Pressure Sensitivity of Low-permeability Gas Reservoir Rock and its

Pressure Sensitivity of Low-permeability Gas Reservoir Rock and its
Influence on Result of Numerical Simulation*
，
ZHANG Ji-Cheng, YANG Hao CUI Xiang-Hua
Key Laboratory of Ministry of Education of china on Enhanced Oil and Gas Recovery, Daqing
Petroleum Institute, Daqing, Heilongjiang 163318, China
[email protected]
Abstract: This paper investigated the variation rule of porosity and permeability as effective pressure
changes for low permeability gas reservoir using experiments on natural cores. The influence of
coupling effect on the result of numerical simulation was then studied taking Wuzhan gas field as an
example. The research shows that both pore volume and porosity decrease with the increase of pressure.
Besides this, the research also shows that the relationship between net ambient pressure and pore
volume and that between net ambient pressure and porosity obey very good exponential power law. The
controlled dynamic reserves of single well and whole gas reservoir and forecasting results of the
development index derived by numerical simulation method accorded with the real situation very
closely, under the condition that pressure sensitivity effect was taken into consideration.
Keywords: gas reservoir; pressure sensitivity; numerical simulation; laboratory experiment
*
Supported by the National Natural Science Foundation of China under Grant No. 50634020
1 Introduction
Many scholars have done research on fluid-solid coupling in gas reservoir. Very strong
stress-sensitivity exists in low permeability reservoir because of its small permeability and porosity.
Study of coupling effect is of great importance. Before the 1980s, fluid mechanics in porous medium
was studied only for homogeneous reservoir. Thence after, many investigations were conducted for
heterogeneous reservoirs. Li Yun and Zhang Liehui et al have done numerical simulations on fluid-solid
coupling effect. In this paper, pressure sensitivity of permeability and porosity was both taken into
consideration to establish coupling numerical simulation for gas reservoir.
2 Pressure sensitivity experiment on low permeability natural cores
Six natural cores, the permeability of which was between 1.98~14.2×10-3µm2 were used for
experiment. In the experiment, their pore volume and porosity vary with the ambient pressure when
pressure in gas reservoir decreases. The variation law of pore volume and porosity with ambient
pressure is shown as in figure 1 and figure 2.
It shows that with the ambient pressure increasing, the core is compressed and the pore volume
decreases. This process simulates the increasing pressure difference between overlying sand and gas
reservoir after it was developed. The decreasing pressure in gas reservoir makes rock particles and
cementing material swell and makes pore volume decrease. On the other side, with the increasing
effective pressure, the gas reservoir is re-compacted, the pore structure is changed and the pore volume
is reduced further more. The variation ratio of pore volume (∆Vp/Vp) is increasing when the ambient
pressure is increasing. But the value of the ratio decreases continuously. Because of the difference of
pore structure and pore component, the variation ratio of pore volume of every core is different from
others. For instance, when the ambient pressure is 20.01MPa, the variation ratio of pore volume of
1739-1# core is 3.65%, but that of 13-1-1# core is 7%.
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5
3
4
m
c
/
e
m3
u
l
o
v
2
e
r
o
p
1
0
0
13-1-1# core
13-1-2# core
14-2-1# core
1739-1# core
14-2-2# core
1# core
5
10
15
20
net ambient pressure/MPa
Fig.1 Relationship of pore volume vs. net ambient pressure
20
18
%16
/
y
t
i
s14
o
r
o
p12
13 -1-1# core
13-1-2# core
14 -2-1# core
14-2-2# core
17 39-1# core
1# core
10
8
0
5
10
15
net ambient pressure/MPa
20
Fig.2 Relationship of porosity vs. net ambient pressure
With the ambient pressure increasing, the core is compressed and the pore volume decreases. Therefore
the porosity decreases gradually. But the value of porosity decline will decrease with the increase of
ambient pressure. With the ambient pressure increasing, the variation ratio of porosity (∆Φ/Φ) is almost
the same as the variation ratio of pore volume. The value of porosity decline and the value of porosity is
directly proportional. For instance, when the ambient pressure is 20.01MPa, the porosity of 13-1-1# core
dropped to 17.407% from 18.719%, the difference is 1.312%, and the variation ratio is 7%. But the
porosity of 1# core dropped to 10.003% from 10.705%, the reduction is 0.702%, and the variation ratio
is 6.56%. The variation ratio of porosity is related to pore structure, core component, cement texture and
cementing strength. The porosity of 14-2-2# core varies abnormally. The porosity of it is 16.117%, when
the ambient pressure is 20.01MPa, the reduction of porosity is 0.831%, and the variation ratio is 5.16%.
But the porosity of 13-1-1# core is 18.655%, higher than that of 14-2-2# core. When the ambient
pressure is 20.01MPa, the reduction is 0.787%, and the variation ratio is 4.22%.
It is known from the above analysis that pore volume and porosity of core sample will decrease
when the pressure increases. Furthermore, the relationship between ambient pressure and pore volume
and that between ambient pressure and porosity obey with exponential power law. This shows that in the
early period, pressure variation has much greater influence on pore volume and porosity. But with the
pressure increasing, the variation of pore volume and porosity is decreasing.
3 The basic mathematical model of numeral simulation for gas reservoirs with
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low permeability
Comprehensively considering the influence of gravity, capillary pressure, fluid and rock
compression, a mathematical model for three-dimensional gas/water two-phase gas reservoirs is
established, the expression is as following.
 k ( p1 )

∂  φs 
div 
grad ( p1 − ρ1 gD )  + q1 =  1 
∂t  B1 
 µ1 B1

The auxiliary equation is
S g + Sw = 1
pcgw ( S w ) = p g − pw
Wherein, k(p1) permeability of rock, a function of pressure, m2; g refers to gas phase; w is water phase;
µ1 is viscosity of formation gas or formation water, Pa.s; B1 is volume factor of gas phase or water phase;
P1 is pressure of gas phase or water phase, Pa; ρ1 is density of formation gas or formation water, kg/m3;
g is acceleration of gravity, 9.8m/s2; D is vertical depth below the datum level; q1 is ground volumetric
production/injection rate of gas/water per unit volume of reservoir rock, m3/(m•s); t is production time, s;
S1 is gas saturation or water saturation; Sg is gas saturation; Sw is water saturation; pcgw(Sw) is gas/water
capillary pressure, a function of water saturation, Pa; pg is gas phase pressure, Pa; and pw is water phase
pressure, Pa.
4 Numerical simulation of Wuzhan gas field
The pay zone of Wuzhan gas field is Fuyang oil layer. The gas reservoir pressure is 5-7.5MPa. The
temperature is 50-60 . The buried depth is 700-1100m. The pressure coefficient is 0.662-0.799. The
gas bearing area is 46.0km2. The proved reserves of natural gas is 15.45×108m3. The are 5 production
wells at present. By now, the cumulative gas production is 0.517×108 m3.
(1) The establishment of geologic model
It is divided into 80×65 grids horizontally. Grid spacing is 100m in both X and Y direction. The
Fuyang oil layer in Wuzhan gas field is thicker than other oil layers. Sandstone of Fuyu, Yangsan and
Yangwu layer unit is well-developed, but sandstone of Yangyi and Yanger layer unit is not well
developed. Depth of mudstone is 100-120m. So the reservoir is vertically divided into 3 grids, i.e., Fuyu
oil layer, tight layer and Yangdachengzi oil layer. The whole reservoir model has 80×65×3=15600 grids.
(2) History match
According to the geologic model, the geologic reserves is fitted. The natural gas reserves of Fuyu
oil layer is 13.35×108m3. The natural gas reserves of Yangdachengzi oil layer is 1.84×108m3. The total
reserves is 15.19×108m3. The relative error is 1.68% between calculated and actual reserves. Some
development indexes such as daily gas production rate, cumulative gas production, bottomhole flowing
pressure of single well and whole field are history matched. The relative errors are 4.64%, 2.43%,
2.76% respectively. The model is reliable because of the higher goodness of history match.
(4) forecasting development effect
On the basis of history match, the whole development plan of Wuzhan gas field is researched by
numerical simulation method. It shows that during the simulation, the cumulative gas production is
0.943×108m3 when the pressure sensitivity is not taken into consideration. If pressure sensitivity is
considered, the cumulative gas production is 0.875×108m3. The ratio of difference is 7.78%. According
to the dynamic data in 2006, the forecast result which considered the pressure sensitivity is more precise,
being much closer to the actual value.
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5 Conclusions
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(1) As to the low permeability reservoir, pressure sensitivity has a greater impact on development
effect. So it should be fully considered during the development decision process.
(2) Wuzhan gas reservoir belongs to shallow gas reservoir. Its pressure and deliverability are low.
On the other side, because there are just 5 production wells, controlled dynamic reserves of the 5 wells
is only 1.81×108m3 though the total reserves is as large as 15.19×108m3. The ratio of controlled dynamic
reserves is only 12%. It is proposed that new wells should be dilled in area which has gas production
potential and has large effective reservoir thickness.
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