CN106677750A - Carbonate rock reservoir karst cave-fracture reservoir body water injection indication curve interpretation model - Google Patents

Abstract

The present invention provides a water injection indication curve interpretation model for cave-fracture reservoirs in carbonate rock reservoirs. The model distinguishes the influence of the elastic energy provided by the model on the shape of the water injection indication curve for different compression coefficients of caves and fractures in different reservoir media. , taking into account the influence of the elastic energy of the oil-water two phases on the shape of the water injection indicator curve. The new model can be used to distinguish different elastic compression coefficients of caves and fractures, and can be used to calculate the respective proportions of caves and fracture reservoirs, thereby calculating their corresponding volumes.

Description

Interpretation Model of Water Injection Curves for Dissolved-Vug-Fractured Reservoirs in Carbonate Reservoirs

technical field

The invention relates to the field of oil reservoir geology and development technology, in particular to a water injection indication curve interpretation model of a carbonate rock oil reservoir karst cave-fracture reservoir body.

Background technique

At present, the traditional model is that the oil well directly drills into the karst cave, and does not consider the influence of the fracture reservoir. However, in field practice, the reservoir unit composed of fractures and karst caves is more common. When the proportion of the fluid stored in the fracture is When it is higher, it is necessary to consider the influence of fractured reservoirs. Therefore, it is necessary to consider the pressure changes of fractured and dissolved cave reservoirs after water injection to establish a model for the water injection indicator curve of carbonate reservoirs dissolved caves and fractured reservoirs for analysis. . However, the traditional model is difficult to distinguish the influence of different compressibility coefficients of caves and fractured reservoirs on the slope of the water injection indicator curve, and it is impossible to explain the proportion of caves and fractured reservoirs and calculate the oil-water volume of various types of reservoirs through the existing model.

Contents of the invention

The purpose of the present invention is to solve the above-mentioned defects in the prior art, and provide a water injection indication curve interpretation model for carbonate rock reservoir cave-fracture reservoir body.

An interpretation model for water injection indication curves of dissolved cave-fracture reservoirs in carbonate reservoirs, including:

(1) For the fracture system

Under the original condition, the volume of the unit fracture is V _pf , the volume of crude oil is V _of , and the volume of formation water is V _wf , then

V _pf =V _of +V _wf (1)

The oil saturation S _of in the fracture satisfies the following relationship with V _of and V _wf

When a certain amount of water is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure _pi to the current formation pressure p, and the value of the reservoir pressure increase is Δp=p- _pi . For a closed reservoir, although the water in the water body It will not invade the reservoir, but the pore volume of the reservoir will increase due to the rise of pressure, and the volume of bound water in the reservoir will decrease due to the rise of pressure,

The pore volume increase in the fracture part is:

ΔV _pf = V _pf C _pf Δp (3)

where, C _pf is the compressibility coefficient of fracture pore volume, MPa ^-1 ,

The compression amount of formation water in the fracture part is:

ΔV _wf = V _wf C _w Δp (4)

where, C _w is the compressibility coefficient of formation water, MPa ^-1 ,

Both the increase of the fracture pore volume and the decrease of the formation water volume in the fracture will increase the volume of the reservoir in the fracture. When the pressure of the fracture system rises to p, the volume of the reservoir is:

V _cf ＝V _cfi +ΔV _pr +ΔV _wf (5)

In the formula, V _cfi is the initial volume of fractured reservoir, m ³ ;

Substitute (3) and (4) into (5) to get

V _cf ＝V _cfi +V _pf C _pf Δp+V _wf C _w Δp (6)

The pore volume of the fracture part is expressed as formula (7)

In the formula, _SW is the water saturation of fractured reservoir, decimal;

The volume of formation water in fractures is expressed as formula (8)

Substituting Equation (7) and Equation (8) into (6), the relational expression between reservoir volume and pressure in the fractured part is:

In the formula, the compressibility coefficient of C _cf fracture volume, MPa ^-1 ;

(2) For the cave system

Under the original conditions, the volume of the unit cave is V _pr , the volume of crude oil is V _or , and the volume of formation water is V _wr , then:

V _pr =V _or +V _wr (10)

When a certain amount of water is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure p _i to the current formation pressure p, and the pressure increase value of the reservoir is Δp=p-p _i . For a closed cave, although the water in the water body does not There will be exchange with the outside world, but the volume of bound water in the reservoir will shrink due to the pressure rise, ignoring the volume of the cave rock in the reservoir will change due to the change of pressure;

The compression amount of part of the formation water in the cave is:

ΔV _wr =V _wr C _w Δp (11)

In the formula, C _w is the compressibility coefficient of formation water, MPa ^-1 ;

The compression of the formation water volume in the cave will increase the volume of some oil reservoirs in the cave. When the pressure of the cave system rises to p, the volume of the reservoir is:

V _cr =V _cri +ΔV _wr (12)

In the formula, V _cri is the initial volume of dissolved-vug reservoir, m ³ ;

Substituting formula (11) into formula (12), we can get

V _cr =V _cri +V _wr C _w Δp (13)

From the definition of water-oil ratio in the cave R=V _wr /V _cri we can know:

V _wr = RV _cri (14)

In the formula, R is the water-oil volume ratio of the cave, decimal;

Substituting Equation (14) into Equation (13), we can get the relationship between the volume of the cave reservoir and the pressure:

V _cr =V _cri (1+RC _w Δp) (15)

(3) For the whole system of cracks and caves

Through the above analysis, it can be obtained that the relationship between reservoir volume and pressure in the whole system of caves and fractures is:

In the formula, V _ci is the initial total volume of the cave and fracture reservoir, m ³ ;

If the ratio α of the fracture volume to the cave volume is known, the above formula can be further written as:

The volume occupied by injected water is: N _w B _w , B _w is the volume coefficient of water, decimal;

Then the volume occupied by crude oil in the reservoir after water injection is:

Equation (18) is the reservoir volume calculation formula during the development of closed karst cave fractured reservoirs. It can be seen from this equation that the reservoir volume decreases continuously with the increase of injected water;

The volume occupied by crude oil if crude oil was stored in the reservoir volume under original conditions

V _oi =V _ci (19)

Convert the underground volume to surface conditions to get the geological reserves of the oil reservoir, and use the symbol N to express, the calculation formula is:

B _oi is the volume coefficient of crude oil under the original pressure, decimal

According to the material balance of crude oil before and after water injection, it can be obtained

B _o is the volume coefficient of crude oil under the current pressure, decimal

NB _o +N _w B _w ＝NB _oi [1+[αC _cf +(1-α)RC _w ]Δp] (22)

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+(B _oi -B _o )N (23)

Obviously, formula (23) also satisfies the linear relationship between cumulative water injection _Nw and pressure difference Δp:

And by the compressibility coefficient of crude oil, namely

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+C _o B _oi NΔp (25)

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w +C _o ]Δp (26)

The form written as pressure is: by Δp=p-p _o

Equation (27) is the expression of the water injection indicator curve corresponding to the cave-fracture dual-media reservoir.

This application takes the karst cave-fracture reservoir model as the research target, and aims at the different compressibility coefficients of karst caves and fractures in different reservoir media, distinguishes the influence of the elastic energy provided by them on the shape of the water injection indication curve, and considers the influence of the elastic energy of the oil-water two phases on Influence of water injection indication curve shape. The new model can be used to distinguish different elastic compression coefficients of caves and fractures through multiple rounds of water injection indication curves, and can be used to calculate the respective proportions of caves and fracture reservoirs, thereby calculating their corresponding volumes.

Description of drawings

Fig. 1 is the water injection indication curve diagram (different volume ratio а) of fracture cave reservoir body of the present invention;

detailed description

In order to make the purpose, technical solutions and advantages of the present invention clearer, the following technical solutions in the present invention are clearly and completely described. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

The derivation of the model still assumes that the entire reservoir system reaches stability instantaneously and rapidly after water injection. Divide the entire closed carbonate rock reservoir controlled by a single well into two parts: fractures and karst caves. The ratio of the fractures to the total volume is assumed to be a, and considering the elastic energy of fluid water and reservoir rocks, the compressibility coefficient are C _o and C _w , respectively.

(1) For the fracture system

Under the original condition, the volume of unit fracture is V _pf , the volume of crude oil is V _of , and the volume of formation water is V _wf , then

V _pf =V _of +V _wf (1)

The oil saturation S _of in the fracture satisfies the following relationship with V _of and V _wf

When a certain amount of water (N _W ) is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure ( _pi ) to the current formation pressure (p), and the value of the reservoir pressure increase is Δp=p- _pi . For closed reservoirs, although the water in the water body will not invade the reservoir, the pore volume of the reservoir will increase due to the rise in pressure, and the bound water volume in the reservoir will decrease due to the rise in pressure.

The pore volume increase in the fracture part is:

ΔV _pf = V _pf C _pf Δp (3)

In the formula, C _pf is the compressibility coefficient of fracture system rock (pore volume), MPa ^-1 .

The compression amount of formation water in the fracture part is:

ΔV _wf = V _wf C _w Δp (4)

In the formula, C _w is the compressibility coefficient of formation water, MPa ^-1 .

Both the increase of fracture pore volume and the decrease of formation water volume in fractures will increase the volume of reservoirs in fractured parts. The volume of the fracture system when the pressure rises to p is:

V _cf ＝V _cfi +ΔV _pf +ΔV _wf (5)

Substitute (3) and (4) into (5) to get

V _cf ＝V _cfi +V _pf C _pf Δp+V _wf C _w Δp (6)

The pore volume of the fracture part is formula (7)

In the formula, _SW is the water saturation of fractured reservoir, decimal;

The volume of formation water in fractures is expressed as formula (8)

Substituting Equation (7) and Equation (8) into (6), the relational expression between reservoir volume and pressure in the fractured part is:

In the formula, C _cf is the compressibility coefficient of fracture volume, MPa ^-1 .

(2) For the cave system

Under the original conditions, the volume of the unit cave is V _pr , the volume of crude oil is V _or , and the volume of formation water is V _wr , then:

V _pr =V _or +V _wr (10)

When a certain amount of water (N _W ) is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure ( _pi ) to the current formation pressure (p), and the value of the reservoir pressure increase is Δp=p- _pi . For closed caves, although the water in the water body will not exchange with the outside world, the volume of bound water in the reservoir will shrink due to pressure rise, and the rock volume of reservoir caves will change due to pressure changes.

The compression amount of part of the formation water in the cave is:

ΔV _wr =V _wr C _w Δp (11)

In the formula, C _w is the compressibility coefficient of formation water, MPa ^-1 .

The compression of the formation water volume in the cave will increase the volume of some oil reservoirs in the cave. When the pressure of the cave system rises to p, the volume of the reservoir is:

V _cr =V _cri +ΔV _wr (12)

In the formula, V _cri is the initial volume of dissolved-vug reservoir, m ³ ;

Substituting formula (11) into formula (12), we can get

V _cr =V _cir +V _wr C _w Δp (13)

From the definition of water-oil ratio in the cave R=V _wr /V _cri we can know:

V _wr = RV _cir (14)

In the formula, R is the water-oil volume ratio of the cave, decimal.

Substituting Equation (14) into Equation (13), we can get the relationship between the volume of the cave reservoir and the pressure:

V _cr =V _cir (1+RC _w Δp) (15)

(3) For the whole system of cracks and caves

Through the above analysis, it can be obtained that the relationship between reservoir volume and pressure in the whole system of caves and fractures is:

In the formula, V _ci is the initial total volume of the cave and fracture reservoir, m ³ ;

If the ratio α of the fracture volume to the cave volume is known, the above formula can be further written as:

The volume occupied by the injected water is: N _w B _w, , B _w is the volume coefficient of water, decimal;

Then the volume occupied by crude oil in the reservoir after water injection is:

Equation (18) is the reservoir volume calculation formula during the development of closed reservoirs. It can be seen from this equation that the reservoir volume decreases continuously with the increase of injected water.

The volume occupied by crude oil if crude oil was stored in the reservoir volume under original conditions

V _oi =V _ci (19)

Convert the underground volume to surface conditions to get the geological reserves of the oil reservoir, and use the symbol N to express, the calculation formula is:

B _oi is the volume coefficient of crude oil under the original pressure, decimal

According to the material balance of crude oil before and after, it can be obtained

B _o is the volume coefficient of crude oil under the current pressure, decimal

NB _o +N _w B _w ＝NB _oi [1+[αC _cf +(1-α)RC _w ]Δp] (22)

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+(B _oi -B _o )N (23)

Obviously, formula (23) also satisfies the linear relationship between cumulative water injection _Nw and pressure difference Δp:

And by the compressibility coefficient of crude oil, namely

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+C _o B _oi NΔp (25)

N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w +C _o ]Δp (26)

The form written as pressure is: by Δp=p-p _o

Equation (27) is the expression of the water injection indicator curve corresponding to the cave and fracture dual medium reservoir. The slope of the curve is not only related to the geological reserves of crude oil, but also to the ratio of crude oil reserves in fractures and caves, the ratio of water to oil in caves and other parameters. The model considers more comprehensive factors, so the model needs to provide more detailed parameters when it is actually used. The values of these parameters can be properly combined and used with the results of well test interpretation.

In the model of dual-media reservoirs with caverns and fractures, it is assumed that the initial pressure of the reservoir is the same. Due to the compressibility of the fractures, the comprehensive elastic compressibility coefficient of the reservoirs in the fractured part is higher than that of the caves. The ratio а is different, and the size of its elastic energy is also different, which will also lead to the change of the slope of the water injection indication curve. The influence of different α values on the indicator curve is shown in Figure 1. It can be seen that the larger the proportion of fractures, the greater the total elastic energy of the reservoir body, the easier the water injection, and the smaller the slope of the indicator curve. When α=1 , it is pure fracture reservoir, when а=0, it is pure karst cave reservoir.

In addition, the new model of this application can consider the influence of water-phase elastic energy on the shape of the water injection indicator curve, so it is suitable for the calculation of the oil-water volume of the reservoir body in the following two situations: ① The initial situation in the cave reservoir is oil-water coexistence; ② Later water injection During the process of oil replacement, the internal water ratio of the cave reservoir changes step by step. The initial conditions of the improved new model are more in line with the real situation of the reservoir body, and the change of water storage rate during the process of replacing oil with water is closer to the actual situation of the mine. The theoretical model can be used to preliminarily judge the type of reservoir, and more accurately determine the volume of caves, fractured reservoirs, crude oil and formation water.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still be Modifications are made to the technical solutions described in the foregoing embodiments, or equivalent replacements are made to some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (1)

1. A carbonate reservoir cave-fracture reservoir water injection indication curve interpretation model, characterized in that it includes: (1) For the fracture system Under the original condition, the volume of the unit fracture is V _pf , the volume of crude oil is V _of , and the volume of formation water is V _wf , then V _pf =V _of +V _wf (1) The oil saturation S _of in the fracture satisfies the following relationship with V _of and V _wf ${\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; f</span>}}}{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; f</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ When a certain amount of water is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure p _i to the current formation pressure p, and the increase value of the reservoir pressure is Δp=p-p _i . For a closed reservoir, although the water in the water body It will not invade the reservoir, but the pore volume of the reservoir will increase due to the rise of pressure, and the volume of bound water in the reservoir will decrease due to the rise of pressure, The pore volume increase in the fracture part is: ΔV _pf = V _pf C _pf Δp (3) where, C _pf is the compressibility coefficient of fracture pore volume, MPa ^-1 , The compression amount of formation water in the fracture part is: ΔV _wf = V _wf C _w Δp (4) where, C _w is the compressibility coefficient of formation water, MPa ^-1 , Both the increase of the fracture pore volume and the decrease of the formation water volume in the fracture will increase the volume of the reservoir in the fracture. When the pressure of the fracture system rises to p, the volume of the reservoir is: V _cf ＝V _cfi +ΔV _pr +ΔV _wf (5) In the formula, V _cfi is the initial volume of fractured reservoir, m ³ ; Substitute (3) and (4) into (5) to get V _cf ＝V _cfi +V _pf C _pf Δp+V _wf C _w Δp (6) The pore volume of the fracture part is expressed as formula (7) ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ In the formula, _SW is the water saturation of fractured reservoir, decimal; The volume of formation water in fractures is expressed as formula (8) ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ Substituting Equation (7) and Equation (8) into (6), the relational expression between reservoir volume and pressure in the fractured part is: ${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$ In the formula, the compressibility coefficient of C _cf fracture volume, MPa ^-1 ; (2) For the cave system Under the original conditions, the volume of the unit cave is V _pr , the volume of crude oil is V _or , and the volume of formation water is V _wr , then: V _pr =V _or +V _wr (10) When a certain amount of water is injected into the reservoir, the pressure of the reservoir rises from the original formation pressure p _i to the current formation pressure p, and the pressure increase value of the reservoir is Δp=p-p _i . For a closed cave, although the water in the water body does not There will be exchange with the outside world, but the volume of bound water in the reservoir will shrink due to pressure rise, ignoring the volume of cave rock in the reservoir will change due to pressure changes; The compression amount of part of the formation water in the cave is: ΔV _wr =V _wr C _w Δp (11) In the formula, C _w is the compressibility coefficient of formation water, MPa ^-1 ; The compression of the formation water volume in the cave will increase the volume of the reservoir in the cave. When the pressure of the cave system rises to p, the volume of the reservoir is: V _cr =V _cri +ΔV _wr (12) In the formula, V _cri is the initial volume of dissolved-vug reservoir, m ³ ; Substituting formula (11) into formula (12), we can get V _cr =V _cri +V _wr C _w Δp (13) From the definition of water-oil ratio in the cave R=V _wr /V _cri we can know: V _wr = RV _cri (14) In the formula, R is the water-oil volume ratio of the cave, decimal; Substituting Equation (14) into Equation (13), we can get the relationship between the volume of the cave reservoir and the pressure: V _cr =V _cri (1+RC _w Δp) (15) (3) For the whole system of cracks and caves Through the above analysis, it can be obtained that the relationship between reservoir volume and pressure in the whole system of caves and fractures is: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$ In the formula, V _ci is the initial total volume of the cave and fracture reservoir, m ³ ; If the ratio α of the fracture volume to the cave volume is known, the above formula can be further written as: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&alpha;V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&rsqb;</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$ The volume occupied by injected water is: N _w B _w , B _w is the volume coefficient of water, decimal; Then the volume occupied by crude oil in the reservoir after water injection is: $\begin{array}{c}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$ Equation (18) is the reservoir volume calculation formula during the development of closed karst cave fractured reservoirs. It can be seen from this equation that the reservoir volume decreases continuously with the increase of injected water; The volume occupied by crude oil if crude oil was stored in the reservoir volume under original conditions V _oi =V _ci (19) Convert the underground volume to surface conditions to obtain the geological reserves of the oil reservoir, which is expressed by the symbol N, and the calculation formula is: $\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$ B _oi is the volume coefficient of crude oil under the original pressure, decimal According to the material balance of crude oil before and after water injection, it can be obtained $\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; \&rsqb;</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}<span\; class="notranslate">\; )</span>$ B _o is the volume coefficient of crude oil under the current pressure, decimal NB _o +N _w B _w ＝NB _oi [1+[αC _cf +(1-α)RC _w ]Δp] (22) N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+(B _oi -B _o )N (23) Obviously, formula (23) also satisfies the linear relationship between cumulative water injection _Nw and pressure difference Δp: And by the compressibility coefficient of crude oil, that is ${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}}{{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$ N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w ]Δp+C _o B _oi NΔp (25) N _w B _w ＝NB _oi [αC _cf +(1-α)RC _w +C _o ]Δp (26) The form written as pressure is: by Δp=p-p _o $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}{\mathrm{<span\; class="notranslate">\; B</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}}{{\mathrm{<span\; class="notranslate">\; NB</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&alpha;C</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; RC</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; o</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 27</span>}<span\; class="notranslate">\; )</span>$ Equation (27) is the expression of the water injection indicator curve corresponding to the cave-fracture dual-media reservoir.