Horizontal well (HW) has been widely applied to enhance well productivity and prevent water coning in the anisotropic reservoir subject to bottom-water drive. However, the water-cut increases quickly after only one or two years’ production in China while oil recovery still keeps at a very low level. It becomes a major challenge to effectively estimate production distribution and diagnose water-influx locations. Ignoring the effect of nonuniform production distribution along wellbore on pressure response may cause erroneous results especially for water-influx location determination. This paper developed an analytical method to determine nonuniform production distribution and estimate water-influx sections through well-testing analysis. Each HW is divided into multiple producing segments (PS) with variable parameters (e.g., location, production, length, and skin factor) in this model. By using Green’s functions and the Newman-product method, the novel transient pressure solutions of an HW can be obtained in the anisotropic reservoir with bottom-water drive. Secondly, the influences of nonuniform production-distribution on type curves are investigated by comparing the multisegment model (MSM) with the whole-segment model (WSM). Results indicate that the method proposed in this paper enables petroleum operators to interpret parameters of reservoir and HW more accurately by using well-testing interpretation on the basis of bottom-hole pressure data and further estimate water-influx sections and nonproducing segments. Additionally, relevant measures can be conducted to enhance oil production, such as water controlling for water-breakthrough segments and stimulation treatments for nonproducing locations.
Horizontal well technology is well established for enhancing well productivity of low-permeability reservoirs, especially for reservoirs with bottom water or gas cap [
Pressure transient analysis (PTA) has been extensively used for evaluating production performance of horizontal wells [
However, these models are not applicable for an HW in the reservoir subject to bottom-water drive. To fill this gap, this paper develops a novel approach to detect water entry of a horizontal well in a low-permeability bottom-water drive reservoir considering nonuniform production rate distribution through PTA.
The physical model is shown in Figure There is an MSHW located in the horizontal-slab reservoir with an upper impermeable stratum and a lower bottom-water boundary. The formation is infinite in the horizontal direction. The horizontal-slab reservoir is considered to be anisotropic and homogeneous, and it has a constant thickness ( The HW is parallel to the The fluid is single-phase, and the total production rate is The effects of capillary and gravity are ignored.
Physical model of MSHW subject to bottom water drive.
The transient-flow equation can be written as
In the horizontal-slab reservoir, the individual horizontal segment can be considered as a line source with length
Dimensionless variables are defined by
The analytical solution of pressure drop of an MSHW subject to bottom water drive can be expressed as
There exists formation damage around the HW during the process of drilling, completion, production, and other operations [
First, type curves are developed and flow regimes of MSHW subject to bottom water drive are discussed. Further, we analyze the effects of main parameters on pressure transient behavior (PTB).
The pressure response of WSM for different lengths of HW is shown in Figure
Type curves of WSM of HW subject to bottom water drive.
We assume that the HW is divided into three PS with the same interval, and each PS has the same length, since production rate distribution has a distinct effect on PTB and flows regime. Here, we take
(long HW (
For short length of PS (
For the long length of PS (
(short HW (
For short length of PS (
For the long length of PS (
Type curves of MSM when the length of HW is long: (a) with short length of PS and (b) with long length of PS.
Type curves of MSM when the length of HW is short: (a) with short length of PS and (b) with long length of PS.
The total production rate should be kept the same for different cases. The effect of crucial parameters (e.g., production rate distribution, the length of HW, the length of PS, the number of PS, PS spacing, skin factor, and anisotropy degree) is shown in Figures
Effect of production rate of specific PS on PTB: (a)
Effect of production rate distribution on PTB under different lengths of HW: (a)
Effect of distribution pattern with four PS: (a) effect of
Effect of number of PS on PTB when the total length of PS is (a) constant and (b) variable.
Effect of length of PS on PTB: (a) UDLPS and (b) NDLPS.
Effect of PS spacing on PTB.
Effect of skin factor on PTB: (a) with variable total skin factor of PS and (b) with constant total skin factor of PS.
Effect of AD on PTB.
An HW with a length of 1200 m is divided into four PS with equal length of 300 m. The dimensionless production rate of each PS is defined as
Since the length of HW affects flow regimes of MSHW subject to bottom-water drive distinctly, three cases are selected according to the length of HW to eliminate the possibility that the length of HW may disturb the effect of production rate distribution on PTB.
The HW with length of
In general, the following flow regimes (transitional flow, the early radial flow, and steady flow) are influenced by production rate distribution. It is clearly found that the magnitude of influence caused by production rate distribution on pressure drop are shown as (from high to low)
In addition, by comparing the results from Figures
In this part, an HW with the length of 1200 m is divided into four PS. Figure
In this section, the number of PS (N) ranges from 2 to 5. For further discussion, this section is divided into two parts.
In this part, the total length of PS equals to 0.36 L/N for MSM, while it is equal to
In this part, the length of each PS equals to 0.12 L for MSM so that the total length of PS is variable for MSM. The length of PS for WSM still equals to
The length of PS distribution can be classified into two categories: uniformly and nonuniformly. First, we discuss the effect of uniformly distributed length of PS (UDLPS) on type curves in this section. An HW is divided into three PS with equal length (e.g.,
For further discussion, we investigate the effect of nonuniformly distributed length of PS (NDLPS) (e.g.,
A horizontal well with the length of 1000 m consists of two PS with the length of 200 m, one of which is located at the heel of HW. The dimensionless spacing between PS is defined as
A horizontal well with the length of 1000 m consists of four segments with the same length of PS (
In this situation, the skin factor of each PS is equal so that the total skin factor of PS is different for different situations. With the decrease in total skin factor (
In this case, the total skin factor is constant. If the length and production rate of each PS are the same, the effect of the nonuniform distribution of the skin factor on PTB is unapparent. This is because total pressure drop caused by skin effect depends on the length, production rate, and skin factor of each PS. When the length and production rate of each PS are different, slight distinctions can be observed on type curves, shown in Figure
The HW with the length of 800 m consists of two segments located at the heel and toe of HW, respectively, as shown in Figure
The strong influence caused by bottom water will increase the multiplicity of well-testing interpretation, so that this model is available when
Therefore, the multiphase model of MSHW may be established to better distinguish the water and oil production profile based on field test data. Furthermore, novel methods need to be developed to reduce the nonuniqueness of pressure interpretation with strong bottom water drive.
A novel approach was presented for determining nonuniform production distribution as well as detecting the location of water entry. First, HW is divided into multiple segments with arbitrary parameters (e.g., production, length, location, and skin factor). Then, new pressure transient solutions for HW are derived in the anisotropic reservoir with bottom-water drive. Clear distinctions can be observed between type curves of MSM and WSM. As a result, neglecting nonuniform production distribution along the wellbore could lead to erroneous results for detecting the location of water entry. The early radial flow regime of MSM appears later than WSM. Spherical flow and elliptical flow regimes appear on type curves of MSM which do not exist on that of WSM.
Sensitivity analysis shows that anisotropy degree and production rate distribution play important roles in pressure response, followed by length, number, spacing, and skin factor of PS. When the total skin factor remains constant, the effect of the nonuniform distribution of skin factor on pressure response can be ignored. Additionally, the late stable flow appears earlier with increasing vertical permeability, which covers up the early radial flow and is bad for parameter estimation. Besides, water controlling for water-out segments and stimulation treatments for nonproducing segments can be carried out to improve oil recovery based on interpretation results.
Wellbore storage coefficient, atm−1
Dimensionless wellbore storage coefficient
Total compressibility, atm−1
Formation thickness, cm
Formation thickness considering permeability anisotropy, cm
Dimensionless formation thickness considering permeability anisotropy
Horizontal permeability, D
Vertical permeability, D
Total length of HW, cm
Dimensionless length of HW
Ratio of the
Length of the
Ratio of the
Number of PS, dimensionless
Pressure, atm
Initial reservoir pressure, atm
Dimensionless pressure drop
Dimensionless transient pressure solution considering the effect of skin factor
Dimensionless transient pressure solution considering wellbore-storage effect
Total production rate, cm3/s
Production rate of the
Dimensionless production rate of the
Wellbore radius, cm
Dimensionless wellbore radius
Skin factor
Skin factor of the
Time, s
Dimensionless time
Laplace transform variable
Cartesian coordinates
Dimensionless Cartesian coordinate
Coordinates of the center of the
Dimensionless coordinates of the center of the
Porosity, fraction
Diffusivity in horizontal direction, cm3/s
Diffusivity in vertical direction, cm3/s
Fluid viscosity, cP
Anisotropy coefficient
Time variable
Pressure drop caused by the
Dimensionless pressure solution in Laplace space.
The authors declare that they have no conflicts of interest.
The authors would like to thank the National Natural Science Foundation of China (No. U1762101) and National Science and Technology Major Projects (No. 2017ZX05009-003).