книги / Разработка нефтяных и газовых месторождений. Ч. 2

selective treating this or that interlayer; and characteristics of particular interlayers and their potential. The above information and data can be obtained by well flow rate metering. Such type of study is performed by special devices: flow meters for production wells and flow rate meters for injection wells. Movement of such subsurface devices along the studied perforated interval makes it possible to obtain data on inflow or intake rate distribution by intervals and share of pay intervals in the total thickness of formation.

The simplest subsurface flow (rate) meter is a device fitted with turbine as metering element. Turbine rotation speed is proportional to flow (rate). Number of revolutions of the turbine is converted to electric pulses of definite frequency and they are transmitted to the surface via electrical cable on which flow (rate) meter is run. In measuring complex, for instance, AIST field research station, electric pulses are recorded by pulse counter and stored, and, simultaneously, the movement of subsurface device is recorded on the surface. Relationship between inflow (flow rate) or intake (flow rate) and depth of device location in well is termed a flowmeter curve or flow log. Various types of flowmeter curves are given in fig. 5. They show an inflow from homogenous formation (1) and inflow from uniform reservoir represented by four interlayers (2), one of which (the second top interlayer) is nonproductive. In this case, the nonproductive part of formation thickness β (vertical sweep efficiency):

where h2 and h are, respectively, thickness of nonproductive interlayer and total thickness of formation, m.

If development target is a sandwich-type reservoir, each formation can be flow (rate) metered under stable and unstable conditions (steady-state and unsteady-state flow) of well operation, thus, the objective information about the processes in this complicated structure is obtained. To date, multifunctional devices for well flow (rate) metering have been developed. They make it possible to measure and record the following parameters: flow (rate), pressure, temperature, water cut, tubing integrity violation, for instance, tubing shoe depth. As a rule, subsurface flowmeters are equipped with special light umbrella-type packers, which are controlled from the surface by electric pulsing, and, in open position, they cover the annular clearance of annulus (clearance between the outside diameter of flowmeter and inside casing diameter). POTOK (flow) device relates to such multifunctional remote controlled integrated subsurface devices fitted with packer.

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в г

Fig. 5. Flowmeter Curves of Various Wells:

а – uniform reservoir; б – reservoir with two interlayers; в – reservoir with two interlayers, and the upper interlayer contains nonproductive intervals; г – reservoir with three interlayers, the center interlayer is nonproductive; 1 – reservoir is homogeneous and inflow is uniform along the entire thickness; 2 – uniform reservoir with four interlayers, one of which is nonproductive (the second

top interlayer)

5. Gas Well Testing

Depending on the reservoir development stage and tasks to be solved, gas well tests are subdivided into primary, routine and special tests.

The primary tests are performed at the exploration stage for all wells to obtain large body of data on reservoir characteristics, to determine well productivity and production capacity, so on. The scope of the primary testing should include: wellhead, formation and bottomhole pressure determination, well flow rate determination, and gas-hydrodynamic surveys under steady-state and unsteadystate gas flows.

Well test equipment layout at undeveloped areas (at exploration stage) is given in fig. 6. Lubricator 1 is installed at wellhead (well is not hooked up the gas gathering station). Flow line 2 is connected with separator 3 fitted with metering tank 6.

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Separator gas flows to flare line 5 equipped with orifice flow meter 7. Pressure gages 4 and temperature gage are installed at X-tree.

Before testing new well, it should be developed to prevent sand-clay plugging the bottomhole. That is why, no high formation underbalance is allowed. Well should be developed by multi-cycle method which is sequential changing choke diameter installed in flow line. First, choke of small diameter should be installed and, then, the choke diameter is sequentially enlarged. After that, the choke diameter is sequentially diminished to the initial diameter.

As a rule, such operations (cycles) should be performed 2–3 times, provided that duration of well operation under each choke diameter is 30–40 minutes.

Fig. 6. Gas Well Wellhead Equipment Layout

At developed areas, gas wells are hooked up to gas gathering station. For well testing, a working line valve should be closed and a test line valve should be opened. Well test can be performed without gas popping. In such case, gas flows via the test line to the separator and, then, to the gas gathering system through the gas flow meter. Separator water is directed to the water line through the flow meter. When gas flows into gas manifold, gas flow resistance becomes higher. So, in some cases (low formation pressure and substantial losses in lines), a flare line should be provided for gas well testing under various test conditions.

Well tests under unstable-steady flow are grouped with flow-after-flow test. The objective of flow-after-flow test is also to determine pressure and flow rate stabilization after recurrent changing well operation processes, and, sometimes, pressure build-up to formation pressure value (shut-in well). As a rule, it is necessary to conduct tests under 5–6 flows with flow rate increase and under 2–3 flows with flow rate decrease, and measure pressure, temperature, gas flow rate, fluid flow rate and amount of particulates for each flow.

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The gas well inflow performance relationship in the coordinates

(∆Р = Рпл–Рзаб, Qат is a mass rate of gas flow under atmospheric conditions) is a parabolic curve (fig.7), and it is not a subject to be processed. That is why, it is a common practice to plot the inflow performance relationship in the coordinates

Рпл2 − Рзаб2 ,Qат , i.e. linear relationship (fig. 7, б).

Fig. 7. Gas Well Inflow Performance Relationships under Linear Filtration Law

Under high well gas flow rate, and, consequently, high rate of flow in reservoir, deviation from the linear filtration law can occur. For solving this task, the so termed two-term inflow formula should be used:

where А is gas flow coefficient that consider friction pressure drop; В is factor that considers inertial component of gas flow coefficient:

where β is experimental constant magnitude of porous rock medium; ρат – gas density under atmospheric conditions; and Рат is atmospheric pressure.

straight line with the slope В and intercept А in the axis of ordinates. Based on such intercept, reservoir deliverability can be determined.

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If bottomhole pressure is equal to formation pressure, well flow is termed Absolute Open Flow.

Fig. 8. Inflow Performance Relationship Processing by Two-Term Formula of Inflow

Pressure, temperature, gas and fluid flows, as well as all changes in them, are taken by wellhead and subsurface devices. It is preferable to apply subsurface devices, especially in wells characterized by high fluid flow, and high flow-rate wells operated under low formation underbalance and penetrated high-temperature formations.

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Course of lectures in

OOO LUKOIL-PERM

WELL HYDRODYNAMIC STUDYING

INTRODUCTION

The objective of well hydrodynamic study is to provide data for monitoring hydrocarbon reservoir energy and hydrodynamic conditions under development. The task of well hydrodynamic study is to obtain data for subsequent determining productivity factor, permeability factor, hydroconductivity (flow capacity) factor and other filtration characteristics of oil rocks. Moreover, studying hydrodynamic parameter change in the course of time and development makes it possible to plan and successfully implement measures aimed at achieving the most complete oil extraction: implementation of formation pressure maintenance system, bottomhole zone treatment and other. Well hydrodynamic study data can be also used for determining lateral (horizontal) and vertical (sectional) interconnection between formation parts and formations.

1. WELL AND FORMATION HYDRODYNAMIC STUDY

DATA INTERPRESTATION

All hydrodynamic study methods are based on studying changes in bottomhole pressure and consequent changes in fluid flow rate in reservoir. Bottomhole pressure is either increased, or decreased relative to formation pressure. In the first case, fluid flows from reservoir to bottomhole, and, in the second case, form the bottomhole to reservoir. Bottomhole pressure can be changed by fluid extraction or injection. There are three basic trends of hydrodynamic study:

1.Flow-after-flow test (Well hydrodynamic study under steady-state flows);

2.Unsteady-state flow test (Well hydrodynamic study under unsteady-state flows); and

3.Pressure interference test (Study of hydrodynamic interconnection between wells and formations).

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1.1. FLOW-AFTER-FLOW TEST

The essence of flow-after-flow test is that well operation conditions are changed several times under well hydrodynamic study. At each well operation conditions, stabilized bottomhole pressure and relevant fluid flow rate (oil and gas) are measured. Well operation is considered to be stable if bottomhole pressure and fluid flow rate are stabilized. Formation pressure in operating well is measured after well shutdown for the time period required for bottomhole pressure build-up to formation pressure. For flowing well testing, flowing well operation conditions are changed by choke of different diameters. For injection well testing, injection well operation conditions are changed by changing the amount (flow rate) of injection fluid. For testing pumping wells equipped with sucker rod pumping units, pumping well operation conditions are changed by changing pumping speed and length of stroke of polished rod; pumping wells equipped with electric centrifugal pumps – by changing downhole motor speed or by changing wellhead pressure. Downhole motor speed is controlled by changing electric current oscillation frequency using frequency converter (40–60 Hz).

The objective of flow-after-flow test is to monitor well productivity, to study influence of well operation conditions on well productivity, to determine deliverability properties of bottomhole formation zone and select the optimal well operation conditions.

Theoretical Background. Modern hydrodynamics is substantially supported by the theoretical principles of mathematical physics that studies physical fields (including hydrodynamic fields). The fields are described by differential equations with derived quantities. The task of hydrodynamics is to determine a filtration field and nature of its potential or pressure distribution within the Earth’s crust area under study at specified initial and boundary conditions.

Filtration theory treats all porous bodies as continuous medium with known flow rate, hydraulic pressure, porosity and permeability at each point. Spatial fluid filtration flow in real reservoirs can be characterized by complex configuration of flowing fluid particle trajectories. Such trajectories can be schematically represented in the form of simple filtration flows in various combinations, and, ultimately, it makes it possible to simulate filtration flows and study them by using methods of mathematical physics. The simple one-dimensional filtration flows are rectilinear-parallel flow (linear filtration flow), radial two-dimensional filtration flow and radial spherical filtration flow (fig. 1).

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Fig. 1. Simple One-Dimensional Filtration Flow Patterns

At some distance from well, fluid and gas flow at fairly low speed, and, that is why, they obey the Linear Filtration Law that establishes that well flow rate is in direct proportion to difference between reservoir pressure and bottomhole pressure, i.e. underbalance. Relationship between hydraulic pressure and fluid or gas flow rate in porous rock medium can be determined by the Linear Filtration Law – Darcy law:

where υ is filtration rate;

Q is fluid flow rate;

S is cross-sectional area of filtration; k is permeability;

µ is fluid dynamic viscosity;

dp is pressure change (infinitely low); and

dr is change of distance from well (infinitely small).

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Taking into consideration, that filtration depends on flow rate Q and filtration area S (area of drilled-in reservoir is mathematically described as lateral surface of cylinder S=2πrh), Darcy law can be put down as follows:

where h is thickness of reservoir.

On integrating the above equation and selecting variable r limits from rc to Rк and variable p limits from рзаб to рпл, we obtain Dupuis formula:

µln Rк rc

where Rк is radius of external reservoir boundary; and rc is radius of hydrodynamically perfect well.

This equation characterizes the stable conditions of well operations under linear filtration, i.e. fluid flow rate and magnitude of bottomhole pressure are continuous in the course of time. Then, well productivity factor Кпрод can be determined:

rс

Reservoir hydroconductivity factor (ε) and permeability (k) can be determined using well productivity factor:

Well radius can be determined using drill bit diameter considering enlargement factor. Half of well spacing distance or equivalent radius of oil drainage area is taken as radius of external reservoir boundary:

к π

where σ is half well spacing distance; and l is distance between well rows.

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The above method for determining hydrodynamic parameters of reservoir can be applicable only to perfect wells penetrated reservoir through the entire thickness with open hole. Partial penetration causes fluid flow line curvature due to additional filtration resistance in bottomhole zone. Such man-made imperfectness of wells should be considered by introducing additional filtration resistance С1, which is appeared because of imperfectness of well in terms of penetration, into Dupuis formula. Imperfectness of well in terms of penetration С2 is caused by perforated casing string, and it depends on shot density, diameter of perforations and rock penetration depth of perforations. It should be noted that failure to consider such natural imperfectness of well can cause obtaining incorrect (low) hydroconductivity determined by productivity factor. Factors С1 and С2 can be determined by V.I. Shchurov curves or calculated using analytical methods. Considering imperfectness of well, Dupuis formula is as follows:

where C =C1 + 1δC2 + 2,31 −δδ; δ =b/h ; and b is penetrated thickness of reservoir.

Inflow Performance Relationships. Obtained stabilized flow rate and bottomhole pressure data under various drives make it possible to plot Inflow Performance Relationship (Curve). For this purpose, in (fig. 1.1.2), flow rates are plotted in rectangular coordinates on horizontal axis, and underbalance or relevant bottomhole pressure is plotted on vertical axis (at ∆р = 0 рbh = рf).

Under the Linear Filtration Law for homogeneous fluid in porous reservoir, when fluid properties and reservoir properties does not depend on pressure, the curve plotted in the flow rate-underbalance coordinates is a straight line (curve 1). Inclination of the line relative to the flow rate axis characterizes productivity factor (in this case, it is the identical for various well operation conditions).

Productivity factor is used for determining reservoir characteristics and effectiveness of applied geological-engineering works (bottomhole zone treatment).

However, in practice, inflow performance relationship curves are not always straight lines. All inflow performance relationship curves can be subdivided by form into four types: straight lines convex to the flow rate axis, straight lines convex to the bottomhole pressure axis, and S-shaped lines (under low drive the inflow performance relationship curve is convex to the flow rate axis, and convex to the bottomhole pressure axis under high drive).

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