Application of water injection curves for the dynamic analysis of fractured-vuggy carbonate reservoirs

Accepted Manuscript Application of water injection curves for the dynamic analysis of fractured-vuggy carbonate reservoirs Ping Yue, Zhiwei Xie, Haohan Liu, Xiaofan Chen, Zhongliang Guo PII:

S0920-4105(18)30456-X

DOI:

10.1016/j.petrol.2018.05.062

Reference:

PETROL 4991

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 15 March 2018 Revised Date:

12 May 2018

Accepted Date: 21 May 2018

Please cite this article as: Yue, P., Xie, Z., Liu, H., Chen, X., Guo, Z., Application of water injection curves for the dynamic analysis of fractured-vuggy carbonate reservoirs, Journal of Petroleum Science and Engineering (2018), doi: 10.1016/j.petrol.2018.05.062. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Application of Water Injection Curves for the Dynamic Analysis of Fractured-vuggy Carbonate Reservoirs

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Abstract: In Tahe Oilfield, Tarim Basin, NW China, the carbonate reservoir displays poor porosity and permeability in its matrix, while the fractured-vuggy system is distributed in a random, discreet and discontinuous way, which yields significant oil rates once the fractured-vuggy system is connected by production

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wells. The fractured-vuggy carbonate reservoirs are consisting of a group of large carves and inter-connected by high permeability fractures. Due to lack of powerful

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and suitable EOR (Improved Oil Recovery) strategies, depletion-drive recovery is commonly adopted for practical production at the beginning. After a period of production, the elastic energy of the cave formation weakens, causing insufficient liquid supply, the water injected for water flooding is used to improve the oil recovery of the fractured-vuggy carbonate reservoirs. However, the water injection

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curves of the carbonate reservoir are different from that of the sandstone reservoir as their fundamental flow mechanisms are different. For the fractured-vuggy reservoirs with high permeability, the water injection curves can be adopted to calculate the

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volumes in place of crude oil and formation water in a single or multi-caves. This paper presents a new model of injection curves. Using the proposed model with multi-round water injection curves, we can initially judge reservoir type and

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determine the volumes of cave, crude oil and water in the caves reasonably. Besides, as testified by the practical case, the parameters interpreted by the new models are proved to be reasonable and reliable. This new model is a useful tool to estimate the crude oil reserves, to demonstrate how much remaining oil in the caves, and to identify where the water-oil contact is. Keywords: Fractured-vuggy formation; Carbonate reservoir; Water injection curves; Crude oil reserve; Dynamic analysis 1. Introduction There are varieties of carbonate reservoirs in China, however, the main oil

ACCEPTED MANUSCRIPT reserves are the paleokarst reservoirs (Li et al., 2018; Wang et al., 2016; Kuanzhi et al., 2015) in Tahe Oilfield, which is located on the central of the North Tarim Uplift in Tarim Basin as is shown in Fig. 1. There are mount of researches have been investigated extensively on the general geological and stratigraphical setting in

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Tarim Basin (Yang et al., 2014; Lu et al., 2017; Tian et al., 2016; Yan et al., 2011; Chen et al., 2012). The Tahe Oilfield is 2400 km2 in size and is located on the southwestern slope of the south-central Akekule Arch (Fig. 1（a）). The Akekule Arch is located within the North Uplift (Shaya Uplift) of the Tarim Basin. The Akekule

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Arch has undergone multiple stages of tectonic movements, including the Caledonian, Hercynian, Indo-Yanshanian, and Himalayan movements (Yang et al.,

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2014; Lu et al., 2017). The Akekule Arch experienced a series of erosional episodes during the Caledonian and Hercynian movements. The remaining Ordovician formations are uneven, and their contact relationships are complex (Lu et al., 2017; Tian et al., 2016). The strata in the northern Tahe Oilfield have been denuded, and there the Carboniferous Bachu Formation unconformably overlies the Yingshan

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Formation. Stratigraphic column of the Tahe Oilfield is shown in Fig. 2, in which the global stages/ages are those of the International Commission on Stratigraphy of 2012, and the stages of the northern Tarim Basin are those of Yan et al. (2011).

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Hydrocarbon reservoirs have been identified in the Triassic, Carboniferous, Devonian, and Ordovician strata of the oilfield, and production from the Ordovician paleokarst reservoirs. The Cross-Section AA’ as is shown in Fig.1(b) illustrates that

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the paleokarst system of the Tahe Oilfield from top to bottom formation of the Ordovician paleokarst reservoir. The main reservoirs are located in the northern part of the Tahe Oilfield in the Yingshan Formation (O1-2ys) (Tian et al., 2016).

From

bottom to top (Fig.2), the Ordovician strata are divided into the Penglaiba Formation (O1p, predominantly dolomite), Yingshan Formation (O1-2ys, limestone), Yijianfang Formation (O2yj, predominantly nodular limestone), Querbake Formation (O3q, knotty limestone containing mud), Lianglitage Formation (O3l, argillaceous limestone and grainstone) and Sangtamu Formation (O3s, mudstone, marlite interbedded with siltstone and limestone) (Lu et al., 2017; Tian et al., 2016; Chen et

ACCEPTED MANUSCRIPT al., 2012). The Tahe Oilfield represent a special type of hydrocarbon reservoir consisting primarily of paleokarst caves and fractures. The outcrops are shows that there are many scales of caves and fractures in the Ordovician strata as is shown in Fig. 3. It also be testified by well drilling that serious drilling fluid leakage occurred

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in many wells since there are big caves and fractures. For instance, the well TH10114X happened three drilling fluid leakage on the depth 5640.92-5645.94m, 5671.31-5672.83m, 5677.29-5678.37m in the yingshan (O1-2y) formation, which total volume of fluid leakage is 2382.2 m3. Beijing

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Southern Tianshan

200km

0 Xin Jiang Tarim Basin

100km

0

Kuqa Depression

Korla

Kuqa

Korla nose-like arch

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A’

Shaya Uplift

Caohu sag

Akekule arch

Sha Ya

Manjiaer Depression

Shaxi arch

Structural Zone

A South

5400

Tahe Oilfield

Study area Tahe Oilfield

0

5300

Third Unit Boundary

Major Faults

1

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Depth (m)

Second Unit Boundary

A

Shuntuogoule lower Uplift

Outline of Tarim Basin

(a)

City

TH -B ’ North A’

2km

C1Kalashayi Formation

5500

C1Bachu Formation

5600

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5700 5800

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5900

O1-2Yijianfang Formation

6000 6100

O1Penglaiba Formation

(b) (c)

Limestone

Dolomite

Nodular limestone

Marlstone

Sandstone

Mudstone

Calcium sandstone

Caledonian caves

Hercynian caves

Fig. 1 Location and Cross-Section of study area of Tahe Oilfield, Tarim Basin, Xinjiang, China

ACCEPTED MANUSCRIPT System Series Global Period Epoch Stage

Fomation

Thickness (m)

Lithology

Dapingian

Middle

Well TH-B ·

·

·

·

·

·

·

· 200~1000

Floian

Yingshan

·

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·

·

·

·

Lower

Ordovician

·

·

·

·

·

·

Tremadocian

·

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Penglaiba

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·

Micrite limestone

Dolomite

240~600

·

·

·

·

·

·

· ·

Peloidal limestone

·

·

·

· ·

·

·

Peloidalbioclastic limestone

Microbail limestone

Microbail dolomite

Ooidal dolomite

· ·

·

·

Peloidal dolomite

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Fig. 2 Stratigraphic column of the Tahe Oilfield

Sed im ent

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Sed im ent

①

U nfilled

②

③

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Fig. 3 Outcrops of caves and fractures in the Ordovician strata (modified from

Tian et al., 2016). ①typical half-filled cave. ②typical completely filled cave with fractures. ③half-filled cave with fractures.

Because of various scales, poor continuity and strong heterogeneity (Shafiei et

al., 2013; Sun et al., 2017; Li et al., 2017; Manrique et al., 2007; Farhadinia Kurtzman et al., 2011) of the caves and fractures with complex flow behaviors (Wang et al., 2014; Popov et al., 2009; Wu et al., 2011), lots of IOR methods are researched in laboratory (Mahzari et al., 2018; Sohal et al., 2017; Mayorquin et al., 2016; Wang et al., 2017), but the efficient development of fractured-vuggy

ACCEPTED MANUSCRIPT carbonate reservoirs in Oilfield practice is quite challenging (Li et al., 2018; Wang et al., 2016; Izgc, 2018; Artun et al., 2014). In Tahe oilfield of China, the carbonate reservoir displays poor porosity and permeability in its matrix, while the fractured-vuggy system is distributed in a random, discreet and discontinuous way.

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According to Reference (Wang et al., 2016), four types of fractured-vuggy reservoir are identified combing drilling & well logging response, numerical well test analysis and production test in Tahe Oilfield. Type I “large fractured-vuggy systems” and Type II “Karst caves” are our research objects in this paper (Fig.

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4). The large vuggy, also called cave, is the main reservoir body in the types I and II formations, which yields significant oil rates once the fractured-vuggy system

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are connected by production wells. The fractured-vuggy carbonate reservoirs are consisting of a group of large carves and inter-connected by high permeability fractures. The reservoirs are highly heterogeneous reservoirs and ultra-deep ranging from 5000m to 6000m, which makes the resolution of the seismic data too low to have a predictive reservoir characterization (Li et al., 2016) of the spatial

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distribution of fractured-vuggy system. For this fractured-vuggy system is commonly development by one well, after the primary depletion period, nowadays, the water injected by the same well is performed in the oilfields (Wang et al., 2016;

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Olson and Kabir, 2014; Nguyen and Somerville, 2014; Shehata et al., 2014). The mainly mechanism of IOR is use the effect of gravity segregation to prevent the water cresting (Yue et al., 2012, 2014, 2015) and supply the reservoir pressure. The

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wells have presented good effects on increasing oil (Wang et al., 2016; Tu, 2008) in this type formation of Tahe Oilfield. However, the sandstone water injection curve reflects the relationship between injection pressure and injection rate. While in the carbonate reservoir the injection pressure often associates with the cumulative injecting water in the process of water injection for replacing oil (Tu, 2008; Raju, 2005), therefore sandstone reservoir flooding theories do not apply to the carbonate reservoir of Tahe oilfield. For the fractured-vuggy carbonate reservoir, the injection curves are redefined as relationship between cumulative injection water and injection pressure. The

ACCEPTED MANUSCRIPT difference of injection curves between sandstone and carbonate is that the basic foundations of models are different. The former bases on Darcy theory and the latter bases on stock tank flow model which regards reservoir as a group of caves and connected by high permeability fractures (Tu, 2008; Belayneh et al., 2006). Large

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numbers wells of Tahe oilfield production practice makes it clear that there are sets of high permeable reservoirs with large scale fractures and big caves with high porosity and permeability (Li et al., 2018; Wang et al., 2016; Kuanzhi et al., 2015; Tu, 2008). The porosity of caves ranges from 15% to 60% which bases on the cave

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filled condition. The permeability of unfilled cave ranges from 0.62D to 6D with mean value 5D and the permeability of collapsed and half-filled cave ranges from

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0.1D to 0.62D with mean value 0.35D. The permeability of big fracture mostly is more than 1D, the one of small fracture is more than 5mD with mean value 50mD. Based on the basic model described for single-cave in formation, which does not consider both the oil and water elastic energies effecting on the injection curve and cannot be used for two or multiple caves, therefore, this paper given a new model of

more than one cave.

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injection curve to demonstrate the effects of both oil and water phase energies and

Multi-rounds water injection curves can be used to solve the volumes of one or

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more caves in reservoir as well as oil, water volumes. Initial conditions of the new models are according to actual produce condition of the reservoir, such as the properties of formation and fluids and the change of water storage during water

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injection. Using the proposed model can initially estimate reservoir type, determine the volumes of cave, crude oil and water in the caves. It is a useful tool to assume the crude oil reserves, to demonstrate how much remaining oil in the caves, and to make sure where the water-oil contact surface is. The case applications of typical oil wells in Tahe oilfield shows that the parameters obtained by our models are reasonable and reliable.

ACCEPTED MANUSCRIPT 40m

Type II : Karst caves

Type I : Large fracturedvuggy systems

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0

Fig. 4 Two types of fractured-vuggy reservoir (modified from Wang et al, 2018)

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2. Water flooding theory of carbonate reservoir

There is a good linear relationship between the injection pressure and

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accumulated water for the type II “Karst caves” reservoir body. Thus, it can be equivalent to a single cave unit reservoir with high permeability which shows good effects on increasing oil by using water flooding for replacing oil (Tu, 2008; Yuan et al., 2015; Hassani et al., 2014). For the type I “large fractured-vuggy systems”, if the fracture connected the caves extremely well, the caves can be together considered to

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a big cave. If there are a small amount fractures or the fractures are badly connected for the caves, the multi caves model will be established, which is our main works in this paper.

Take the single cave model to demonstrate the water flooding theory of

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carbonate reservoir. For the type II “Karst caves” reservoir body in Tahe oilfield, a single well in a certain volume of a large cave relies on fluid elastic energy for

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production. After a period of production, the elastic energy of the cave formation weakens, causing insufficient liquid supply, the water has to be inject to the cave. After that, the single well will be shut for soaking process after high density water injection. Due to high porosity and permeability of fractured-vuggy system, capillary pressure can be ignored. During the soaking process, oil is displaced by the injected water and the oil-water contact interface raises due to Gravity segregation by oil-water density difference, so that remaining oil enriches in the upper location of the cave unit again. The injection and soaking process, as shown in Fig. 5, suppled energy and

ACCEPTED MANUSCRIPT adjusted oil-water contact interface, let the well re-produce again to increase the amount of oil recovery. The main mechanism of IOR is that: the cave reservoir pressure increases, and oil elastic energy improves due to the injected water occupies the bottom space of the units, reduces the space of the oil phase and

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supplied the driving energy. Then the wells can produce oil by elastic energy or pumping. this well takes water injection-soaking-production process as a cycle, gradually increasing the oil recovery of fractured-vuggy system after many rounds of water flooding for oil (Tu, 2008; Yuan et al., 2015). It is worthy to mention that

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the basic water injection model only considers the oil compression energy, without taking account of the elastic energy of water. While the elastic energy of heavy oil in

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Tahe oilfield is in the same order of magnitude as the energy of the water, therefore, it can also be seen from the above mechanism that major errors may occur if water energy is ignored. Moreover, common situation of Tahe carbonate reservoir is that there ara more than one fractured-vuggys in the formation as Types I “large fractured-vuggy systems” in Fig. 4 (Wang et al., 2018). So, we need a new model

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to study these complex issues.

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Water flooding 注水

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Initial production rely on elastic displacing oil from the spray or machine pumping

Opening wells and making oil-well producing

There are difficulties in well liquid supply because of shortage of elastic energy

Injecting high-density water and controlling oil pressure in the wellhead affordable range

Shutting down Wells to make oil-water gravity segregation

注水 Water flooding cycle in 注采循环 injection and production

There are shortages in well liquid supply

Injecting high-density water again

Fig. 5 Process of single well injection-soaking-production for the oil by gravity segregation (Tu, 2008)

ACCEPTED MANUSCRIPT 3. Basic model of water injection curves The assumptions of basic model in Fig. 6 are as follows. Without consider the storage property of fracture, the entire reservoir is simplified as a cave. The cave is closed and constant-volume. Production well is drilled on cave. Elastic energy of oil

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is the driving energy for well producing and elastic energies of formation water, injection water and formation rock are ignored. Reservoir pressure has approximately same changes with well head pressure, namely both pressures have similar increase or decrease. Without considering compressibility of injected water

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and formation water. Based on above assumptions, on the injection process, the compressed volume of crude oil ∆V approximates to the volume of injected water

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Nw. ∆V=Voi-V'o=Nw

（1）

According to the definition of compressibility of crude oil, Co =

40m

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（2 ）

p

Vo

V'o

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pi

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20m

0

1 ∆V 1 Nw = Vo ∆p ∆p Vo

Before shut well by producing

After shut well by inject water flooding

Fig. 6 diagram of water flooding for oil by gravity segregation

If ignoring the friction of vertical well bore, the formation pressure changes can be measured by wellhead pressure changes, namely

∆p=p-pi

（3 ）

From Eq. (1) to Eq. (3), the relationship between the pressure and the injected water volume can be demonstrated by Eq. (4).

ACCEPTED MANUSCRIPT p=

Nw + pi CoVo

（4 ）

The oil compressibility Co is approximately constant when the temperature is constant. When formation compressibility is ignored, wellhead pressure has a linear

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relationship with cumulative injected water Nw. Thus, according to slope changes of water injection curves of different rounds, the volume of crude oil in caves (Vo) and remaining oil volume (Voi -Vo) can be calculated.

4. New models of water injection curves

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4.1. The new model for one cave

When the cave reservoirs both contain oil and water phase, the elastic energy of

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water phase cannot be ignored. For some cave reservoirs with larger volume of water, as the proportion of water in the cave is large, the elastic energy of formation water and injected water is numerous and should not be ignored. But elastic energy of formation rocks remains negligible. It is still assumed that reservoir pressure has approximately same changes with wellhead tubing pressure.

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For one cave, define the cave volume is Vp, the initial oil volume is Voi and initial formation water volume is Vwi. And define the original water-oil volume ratio in the cave is

So,

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R=Vwi /Voi

Vp =Voi+ Vwi

（5 ）

（6 ）

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When a certain amount of water, NW, is injected into the reservoir, the reservoir

pressure increase value is ∆p (∆p=p–pi). For closed caves, ignoring reservoir rock volume change as pressure changes, although the water cannot be in exchange with outside, the original formation water volume in the reservoir will be compressed because of reservoir pressure increased. The compression volume of water in cave is

∆Vw = VwiCw ∆p

（7 ）

Cave formation water volume compression will increase the reservoir volume.

ACCEPTED MANUSCRIPT When system’s pressure rise to p, the volume of cave is Vc = Vci + ∆Vw

（8 ）

Take Eq. (7) into Eq. (8) Vc = Vci + VwiCw ∆p

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（9 ）

Take Eq. (5) into Eq. (9) Vc = Vci (1 + RCw ∆p )

（10）

Relationship between volume and pressure in the reservoir of the cave system

volume of crude oil in the reservoir is as follows

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Vo = Vc − N w Bw

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can be demonstrated by Eq. (10). Assume injected water volume is NwBw, the

= Vci [1 + RCw ∆p ] − N w Bw

（11）

Eq. (11) can be used to calculate the oil volume in the process of reservoir development. It can be seen that oil volume decreases with the increasing water injection. The volume of crude oil on original condition of cave reservoir is

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Voi = Vci

（12）

Converse underground volume to surface conditions

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N=

Voi Vci = Boi Boi

（13）

Based on material balance theory

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N=

Vo Vci [1 + RCw ∆p ] − N w Bw = Bo Bo

（14）

Obviously, Eq. (14) gratifies the linear relationship between cumulative

water injection N w and pressure difference ∆p . Put Eq. (13) into Eq. (13), it can get NBo + N w Bw = NBoi [1 + RCw ∆p ] N w Bw = NBoi RCw ∆p + ( Boi − Bo ) N

From the compressibility of crude oil, which

（15）

ACCEPTED MANUSCRIPT Co =

Boi − Bo Boi ∆p

（16）

Take Eq. (16) into Eq. (15), it can get N w Bw = NBoi ( RCw + Co )∆p

And ∆p=p-po, so p=

N w Bw + p0 NBoi ( RCw + Co )

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（17）

（18）

This formula also shows that when there is more original water in the caves the

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elastic energy of formation water is not negligible. It is recommended that if RCw

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and Co are the same magnitude, the model should consider the influence of elastic energy of formation water on the injection curve. For Tahe oilfield Cw is in an order of magnitude with Co . If R>1, it also apparently meets that RCw is in an order of magnitude with Co , so that the elastic energy of water cannot be ignored.

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4.2. The new model for several caves

For the type I “large fractured-vuggy systems”, If there are a small amount fractures or the fractures are badly connected for the caves, the multi caves model

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should be established. Choose the simple cave reservoir with two caves as an example and suppose that both water and oil phase exist in caves, so the model will

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be expanded as follows.

Nw Bw   p = N B (RC + C ) + p0 , Nw ≤ Nw0  1 oi 1 w o  (Nw − Nw0 )Bw Nw0 Bw p = + + p0 , Nw > Nw0  N1Boi (RC N1Boi (RC 1 w + Co ) + N2 Boi (R2Cw + Co ) 1 w + Co )

（19）

Fig. 7 is the water injection curves of model for two caves with different volume of cave 2 base on Eq. 19. For the original condition of cave 1 is the same, the water injection curves are the same before the cumulative injection quantity exceed the value, Nw0, at the inflection point in the corves. When the cumulative injection volume more than Nw0, the greater the volume of cave 2, the second part of

ACCEPTED MANUSCRIPT the elastic energy of the cave is more, the injection of water is easier to inject, the slope of the second line reduces the more obviously contrast to slope of the first line.

p1 p2 p3

N22

N21
NW0

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Amount of cumulative water injection 累积注入量

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N23

注入压力

Pressure of injection

N21

Fig. 7 Water injection curve of model for two caves

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4.2.1. R with a little variation

When the R (water-oil volume ratio in cave) changes little, it can be considered as a constant. This means that R1 and R2 are unchanged during the injection process. Due to not known that the produced oil comes from which cave, the unknown parameters could be solved through 3 rounds injection curves with inflection points.

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Assume that injection curves n, m and l satisfy the above equation, the following equations can be established according to the slope.

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Bw  k1n = N B (RC + C ) 1n oi 1 w o   Bw k2n = N B (RC + C ) + N B (R C + C ) 1n oi 1 w o 2n oi 2 w o   Bw k1m = N B ( RC 1m oi 1 w + Co )   Bw k2m = N B (RC + C ) + N B (R C + C ) 1m oi 1 w o 2m oi 2 w o   Bw k1l = N1l Boi (RC 1 w + Co )   Bw k2l = N1l Boi (RC 1 w + Co ) + N2l Boi (R2Cw + Co )  N + N = N + N +∆V 2n 1m 2m onm  1n N1n + N2n = N1l + N2l +∆Vonl

（20）

Where, the cumulative oil production ∆Vonm , ∆Vonl can be obtained from production data. There are 8 unknowns in the above equations corresponding to 8

ACCEPTED MANUSCRIPT equations, so the Eq. (20) can be solved.

4.2.2. R with a big variation When R changes greatly, the water-oil ratio in each cave of every injection curve also changes. Because produced oil and water cannot be distinguished from cave,

so

it

can

be

approximately

assumed

that

during

each

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which

injection-production round the produced oil volume is equal to amount of water injected in the next round. Thus, when the next round injection begins, the ratio of water to oil can be calculated by Eq. (21).

（21)

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Bw  k1n = N B (R C + C ) 1n oi 1n w o   Bw k2n = N B (R C + C ) + N B (R C + C ) 1n oi 1n w o 2n oi 2n w o   Bw k1m = N1mBoi (R1mCw + Co )   Bw k2m = N1mBoi (R1mCw + Co ) + N2mBoi (R2mCw + Co )   Bw k1l = N B ( R 1l oi 1l Cw + Co )   Bw k2l = N B (R C + C ) + N B (RC + C ) l w 1l oi 1l w o 2l oi o  N1n + N2n = N1m + N2m +∆Vonm  N1n + N2n = N1l + N2l +∆Vonl  N R + (N1n − N1m )Bo R1m = 1n 1n N1m   N R + (N2m − N2m )Bo R2m = 2m 2m N2m   N R + (N1l − N1l )Bo R1l = 1l 1l N1m   R2l = N2l R2l + (N2l − N2l )Bo  N2l

Where, the produced oil ∆Vonm , ∆Vonl , the difference between cumulative

water injection and cumulative water production ∆Vw nm ， ∆Vw nl can be obtained from production data. There are 12 unknowns in the above equations corresponding to 12 equations, so the Eq. (21) also can be solved.

5. Results and Discussion

ACCEPTED MANUSCRIPT 5.1. The Results and Discussion in case of single-cave A typical cave reservoir is used to comparison and application analysis of the models. Typical well TH10229 is a multi cycle production and injection well. Each round water injection curve is linear, presents obvious characteristics of constant

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volume (Fig. 8). From the 1st round to 7th round of water flooding, it recovered 1.50×104t crude oil. The density of crude oil is 0.994g/cm3. Oil compressibility Co is 10×10-4 MPa-1. Formation water compressibility Cw is 4×10-4MPa-1. According to the water injection curve, the interpretation process and results using the above

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models are as follows.

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Fig. 8 water injection curve of well TH10229

(1) The calculation results of basic model

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According to the slope of the 1st round water injection curve, the calculated

volume of crude oil by Eq. (4) is 22.73×104m3. With the increase of water injection rounds, the slope tends to be larger and the residual oil in reservoir is decrease. After the 7th round injection, the calculated volume of crude oil by Eq. (4) is 20.00×104m3, the oil volume reduced 2.73×104m3. That is, while the oil density is 0.994g/cm3, the crude oil in this cave should be reduce 2.71×104t based on basic model. Actually, in this period from production data, the total recovered oil was 1.50×104t which it was 80% less than predicted result of basic model. Obviously, the result based on basic model is inappropriate.

ACCEPTED MANUSCRIPT (2) The calculation results of new model New model should consider the elastic energy of formation water in the cave, and compressibility Cw is 4×10-4MPa-1. For initial water-oil ratio R in cave reservoir is unknown, the new model need to take different R by trial and error. When R=2,

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according to the slope of the 1th round water injection curve, the calculated volume of crude oil is 12.63×104m3. After the 7th round injection, the calculated volume of crude oil is 11.11×104m3. The calculated oil volume reduces 1.52×104m3, that is, crude oil in reservoir reduced 1.506×104t. In this period, the actually produced oil

single-cave, the calculation error is only 0.27%.

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was 1.502×104t. If the elastic energy of water is considered in new model of

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Based on the above results, it can be determined that the cave contains two-phase, oil and water, in the initial condition. Water-oil volume ratio R is roughly equal to 2. Initial volume of oil, water is approximately 12.63×104m3, 25.26×104m3 respectively. Based on the new model, the volumes of cave, oil, water phase can be calculated quantitatively.

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5.2. The Results and Discussion in case of two-cave 5.2.1. Parameters Analysis and Discussion

Three rounds of water injection curves in the complex two-cave reservoir are

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selected to be solved by MATLAB programming. “Fsolve” Function is used to solve 12 equations, 12 unknowns’ nonlinear equations. During the process of solving, it is found that given different initial values for

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iteration, the results are different, that is, multiple solutions exists for the equations. When set, y=Fsolve('zfz',[10,20,7.5,19.5,6,19,20,10,60,13,99,16],1), iterative

solutions of this model is shown in Table 1. Table 1 solutions 1

Round

Ni

∆Vij

Ri

Ki

1st

10

/

0.200

92.5926

20

/

0.100

31.6456

7.5

2.5

0.600

107.5269

2ed

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3th

19.5

0.5

0.128

33.5570

6

1.5

1.000

119.0476

19

0.5

0.158

34.9650

When set, y=Fsolve('zfz',[20,20,15,15,10,10,20,20,30,30,40,40],1), iterative

Table 2 solutions 2

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solutions of this model is shown in Table 2.

Ni

∆Vij

Ri

Ki

1st

10.1656

/

0.156

92.5929

15.6611

/

0.820

31.6456

7.6656

2.5

0.533

15.1611

0.5

0.880

6.1656

1.5

0.906

119.0481

14.6611

0.5

0.944

34.9651

3th

107.5273 33.5571

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2ed

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Round

When set, y=Fsolve('zfz',[20,20,18,18,16,16,20,20,40,40,60,60],1), iterative solutions of this model is shown in Table 3.

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Table 3 solutions 3

Round

∆Vij

Ri

Ki

10.0681

/

0.182

92.5928

18.2566

/

0.348

31.6456

7.5681

2.5

0.572

107.5272

17.7566

0.5

0.386

33.5571

6.0681

1.5

0.961

119.0480

17.2566

0.5

0.426

34.9651

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1st

Ni

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2ed

3th

The results of the above 3 solutions can be drawn to the following water

injection curves (Fig. 9), that is, they are all the solutions of this water injection curves. For this issue, it needs to combine the well testing and interpretation seismic data to obtain the volume of cave, that is, more restriction conditions are required for the equations. For example, add the volumes of cave 1 and cave 2, as following conditions. N11=10

ACCEPTED MANUSCRIPT N12=20

The only specific solutions 1 can be obtained. 300000 30 2 3th round 3 1st round1 2ed round 11 22 33

200000 20

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压力，MPa

Pressure (MPa)

250000 25

15 150000 10 100000

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5 50000 00 0

500

1000

Cumulative

1500 2000 2500 3000 3500 累积注入量，m3 amount of injection (m3)

4000

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Fig. 9 Comparison between three rounds of water injection curves

5.2.2. Case Application and Discussion

Due to Well TH10114X, the 6th, 9th, 10th round water injection curves have the obvious characteristics of two-cave model, this well is selected for case application and discussion for the complex two-cave model.

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Combined the well testing which can be used to quantitatively calculate well controlled volume and interpretation seismic data whose RMS (Root-Mean-Square) and Coherent Volume Interpretation can be used to qualitative describe the caves

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and fracture property respectively, the approximate volumes of the two caves can be got. So the restriction conditions are given as N11=2.5, N12=20. The results in Table

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4 can be obtained by the above method of new model. The cave 1 volume is 2.5×104m3, the water-oil volume ratio in cave 1 is 1.453. The cave 2 volume is 20×104m3, the water-oil volume ratio in cave 2 is 12.287. The comparison between theoretical results and actual data are shown in Fig. 10. Table 4 The solutions of well TH10114X

Round 6th 9th

Ni

∆Vij

Ri

Ki

2.5

/

1.453

252.9724

20

/

12.287

8.1800

1.6

0.90

2.833

292.9974

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10th

20.7

-0.70

11.838

8.1881

1.6

0.00

2.833

292.9974

20.66

0.04

11.863

8.1897

25

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15 10 5

th轮 66 Round

9th9轮 Round

66th轮线性 Linear

9th9轮线性 Linear

0 500

1000

1500

2000

2500

th Linear 1010 轮线性

3000

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0

th轮 1010 Round

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Pressure (MPa) 压力，MPa

20

3

Cumulative amount of water m injection 累积注入量，

3500

4000

(m3)

Fig. 10 Comparison between model results and the actual curves of TH10114X

From the contrast in the Fig. 10, theoretical models and water injection curves have high fitting degree. The results can reflect the variation law of water injection

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curves in the condition of corresponding model. From this interpretation we know that the Well TH10114X have two fractured-vuggy formations, the initial volume of oil, water in first cave is 1.02×104m3, 1.48×104m3 respectively, the initial volume of

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oil, water in second cave is 1.51×104m3, 18.49×104m3 respectively. Moreover, we can calculate more detail information, such as that the oil reserve controlled by this

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well is 2.52×104m3, the aquifer multiple is 7.9.

6. Conclusions

Based on the results obtained from this study, the following main conclusions

can be drawn:

(1) The mechanism of water-flooding and replacing oil by gravity segregation in fractured-cave reservoir is different from the flow mechanism in sandstone. The water injection curve of carbonate reservoir is completely different from that of sandstone reservoir. Its parameters values (slope, intercepts) are the functions of oil, water volumes in place.

ACCEPTED MANUSCRIPT (2) Our proposed water injection models can be used in the case that both oil and water phase exist in caves. New models can be considered that the influence of the gradually changes of total water storage in cave reservoir, and the results can be obtained by multiple rounds of water injection. Our proposed models not only can

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be used to calculate in single cave carbonate formation, but also can be used to calculate in multi-cave carbonate formation and more detail information can be obtained.

(3) The more caves the reservoir has, the more rounds of water injection curves

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are needed to get the solutions, and the computing process is more complex and time-consuming. The field example applications show that the calculated results

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from our proposed models are reasonable and reliable for this kind of Fractured-vuggy Carbonate Oil Reservoirs which have caves and fractures in the paleokarst reservoirs.

Acknowledgements

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This work was supported by the National Major Projects of China (No.2016ZX05048-002), visiting scholar program by the China Scholarship Council (No. 201608515035) and Texas Tech University, Fund of SKL of Petroleum

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Resources and Prospecting, Beijing (No. PRP/open 1501), Science and Technology Department of Sichuan Province (No. 2015JY0076).

Nomenclatures

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Boi—the initial volume factor of formation oil, m3/m3 Bo—the volume factor of formation oil, m3/m3 Bw—the volume factor of formation water, m3/m3 Co—compressibility of formation oil, MPa-1 Cw—compressibility of water, MPa-1 k1—the slope of the first line on the 1st round water injection curve, f k2—the slope of the second line on the 1st round water injection curve, f k1m—the slope of the first line on the mth round water injection curve, f k2m—the slope of the second line on the mth round water injection curve, f

ACCEPTED MANUSCRIPT N—the geologic reserve of cave reservoir, m3 Nw—the volume of injected water, m3 Nw0—the injected water volume at inflection point on water injection curve, m3 N1n—the cumulative oil production between the 1st and nth round in the 1st cave, m3

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N2n—the cumulative oil production between the 1st and nth round in the 2ed cave, m3 p—the tubing pressure after water injection, MPa pi—the tubing pressure before water injection, MPa R—the initial water-oil ratio, m 3/m3

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R1—the initial water-oil ratio in first cave, m 3/m3

R1m—the water-oil ratio after mth round water injection in the 1st cave, m 3/m3

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R2—the initial water-oil ratio in second cave, m 3/m3

∆p—the change of pressure after water injection, MPa Vc—the volume of cave after injecting water, m3 Vci—the initial volume of cave reservoir, m3

Voi—the initial volume of oil in the reservoir, m3

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V'o—the volume of oil after injecting water, m3

Vp—the reservoir volume when the pressure is p, m3 Vwi—the initial volume of formation water, m3

∆Vw—the volume change of formation water, m3

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∆V—the changed volume of oil, m3

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∆Vonm — the cumulative oil production between the nth and mth round production, m3 ∆Vw nm —the cumulative water injection minus cumulative water production between

the nth and mth round, m3

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Highlights (1) With multi-round water injection curves, reservoir type and volumes of cave, oil, water can be got.

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(2) New model considered the influence of the gradually changes of water storage in cave reservoir.

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(3) New method is a useful tool to estimate the crude oil reserves of fractured-vuggy system.