1/rs. The production stream might consist of reservoir oil, reservoir gas and injection gas when Rp > Rs without necessarily meeting the condition of Rp > 1/rs. In this paper we developed a new black-oil delumping procedure using an approach similar to that of the Hoda method. Our main goal is to improve the delumping procedure for handling of the injection gas recovery process.

When the reservoir oil, reservoir gas and injection gas exist in the production stream, the correlation between the surface volume rate and reservoir volume rate can be defined as follows (Kuntadi 2012)

VV goV = + ro sB Bo g

(1)

V VV g igoV = R + +g s B B Bo g g ig

(2)

where Vo andVg are the volume of surface oil and gas, repectively. Vo, Vg and Vig are the volume of reservoir oil, gas and

injection gas at reservoir condition, repectively. Bo, Bg and Bg ig are the formation volume factor of reservoir oil, gas and injection gas, repectively.

Rearranging Eqs. (1) and (2) and introducing parameter, that is defined as a volumetric contribution of the injection gas to the total surface gas, to the equations yields

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V (1- a)r1o s= V - Vo gB 1-r R 1- r Ro s s s s

(3)

Vg R1- a s= V - Vg oB 1- r R 1- r Rg s s s s

(4)

where

g ig

g

ig g ig

g

Va

V

V / B=

V

(5)

g igV is the volume of the injection gas at surface condition. We utilize split factors to perform the conversion from Vo/Bo,

Vg/Bg, and Vig/Bg ig to moles of component j ( jn ) as given by

g igoj o j j ig j

o g g ig

g

V VVn S S S

B B B (6)

where o jS , g jS and ig jS are split factors of reservoir oil, gas and injection gas, respectively.

The split factor is calculated from the molar volume and composition of the equilibrium phase of simulated depletion PVT experiments using a detailed-EOS model. A complete set of split factors is provided by pressure-dependent table and there are three sets of split factors at each pressure point for the conversion of reservoir oil, gas and injection gas volumes to the corresponding reservoir phase composition. To recognize the presence of reservoir phases in the production stream for the depletion recovery process, we use the same assumption as proposed by Hoda (2002). For injection gas recovery process, we propose to utilize the tracer tracking feature to provide the parameter as an indicator of the injection gas presence in the production stream. For the producing GOR in the range of Rs ≤ Rp ≤ 1/rs, the production stream is assumed to contain RO, RG and IG if > 0. Fig. 1 shows how we identify the flowing reservoir phases on reservoir simulation outputs for both depletion and gas injection recovery processes. The injection gas breakthrough of Fig. 1b was identified by the tracer tracking of the reservoir simulation. For further discussion on this paper, we refer our black-oil delumping to as “the proposed BOz delumping”.

(a) Depletion Case (b) Gas Injection Case

Fig. 1 — Identification of the flowing reservoir phases on reservoir simulation outputs.

Compositional Delumping Schlijper and Drohm (1988) performed a study of delumping or inverse lumping to recover a detailed fluid description

from the lumped-components. They used tshe lumped-component liquid vapor equilibrium composition, split parameters and detailed EOS parameters to approximate the detailed-component K-values and then used the material balance to calculate the detailed composition. Danesh et al. (1990) proposed a different delumping method by modifying the Wilson equation to correlate the detailed-component K-values with the acentric factor and reduced temperature at a constant pressure and temperature. Leibovici et al. (1996) proposed a similar approach but they correlated K-values with EOS parameters a and b. They conducted their study using Soave-Redlich-Kwong (SRK) and Peng Robinson (PR) EOS models. If the EOS models have zero binary interaction parameters (BIPs), the K-values logarithms have a linear correlation with EOS parameters at a given pressure and temperature and the constants can be analytically calculated from the lumped EOS model. For the non-zero BIPs EOS model, a regression procedure is required. This approach is referred to as the LSK delumping method. Stenby et al.

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(1996) tested the LSK delumping on the constant volume depletion experiment and reservoir simulation of the fifth SPE Comparative example. Faissat and Duzan (1996) proposed a delumping method based on a set of split factors on depletion recovery. The split factors were generated from two single-cell simulations, one for lumped fluids and the other for detailed fluids. Leibovici et al. (1998) proposed implementation of LSK delumping on a compositional reservoir simulation; their approach is referred to as the LBW delumping method. Baker and Leibovici (1999) implemented the LBW delumping procedure on a real field case. They reported that the time required for the delumping calculation was only a small fraction of the total time required to run the reservoir simulation.

Nichita and Leibovici (2006) proposed an analytical correlation to extend the LSK delumping procedure to the non-zero BIPs EOS model. Their correlation is based on the concept that the equilibrium coefficients are related only to the component properties and EOS coefficients, independent of the phase compositions. They proposed to the application of a reduction method to obtain the equilibrium coefficients from the lumped fluid flash and then use them to retrieve the detailed fluid composition. Further, Nichita et al. (2007) tested this method on more complex cases for several reservoir fluids and reservoir processes. Recently, De Castro et al. (2011) compared the implementation of the analytical delumping (Nichita and Leibovici 2006) and LSK delumping (Leibovici et al. 1996) in the reservoir simulation results. They reported that analytical delumping provides systematically better results than LSK delumping.

Our proposed black-oil delumping method was developed based on the similarity between the reservoir simulation and depletion PVT experiment on a pressure and phase composition correlation. We used the same approach to develop a new method to delump a lumped-component into the corresponding detailed-components based on the unique correlation of the phase composition and pressure of the lumped EOS reservoir simulation and the detailed EOS depletion experiment. We use the split factor to split the lumped-component (l) into the contributing detailed-components (d). The split factors (S) used to convert lumped EOS fluid containing Nl components to a detailed EOS containing Nd components can be described by

1

, for 1,2,...lN

d ld l dl

q S q d N

(7)

where Sld = split factor used to convert the lumped-component d to the detailed-component l and q = quantity. To generate the split factor, we conducted a depletion PVT experiment (the CCE is recommended) on reservoir fluid at the

reservoir temperature using a detailed EOS model. From each pressure point, we collected equilibrium liquid (EQL) and equilibrium vapor (EQV) compositions and then calculated the split factors of both phases. The pressure range of the depletion PVT experiment should cover the expected pressure range of the reservoir simulation. The phase depletion split factor represents the delumping split factor of reservoir simulation well-connection phase streams as given by ( )DS S p , where

DS = the phase-specific split factor generated from the depletion PVT experiment and p = saturation pressure of the depletion

PVT experiment. We used the C7+ mole fraction as the control variable to distinguish the liquid and vapor phases. The complete split factor table consists of sets of the split factor as a function of pressure and composition (C7+ mole fraction).

The compositional delumping procedure for depletion recovery process includes flashing the well-connection production streams at well-connection pressure and temperature and then applying the split factor tables phase-wise to get the detailed compositional profile. This is done for every time step of the reservoir simulation. The two phase streams are finally combined to get the mixture well-connection stream. For gas injection processes, the amount of injection gas is estimated from stream information and, accordingly, removed from the stream before applying the phase-specific pressure-dependent split factors. The compositional delumping procedures are summarized in Fig. 2.

(c) Depletion Case (d) Gas Injection Case

Fig. 2 — Compositional delumping procedures.

To split the injection gas stream from the connection-well stream, we introduce the parameter to quantify the amount of

injection gas in the well-connection production stream

ig

t

n

n (8)

o g ig tn n n n (9)

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where nig = moles of injection gas in the well-connection stream, nt = total moles of well-connection stream, no = moles of reservoir oil in the well-connection stream and ng = moles of reservoir gas in the well-connection stream. We used “a key component” content in the gas phase as the parameter to estimate . The key component is a lumped-component that its

compositional change is proposional with the amount of injection gas in the production stream when the well-connection stream experiencing an injection gas breakthrough. Based on our study, we found that the intermediate components (C3 - C5) give a very good indication of the presence of injection gas. Fig. 3 shows the compositional change of an oil reservoir undergoing partial pressure maintenance by rich injection gas, compared to the composition of the equilibrium phases from simulated CCE experiment. Path 1-2-3 indicates the depletion process, which consists of the depletion process for under-saturated conditions (path 1-2) and the depletion process for saturated conditions (path 2-3). Path 3-4-5 shows the condition after injecting rich gas into the reservoir. The components undergo a compositional change toward that of the injection gas. The parameter can be estimated by

* *

* *

l Dl

ig l Dl

y y

y y

(10)

where yl* = mole fraction of the key lumped-component l in the reservoir gas in well-connection stream, yDl* = mole fraction of key lumped-component l in the equilibrium vapor of the PVT depletion and yig l* = mole fraction of key lumped-component l in the injection gas. The total and lumped-component molar amounts of the injection gas are given by

ig tn n (11)

for 1, 2,.... ,igig l ig l ll Nn y n (12)

where nig l = moles of lumped-component l in the injection gas, yig l = moles fraction of the lumped-component l in the injection gas and Nl = number of lumped-component in the fluid model. The component material balance was used to calculate the lumped-component molar amount in the injection-gas-free production stream as given by

, for 1,2,...Rl l t ig l ln z n n l N (13)

where nRl = moles of lumped-component l in the reservoir oil and gas in well-connection stream and zl = mole fraction of the lumped-component l in well-connection stream. We recommend intermediate components (C3-C5) as the key lumped-component used in the injection gas separation. If we inject a pure injection gas (e.g. CO2) then this pure component becomes the key lumped-component. Split factors generated from the depletion PVT experiment (SD) are used to convert the molar amount of the lumped-components as given by Eq. (13), while the split factors generated from the injection gas composition (SIG) are applied to convert the lumped-components calculated by Eq. (12) to a detailed compositional profile.

(a) nC5 (b) nC4

Fig. 3 — Composition comparison (CCE experiment vs. reservoir simulation of partial pressure maintenance by rich gas injection).

We propose a second procedure to split the injection gas stream from the connection-well stream using the tracer tracking

option available in most reservoir simulators. In compositional reservoir simulation, the amount of injection gas stream in the well-connection production stream can be estimated by the concentration of injection gas tracer component in the production stream. The molar amount of injection gas is given by

1

lN

ig ttll

n z n

(14)

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where nig = moles of lumped-component l in the injection gas; nt = total moles of lumped-component l in the well-connection stream; ztl = concentration of the injection gas tracer lumped-component l in the well-connection stream. The lumped-component molar amount of the injection-gas-free production stream is calculated by

1

( )lN

tRl l tll

n z z n

(15)

where nRl = moles of lumped-component l in the reservoir oil and gas in well-connection stream; zl = mole fraction of the lumped-component l in well-connection stream. . For further discussion on this paper, we refer our proposed compositional delumping to as “the z2z delumping”. Example Cases We ran different example cases to test the proposed black-oil and compositional delumping methods. Depletion and gas injection simulations are performed. Three reservoir fluids and three injection gases are used as the reference fluids. We use a multi-layer with permeability variation reservoir model for all cases. For black-oil delumping cases, we ran both black-oil and detailed-EOS compositional reservoir simulations. The black-oil tables used in the black-oil simulation are generated by the detailed EOS model as was used in the compositional simulation. For compositional delumping cases, we ran both lumped and detailed EOS compositional reservoir simulations. The lumped EOS models were developed based on the detailed EOS model.

PVT Models

The first EOS model utilized in this study was developed by Fevang et al. (2000). It is a Soave-Redlich-Kwong (SRK) EOS model with 22 components. It has 13 individual components and nine lumped-components that describe the decanes-plus fraction. Fevang et al. (2000) generated the EOS-SRK22 model based on a gas condensate sample from a North Sea field with a reservoir temperature of 163 oC. Table 2 gives the detailed EOS parameters of the EOS-SRK22 model. We took a volatile oil fluid and injection gases from Fevang et al. (2000) study. We applied an isothermal gravitational segregation at 163 oC on the volatile oil fluid to obtain the oil compositions. Table 3 provides the reference fluids used in the black-oil delumping testing. To generate the black-oil table for the black-oil reservoir simulation we applied the Whitson and Torp (1983) method as recommended by Singh (2002). The corresponding black-oil delumping split factor table was generated for each black-oil table. We took the CCE experiment as the standard depletion PVT experiment for generation of the black-oil table.

Table 2 — Detailed EOS-SRK22 parameters

We utilized a lumped EOS model developed by Fevang et al. (2000) based on EOS-SRK22. They performed a stepwise lumping procedure (22 12 10 9 8) to obtain the final lumped EOS-SRK8 model. They used EOS-SRK22 to provide the “experimental PVT data” (e.g. depletion, separator test, and multi-contact) during lumping process, and finally, they tuned the lumped EOS to match the “experimental PVT data”. Table 5 shows the EOS parameters of the EOS-SRK8 model. Table 6 provides the composition of the reference fluids and injection gas used in this study. Fig. 4 shows a comparison between the EOS-SRK22 and EOS-SRK8 models regarding composition, liquid saturation and relative volume from the CCE experiment of the volatile oil at 163 oC. The two models showed good agreement, but there was a slight difference in the C4-5 composition in the oil and gas phases. Later, we will find that this difference will significantly impact the accuracy of the delumping results.

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Table 3 — Reference fluid compositions (EOS-SRK22)

a GORs are calculated based on two-stage separator condition in Table 4

Table 4 — Two-stage and three-stage separator conditions

Table 5 — Lumped EOS-SRK8 parameters

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Table 6 — Reference fluid compositions (EOS-SRK8)

(a) Oil Phase (b) Gas Phase

Fig. 4 — Phases composition comparison between the EOS-SRK22 and EOS-SRK8 models on the CCE experiment at 163oC.

The second EOS model is a Peng-Robinson (PR) EOS model (Nichita et al. 2007). The detailed model (EOS-PR20)

consists of 20 components with the heaviest component C48+. Nichita et al. (2007) adopted the lumping scheme “D” proposed by Stenby et al. (1996) to obtain a lumped EOS model that consists of 10 components (EOS-PR10). The lumped-components properties and BIPs were estimated by the method of Leibovici (1993). Table 7 gives the detailed EOS parameters of the EOS-PR20 and Table 8 does of EOS-PR10 models. Table 9 gives the composition of the reference fluids used in this study. The EOS-PR10 and EOS-PR20 models are in good agreement in the results of the CCE experiment for the given reference fluid, except for the C7+ gas composition as shown in Fig. 5. This difference is not an issue for a low GOR (100 Sm3/Sm3) reservoir oil.

Table 7 — Detailed EOS-PR20 parameters

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Table 8 — Lumped EOS-PR10 parameters

Table 9 — Reference fluid compositions (EOS-PR20 and EOS-PR10)

a GOR is calculated based on three-stage separator condition in Table 4

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(a) Oil Phase (b) Gas Phase

Fig. 5 — Phases composition comparison between the EOS-PR20 and EOS-PR10 models on the CCE experiment at 71.1 oC.

Reservoir Model

The reservoir simulation model is given in Table 10 (Fevang et al. 2000). It has a 50x10x10 grid system. The reservoir has an average permeability of 200 md and each numerical layer has a constant kh with varying thickness. The reservoir model has a dip of 3.8 degrees. For the depletion recovery process the producer is located down-dip in cell (50,10). For the gas injection recovery process the producer is located in cell (50,5), and the injector is placed in cell (1,5). Both the producer and injector are perforated in all layers.

In this study, we use Eclipse software (Schlumberger) as the reservoir simulator: ECLIPSE 100 (ECL100) for the black-oil simulation and ECLIPSE 300 (ECL300) for the compositional simulation. We also use PhazeComp (Zick Technologies) for the PVT behavior simulation and Pipe-It (Petrostreamz AS) for the post-processing of the reservoir simulation output: petroleum stream management and dynamic delumping conversion.

Table 10 — Reservoir model

Dynamic Delumping Quality Assesment

Two procedures are performed to assess the accuracy of the proposed BOz delumping method. First, the delumped compositional profile is reprocessed to obtain the surface gas and surface oil rates with the same process conditions as those used to generate the black-oil table. The comparison is performed on either a producing GOR or surface phase rate basis

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between the reprocessed and the black-oil simulation results. The second procedure is to compare the delumped compositional profile with that resulting from the compositional reservoir simulation. For the sake of consistency, a close production performance between the black-oil and the compositional reservoir simulation runs is required.

The z2z delumping was tested using several example cases including the depletion and gas injection recovery processes. For each case, we ran a reservoir simulation with detailed and lumped EOS models. To avoid the effects of the different PVT behaviors between the detailed EOS and lumped EOS on the delumping results, we used a special quality assessment procedure. We took the well-connection stream of the detailed EOS reservoir simulation and flashed it at the reservoir temperature and well-connection pressure to obtain reservoir oil and gas streams. We lumped these streams to obtain the reservoir phases described in the lumped EOS model. Then, these streams were delumped based on the z2z delumping split factor table to re-obtain the detailed EOS description. This special procedure gives the ideal result yielded by the z2z delumping. In the discussion that follows, we refer to this procedure as the “ideal z2z delumping”. The normal z2z delumping of a lumped EOS simulation is later referred to as the “standard z2z delumping”.

In all delumping quality assessment figures in this paper we show a composition comparison between results of the detailed EOS simulation, standard z2z delumping and ideal z2z delumping. For the SRK EOS model, we use the figure legends of “EOS22”, “z2z-EOS8” and “z2z-EOS22” to represent the detailed EOS simulation, standard z2z delumping and ideal z2z delumping cases, respectively. For the PR EOS model, we use the figure legends of “EOS20”, “z2z-EOS10” and “z2z-EOS20” to represent the detailed EOS simulation, standard z2z delumping and ideal z2z delumping cases, respectively.

We also performed sensitivity analysis to exemine the effect of two different approaches to splitting the injection gas stream from the production stream before conducting the z2z delumping in the gas injection recovery cases. In this section, we compare four methods: the “ideal z2z delumping” and “standard z2z delumping” using the key component, the “standard z2z delumping” using the tracer, and the detailed EOS reservoir simulation. For these four methods we use figure legends: “z2z-EOS22-KeyComponent”, “z2z-EOS8-KeyComponent”, “z2z-EOS8-Tracer” and “EOS22”, respectively.

Black-oil Delumping Case 1: Volatile Oil Depletion Case

We initialized the reservoir with a constant composition of volatile oil as given in Table 3. The reference fluid has a saturation pressure of 456.2 bar of 163 oC. The reservoir was defined as an undersaturated reservoir with an initial pressure of 494.68 bar. We ran a depletion reservoir simulation by specifying that the production well must produce a reservoir volume rate of 10% hydrocarbon pore volume per year with a minimum bottom hole pressure of 100 bar. The simulation was run for 10 years. The CCE experiment was conducted to generate the black-oil table and delumping split factor table. Fig. 6a shows the well producing GOR comparison between ECL100, ECL300 and the delumped stream.

The reprocessed surface rates of the delumped stream give an identical producing GOR as the ECL100 simulation result. We suggest that ECL100 and ECL300 have similar production profiles based on the close producing GOR profiles. Therefore, we can use the ECL300 simulation results as a reference composition profile for the quality assessment. Fig. 6b depicts the production stream composition for light, intermediate and heavy components. The proposed BOz delumping approach yields nearly identical results to the compositional simulation for all components.

(a) Producing GOR vs. Reproduced GOR (b) Composition

Fig. 6 — Black-oil delumping quality assessment on Volatile oil depletion case. Well level GOR and component composition comparison.

Black-oil Delumping Case 2: Full Pressure Maintenance in an Oil Reservoir by Lean Gas Injection

To address the injection gas effect on the accuracy of BOz delumping, we ran a full pressure maintenance reservoir simulation in an oil reservoir by injecting a lean gas into the reservoir on day 1. Table 3 gives the details related to the reservoir oil and lean gas compositions used in this example case. We used a tracer tracking system available in the ECL100 simulator to obtain the injection gas flow rate produced by the producing well-connections. The parameter is calculated as

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the ratio of the produced injection gas rate relative to the total produced gas rate. The proposed BOz delumping procedure was performed to generate the compositional profile. We also performed the Hoda (2002) BOz delumping procedure to provide a quantitative comparison with the currently available black-oil delumping method. The reservoir simulation was carried out for a 30-year period.

Fig. 7a shows a comparison of the producing GOR from the compositional simulation, black-oil simulation and the reproduced GOR from the BOz delumping results. The black-oil reservoir simulation is only able to match the producing GOR of the compositional run for the first 2,500 days; after this period, the black-oil run yields lower producing GORs. This figure also suggests that both BOz delumping methods perfectly reproduce the producing GOR of the black-oil reservoir simulation throughout the entire simulation period. The compositional profile comparison is performed on the well level and is depicted in Fig. 8. For the period in which ECL100 and ECL300 have comparable profiles (0-2,500 days), the proposed BOz method yields a perfect match for the C1, nC4 and C7p components and a reasonably good match for the other light components CO2 and C2. Thus, the proposed BOz method is able to handle the compositional change after an injection gas breakthrough.

We plotted the well-connection producing GOR of the first two top layers against the solution gas-ratio and the inverse of the solution oil-gas ratio of the black-oil table. Fig. 7b shows that the producing GOR never exceeds 1/rs. This is the reason why the Hoda BOz method estimates an increasing CO2 profile after an injection gas breakthrough while the ECL300 has a decreasing trend. In Hoda method, the production streams are assumed to consist of reservoir oil and reservoir gas because the producing GOR is between Rs and 1/rs. The proposed BOz method is an improvement of Hoda's approach and enables a proper estimation to distinguish between the two-phase or three-phase production streams.

(a) Producing GOR vs. Reproduced GOR and Injection Gas Tracer

(b) Producing GOR vs. Black-Oil properties (Rs and 1/rs)

Fig. 7 — Black-oil delumping quality assessment on the full pressure maintenance gas injection case. Well level GOR and injection

gas tracer comparisons.

(a) CO2, C2 and nC4 (b) C1 and C7+

Fig. 8 — Black-oil delumping quality assessment on the full pressure maintenance gas injection case. Well level component composition comparison.

As shown in Fig. 8a, the proposed BOz approach does not yield close CO2 and C2 profiles in the early period despite

ECL100 and ECL300 having the same GOR profile. To verify this, we reran ECL300 with tracer tracking and compared the

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tracer concentration between ECL100 and ECL300 outputs. Fig. 7a shows that the ECL100’s and ECL300’s timing of the injection gas breakthrough and development are slightly different. Therefore, the difference between the ECL100 and ECL300 profiles rather than the limitation of the proposed BOz, is most likely the determining factor impacting the imperfect match of the CO2 and C2 profiles.

We performed BOz delumping on the black-oil rates of the ECL300 simulation to avoid the inconsistent profiles of the ECL100 and ECL300 outputs. Any difference observed in the composition comparison, should be considered as a result of the BOz delumping method. Fig. 9 shows the composition comparison between the ECL300 output and the BOz method results. The proposed BOz approach gives an almost perfect match of all components. The distinct profiles of CO2 and C2 given by ECL100 BOz delumping are not observed. The proposed BOz method can perfectly retrieve the compositional profile of ECL300 from ECL100 black-oil rates as long as there is consistency between the ECL300 and ECL100 profiles. Alterations of the compositional profile after an injection gas breakthrough can be properly handled using the proposed BOz delumping method.

(a) CO2, C2 and nC4 (b) C1 and C7+

Fig. 9 — Black-oil delumping quality assessment on the full pressure maintenance gas injection case from ECL300 runs. Well level component composition comparison.

Black-oil Delumping Case 3: Partial Pressure Maintenance in an Oil Reservoir by Rich Gas Injection

In this case, we ran another injection gas recovery simulation on the same oil reservoir that we used in case 2. The undersaturated oil reservoir is depleted for 200 days; afterward, a rich injection gas is injected into the reservoir to maintain the reservoir pressure. The composition of the rich injection gas is given in Table 3. We ran the reservoir simulation with the tracer tracking option to obtain the injection gas profile of the well-connection production stream. Again, we compare our proposed method to the Hoda method.

(a) Producing GOR vs. Reproduced GOR and Injection Gas Tracer

(b) Producing GOR vs. Black-Oil properties (Rs and 1/rs)

Fig. 10 — Black-oil delumping quality assessment on the partial pressure maintenance gas injection case. Well level GOR and

injection gas tracer comparisons. Fig. 10a shows the producing GOR profiles as a function of time. This figure shows that the producing GOR given by

ECL100 can be perfectly reproduced by both BOz methods throughout the entire period. For the period spanning 0-5,000 days, both ECL100 and ECL300 yielded the same GOR profiles. Fig. 11 depicts that the proposed BOz method, which is expected

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to provide a better estimation in the case of the incorporation of injection gas, fails to match the ECL300 profile after the injection breakthrough until 5,000 days, with exception of C7+ components. The different production profile between ECL100 and ECL300 is the reason of the imperfect match. As shown in Fig. 10a, the injection gas breakthrough of ECL300 comes almost 800 days after that is of ECL100. This difference also explains why the Hoda BOz method yields results matching those of the ECL300 simulation for the period of 2,200-4,000 days. The ECL300 simulation yields a combination of reservoir oil and gas production stream from the beginning until the injection gas breakthrough is achieved (at approximately day 2,900). This two-phase stream perfectly matches the Hoda BOz assumption where there is no injection gas exists when Rp ≤ 1/rs as shown in Fig. 10b.

As we did in example case 3, we performed another BOz delumping on the black-oil rates of the ECL300 to avoid the production profile inconsistency effect on the BOz delumping results. Fig. 12 shows the comparison between the ECL300 output and the proposed BOz delumping applied to the ECL300 black-oil rates. The proposed BOz method yields a perfect match for most of the components. The presence of the injection gas in the production stream can be identified and treated properly and yields a perfect match with the ECL300 output.

(a) CO2, C2 and nC4 (b) C1, C7 and F9

Fig. 11 — Black-oil delumping quality assessment on the partial pressure maintenance gas injection case. Well level component composition comparison.

(a) CO2, C2 and nC4 (b) C1, C7 and F9

Fig. 12 — Black-oil delumping quality assessment on the partial pressure maintenance gas injection case from ECL300 runs. Well level component composition comparison.

Compositional Delumping Case 1: Oil Depletion Case

In the first test case of the compositional delumping, we used EOS-PR20 and EOS-PR10 as the reference EOS models. We initialized the reservoir with a constant oil composition as given in Table 9. The reference fluid had an original saturation pressure of 297.88 bar at 71.1oC. The initial reservoir pressure was 400 bar, which is higher than the original saturation pressure. The reservoir was depleted by controlling the production well to produce a reservoir volume rate of 10% hydrocarbon pore volume per year with a minimum bottom hole pressure of 100 bar. We ran the simulation for a 10-years period. Fig. 13a shows the identical well surface rates obtained in the detailed and lumped EOS simulations. Fig. 13b compares the well production stream composition of intermediate and heavy components. The standard and ideal z2z

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delumping approaches yield nearly identical results to those obtained using the detailed EOS simulation for all of the components.

(a) Well surface rates (b) Composition

Fig. 13 — z2z delumping quality assessment of oil reservoir depletion case. Well surface rates and component composition comparisons.

Compositional Delumping Case 2: Volatile Oil Depletion Case

We ran a similar depletion reservoir simulation on the second test case using the EOS-SRK22 and EOS-SRK8 models. We used volatile oil fluid as given in Tables 3 and Error! Switch argument not specified.. to initialize the reservoir with a constant composition, initial pressure of 494.68 bar and reservoir temperature of 163oC. Fig. 14 shows a well stream compositional comparison for some components representing light, intermediate and heavy components. The ideal z2z delumping method gives nearly identical results. The agreement is very good for the standard z2z delumping method except for the intermediate component (nC4). The deviation of the nC4 composition is approximately 20%. This difference is due to different vapor liquid equilibrium behaviors of intermediate components between the detailed EOS and lumped EOS models, as we found earlier.

(a) CO2, C1 and nC4 (b) C7, C9 and F4

Fig. 14 — z2z delumping quality assessment of volatile oil reservoir depletion case. Well component composition comparison. Compositional Delumping Case 3: Full Pressure Maintenance in an Oil Reservoir by CO2 Injection

The third example is an extension of the compositional delumping example case 1. We conducted a full pressure maintenance in this oil reservoir by injecting CO2 gas from the start to maintain the reservoir pressure at levels higher than the original saturation pressure. The well produced reservoir oil at a constant rate for approximately 1,350 days, at which the injection gas was breakthrough to the well bore. Thereafter, the producing GOR rapidly increased due to a greater amount of injection gas being produced at the well bore.

Fig. 15a compares the well surface rates resulted from the detailed and lumped EOS simulation. Both simulations yielded similar results. Fig. 15b shows a component composition comparison between detailed and delumped fluids at the well level.

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Again, the ideal z2z delumping procedure gives almost identical results for all components. The standard z2z delumping procedure results are very similar to those of the detailed fluids.

(a) Well surface rates (b) Composition

Fig. 15 — z2z delumping quality assessment of the full pressure maintenance on an oil reservoir by CO2 injection gas. Well surface rates and component composition comparisons.

Compositional Delumping Case 4: Partial Pressure Maintenance in a Volatile Oil Reservoir by Rich Gas Injection

In the fourth test example, we conducted a partial pressure maintenance by injecting rich gas into the same volatile oil reservoir as used in the second example. For the first 200 days, we depleted the reservoir until reached 410 bar and then injected the rich gas to maintain the reservoir pressure. The rich gas composition is given in Tables 3 and Error! Reference source not found.. Fig. 16a shows that the well surface rates for the detailed and lumped EOS simulations are very similar.

To split the injection gas stream and reservoir fluid stream at the well connection level, we used two different approaches, the key component and tracer approaches, to evaluate their impact on the z2z delumping results. For the key component approach, we took C4-5 as the key component. The ideal z2z delumping yielded very similar results for the composition of all components as seen at Figs. 16a and 17. The standard z2z delumping procedure, yielded similar results, using both the key component and tracer approaches, with exception of the intermediate component (nC4). Although not presented in this thesis, the comparison for the C4 and C5 components yielded similar results. The different PVT behavior of the detailed and lumped EOS, affects the accuracy of the compositional delumping results. From the comparison plots, we found that the two approaches (key component and tracer) do not have significantly different compositional delumping accuracies.

(a) Well surface rates (b) C1

Fig. 16 — z2z delumping quality assessment of partial pressure maintenance on volatile oil reservoir by rich gas injection. Well surface rates and component composition comparisons.

Computational Time

A lower computational time is the main reason for engineers' preference to run a reservoir simulation with a black-oil or lumped EOS rather than a detailed EOS even though the later may provide better fluid description. Application of the dynamic delumping procedure may yield a black-oil or lumped EOS reservoir simulation to retrieve the detailed fluid description while putting a lower demand on the simulation time. In this section, we investigate the extra time required to perform dynamic delumping relative to the reservoir simulation computational time.

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Table 11 shows the computational time summary of all example cases that were simulated on the BOz delumping study. The black-oil reservoir simulation is between 40-130 times faster than the detailed EOS simulation. The extra time required for BOz delumping is very small compared to the computational time of the detailed EOS reservoir simulation and is less than that of the black-oil reservoir simulation. Running the black-oil reservoir simulation and combined with the BOz delumping are about 20-80 times faster than the detailed EOS reservoir simulation.

(a) iC5 (b) C7

Fig. 17 — z2z delumping quality assessment of partial pressure maintenance on volatile oil reservoir by rich gas injection. Well component composition comparison.

Table 11 — Reservoir simulation and BOz delumping computational time

Table 12 shows the computational time summary of all example cases that were simulated on the z2z delumping study. The lumped EOS reservoir simulation is almost four times faster than the detailed EOS simulation. The extra time required for z2z delumping is almost negligible for depletion cases because it is a straight-forward conversion and does not require a splitting injection gas step. For the injection case, injection gas splitting is the largest contributor to z2z delumping implementation. In general, this splitting step requires 60-70% of the total z2z delumping time. For z2z conversion we used the commercial software Streamz (Petrostreamz AS). We have written MATLAB codes to split the injection gas from the production stream. Although these codes require improvement prior to commercial implementation, they have a reasonably good performance for research purpose. For the combination of the lumped EOS reservoir simulation and z2z delumping, these codes operate approximately three times faster than the detailed EOS reservoir simulation.

Table 12 — Reservoir simulation and z2z delumping computational time

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Table 13 summarizes the effect of using tracer tracking on the computational time of z2z delumping. Running a lumped EOS reservoir simulation with tracer tracking increases the run time by approximately 28% compared to the simulation without tracer, but the tracer require less run time when performing z2z delumping, so both cases require similar total run time for reservoir simulation and z2z delumping, which is three times shorter than the time required for the detailed EOS reservoir simulation.

We also studied the effect of the total number of grid cells used in the reservoir model on the computational time. In our base reservoir model we used 50x10x10 gridding. To obtain a different number of grid cells we developed three new reservoir models with 15x5x3, 50x10x30 and 50x10x99 gridding. Thus, we have four cases with total grid cell numbers of: 225, 5,000 (base case), 15,000 and 495,500. We perforated these new models in all layers as we did for the base case. We used Example Case 4 as the case reference. Fig. 18 shows the computational time of the reservoir simulation (detailed and lumped EOS) and z2z delumping as a function of the total number of perforated cells. All plots show relatively linear trends where the total CPU times required by the lumped EOS reservoir simulation and z2z delumping process are consistently about three times faster than those of the detailed EOS reservoir simulation. This figure also shows that the injection gas splitting process requires the largest portion of the z2z delumping run time. As the model uses more perforated cells, the total run time of z2z delumping becomes dominated by injection gas splitting. The z2z conversion run time has little to no impact in complex reservoir models.

Table 13 — Tracer tracking effect on the computational time

Fig. 18 — Computational time required by the reservoir simulation and z2z delumping as a function of total number of perforated grid

cells (injection gas case).

Conclusion We have presented a dynamic delumping method to generate detailed compositional streams from either black-oil or compositional (lumped-EOS) reservoir simulations. It is implemented as a post-processing step of reservoir simulation and performed phase-wise at the well-connection level, for each time step of the reservoir simulator. The delumping conversion is performed using a set of split factor tables that are dynamically related to multiple variables (e.g. pressure, composition). The split factors are generated from simulated depletion PVT experiments using a detailed-EOS model (the CCE experiment is recommended). The proposed black-oil delumping method gives nearly identical results in the depletion recovery cases and excellent agreement in the gas injection cases. For injection gas cases, we propose use of the tracer tracking of the reservoir simulation to identify and quantify the injection gas. The proposed compositional delumping method works very well in both depletion and gas injection cases independent of the PVT model. The accuracy of compositional delumping results is highly dependent on the quality of the lumped EOS model relative to the detailed EOS model. Under ideal condition, when the detailed and lumped EOS models have exactly the same PVT behavior, the proposed compositional delumping method can

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retrieve the detailed fluid composition with nearly perfect. Both black-oil and compositional delumping methods are fast and require only a very small additional amount of computational run time relative to the detailed EOS reservoir simulation.

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