книги / Разработка нефтяных и газовых месторождений. Ч. 2

Fig. 2. Inflow Performance Relationship Curves

Different forms of inflow performance relationship curves are dictated by the following factors: deviation from linear filtration law; phase permeability decrease in bottomhole zone in case if bottomhole pressure becomes lower than bubble point pressure; permeability decrease due to reservoir compressibility under pressure drop and fracture closing; change in fluid physical properties – relationship between fluid viscosity and pressure; change in working thickness of reservoir due to connecting low permeable stringers in case if underbalance becomes higher; and inaccurate test (well test under unsteady-state flow).

Deviation from linear filtration law can be accounted for by imperfectness of wells in terms of penetration (including, high fluid flow speed through perforations).

Change in fluid properties in case if bottomhole pressure becomes lower than bubble point pressure, is a significant factor for reducing well productivity factor.

Connecting additional thickness under high underbalance is reflected by changing convexity of inflow performance relationship curve to the bottomhole pressure axis (dot-and-dash line) (fig. 2).

51

Permeability becomes lower if pressure lowers during fluid withdrawal, when a portion of underground pressure, which was taken earlier by fluid, is transferred to rock matrix, and it causes rock matrix deformation, at the same time, size of porous channels and fractures is reduced, and reservoir becomes compressed. The form of inflow performance relationship curve under the above factor is convex to the flow rate axis (curve 2) (see fig. 2).

Practical application of flow-after-flow test data interpretation. For determining well parameters by flow-after-flow test, it is necessary to record bottomhole and wellhead pressure, fluid and gas flow rates, water cut and take fluid and gas bottomhole and surface samples under various drives. In addition, it is necessary to determine formation pressure in shutdown well. In the majority of cases, formation pressure can be determined by direct measuring before reservoir development (at exploration stage) or by pressure build-up curves (to be discussed below). Flow rate and bottomhole pressure under steady-state flows shall be constant.

Using flow rate and bottomhole pressure magnitudes, inflow performance relationship curve in the coordinates ∆p – Q is plotted, its form is studied and relevant data of reservoir compressibility, phase permeability decrease and other are obtained.

Then, well productivity factor is determined using inclination of the inflow performance relationship curve to the flow rate axis i or by formula:

Using productivity factor Кпрод, hydroconductivity ε of bottomhole formation zone is determined by formula:

where 0,159=1/2π is radial flow factor for bottomhole zone; 11,57 10–12 m3/d to m3/sec conversion factor;

b is volumetric coefficient;

С is factor that considers imperfectness of well in terms of penetration. Permeability in bottomhole zone is determined by formula:

where µ is viscosity, Pa sec; and h is net pay zone, m.

52

Fluid characteristics µ, ρ and b under reservoir conditions are determined by deep samples, and surface – by surface samples.

Fig. 3 provides an example of inflow performance relationship curve plotting for exploration well 316, Sibirskoye field. The form of the inflow performance relationship curve – convex to the bottomhole pressure axis – indicates bottomhole zone cleaning.

Fig. 3. Well 316, Sibirskoye Field.

Inflow Performance Relationship

Based on well hydrodynamic data interpretation, the optimal well operation conditions should be selected. The main criteria for selecting optimal well operation conditions are as follows: well operation must be stable with constant flow rate, bottomhole pressure must be not lower than bubble point pressure (Рbh ≥ Рbpp), underbalance in case of poor interconnection of well with external reservoir boundary (rate of formation pressure build-up or reduction is very low) must be low. For selecting, it is also necessary to consider water cut and water quality (composition).

Then, Appraisal Curve should be plotted based on flow-after-flow test data (flow rate, bottomhole and flowing tubing head pressure). Choke diameter is plotted on the x-axis, and bottomhole and flowing tubing head pressure – on the y-axis (fig. 4).

53

Q Рfp Рbh

Fig. 4. Well 316, Sibirskoye Field.

Appraisal Curve

In the given case, well is operated with 6mm choke. Such operation meets the condition – Рbh > Рbpp (Рbpp = 12.6 MPa).

1.2. UNSTEADY-STATE FLOW TEST

Unsteady-state flow test became of common use in hydrodynamic studying. Unlike flow-after-flow test, such test can be characterized by higher resolution. It makes it possible to determine separately characteristics of bottomhole formation zone and remote formation zone, formation homogeneity, and identify lithological screens.

Theoretical Background. The task of unsteady-state flow test is to determine relationship between bottomhole pressure change and time when transferring from one stead-state condition to another one. Such relationship between bottomhole pressure change and time after well shutdown is termed Pressure Build-up Curve.

Let us discuss the basic methods for pressure build-up curve interpretation used in OOO LUKOIL-PERM oil fields of Perm Krai.

54

Standard Method (Tangent Method). Instantaneous fluid influx stop after well shutdown can be represented in the form of plotting negative flow rate equal to the previous one. Such case can take place if bottomhole is fitted with device that instantaneously closes fluid influx.

If well with infinite reservoir drainage and flow rate Q is to be shutdown for long period of time Т (provided that Т>24t, where t is pressure build-up curve), wellbore wall pressure change can be described by the following equation:

where Еi is exponential integral function;

χ is reservoir piezoconductivity; and

Р0 is bottomhole pressure at the moment of shutdown.

In case of shutting down a production well operating under stable conditions (steady-state flow), magnitude ∆P(t) will be increasing from the moment of well shutdown (table 1). The form of pressure build-up curve in Cartesian coordinates will look like as provided in (fig. 5).

Table 1

Well 282, Shatovskoye Field.

Initial Data for Pressure Build-up Curve Interpretation

Fig. 5. Well 282, Shatovskoye Field.

Pressure Build-up Curve in Cartesian coordinates

Let us substitute the exponential integral function with its form for its minor argument. The equation will look like as follows :

Under algebraic law ln(xy)= ln x+ ln y – we obtain the equation of the first straight line y=ix+A in the coordinates ∆p (rc, t), lg t:

Thus, by replotting the pressure build-up curve in semi-logarithmic coordinates

∆p (rc, t), ln t, we obtain the straight line of the final curve portion (fig. 6), and, can determine characteristics of the remote formation zone by inclination of line to the x-axis and intercept A on the y-axis:

56

Ln t, min

Fig. 6. Well 282, Shatovskpye Field.

Pressure Build-up Curve in Semi-Logarithmic Coordinates

Then, we determine numerical value of tangent of inclination angle by formula:

where ∆p1, ln t1 и ∆p2, ln t2 are, respectively, the coordinates of the origin and end of straight-line portion.

Now, we can determine reservoir hydroconductivity ε (м2·м/(Па·с)):

where 1/4π is radial flow factor; and b is fluid volume factor.

By comparing hydroconductivity factors obtained by inflow performance relationship curve and pressure build-up curve, bottomhole plugging factor, which shows how bottomhole zone is contaminated or circulated, is determined:

П = εεквд . (18)

ид

57

Then, reservoir permeability and piezoconductivity can be determined by pressure build-up curve (m2):

where m reservoir porosity, unit fraction;

Βж is fluid compressibility factor Pa-1;

Βск is rock matrix compressibility factor Pa-1.

Then, reduced radius is determined. The physical meaning of reduced radius, under conditions of perfect well and given hydrodynamic characteristics, is a radius of influx (the larger the radius relative to well radius rc, the larger fluid influx area and higher the bottomhole zone parameters):

r = 2, 25χ . (21)

Then, skin factor is determined. The physical meaning of skin factor is pressure loss under fluid filtration in bottomhole zone. Skin factor magnitude depends on reservoir penetration degree and bottomhole zone conditions:

If skin factor is negative, there is no additional pressure loss – as a rule, it is true for carbonate reservoirs after acid treatment. The lower limit of skin factor is equal to – ln(Rк/rс). If skin factor is positive, there is pressure loss in bottomhole zone – deliverability of remote zone of formation is higher than that in bottomhole zone. As a rule, positive skin factor is typical for terrigenous reservoirs which were not subjected to stimulation. Positive skin factor magnitude does not exceed 50.

Horner Method. Horner method is used in case if well operation time period before shutdown Т is commensurable with pressure build-up measurement time t

(at Т < 24t). The essence of the method: we assume that well, which is shutdown for pressure build-up measurement, was not in fact shutdown, and continuous fluid withdrawal is compensated with fluid injected to the neighboring injection well.

58

Thus, well shutdown problem situation is met. Then, pressure change from initial time to time t can be determined using superposition of source and drain. We obtain the equation:

From knowledge of ln(x/y)=ln x–ln y, we obtain straight line equation y=ix+A in Horner coordinates ∆p (rc, t), ln(T+t)/t (table 1.1.1, fig. 1.7.3).

Further calculations should be made similar to tangent method. In addition, Horner method makes it possible to determine formation pressure by extrapolation of straight-line segment of pressure build-up curve before crossing the axis of ordinates (fig. 7).

Fig. 7. Well 282, Shativskoye Field.

Pressure Build-up Curve in Horner Coordinates

Filtration Flow Description. Unsteady-state fluid flow in reservoirs to wells is characterized by complex flow trajectories. For approximate mathematical modeling of complex flows – theoretical modeling of the reservoir filtration systems and subsequent analyzing by subsurface hydromechanics methods - the method of substitution of complex trajectories with simple one-dimensional flows and their combinations is used. Comparison of obtained test data with such models makes it possible to describe fairly accurate the fluid flow pattern in reservoir and distance to boundaries of non-uniformities. For this purpose, the

59

measured pressure build-up curve should be replotted in the coordinates ∆p – t and derivative ∆p’ – t, on the both sides of the curve the magnitudes are plotted in the logarithmic scale – Diagnostic Graph (table 1, fig. 8). Derivative behavior and form are compared with simple flow models.

Derivative ∆p’ can be determined by equation:

There are the following flow types (fig. 1.2.4):

•borehole effect – gradient is equal to 1 cycle (original segment of derivative);

•linear flow – derivative gradient is 0.5 cycle;

•bilinear flow – derivative gradient is 0.25 cycle;

•spherical flow – derivative gradient is –0.5 cycle; and

•radial filtration flow – gradient is 0.

As a rule, radial filtration flow appears in 1.5 cycles after divergence of ∆p and derivative ∆p’ curves, and, usually, it corresponds to the last straight-line segment of pressure build-up curve plotted in semi-logarithmic coordinates ∆p (rc, t), ln t

(see fig. 7).

Fig. 8. Well 282, Shatovskoye Field.

Pressure Build-up Curve Diagnostic Graph

60